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Helical magnetic structure and hyperfine interactions in FeP studied by 57Fe Mössbauer spectroscopy and 31P NMR
Journal of Alloys and Compounds 675 (2016) 277e285
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Helical magnetic structure and hyperfine interactions in FeP studied € ssbauer spectroscopy and 31P NMR by 57Fe Mo Alexey V. Sobolev a, *, Igor A. Presniakov a, Andrey A. Gippius b, c, Ivan V. Chernyavskii a, Martina Schaedler c, Norbert Buettgen c, Sergey A. Ibragimov a, Igor V. Morozov a, Andrei V. Shevelkov a a b c
Department of Chemistry, Lomonosov Moscow State University, 119991, Moscow, Russia Department of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia Experimental Physics V, University of Augsburg, 86159, Augsburg, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2015 Received in revised form 14 March 2016 Accepted 16 March 2016 Available online 18 March 2016
€ ssbauer and 31P NMR studies of a phosphide FeP powder sample performed We report results of 57Fe Mo in a wide temperature range including the point (TN z 120 K) of magnetic phase transitions. The 57Fe € ssbauer spectra at low temperatures T < TN present a very complex Zeeman pattern with line Mo broadenings and sizeable spectral asymmetry. It was shown that the change of the observed spectral shape is consistent with the transition into a space-modulated helicoidal magnetic structure. Analysis of the experimental spectra was carried out assuming an anisotropy of the magnetic hyperfine field Hhf at the 57Fe nuclei when the Fe3þ magnetic moment rotates with respect to the principal axis of the electric field gradient (EFG) tensor. The obtained large temperature independent anharmonicity parameter m z 0.96 of the helicoidal spin structure results from easy-axis anisotropy in the plane of the iron spin rotation. It was assumed that a very low maximal value of Hhf(11 K) z 36 kOe and its high anisotropy DHanis(11 K) z 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (SFe ¼ 1/ 2). The 31P NMR measurements demonstrate an extremely broad linewidth reflecting the spatial distribution of the transferred internal magnetic fields of the Fe3þ ions onto P sites in the magnetically ordered state. © 2016 Elsevier B.V. All rights reserved.
Keywords: Iron phosphide Mossbauer spectroscopy Noncollinear magnetism NMR
1. Introduction Binary compounds MX (where M is transition metal, X is pnictogen) of the MnP structure type are numerous, and many of them display magnetic properties that attract rapt attention. For instance, the first-order ferromagnetic phase transition in MnAs near room temperature gives rise to a pronounced magnetocaloric effect (MCE), with the change in magnetic entropy exceeding 20 J kg1 K1 at 293 K and 15 kOe, placing MnAs and its substituted variants among the most studied MCE materials [1,2]. But arguably the most attractive property is helimagnetism displayed by such compounds as MnP, FeP, and CrAs [3,4]. The scientific interest into iron phosphide, which seems rather simple at the first glance, is largely associated with intrinsic complexity of its unusual helical
* Corresponding author. Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1-3, 119991, Moscow, Russia. E-mail address: [email protected] (A.V. Sobolev). http://dx.doi.org/10.1016/j.jallcom.2016.03.123 0925-8388/© 2016 Elsevier B.V. All rights reserved.
magnetic structure, details and generation mechanisms of which are still a matter of discussions. This FeP phosphide has an orthorhombic structure with the Pnma space group at room temperature [1]. The structure consists of iron ions Fe3þ that occupy equivalent crystal sites with distorted octahedral phosphorus (P3) atoms surrounding them (FeP6), and bears four formulas units per unit cell (Fig. 1a). According to magnetic data for FeP [2], this compound exhibits a magnetic transition at TN z 120 K to the double antiferromagnetic helix with the iron moments lying in the (ab) plane. Following the helicoidal structure proposed in Ref. [5], the magnetic moments are parallel within the planes 1, 2, 3, 4 normal to the c axis (Fig. 1 b). As the plane changes 1e3 or 4e2, the direction of the spin rotates by ~36 (the difference of the angles between the spin directions of two Fe atoms separated by 0.4 c) with the relative angle 176 between adjacent planes separated by 0.1 c (Fig. 1 b). Taking into account that the propagation vector, k z (2p/c) 0.20, is only approximately commensurate with the c axis, such rotation between adjacent moments along the
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Fig. 1. (a) The crystal structure of FeP with the cations octahedrally coordinated by phosphorus anions (not shown). (b) Schematic view of the double helical spin structure and its ab projections proposed in Ref. [5] from neutron diffraction study. The orange, blue, white and dark colored circles illustrate the iron atoms lying in different (ab) planes (the spins are parallel within each plane normal to the c axis). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
c axis implies the presence of a quasi-continuum of possible orientations of iron moments mFe lying in the (ab) plane. According to the results obtained in Ref. [5], the magnetic structure of FeP may be described assuming two nonequivalent iron positions with different magnetic moments, m1 ¼ 0.37 mB and m2 ¼ 0.46 mB. At the same time, in the case of isostructural arsenide FeAs with nearly the same magnetic structure [6], polarized neutron scattering showed that magnetic helicoid has elliptic deformation within the (ab) plane with the longest axis of the ellipse being aligned with the b axis. It should be noted that the powder neutron diffraction applied to study the magnetic properties of the iron pnictides FeP and FeAs cannot distinguish between a simple double spiral model with two discrete iron positions and a quasi-continuous elliptically polarized distribution of iron moments, thus suggesting that other techniques should be employed. €ssbauer works performed for FeP [6,7] in the Early 57Fe Mo paramagnetic temperature region (T > TN) showed that all iron cations occupy unique crystallographic positions, being in accordance with the crystal data [8,9]. However, identification and selfconsistent analysis of the very complex magnetic hyperfine spectra at T < TN caused serious difficulties [7] and left a number of ques€ssbauer studies of FeP tions. One of the most comprehensive Mo single crystals in an external magnetic field was performed by
€ggstro € m et al. [6]. A reasonable fit was obtained by using a suHa perposition of several Zeeman patterns with different values of magnetic hyperfine fields on the 57Fe nuclei and partial contributions. According to [6], each discrete Zeeman pattern arises from different orientations of the magnetic hyperfine field in the (ab) plane. It was shown that in order to get a good fit, a bunching of spins along certain directions in the (ab) plane is necessary. Unfortunately, the authors did not discuss the origin of such bunching in context of the electronic structure of iron ions in FeP. Moreover, there is no information on the temperature evolution of the hy€ssbauer spectra, in particular, near perfine Zeeman structure of Mo the critical point (T z TN) that would be very useful to clarify the nature of the magnetic phase transition. €ssbauer study of isostructural monoRecently, a detailed Mo arsenide FeAs was published by Błachowski et al. [10], where the quasi-continuous variation of the hyperfine magnetic field amplitude with the iron spin orientation varying in the (ab) plane was taken into account. However, despite good fitting of all experimental spectra measured in a wide temperature range below TN, this model still leaves some unanswered questions. In particular, it is assumed the existence of two nonequivalent Fe1 and Fe2 positions, which disagrees with the high temperature spectra (T > TN) and structural data for FeAs [11]. Moreover, the authors [11] did not
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explain a rather unusual profile of the spatial anisotropy of Fe1 and Fe2 magnetic moments that points at a lack of proportionality between the hyperfine field and the magnetic moments on the iron atoms. We can not exclude that the above conclusions are the result of constrains made by the authors in their model fitting of experimental spectra. In particular, one could assume that the angle defining the relative orientation of the spins for a given propagation wave vector (k) of helicoid is constant upon moving along the caxis. This statement requires independent experimental confirmation. In the present work we tried to combine the advantages of the € m et al. [6] and Błachowski above two models used by H€ aggstro € ssbauer spectra for FeP and FeAs, et al. [10] for the analysis of Mo respectively. Firstly, we took into account that period of the helicoidal magnetic structure of FeP is incommensurate with the crystal lattice. Therefore, we used the quasi-continuous distribution of the hyperfine magnetic field amplitude and the angle that determines its orientation with the spin rotation in the (ab) plane. Such approach allows us to reproduce from experimental spectra the profile (polar diagram) of the spatial anisotropy of the hyperfine magnetic field. Secondly, we took into account the possible anharmonicity (bunching) of Fe3þ magnetic moments related to magnetocrystalline anisotropy. High efficiency of this approach was demonstrated by us in a recent preliminary study [12], the main result of which is the possibility of a good fitting of the experimental spectra without the involvement of two magnetic iron sites. In the present work, we show the elliptic contour of the magnetic anisotropy indicating proportionality between the hyperfine field and the magnetic moments of iron ions. In addition, we carried out a detailed analysis of the temperature dependence of hyperfine parameters and their discussion in light of the peculiarities of the electronic and magnetic state of the iron cations in FeP. The results €ssbauer study in a wide range of temperatures including of the Mo the magnetic transition temperature (TN) supplemented by first results of 31P NMR spectroscopy in iron phosphide FeP. Analysis of the experimental spectra was carried out assuming the anisotropy of the magnetic hyperfine field Hhf at the 57Fe nuclei, when the Fe3þ magnetic moment rotates with respect to the principal axis of the EFG tensor.
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the time domain. To avoid skin-depth effects and the reduction of the resonance circuit quality factor due to high metallic conductivity the fine powder sample was fixed in paraffin. This also prevents the sample grains from re-orienting in the applied field. 3. Results and discussion €ssbauer spectrum in paramagnetic state 3.1. Mo € ssbauer spectrum of the 57Fe nucleus (Fig. 2 a) measured The Mo above the magnetic ordering temperature of FeP (TN z 120 K) presents a single quadrupole doublet with narrow (W ¼ 0.31(1) mm/s) and symmetrical lines, thus emphasizing the uniformity of structural positions of iron atoms in the phosphide [12]. The value of the isomer shift d300K ¼ 0.31(1) mm/s corresponds to iron atoms in a formal oxidation state of “þ3” [14]. It is interesting that the observed d value matches typical values of isomer shifts for high-
2. Experimental part Synthesis was carried out by heating the stoichiometric mixture of Fe and P (red) powders in an evacuated quartz ampoule. The mixture was slowly (over 30 h) heated up to 1123 K and annealed at this temperature for 48 h, after which the furnace was switched off. Powder X-ray diffraction analysis was performed on a Bruker D8 Advance diffractometer (Cu-Ka1 radiation, Ge-111 monochromator, reflection geometry) equipped with a LynxEye silicon strip detector. It revealed the obtained product to be pure FeP phase with the orthorhombic unit cell: a ¼ 5.203(1) Å, b ¼ 3.108(1) Å and с ¼ 5.802(1) Å, space group Pnma, which agrees perfectly with the literature data [5,6]. All operations were carried out in a glovebox (pH2O, O2) < 1 ppm) to prevent surface oxidation in a moist air. €ssbauer spectra on the 57Fe nucleus were obtained employMo ing a MS-1104Em spectrometer, operating in a constant acceleration mode. Spectra were processed with SpectrRelax program [13]. €ssbauer spectra of a-Fe All isomer shifts are given relative to the Mo at room temperature. The 31P NMR measurements were performed both in the paramagnetic (at 155 K) and in the magnetically ordered state (at 1.55 K) utilizing a home-built phase coherent pulsed NMR spectrometer. NMR spectra were measured by sweeping the magnetic field at several fixed frequencies in the wide range of 18e120 MHz, the signal was obtained by integrating the spin-echo envelope in
€ssbauer spectrum of FeP recorded at T ¼ 300 K (T >> TN). The solid Fig. 2. (a) 57Fe Mo red line is the result of the simulation of the experimental spectra as described in the 57 € ssbauer spectrum at 11 K (T < TN) fitted (solid red line) using a text. (b) Fe Mo modulation of the hyperfine interactions as the Fe3þ magnetic moment rotates with respect to the principal axis of the EFG tensor, and the anisotropy of the magnetic hyperfine interactions at the Fe3þ sites. The blue shaded area shows the results of the model fitting assuming the equivalence of crystal and magnetic iron sites (the solid line in the upper part of the figure corresponds to the resulting error curve). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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spin cations Fe3þ(d5), octahedrally surrounded by oxygen [15], where, in contrast to phosphides, the FeO chemical bonds are considered to be almost entirely ionic. Apparently, this coincidence is due to the fact that the Fe)Х transfer of the electron density, caused by a high degree of covalency in metal-pnictogen bonds (X ¼ P, As, Sb), induces a simultaneous increase in the 4s- and 3dorbital populations, which affects the value of the isomer shift in the opposite direction [14,15]. Mutual compensation of these two effects possibly renders the resulting isomer shift “less sensitive” to specific chemical bonds of iron cations in pnictides, in contrast to iron oxides, in which the isomer shift value allows estimating the symmetry of local surrounding and spin state of Fe3þ ions [15]. High quadrupole splitting of the doublet, D300K ¼ 0.57(1) mm/s, means that a strong electric field gradient (EFG) appears on the 57Fe nuclei. In the case of high-spin ions Fe3þ(SFe ¼ 5/2) with a spherically symmetric 3d5 (6S) electron shell, the major contribution to the EFG must be associated with the distortion of the crystalline environment of the target nucleus. However, our calculations of the “lattice” contribution to the EFG tensor {Vijlat}i,j¼x,y,z using the crystallographic data for FeP [5] showed that it is impossible to reach an agreement between the experimental and theoretical values under any physically reasonable values of effective charges of iron (ZFe) and phosphorus (ZP) ions. Thus, the symmetry of the crystal environment of the iron cations in the FeP crystal structure cannot cause such high values of the EFG at the 57Fe nuclei. This result indicates the necessity of considering the electronic contributions to the EFG that are related to different electronic populations of 3dorbitals of iron [15] and the overlapping effects of filled 3р-orbital of Fe3þ and valence 3(sp) orbitals of phosphorus (overlap distortion) [17]. According to the Vlat calculations, irrespective of the ZFe and ZP values, the principal VYY axis for the four crystallographically equivalent Fei atoms in the orthorhombic unit cell lies along the b axis (Fig. 3 a). The largest VZZ components for all Fei sites have the same negative values and are located in the (ac) plane, but the angles (Qi), which these components make with the a-axis, are different for the four iron atoms (see Fig. 1 a): Q1 z 78 , Q2 ¼ pQ1, Q3 ¼ p þ Q1, Q4 ¼ pQ1 (Fig. 3 a). Variation of the ZFe and ZP charges leads only to a slight turn of the principal axes VZZ and VXX in the plane (ac) of the FeP lattice. This conclusion is in €ggstro €m et al. [6] using disagreement with the data obtained by Ha €ssbauer measurements on the FeP single crystals in an external Mo magnetic field. It was found that the EFG tensor has a positive VZZ component parallel to the b-axis and negative VXX one making an angle of z60 with the c-axis [6]. Such disagreement with our data may be related to a very large value of the asymmetry parameter h ¼ (VYYVXX)/VZZ (h z 0.7 [6]) and, as a consequence, of the closeness of the values jVZZj z jVXXj. This fact leads to considerable uncertainty in the determination of the true value of the principal axis for the EFG tensor and its direction in crystal lattice under investigation. €ssbauer spectra for the magnetically ordered state 3.2. Mo Decreasing the temperature down to T z TN did not reveal any specific features in the monotonic temperature dependence of the hyperfineeinteraction parameters (d, D) that is usually observed for the Fe3þ ions. At the same time, a complex Zeeman structure appears in the spectra upon moving into the low-temperature region T < TN (Fig. 2b), indicating the hyperfine magnetic fields Hhf induced at 57Fe nuclei. Since the maximum value of the field Hhf does not exceed 36 kOe even at the lowest temperature (11 K) and the quadrupole coupling constant reaches the value of eQVZZ ¼ j1.15(1)j mm/s (300 K), we used the full Hamiltonian of hyperfine interactions having the simplest form in the coordinate system of the
Fig. 3. (a) Directions of the principal EFG axes for four equivalent Fei sites in the unit cell of FeP. (b) The local magnetic structure (for one iron site) of FeP. The angle w gives the orientation of the hyperfine field Hhf in the (ab) plane, varying continuously between 0 and 2p; the polar angle Q gives the orientation of the principal VZZ component in the (ac) plane (when the c axis is normal to the plane of the Hhf(w) ellipse); the polar (q) and azimutal (4) angles give orientation of the Hhf field in the coordinate system of the principal axes of the EFG tensor.
principal axes of the EFG tensor [12]:
b H mQ ¼
2 h 2 i eQVZZ h b2 b2 3 I Z I þ h bI X bI Y g mN Hhf bI X cos 4 4Ið2I 1Þ i þ bI Y sin 4 sin q þ bI Z cos q ; (1)
where bI X , bI Y , bI Z are the angular momentum operators of the 57Fe nucleus in its exited state; g is the nuclear g-factor; mN is the nuclear Bohr magneton, and h ¼ (VYYVXX)/VZZ is the parameter of asym^ mQ depend not only on the hyperfine pametry. The eigenvalues H rameters of the system (d, eQVZZ, Hhf, h) but also on spherical angles (q, 4) that determine the orientation of the hyperfine field Hhf in the system defined by the principal axes of the EFG tensor (X,Y,Z) (Fig. 3 b). It is important to note that in the case of the FeP lattice there are four crystallographically equivalent Fei sites with different directions of local principal EFG axes (Fig. 3 a), and, as a consequence, different qi and 4i values. However, due to the symmetry of the
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complete hyperfine Hamiltonian (1), if the magnetic structure of FeP were collinear, then for these four values of qi and 4i, angles the positions and the relative intensities of the nuclear Zeeman patterns would be the same irrespective of the value of h [6]. The eigenvalues of such Hamiltonian depend on a number of parameters (d, eQVZZ, Hhf, h, q, 4), many of them are correlated, i.e., €ssbauer spectra, but cannot be determined independently from Mo only in certain combinations. However, despite the large number of variable independent hyperfine parameters we could not adequately describe the experimental spectra profiles at T < TN according to this simple model. In Fig. 2b (blue shaded area), we present an example of the best possible description of the experimental spectrum at T ¼ 11 K, which accounts for the main features, but can not reconstruct the profile completely.
3.3. Helicoidal structure As long as the model with a unique iron site failed to completely describe the experimental spectrum, in the next step of the analysis at T < TN we used a more sophisticated model by taking into account the features associated with an incommensurate planar elliptical structure for FeP, which is schematized in Fig. 1b. The angle w, which gives the orientation of the hyperfine field Hhf in the (ab) plane, is varying continuously between 0 and 2p. We found the expressions q(w, Q) and 4(w, Q) connecting the spherical angles in ^ mQ (1) with the rotation angle (w) of the magnetic Hamiltonian H moments of iron ions and also with the angle Q that the principle VZZ component makes with the normal (the c-axis) to the helical plane (Fig. 3b):
cosq ¼ sinQcosw
(2a)
tan f ¼ tanw=cosQ
(2b)
The values wi(z) depend on the coordinates of iron atoms (z) along the helix propagation, in particular, for the harmonic approximation w(z) ¼ qz þ t (where t is the phase shift). Our model assumes a linear relation of the magnetic moment mFe and the hyperfine magnetic field Hhf at 57Fe nuclei: Hhf ¼ amFe (neglecting the influence of magnetic neighbors e supertransferred hyperfine field, HSTHF). To account for the possible spatial anisotropy of the magnetic moment mFe(w) ¼ amacosw þ bmbsinw or the anisotropy of ~ both of which lead to anisotropy the magnetic hyperfine tensor (A), of the Hhf field, we used the expression Hhf(w) ¼ Hacos2w þ Hbsin2w, where Ha and Hb are the magnitudes of Hhf when the magnetic moment of Fe3þ is directed along the a and b axis, respectively. Finally, we used Jacobian elliptic function, sn[…], to describe possible anharmonicity (bunching) of spatial distribution of Fe3þ magnetic moments [18]:
coswðzÞ ¼ sn½ð±4KðmÞ=lÞz; m;
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allowed to satisfactorily describe the entire series of experimental spectra measured in the magnetic ordering temperature range 11 K T < TN (Fig. 4).
3.4. Anisotropy and anharmonicity It is possible to make a number of observations and comments based on the acquired data. First of all, one should pay attention to the very small value of the maximal magnetic field Ha(11 K) ¼ 35.9(1) kOe. It is usually assumed that the Fermi contact interaction with an s-electron is the dominant hyperfine coupling, implying that the Fe moment is proportional to the hyperfine field via the relation Hhf ¼ amFe, where the value of the proportionality constant a is compound specific. In our experiments, the average a €ssbauer value was obtained from Hhf and mFe determined from Mo and neutron diffraction studies of isostructural pnictides AFe2As2 (A ¼ Ca, Sr, Ba) [19]. Using the thus obtained average ratio a ≡ Hhf/ mFe z 92 kOe/mB, we estimated the possible value of the magnetic moment to be mFe z 0.39 mB, which appears to be very close to the values of 0.37e0.46 mB deduced from a neutron diffraction study of FeP [5]. It should be noted that despite the small difference in the values of mFe defined by different methods, all of them clearly point at a significant decrease of the resultant spin of iron compared to SFe ¼ 5/2 (mFe ¼ 5 mB) for high-spin cations Fe3þ(d5). Such a reduction of SFe cannot be related to the effects of strong covalency of the FeP bonds in (FeP6) polyhedra of iron phosphide. Our model suggests that the “spatial anisotropy of a hyperfine field” refers to the angular dependency of the Hhf(w) in the (ab) plane of the orthorhombic unit cell or Hhf(qw, 4w) field value in the system defined by principal axes of the EFG tensor (Fig. 3a). The strong spatial anisotropy of the magnetic hyperfine field Hhf, particularly at T ¼ 11 K, Ha ¼ 35.9(1) kOe and Hb ¼ 5.6(1) kOe, is related to the spatial anisotropy of magnetic moment values mFe(w) ~ [5] or hyperfine magnetic interaction constant A(w) (generally, a ~ mFe [20]. Fig. 5a tensor quantity) included in the expression Hhf ¼ A,
(3)
R p=2
where KðmÞ ¼ 0 dw=ð1 m cos2 wÞ1=2 is an elliptic integral of the first kind, l the helical period, and m is the anharmonicity parameter that is found by minimization of the free-energy [18]. One of the main manifestations of anharmonicity is the dependence of the angles (wij) between neighboring i-th and j-th iron spins on the helicoid propagation (k). Without anharmonicity, the angle wij defining the relative orientation of the spins for a given wave vector k is constant wij (≡ kz). However, if anharmonicity is present, the helicoid with w0 ≡ kz no longer describes the minimal energy spin arrangement because the spins bunch along the modulation propagation zjjc direction with modulated rotation angles wij ¼ w0 þ Dwij and the spin distribution given by d(wij)/dz f 4 K(m)/l(1mcos2w)1/2 [18]. The use of this model
€ssbauer spectra (experimental open circles) of FeP recorded at the Fig. 4. 57Fe Mo indicated temperatures. The solid red lines are simulations of the experimental spectra as described in the text. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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the value DHanis ¼ aDmanis z 31.3 kOe that almost completely coincides with the experimental value 30.3(2) kOe. In addition, we can not exclude the anisotropic part of the magnetic hyperfine ~ as the probable cause for the observed interaction constant A anisotropy Hhf responsible for the mechanisms of formation of the magnetic hyperfine structure [20]. One should also consider the ~ that is strongly dependent on the iron spin orbital contribution to A direction with respect to the crystal axes. Within the above model, the best description of all spectra measured at 11К T 120 K (Fig. 4) may only be attained with sufficiently high values of the anharmonicity parameter m that remains almost unchanged (m z 0.96) in the entire temperature range (T < 0.87,TN) of magnetic order (Fig. 5b). The obtained very large and temperature independent anharmonicity parameter of the helicoidal spin structure results from the bunching of the spins along certain directions in the plane of the iron spin rotation. Such type of bunching was suggested by Moon [21] for MnP having the spiral structure with a bunching of the spins along easy axis in the ab-plane. In the used model, the angle w of the iron moments relative to the b-axis is w ¼ kz 2xsin2(kz), where x is the bunching parameter (x4.6K ¼ 0.022(2) for MnP [21]). The same model was € m et al. [6] for the qualitative analysis of used by H€ aggstro € ssbauer data for FeP. However, no quantitative estimates of the Mo bunching parameter were performed. The inset in Fig. 5b shows the dependence of the bunching parameter (x) as a function of the anharmonicity (m). According to our estimation, x11K z 0.18 for FeP that significantly exceeds the similar parameter for MnP [21] containing high-spin Mn2þ ions with quenched orbital angular momentum. In order to visualize the effect of the uniaxial anisotropy that distorts from circular helicoid, the asymmetric (p(Ha) >> p(Hb)) hyperfine field distribution p(Hhf) f (jvHhf(w)/vwj)1 resulting from simulation of the spectra is shown in Fig. 5b. In addition, a modulation along the direction k(jjz) of the x-projection Hx ¼ Hhf(w),sn [(±4 K(m)/l)z, m] (see Eq. (3)) of the Hhf field on the a(jjx)-axis is shown in the inset to Fig. 6 (for comparison, the figure shows the distribution p(Hhf) for a harmonic helicoidal magnetic structure with w0 ≡ kz (blue area)). The anharmonicity is related to the constant of magnetocrystalline anisotropy (Ku) [18]: m f (Ku/)
Fig. 5. (a) Polar diagram demonstrating anisotropy of the hyperfine magnetic fields at 57 Fe nuclei in FeP for selected temperatures; the symbol Ha denotes a hyperfine field component on iron along the a-axis, while Hb stands for an iron hyperfine field component along the b-axis. (b) Temperature dependences of the anharmonicity parameter (m) and the difference DHanis ¼ (HaeHb) extracted from least-squares fits of €ssbauer spectra. The inset shows the dependence of the bunching parameter (x) the Mo as a function of the anharmonicity (m).
represents experimental polar diagrams Hhf(w) at different temperatures. Clearly, the difference (Ha - Hb) ≡ DHanis decreases monotonically with increasing temperature (Fig. 5b). The anisotropy of Hhf usually associates with the dipole contribution Hdip due to the asymmetry of the local magnetic surrounding, but in our case it cannot significantly influence Hhf because of the low mFe value. In our case, the most probable cause of the anisotropy Hhf is related to the anisotropy of the magnetic moment mFe(w) as it rotates in the (ab) plane. This conclusion is consistent with the results of the FeP neutron diffraction study [5], according to which the anisotropy of magnetic moment is Dmanis z 0.34mB (T ¼ 4.6 K); that should lead to
Fig. 6. The hyperfine field distribution p(Hhf) resulting from a simulation of the spectra (red area). For comparison, the figure shows the distribution p(Hhf) for a harmonic helicoidal magnetic structure (blue area). Insert: modulation along the direction k(jjz) of the x-projection (Hx ¼ Hhf,cosw) of the Hhf field on the a axis, derived from the € ssbauer spectrum (red line); for comparison, blue line gives the theoretical curve Mo for harmonic (sin-modulated) spin structure. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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RFeeFe, where is the exchange integral and RFeeFe is the distance between nearest iron atoms along the helicoid propagation. The Ku constant contains two main contributions: Ku ¼ KD þ KSI [15], where KD is a dipole contribution connected to dipoleedipole interactions of magnetic moments mFe, which depend on their orientation in a crystal, and KSI is the single-ion anisotropy determined by the effects of the spin-orbital interaction [22]. In the case of FeP, the KD contribution should not play any significant role due to the very low values of magnetic moment mFe(w). The manifestation of single-ion anisotropy KSI by Fe3þ ions is possible only with consideration of electronic states with a nonzero orbital angular moment [15].
3.5. Low-spin model for Fe3þ € ssbauer data suggest that the orbital angular Thus, the above Mo moment contribution should be taken into account while analyzing the basic electronic state of the Fe3þ cations in iron phosphide FeP. High-spin Fe3þ ions in the distorted octahedral environment of phosphorus anions are characterized by the electronic term 6A1g, which requires orbital angular moment to be completely quenched. Consideration of s 0 is possible only within the second order of perturbation theory that could hardly explain the low value of hyperfine magnetic field Hhf, the high value of anisotropy DHanis, and strongly pronounced anharmonicity (m / 1) of magnetic helicoid observed in our experiments. A possible reason for all these results is the stabilization of iron cations in a low-spin state (LS). Examples of the high-spin to low-spin transition in isostructural compounds were observed for FeAs and P-doped MnAs at 77 and 232 K, respectively [9,23]. In a strong crystal field of octahedral symmetry, the ground state of the Fe3þ ions is 2T2g (t52g, SFe ¼ 1/2). Considering the relation between holes and electrons, we have to take the t52g electron configuration as a t12g hole configuration. If the local symmetry is exactly octahedral, then the 2T2g state is sixfold degenerate. However, under the influence of axial tetragonal or trigonal distortions the sixfold degeneracy is removed (Fig. 7a). According to our estimations, the negative sign of eQVZZ (<0), which is observed at T << TN, is compatible with a crystal field with predominant tetragonal or very large (ε/D > 0.4, see Fig. 7a) and physically unreasonable trigonal distortion (small trigonal character gives a positive sign for the quadrupole interaction). Thus, although there is no direct experimental evidence for the presence of a fourfold local symmetry axis at the Fe3þ positions in the FeP lattice, the sign of the measured EFG tensor shows that the iron ions experience a quasi-tetragonal crystal field. The hyperfine interactions in low-spin iron ions are considerably modified as compared with those of high-spin iron ions. For instance, despite the fact that the axial and rhombic distortions of the (Fe3þP6) polyhedra causes the splitting of sub-levels t2g / a1g þ eg (Fig. 7a), a small difference in energies of the generated terms 2A1g and 2Eg as well as the spin-orbital interaction (lLS) will lead to a partial “unfreezing” of the orbital moment
X〈0jb L i jn〉〈njb L j j0〉 ij ,Sj ; hLi i ¼ lL Sj ¼ l E E n 0 n
(4)
where l is the spin-orbital interaction constant; b L i is the orbital angular momentum operator; <0jand jn> are wave vectors of ground and exited electronic states, respectively; Е0 and Еn are the ~ tensor comenergies of the corresponding states; Lij are the (L) ponents that define the anisotropy of the orbital moment. The observed internal magnetic field Hhf at the 57Fe nucleus may be discussed in term of three dominant contributions [24]:
Fig. 7. (a) Low-spin Fe3þ orbital level scheme in the trigonal crystal field approximation; (b) Quadrupole coupling constant eQVZZ plotted versus temperature; fitting to the experimental data (blue solid line) with the crystal field model (the region I e T < TN) and using semi-empirical relation (see text) in the region II: T > TN. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
~ m Hhf ¼ HF þ lL,S B
.D E Dh i. E r 3 þ 2mB 3rðS,rÞ r 2 S r 5 ;
(5)
where HF is the Fermi contact term, which is created by the polarization of the s electrons by the 3d electrons of iron ions; the second term (HL) is the contribution from the components of the unquenched angular momentum, and the third dipole term (HD) is due to the anisotropy of the spin density distribution. The dipole term is related to the electronic contribution (~Vel/jej) to the EFG, which arises from the aspherical charge distribution (see x1). Under a small tetragonal distortion from the strict cubic symmetry the degeneracy of the t2g triplet is partially removed giving rise to a singlet a1g{dxy} and a doublet eg{dxz,dyz} (Fig. 7a). For the LS configuration (dxz,dyz)4(dxy)1, ignoring the effects of crystal field of lower than tetragonal symmetry, the components of the Hhf parallel (Hjj) and perpendicular (H⊥) to the OZ tetragonal axis (jj Vel ZZ) are given by
E n o D Hjj ¼ HF þ 4 gjj 2 4=7 mB r 3
(6a)
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
(6b)
~ where gjj ≡ gzz and g⊥ ≡ gxx,yy are the main components of the g tensor: {gij} ¼ 2 þ l/2Lij. Using the above equations, one can write the expression DHanis z (HjjH⊥) ¼ {4(gjjg⊥)6/7}mB according to which the dipole term HD is the main source of the observed anisotropy (~DHanis) of the internal magnetic field Hhf at the 57Fe nuclei in FeP. However, as the Fermi (HF) and orbital (HL) contributions to the hyperfine magnetic field have opposite signs, their partial canceling may lead to a significant decrease of the Hhf value. In addition, since the value of the orbital moment is mostly anisotropic (Lxx z Lyy s Lzz), the HL contribution induced by this moment must be anisotropic as well. Finally, “mixing” the main electronic state of low-spin cations FeIII and the term 2Eg leads to the Ising-like anisotropy [22], which could manifest itself as a high anisotropy level of spiral magnetic structures. The above assumption about the low-spin state of Fe3þ ions in FeP provides good explanations for the main features of the experimental temperature dependence of a quadrupole coupling constant eQVZZ at T < TN (Fig. 7b). If in high-spin Fe3þ(t32ge2g) compounds the EFG acting on the iron nuclei is of lattice origin (Vlat), then in the low-spin Fe3þ(t52g) state it is mainly produced by 3d5electrons of iron ions. The temperature dependent electron population on t2g sublevels produces a relatively strong temperature dependent electronic contribution (Vel) to the EFG [16,20]. Taking into account the temperature dependent probabilities of a hole occupying the 2A1g and 2Eg levels, the temperature dependence of the electronic EFG can be described as [16].
VZZ ðTÞ ¼ VZZ ð0Þ½ð1 expðε=RTÞÞ=ð1 þ 2 expðε=RTÞÞ;
(7)
From the thermal variation of eQVZZ we can give an evaluation of the crystal field splitting (ε) between the two lowest orbitals of the low-spin Fe3þ ions (Fig. 7a) in the FeP structure. The EFG is a decreasing function of increasing temperatures; this effect, which arises from the fact that the EFG is a thermal average between the values corresponding to the lowest orbital doublet and singlet. The axial case (only one free parameter, ε) proved to be the best in all fitting procedures. Using the data of Fig. 7b and the simple formula (8) one gets ε ¼ 2.61 kJmol1. As can be seen (Fig. 7b), the agreement of calculated curve with experimental results is quite satisfactory. In the paramagnetic range T > TN, the temperature dependence of the quadrupole interactions is described using a semi-empirical relation VZZ(T) ¼ A(1B,T3/2), where A ≡ VZZ(TN) is the main EFG tensor component at T z TN, corresponding to the D118K ¼ 0.61(1) mm/s value of quadrupole splitting, and B is a constant with positive value 1.17(6),105 K2/3. In this temperature range (T > TN), the observed eQVZZ(T) dependence is mainly due to the temperature variation of the lattice Vlat(T) contribution to the EFG [20]. One notes that at T z TN the quadrupole splitting increases sharply on cooling (Fig. 7b). Similar sudden change in D(T) have been observed in many compounds, for example, MnAs [1], MnFeP1-xAsx [25], NaFeAs [26], FeAs [10], and FeS [27], thus demonstrating a strong coupling magnetic ordering to the lattice deformation. Various mechanisms have been examined in order to interpret this transition, such as exchange magnetostriction [27,28], biquadratic exchange [29] or spin-orbital coupling of magnetization in the presence of orbital degeneracy (Jahn-Teller distortions) [30,31]. However, due to the lack of sufficient structural and thermodynamic data for FeP we are unable to give a definitive explanation of this unusual behavior of the temperature dependence D(T) at the magnetic phase transition. More detailed analysis of hyperfine parameters in a wide range of temperatures
including the magnetic transition temperature TN in comparison €ssbauer data for the isostructural phases will be a with the Mo subject of our next publication. 3.6.
31
P NMR spectra
The remaining question is whether the magnetic anisotropy affects the hyperfine magnetic fields at 31P nuclei transferred from the nearest magnetic Fe3þ ions. Fortunately, apart from the most € ssbauer nuclei, 57Fe, the crystal structure of FeP conpopular Mo tains also very good NMR nuclei 31P (I ¼ 1/2, g/2p ¼ 17.235 MHz/T). This enables us to probe the hyperfine interactions on the phosphorus site in FeP by 31P NMR spectroscopy. The field-sweep 31P NMR spectrum of the FeP powder sample measured at fixed frequency of 80 MHz in the paramagnetic state at 155 K is presented in Fig. 8a. The line is very narrow (FWHM ~ 6,102 kOe) with the peak situated almost at the diamagnetic Larmor field HLar ¼ 46.42 kOe. With decreasing temperature below TN the 31P spectra change dramatically. The spectrum measured at lowest temperature of 1.55 K is presented in the Fig. 8b. First of all, the spectrum is now extremely broad with FWHM ~11.6(4) kOe and width at the line basement ~ 16.4(4) kOe which is more than two orders of magnitude higher than the FWHM in the paramagnetic state. This result unambiguously indicates that in the magnetically ordered state the effective magnetic field on 31P nuclei is strongly affected by the hyperfine field transferred from Fe3þ cations. The spatial distribution of these transferred fields with respect to external magnetic field is reflected in the characteristic trapezoidal 31P line shape. The trapezoidal distribution of the resonance fields Hres in an antiferromagnet can be modeled based on the superposition of the internal magnetic field Hint and the externally applied magnetic field H [32,33]:
! ! Hres ¼ u0 =g ¼ H þ H int ;
(8)
or, equivalently, 2 2 Hres ¼ H2 þ Hint þ 2H,Hint ,cos a;
P NMR spin-echo-intensity (arb. units)
D E H⊥ ¼ HF þ f4ðg⊥ 2Þ þ 2=7gmB r 3 ;
(9)
80 MHz HL = 46.42 kOe
(a) T = 155 K -0.01 0 0.01 0.02
60 MHz HL = 34.8 kOe
(b) T = 1.55 K
31
284
-10
-5
0
5
10
H - HL (kOe) Fig. 8. (a) 31P NMR spectrum of FeP measured in the paramagnetic state at 155 K; (b) 31 P NMR spectrum of FeP measured in the magnetically ordered state at 1.55 K. (the red solid line is the simulation, see text). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
where a is the angle between H and Hint. In a powder sample, the direction of H is randomly distributed with respect to Hint, and the probability for an angle between H and Hint to be in an interval between a and a þ Da is proportional to the solid angle DU ~ sina,Da. The number of nuclei DN ¼ f(H)DH which probe a resonance field between H and H þ DH is proportional to the solid angle DU or f(H)DH ~ sina,Da, giving the NMR line shape f(H):
f ðHÞfsin a
da : dH
Acknowledgments
(11)
This result, inserted into Eq. (10), gives f(H) which represents the number of nuclei which are in resonance at a certain value of the applied magnetic field H. As different values of Hres are only obtained for angles 0 < a < p, the function f(H) is valid only in the region HresHint < H < Hres þ Hint with edge singularities at Hres ± Hint, whereas it is zero out of this range (cf. Eq. (11)). For the simulation of the intensity I(H) of real powder spectra a convolution with a Gaussian distribution of internal fields has to be accomplished: Hres ZþHint
IðHÞf Hres Hint
of hyperfine magnetic field Hhf(11 K) z 36 kOe and its high anisotropy DHanis(11 K) z 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (SFe ¼ 1/2). This assumption is consistent with the high value of the anharmonicity parameter of helical structure obtained from the spectra of interest. Our preliminary 31P NMR measurements on FeP demonstrate extremely broad spatial distribution of the transferred internal magnetic fields on P sites in the magnetically ordered state.
(10)
The latter term da/dH is given by the differentiation of Eq. (9) using the relation: 2 þ H2 da d cos a 1 H2 Hint res ¼ , , ; sin a d cos a dH Hint ,H2
285
" # 2 þ H2 H 2 Hint 1 1 ðt HÞ2 res , ,exp , dt: 2 2 DHint DHint Hint ,H 2 (12)
The red solid line in Fig. 8b is a result of simulation of the experimental spectrum using Eq. (12) with the following parameters: Hres ¼ 34.1 kOe, Hint ¼ 6.8 kOe, DHint ¼ 0.7 kOe. As seen from this figure, the coincidence with the experimental 31P spectrum is quite satisfactory. Some deviation is expected since in the above analysis we assumed an isotropic distribution of the hyperfine field orientation with respect to the external magnetic field. Accounting for the anisotropy and anharmonicity effects will lead to characteristic “bumping” of the spectra (see, for instance, [34]), as well as decreasing of DHint. 4. Conclusions The results obtained in the present study have shown the effectiveness of the suggested approach to the complex hyperfine magnetic structure analysis of the experimental spectra of iron phosphide measured over a wide temperature range. The results presented above show that a good fitting of the experimental spectra can be achieved without assumptions of formation of two nonequivalent crystallographic positions of the Fe3þ cations, as was suggested earlier. The main reason for the observed asymmetry of hyperfine structure is the spatial modulation of the rotation angles w between adjacent moments mFe along the c axis, which induces ^ mQ(q,4) eigenvalues. Low value the modulation of the Hamiltonian H
This work is supported in part by the Russian Science Foundation, grant # 14-13-00089 (nuclear resonance measurement), and Russian Foundation for Basic Research, grant # 15-03-99628 (sample preparation and characterization). A.A.G., M.S., and N.B. kindly acknowledge support from the German Research Society DFG via TRR80 (Augsburg, Munich). References [1] V.I. Mitsiuk, G.A. Govor, M. Budzynski, Inorg. Mater. 49 (2013) 14e17. [2] H.T. Cho, I.J. Park, I.B. Shim, C.S. Kim, S.J. Kim, J. Korean Phys. Soc. 60 (2012) 1049e1051. [3] Z. Gercsi, K.G. Sandeman, Phys. Rev. B 81 (2010) 224426. [4] Y. Shiomi, S. Iguchi, Y. Tokura, Phys. Rev. B 86 (2012) 180404(R). [5] G.P. Felcher, F.A. Smith, D. Bellavance, A. Wold, Phys. Rev. B 3 (1971) 3046. €m, A. Narayanasamy, J. Magn. Magn. Mater. 30 (1982) 249e256. [6] Н€ aggstro [7] R.E. Bailey, J.F. Duncan, Inorg. Chem. 6 (1967) 1444. [8] S. Rundqvist, P.C. Nawapong, Acta Chem. Scand. 19 (1965) 1006e1008. [9] K. Selte, A. Kjekshus, Acta Chem. Scand. 23 (1969) 2047e2049. _ [10] A. Błachowski, K. Ruebenbauer, J. Zukrowski, Z. Bukowski, J. Alloys Compd. 582 (2014) 167e176. [11] E.E. Rodriguez, C. Stock, K.L. Krycka, C.F. Majkrzak, et al., Phys. Rev. B 83 (2011) 134438. [12] I.A. Presniakov, A.V. Sobolev, I.O. Chernyavskii, D.A. Pankratov, I.V. Morozov, Bulletin of the Russian Academy of Sciences, Physics 79 (2015) 984e989. [13] M.E. Matsnev, V.S. Rusakov, AIP Conf. Proc. 1489 (2012) 178e185. [14] G.A. Fatseas, J. Goodenough, J. Solid State Chem. 33 (1980) 219e232. [15] F. Menil, J. Phys. Chem. Solids 46 (1985) 763. [16] R. Ingalls, Phys. Rev. 133 (1964) A787. [17] R.R. Sharma, Phys. Rev. B 6 (1972) 4310. [18] A.V. Zalesskii, A.K. Zvezdin, A.A. Frolov, A.A. Bush, JETP Lett. 71 (2000) 465. [19] S.M. Dubiel, J. All. Comp. 488 (2009) 18. €ssbauer Spectroscopy and Transition [20] P. Gütlich, E. Bill, A.X. Trautwein, Mo Metal Chemistry (Fundamentals and Applications), Springer, 2012. [21] R.M. Moon, J. Appl. Phys. 53 (1982) 1956. [22] A.S. Moskvin, I.G. Bostrem, M.A. Sidorov, JETP 77 (1993) 127. [23] S. Haneda, N. Kazama, Y. Yamaguchi, H. Watanabe, J. Phys. Soc. Jpn. 42 (1977) 1212. [24] Y. Hazony, J. Phys. C. Solid State Phys. 5 (1972) 2267. [25] O. Tegus, G.X. Lin, W. Dagula, B. Fuquan, et al., JMMM 290e291 (2005) 658. [26] I. Presniakov, I. Morozov, A. Sobolev, M. Roslova, et al., J. Phys. Condens. Matter 25 (2013) 346003. [27] M. Wintenberger, B. Srour, C. Meyer, F. Hartmann-Boutron, Y. Cros, J. Phys. Condens. Matter 39 (1978) 965. [28] D.S. Rodbell, I.S. Jacobs, J. Owen, Phys. Rev. Lett. 11 (1963) 10. [29] M.E. Lines, E.D. Jones, Phys. Rev. 139A (1969) 1313. [30] R.J. Elliott, M.F. Thorpe, J. Appl. Phys. 39 (1968) 802; [a] F. Varret, F. Hartmann-Boutron, Ann. Phys. 3 (1968) 157. [31] S. Haneda, N. Kazama, Y. Yamaguchi, H. Watanabe, J. Phys. Soc. Jpn. 42 (1977) 1212. [32] Y. Yamada, A. Sakata, J. Phys. Soc. Jpn. 55 (1986) 1751. [33] J. Kikuchi, K. Ishiguchi, K. Motoya, M. Itoh, K. Inari, N. Eguchi, J. Akimitsu, J. Phys. Soc. Jpn. 69 (2000) 2660. [34] A.A. Gippius, A.S. Moskvin, S.-L. Drehsler, Phys. Rev. B 77 (2008) 180403(R).
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Helical magnetic structure and hyperfine interactions in FeP studied € ssbauer spectroscopy and 31P NMR by 57Fe Mo Alexey V. Sobolev a, *, Igor A. Presniakov a, Andrey A. Gippius b, c, Ivan V. Chernyavskii a, Martina Schaedler c, Norbert Buettgen c, Sergey A. Ibragimov a, Igor V. Morozov a, Andrei V. Shevelkov a a b c
Department of Chemistry, Lomonosov Moscow State University, 119991, Moscow, Russia Department of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia Experimental Physics V, University of Augsburg, 86159, Augsburg, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2015 Received in revised form 14 March 2016 Accepted 16 March 2016 Available online 18 March 2016
€ ssbauer and 31P NMR studies of a phosphide FeP powder sample performed We report results of 57Fe Mo in a wide temperature range including the point (TN z 120 K) of magnetic phase transitions. The 57Fe € ssbauer spectra at low temperatures T < TN present a very complex Zeeman pattern with line Mo broadenings and sizeable spectral asymmetry. It was shown that the change of the observed spectral shape is consistent with the transition into a space-modulated helicoidal magnetic structure. Analysis of the experimental spectra was carried out assuming an anisotropy of the magnetic hyperfine field Hhf at the 57Fe nuclei when the Fe3þ magnetic moment rotates with respect to the principal axis of the electric field gradient (EFG) tensor. The obtained large temperature independent anharmonicity parameter m z 0.96 of the helicoidal spin structure results from easy-axis anisotropy in the plane of the iron spin rotation. It was assumed that a very low maximal value of Hhf(11 K) z 36 kOe and its high anisotropy DHanis(11 K) z 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (SFe ¼ 1/ 2). The 31P NMR measurements demonstrate an extremely broad linewidth reflecting the spatial distribution of the transferred internal magnetic fields of the Fe3þ ions onto P sites in the magnetically ordered state. © 2016 Elsevier B.V. All rights reserved.
Keywords: Iron phosphide Mossbauer spectroscopy Noncollinear magnetism NMR
1. Introduction Binary compounds MX (where M is transition metal, X is pnictogen) of the MnP structure type are numerous, and many of them display magnetic properties that attract rapt attention. For instance, the first-order ferromagnetic phase transition in MnAs near room temperature gives rise to a pronounced magnetocaloric effect (MCE), with the change in magnetic entropy exceeding 20 J kg1 K1 at 293 K and 15 kOe, placing MnAs and its substituted variants among the most studied MCE materials [1,2]. But arguably the most attractive property is helimagnetism displayed by such compounds as MnP, FeP, and CrAs [3,4]. The scientific interest into iron phosphide, which seems rather simple at the first glance, is largely associated with intrinsic complexity of its unusual helical
* Corresponding author. Department of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1-3, 119991, Moscow, Russia. E-mail address: [email protected] (A.V. Sobolev). http://dx.doi.org/10.1016/j.jallcom.2016.03.123 0925-8388/© 2016 Elsevier B.V. All rights reserved.
magnetic structure, details and generation mechanisms of which are still a matter of discussions. This FeP phosphide has an orthorhombic structure with the Pnma space group at room temperature [1]. The structure consists of iron ions Fe3þ that occupy equivalent crystal sites with distorted octahedral phosphorus (P3) atoms surrounding them (FeP6), and bears four formulas units per unit cell (Fig. 1a). According to magnetic data for FeP [2], this compound exhibits a magnetic transition at TN z 120 K to the double antiferromagnetic helix with the iron moments lying in the (ab) plane. Following the helicoidal structure proposed in Ref. [5], the magnetic moments are parallel within the planes 1, 2, 3, 4 normal to the c axis (Fig. 1 b). As the plane changes 1e3 or 4e2, the direction of the spin rotates by ~36 (the difference of the angles between the spin directions of two Fe atoms separated by 0.4 c) with the relative angle 176 between adjacent planes separated by 0.1 c (Fig. 1 b). Taking into account that the propagation vector, k z (2p/c) 0.20, is only approximately commensurate with the c axis, such rotation between adjacent moments along the
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Fig. 1. (a) The crystal structure of FeP with the cations octahedrally coordinated by phosphorus anions (not shown). (b) Schematic view of the double helical spin structure and its ab projections proposed in Ref. [5] from neutron diffraction study. The orange, blue, white and dark colored circles illustrate the iron atoms lying in different (ab) planes (the spins are parallel within each plane normal to the c axis). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
c axis implies the presence of a quasi-continuum of possible orientations of iron moments mFe lying in the (ab) plane. According to the results obtained in Ref. [5], the magnetic structure of FeP may be described assuming two nonequivalent iron positions with different magnetic moments, m1 ¼ 0.37 mB and m2 ¼ 0.46 mB. At the same time, in the case of isostructural arsenide FeAs with nearly the same magnetic structure [6], polarized neutron scattering showed that magnetic helicoid has elliptic deformation within the (ab) plane with the longest axis of the ellipse being aligned with the b axis. It should be noted that the powder neutron diffraction applied to study the magnetic properties of the iron pnictides FeP and FeAs cannot distinguish between a simple double spiral model with two discrete iron positions and a quasi-continuous elliptically polarized distribution of iron moments, thus suggesting that other techniques should be employed. €ssbauer works performed for FeP [6,7] in the Early 57Fe Mo paramagnetic temperature region (T > TN) showed that all iron cations occupy unique crystallographic positions, being in accordance with the crystal data [8,9]. However, identification and selfconsistent analysis of the very complex magnetic hyperfine spectra at T < TN caused serious difficulties [7] and left a number of ques€ssbauer studies of FeP tions. One of the most comprehensive Mo single crystals in an external magnetic field was performed by
€ggstro € m et al. [6]. A reasonable fit was obtained by using a suHa perposition of several Zeeman patterns with different values of magnetic hyperfine fields on the 57Fe nuclei and partial contributions. According to [6], each discrete Zeeman pattern arises from different orientations of the magnetic hyperfine field in the (ab) plane. It was shown that in order to get a good fit, a bunching of spins along certain directions in the (ab) plane is necessary. Unfortunately, the authors did not discuss the origin of such bunching in context of the electronic structure of iron ions in FeP. Moreover, there is no information on the temperature evolution of the hy€ssbauer spectra, in particular, near perfine Zeeman structure of Mo the critical point (T z TN) that would be very useful to clarify the nature of the magnetic phase transition. €ssbauer study of isostructural monoRecently, a detailed Mo arsenide FeAs was published by Błachowski et al. [10], where the quasi-continuous variation of the hyperfine magnetic field amplitude with the iron spin orientation varying in the (ab) plane was taken into account. However, despite good fitting of all experimental spectra measured in a wide temperature range below TN, this model still leaves some unanswered questions. In particular, it is assumed the existence of two nonequivalent Fe1 and Fe2 positions, which disagrees with the high temperature spectra (T > TN) and structural data for FeAs [11]. Moreover, the authors [11] did not
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
explain a rather unusual profile of the spatial anisotropy of Fe1 and Fe2 magnetic moments that points at a lack of proportionality between the hyperfine field and the magnetic moments on the iron atoms. We can not exclude that the above conclusions are the result of constrains made by the authors in their model fitting of experimental spectra. In particular, one could assume that the angle defining the relative orientation of the spins for a given propagation wave vector (k) of helicoid is constant upon moving along the caxis. This statement requires independent experimental confirmation. In the present work we tried to combine the advantages of the € m et al. [6] and Błachowski above two models used by H€ aggstro € ssbauer spectra for FeP and FeAs, et al. [10] for the analysis of Mo respectively. Firstly, we took into account that period of the helicoidal magnetic structure of FeP is incommensurate with the crystal lattice. Therefore, we used the quasi-continuous distribution of the hyperfine magnetic field amplitude and the angle that determines its orientation with the spin rotation in the (ab) plane. Such approach allows us to reproduce from experimental spectra the profile (polar diagram) of the spatial anisotropy of the hyperfine magnetic field. Secondly, we took into account the possible anharmonicity (bunching) of Fe3þ magnetic moments related to magnetocrystalline anisotropy. High efficiency of this approach was demonstrated by us in a recent preliminary study [12], the main result of which is the possibility of a good fitting of the experimental spectra without the involvement of two magnetic iron sites. In the present work, we show the elliptic contour of the magnetic anisotropy indicating proportionality between the hyperfine field and the magnetic moments of iron ions. In addition, we carried out a detailed analysis of the temperature dependence of hyperfine parameters and their discussion in light of the peculiarities of the electronic and magnetic state of the iron cations in FeP. The results €ssbauer study in a wide range of temperatures including of the Mo the magnetic transition temperature (TN) supplemented by first results of 31P NMR spectroscopy in iron phosphide FeP. Analysis of the experimental spectra was carried out assuming the anisotropy of the magnetic hyperfine field Hhf at the 57Fe nuclei, when the Fe3þ magnetic moment rotates with respect to the principal axis of the EFG tensor.
279
the time domain. To avoid skin-depth effects and the reduction of the resonance circuit quality factor due to high metallic conductivity the fine powder sample was fixed in paraffin. This also prevents the sample grains from re-orienting in the applied field. 3. Results and discussion €ssbauer spectrum in paramagnetic state 3.1. Mo € ssbauer spectrum of the 57Fe nucleus (Fig. 2 a) measured The Mo above the magnetic ordering temperature of FeP (TN z 120 K) presents a single quadrupole doublet with narrow (W ¼ 0.31(1) mm/s) and symmetrical lines, thus emphasizing the uniformity of structural positions of iron atoms in the phosphide [12]. The value of the isomer shift d300K ¼ 0.31(1) mm/s corresponds to iron atoms in a formal oxidation state of “þ3” [14]. It is interesting that the observed d value matches typical values of isomer shifts for high-
2. Experimental part Synthesis was carried out by heating the stoichiometric mixture of Fe and P (red) powders in an evacuated quartz ampoule. The mixture was slowly (over 30 h) heated up to 1123 K and annealed at this temperature for 48 h, after which the furnace was switched off. Powder X-ray diffraction analysis was performed on a Bruker D8 Advance diffractometer (Cu-Ka1 radiation, Ge-111 monochromator, reflection geometry) equipped with a LynxEye silicon strip detector. It revealed the obtained product to be pure FeP phase with the orthorhombic unit cell: a ¼ 5.203(1) Å, b ¼ 3.108(1) Å and с ¼ 5.802(1) Å, space group Pnma, which agrees perfectly with the literature data [5,6]. All operations were carried out in a glovebox (pH2O, O2) < 1 ppm) to prevent surface oxidation in a moist air. €ssbauer spectra on the 57Fe nucleus were obtained employMo ing a MS-1104Em spectrometer, operating in a constant acceleration mode. Spectra were processed with SpectrRelax program [13]. €ssbauer spectra of a-Fe All isomer shifts are given relative to the Mo at room temperature. The 31P NMR measurements were performed both in the paramagnetic (at 155 K) and in the magnetically ordered state (at 1.55 K) utilizing a home-built phase coherent pulsed NMR spectrometer. NMR spectra were measured by sweeping the magnetic field at several fixed frequencies in the wide range of 18e120 MHz, the signal was obtained by integrating the spin-echo envelope in
€ssbauer spectrum of FeP recorded at T ¼ 300 K (T >> TN). The solid Fig. 2. (a) 57Fe Mo red line is the result of the simulation of the experimental spectra as described in the 57 € ssbauer spectrum at 11 K (T < TN) fitted (solid red line) using a text. (b) Fe Mo modulation of the hyperfine interactions as the Fe3þ magnetic moment rotates with respect to the principal axis of the EFG tensor, and the anisotropy of the magnetic hyperfine interactions at the Fe3þ sites. The blue shaded area shows the results of the model fitting assuming the equivalence of crystal and magnetic iron sites (the solid line in the upper part of the figure corresponds to the resulting error curve). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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spin cations Fe3þ(d5), octahedrally surrounded by oxygen [15], where, in contrast to phosphides, the FeO chemical bonds are considered to be almost entirely ionic. Apparently, this coincidence is due to the fact that the Fe)Х transfer of the electron density, caused by a high degree of covalency in metal-pnictogen bonds (X ¼ P, As, Sb), induces a simultaneous increase in the 4s- and 3dorbital populations, which affects the value of the isomer shift in the opposite direction [14,15]. Mutual compensation of these two effects possibly renders the resulting isomer shift “less sensitive” to specific chemical bonds of iron cations in pnictides, in contrast to iron oxides, in which the isomer shift value allows estimating the symmetry of local surrounding and spin state of Fe3þ ions [15]. High quadrupole splitting of the doublet, D300K ¼ 0.57(1) mm/s, means that a strong electric field gradient (EFG) appears on the 57Fe nuclei. In the case of high-spin ions Fe3þ(SFe ¼ 5/2) with a spherically symmetric 3d5 (6S) electron shell, the major contribution to the EFG must be associated with the distortion of the crystalline environment of the target nucleus. However, our calculations of the “lattice” contribution to the EFG tensor {Vijlat}i,j¼x,y,z using the crystallographic data for FeP [5] showed that it is impossible to reach an agreement between the experimental and theoretical values under any physically reasonable values of effective charges of iron (ZFe) and phosphorus (ZP) ions. Thus, the symmetry of the crystal environment of the iron cations in the FeP crystal structure cannot cause such high values of the EFG at the 57Fe nuclei. This result indicates the necessity of considering the electronic contributions to the EFG that are related to different electronic populations of 3dorbitals of iron [15] and the overlapping effects of filled 3р-orbital of Fe3þ and valence 3(sp) orbitals of phosphorus (overlap distortion) [17]. According to the Vlat calculations, irrespective of the ZFe and ZP values, the principal VYY axis for the four crystallographically equivalent Fei atoms in the orthorhombic unit cell lies along the b axis (Fig. 3 a). The largest VZZ components for all Fei sites have the same negative values and are located in the (ac) plane, but the angles (Qi), which these components make with the a-axis, are different for the four iron atoms (see Fig. 1 a): Q1 z 78 , Q2 ¼ pQ1, Q3 ¼ p þ Q1, Q4 ¼ pQ1 (Fig. 3 a). Variation of the ZFe and ZP charges leads only to a slight turn of the principal axes VZZ and VXX in the plane (ac) of the FeP lattice. This conclusion is in €ggstro €m et al. [6] using disagreement with the data obtained by Ha €ssbauer measurements on the FeP single crystals in an external Mo magnetic field. It was found that the EFG tensor has a positive VZZ component parallel to the b-axis and negative VXX one making an angle of z60 with the c-axis [6]. Such disagreement with our data may be related to a very large value of the asymmetry parameter h ¼ (VYYVXX)/VZZ (h z 0.7 [6]) and, as a consequence, of the closeness of the values jVZZj z jVXXj. This fact leads to considerable uncertainty in the determination of the true value of the principal axis for the EFG tensor and its direction in crystal lattice under investigation. €ssbauer spectra for the magnetically ordered state 3.2. Mo Decreasing the temperature down to T z TN did not reveal any specific features in the monotonic temperature dependence of the hyperfineeinteraction parameters (d, D) that is usually observed for the Fe3þ ions. At the same time, a complex Zeeman structure appears in the spectra upon moving into the low-temperature region T < TN (Fig. 2b), indicating the hyperfine magnetic fields Hhf induced at 57Fe nuclei. Since the maximum value of the field Hhf does not exceed 36 kOe even at the lowest temperature (11 K) and the quadrupole coupling constant reaches the value of eQVZZ ¼ j1.15(1)j mm/s (300 K), we used the full Hamiltonian of hyperfine interactions having the simplest form in the coordinate system of the
Fig. 3. (a) Directions of the principal EFG axes for four equivalent Fei sites in the unit cell of FeP. (b) The local magnetic structure (for one iron site) of FeP. The angle w gives the orientation of the hyperfine field Hhf in the (ab) plane, varying continuously between 0 and 2p; the polar angle Q gives the orientation of the principal VZZ component in the (ac) plane (when the c axis is normal to the plane of the Hhf(w) ellipse); the polar (q) and azimutal (4) angles give orientation of the Hhf field in the coordinate system of the principal axes of the EFG tensor.
principal axes of the EFG tensor [12]:
b H mQ ¼
2 h 2 i eQVZZ h b2 b2 3 I Z I þ h bI X bI Y g mN Hhf bI X cos 4 4Ið2I 1Þ i þ bI Y sin 4 sin q þ bI Z cos q ; (1)
where bI X , bI Y , bI Z are the angular momentum operators of the 57Fe nucleus in its exited state; g is the nuclear g-factor; mN is the nuclear Bohr magneton, and h ¼ (VYYVXX)/VZZ is the parameter of asym^ mQ depend not only on the hyperfine pametry. The eigenvalues H rameters of the system (d, eQVZZ, Hhf, h) but also on spherical angles (q, 4) that determine the orientation of the hyperfine field Hhf in the system defined by the principal axes of the EFG tensor (X,Y,Z) (Fig. 3 b). It is important to note that in the case of the FeP lattice there are four crystallographically equivalent Fei sites with different directions of local principal EFG axes (Fig. 3 a), and, as a consequence, different qi and 4i values. However, due to the symmetry of the
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complete hyperfine Hamiltonian (1), if the magnetic structure of FeP were collinear, then for these four values of qi and 4i, angles the positions and the relative intensities of the nuclear Zeeman patterns would be the same irrespective of the value of h [6]. The eigenvalues of such Hamiltonian depend on a number of parameters (d, eQVZZ, Hhf, h, q, 4), many of them are correlated, i.e., €ssbauer spectra, but cannot be determined independently from Mo only in certain combinations. However, despite the large number of variable independent hyperfine parameters we could not adequately describe the experimental spectra profiles at T < TN according to this simple model. In Fig. 2b (blue shaded area), we present an example of the best possible description of the experimental spectrum at T ¼ 11 K, which accounts for the main features, but can not reconstruct the profile completely.
3.3. Helicoidal structure As long as the model with a unique iron site failed to completely describe the experimental spectrum, in the next step of the analysis at T < TN we used a more sophisticated model by taking into account the features associated with an incommensurate planar elliptical structure for FeP, which is schematized in Fig. 1b. The angle w, which gives the orientation of the hyperfine field Hhf in the (ab) plane, is varying continuously between 0 and 2p. We found the expressions q(w, Q) and 4(w, Q) connecting the spherical angles in ^ mQ (1) with the rotation angle (w) of the magnetic Hamiltonian H moments of iron ions and also with the angle Q that the principle VZZ component makes with the normal (the c-axis) to the helical plane (Fig. 3b):
cosq ¼ sinQcosw
(2a)
tan f ¼ tanw=cosQ
(2b)
The values wi(z) depend on the coordinates of iron atoms (z) along the helix propagation, in particular, for the harmonic approximation w(z) ¼ qz þ t (where t is the phase shift). Our model assumes a linear relation of the magnetic moment mFe and the hyperfine magnetic field Hhf at 57Fe nuclei: Hhf ¼ amFe (neglecting the influence of magnetic neighbors e supertransferred hyperfine field, HSTHF). To account for the possible spatial anisotropy of the magnetic moment mFe(w) ¼ amacosw þ bmbsinw or the anisotropy of ~ both of which lead to anisotropy the magnetic hyperfine tensor (A), of the Hhf field, we used the expression Hhf(w) ¼ Hacos2w þ Hbsin2w, where Ha and Hb are the magnitudes of Hhf when the magnetic moment of Fe3þ is directed along the a and b axis, respectively. Finally, we used Jacobian elliptic function, sn[…], to describe possible anharmonicity (bunching) of spatial distribution of Fe3þ magnetic moments [18]:
coswðzÞ ¼ sn½ð±4KðmÞ=lÞz; m;
281
allowed to satisfactorily describe the entire series of experimental spectra measured in the magnetic ordering temperature range 11 K T < TN (Fig. 4).
3.4. Anisotropy and anharmonicity It is possible to make a number of observations and comments based on the acquired data. First of all, one should pay attention to the very small value of the maximal magnetic field Ha(11 K) ¼ 35.9(1) kOe. It is usually assumed that the Fermi contact interaction with an s-electron is the dominant hyperfine coupling, implying that the Fe moment is proportional to the hyperfine field via the relation Hhf ¼ amFe, where the value of the proportionality constant a is compound specific. In our experiments, the average a €ssbauer value was obtained from Hhf and mFe determined from Mo and neutron diffraction studies of isostructural pnictides AFe2As2 (A ¼ Ca, Sr, Ba) [19]. Using the thus obtained average ratio a ≡ Hhf/ mFe z 92 kOe/mB, we estimated the possible value of the magnetic moment to be mFe z 0.39 mB, which appears to be very close to the values of 0.37e0.46 mB deduced from a neutron diffraction study of FeP [5]. It should be noted that despite the small difference in the values of mFe defined by different methods, all of them clearly point at a significant decrease of the resultant spin of iron compared to SFe ¼ 5/2 (mFe ¼ 5 mB) for high-spin cations Fe3þ(d5). Such a reduction of SFe cannot be related to the effects of strong covalency of the FeP bonds in (FeP6) polyhedra of iron phosphide. Our model suggests that the “spatial anisotropy of a hyperfine field” refers to the angular dependency of the Hhf(w) in the (ab) plane of the orthorhombic unit cell or Hhf(qw, 4w) field value in the system defined by principal axes of the EFG tensor (Fig. 3a). The strong spatial anisotropy of the magnetic hyperfine field Hhf, particularly at T ¼ 11 K, Ha ¼ 35.9(1) kOe and Hb ¼ 5.6(1) kOe, is related to the spatial anisotropy of magnetic moment values mFe(w) ~ [5] or hyperfine magnetic interaction constant A(w) (generally, a ~ mFe [20]. Fig. 5a tensor quantity) included in the expression Hhf ¼ A,
(3)
R p=2
where KðmÞ ¼ 0 dw=ð1 m cos2 wÞ1=2 is an elliptic integral of the first kind, l the helical period, and m is the anharmonicity parameter that is found by minimization of the free-energy [18]. One of the main manifestations of anharmonicity is the dependence of the angles (wij) between neighboring i-th and j-th iron spins on the helicoid propagation (k). Without anharmonicity, the angle wij defining the relative orientation of the spins for a given wave vector k is constant wij (≡ kz). However, if anharmonicity is present, the helicoid with w0 ≡ kz no longer describes the minimal energy spin arrangement because the spins bunch along the modulation propagation zjjc direction with modulated rotation angles wij ¼ w0 þ Dwij and the spin distribution given by d(wij)/dz f 4 K(m)/l(1mcos2w)1/2 [18]. The use of this model
€ssbauer spectra (experimental open circles) of FeP recorded at the Fig. 4. 57Fe Mo indicated temperatures. The solid red lines are simulations of the experimental spectra as described in the text. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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the value DHanis ¼ aDmanis z 31.3 kOe that almost completely coincides with the experimental value 30.3(2) kOe. In addition, we can not exclude the anisotropic part of the magnetic hyperfine ~ as the probable cause for the observed interaction constant A anisotropy Hhf responsible for the mechanisms of formation of the magnetic hyperfine structure [20]. One should also consider the ~ that is strongly dependent on the iron spin orbital contribution to A direction with respect to the crystal axes. Within the above model, the best description of all spectra measured at 11К T 120 K (Fig. 4) may only be attained with sufficiently high values of the anharmonicity parameter m that remains almost unchanged (m z 0.96) in the entire temperature range (T < 0.87,TN) of magnetic order (Fig. 5b). The obtained very large and temperature independent anharmonicity parameter of the helicoidal spin structure results from the bunching of the spins along certain directions in the plane of the iron spin rotation. Such type of bunching was suggested by Moon [21] for MnP having the spiral structure with a bunching of the spins along easy axis in the ab-plane. In the used model, the angle w of the iron moments relative to the b-axis is w ¼ kz 2xsin2(kz), where x is the bunching parameter (x4.6K ¼ 0.022(2) for MnP [21]). The same model was € m et al. [6] for the qualitative analysis of used by H€ aggstro € ssbauer data for FeP. However, no quantitative estimates of the Mo bunching parameter were performed. The inset in Fig. 5b shows the dependence of the bunching parameter (x) as a function of the anharmonicity (m). According to our estimation, x11K z 0.18 for FeP that significantly exceeds the similar parameter for MnP [21] containing high-spin Mn2þ ions with quenched orbital angular momentum. In order to visualize the effect of the uniaxial anisotropy that distorts from circular helicoid, the asymmetric (p(Ha) >> p(Hb)) hyperfine field distribution p(Hhf) f (jvHhf(w)/vwj)1 resulting from simulation of the spectra is shown in Fig. 5b. In addition, a modulation along the direction k(jjz) of the x-projection Hx ¼ Hhf(w),sn [(±4 K(m)/l)z, m] (see Eq. (3)) of the Hhf field on the a(jjx)-axis is shown in the inset to Fig. 6 (for comparison, the figure shows the distribution p(Hhf) for a harmonic helicoidal magnetic structure with w0 ≡ kz (blue area)). The anharmonicity is related to the constant of magnetocrystalline anisotropy (Ku) [18]: m f (Ku/
Fig. 5. (a) Polar diagram demonstrating anisotropy of the hyperfine magnetic fields at 57 Fe nuclei in FeP for selected temperatures; the symbol Ha denotes a hyperfine field component on iron along the a-axis, while Hb stands for an iron hyperfine field component along the b-axis. (b) Temperature dependences of the anharmonicity parameter (m) and the difference DHanis ¼ (HaeHb) extracted from least-squares fits of €ssbauer spectra. The inset shows the dependence of the bunching parameter (x) the Mo as a function of the anharmonicity (m).
represents experimental polar diagrams Hhf(w) at different temperatures. Clearly, the difference (Ha - Hb) ≡ DHanis decreases monotonically with increasing temperature (Fig. 5b). The anisotropy of Hhf usually associates with the dipole contribution Hdip due to the asymmetry of the local magnetic surrounding, but in our case it cannot significantly influence Hhf because of the low mFe value. In our case, the most probable cause of the anisotropy Hhf is related to the anisotropy of the magnetic moment mFe(w) as it rotates in the (ab) plane. This conclusion is consistent with the results of the FeP neutron diffraction study [5], according to which the anisotropy of magnetic moment is Dmanis z 0.34mB (T ¼ 4.6 K); that should lead to
Fig. 6. The hyperfine field distribution p(Hhf) resulting from a simulation of the spectra (red area). For comparison, the figure shows the distribution p(Hhf) for a harmonic helicoidal magnetic structure (blue area). Insert: modulation along the direction k(jjz) of the x-projection (Hx ¼ Hhf,cosw) of the Hhf field on the a axis, derived from the € ssbauer spectrum (red line); for comparison, blue line gives the theoretical curve Mo for harmonic (sin-modulated) spin structure. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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283
RFeeFe, where
3.5. Low-spin model for Fe3þ € ssbauer data suggest that the orbital angular Thus, the above Mo moment contribution should be taken into account while analyzing the basic electronic state of the Fe3þ cations in iron phosphide FeP. High-spin Fe3þ ions in the distorted octahedral environment of phosphorus anions are characterized by the electronic term 6A1g, which requires orbital angular moment to be completely quenched. Consideration of
X〈0jb L i jn〉〈njb L j j0〉 ij ,Sj ; hLi i ¼ lL Sj ¼ l E E n 0 n
(4)
where l is the spin-orbital interaction constant; b L i is the orbital angular momentum operator; <0jand jn> are wave vectors of ground and exited electronic states, respectively; Е0 and Еn are the ~ tensor comenergies of the corresponding states; Lij are the (L) ponents that define the anisotropy of the orbital moment. The observed internal magnetic field Hhf at the 57Fe nucleus may be discussed in term of three dominant contributions [24]:
Fig. 7. (a) Low-spin Fe3þ orbital level scheme in the trigonal crystal field approximation; (b) Quadrupole coupling constant eQVZZ plotted versus temperature; fitting to the experimental data (blue solid line) with the crystal field model (the region I e T < TN) and using semi-empirical relation (see text) in the region II: T > TN. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
~ m Hhf ¼ HF þ lL,S B
.D E Dh i. E r 3 þ 2mB 3rðS,rÞ r 2 S r 5 ;
(5)
where HF is the Fermi contact term, which is created by the polarization of the s electrons by the 3d electrons of iron ions; the second term (HL) is the contribution from the components of the unquenched angular momentum, and the third dipole term (HD) is due to the anisotropy of the spin density distribution. The dipole term is related to the electronic contribution (~Vel/jej) to the EFG, which arises from the aspherical charge distribution (see x1). Under a small tetragonal distortion from the strict cubic symmetry the degeneracy of the t2g triplet is partially removed giving rise to a singlet a1g{dxy} and a doublet eg{dxz,dyz} (Fig. 7a). For the LS configuration (dxz,dyz)4(dxy)1, ignoring the effects of crystal field of lower than tetragonal symmetry, the components of the Hhf parallel (Hjj) and perpendicular (H⊥) to the OZ tetragonal axis (jj Vel ZZ) are given by
E n o D Hjj ¼ HF þ 4 gjj 2 4=7 mB r 3
(6a)
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(6b)
~ where gjj ≡ gzz and g⊥ ≡ gxx,yy are the main components of the g tensor: {gij} ¼ 2 þ l/2Lij. Using the above equations, one can write the expression DHanis z (HjjH⊥) ¼ {4(gjjg⊥)6/7}mB
VZZ ðTÞ ¼ VZZ ð0Þ½ð1 expðε=RTÞÞ=ð1 þ 2 expðε=RTÞÞ;
(7)
From the thermal variation of eQVZZ we can give an evaluation of the crystal field splitting (ε) between the two lowest orbitals of the low-spin Fe3þ ions (Fig. 7a) in the FeP structure. The EFG is a decreasing function of increasing temperatures; this effect, which arises from the fact that the EFG is a thermal average between the values corresponding to the lowest orbital doublet and singlet. The axial case (only one free parameter, ε) proved to be the best in all fitting procedures. Using the data of Fig. 7b and the simple formula (8) one gets ε ¼ 2.61 kJmol1. As can be seen (Fig. 7b), the agreement of calculated curve with experimental results is quite satisfactory. In the paramagnetic range T > TN, the temperature dependence of the quadrupole interactions is described using a semi-empirical relation VZZ(T) ¼ A(1B,T3/2), where A ≡ VZZ(TN) is the main EFG tensor component at T z TN, corresponding to the D118K ¼ 0.61(1) mm/s value of quadrupole splitting, and B is a constant with positive value 1.17(6),105 K2/3. In this temperature range (T > TN), the observed eQVZZ(T) dependence is mainly due to the temperature variation of the lattice Vlat(T) contribution to the EFG [20]. One notes that at T z TN the quadrupole splitting increases sharply on cooling (Fig. 7b). Similar sudden change in D(T) have been observed in many compounds, for example, MnAs [1], MnFeP1-xAsx [25], NaFeAs [26], FeAs [10], and FeS [27], thus demonstrating a strong coupling magnetic ordering to the lattice deformation. Various mechanisms have been examined in order to interpret this transition, such as exchange magnetostriction [27,28], biquadratic exchange [29] or spin-orbital coupling of magnetization in the presence of orbital degeneracy (Jahn-Teller distortions) [30,31]. However, due to the lack of sufficient structural and thermodynamic data for FeP we are unable to give a definitive explanation of this unusual behavior of the temperature dependence D(T) at the magnetic phase transition. More detailed analysis of hyperfine parameters in a wide range of temperatures
including the magnetic transition temperature TN in comparison €ssbauer data for the isostructural phases will be a with the Mo subject of our next publication. 3.6.
31
P NMR spectra
The remaining question is whether the magnetic anisotropy affects the hyperfine magnetic fields at 31P nuclei transferred from the nearest magnetic Fe3þ ions. Fortunately, apart from the most € ssbauer nuclei, 57Fe, the crystal structure of FeP conpopular Mo tains also very good NMR nuclei 31P (I ¼ 1/2, g/2p ¼ 17.235 MHz/T). This enables us to probe the hyperfine interactions on the phosphorus site in FeP by 31P NMR spectroscopy. The field-sweep 31P NMR spectrum of the FeP powder sample measured at fixed frequency of 80 MHz in the paramagnetic state at 155 K is presented in Fig. 8a. The line is very narrow (FWHM ~ 6,102 kOe) with the peak situated almost at the diamagnetic Larmor field HLar ¼ 46.42 kOe. With decreasing temperature below TN the 31P spectra change dramatically. The spectrum measured at lowest temperature of 1.55 K is presented in the Fig. 8b. First of all, the spectrum is now extremely broad with FWHM ~11.6(4) kOe and width at the line basement ~ 16.4(4) kOe which is more than two orders of magnitude higher than the FWHM in the paramagnetic state. This result unambiguously indicates that in the magnetically ordered state the effective magnetic field on 31P nuclei is strongly affected by the hyperfine field transferred from Fe3þ cations. The spatial distribution of these transferred fields with respect to external magnetic field is reflected in the characteristic trapezoidal 31P line shape. The trapezoidal distribution of the resonance fields Hres in an antiferromagnet can be modeled based on the superposition of the internal magnetic field Hint and the externally applied magnetic field H [32,33]:
! ! Hres ¼ u0 =g ¼ H þ H int ;
(8)
or, equivalently, 2 2 Hres ¼ H2 þ Hint þ 2H,Hint ,cos a;
P NMR spin-echo-intensity (arb. units)
D E H⊥ ¼ HF þ f4ðg⊥ 2Þ þ 2=7gmB r 3 ;
(9)
80 MHz HL = 46.42 kOe
(a) T = 155 K -0.01 0 0.01 0.02
60 MHz HL = 34.8 kOe
(b) T = 1.55 K
31
284
-10
-5
0
5
10
H - HL (kOe) Fig. 8. (a) 31P NMR spectrum of FeP measured in the paramagnetic state at 155 K; (b) 31 P NMR spectrum of FeP measured in the magnetically ordered state at 1.55 K. (the red solid line is the simulation, see text). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
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where a is the angle between H and Hint. In a powder sample, the direction of H is randomly distributed with respect to Hint, and the probability for an angle between H and Hint to be in an interval between a and a þ Da is proportional to the solid angle DU ~ sina,Da. The number of nuclei DN ¼ f(H)DH which probe a resonance field between H and H þ DH is proportional to the solid angle DU or f(H)DH ~ sina,Da, giving the NMR line shape f(H):
f ðHÞfsin a
da : dH
Acknowledgments
(11)
This result, inserted into Eq. (10), gives f(H) which represents the number of nuclei which are in resonance at a certain value of the applied magnetic field H. As different values of Hres are only obtained for angles 0 < a < p, the function f(H) is valid only in the region HresHint < H < Hres þ Hint with edge singularities at Hres ± Hint, whereas it is zero out of this range (cf. Eq. (11)). For the simulation of the intensity I(H) of real powder spectra a convolution with a Gaussian distribution of internal fields has to be accomplished: Hres ZþHint
IðHÞf Hres Hint
of hyperfine magnetic field Hhf(11 K) z 36 kOe and its high anisotropy DHanis(11 K) z 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (SFe ¼ 1/2). This assumption is consistent with the high value of the anharmonicity parameter of helical structure obtained from the spectra of interest. Our preliminary 31P NMR measurements on FeP demonstrate extremely broad spatial distribution of the transferred internal magnetic fields on P sites in the magnetically ordered state.
(10)
The latter term da/dH is given by the differentiation of Eq. (9) using the relation: 2 þ H2 da d cos a 1 H2 Hint res ¼ , , ; sin a d cos a dH Hint ,H2
285
" # 2 þ H2 H 2 Hint 1 1 ðt HÞ2 res , ,exp , dt: 2 2 DHint DHint Hint ,H 2 (12)
The red solid line in Fig. 8b is a result of simulation of the experimental spectrum using Eq. (12) with the following parameters: Hres ¼ 34.1 kOe, Hint ¼ 6.8 kOe, DHint ¼ 0.7 kOe. As seen from this figure, the coincidence with the experimental 31P spectrum is quite satisfactory. Some deviation is expected since in the above analysis we assumed an isotropic distribution of the hyperfine field orientation with respect to the external magnetic field. Accounting for the anisotropy and anharmonicity effects will lead to characteristic “bumping” of the spectra (see, for instance, [34]), as well as decreasing of DHint. 4. Conclusions The results obtained in the present study have shown the effectiveness of the suggested approach to the complex hyperfine magnetic structure analysis of the experimental spectra of iron phosphide measured over a wide temperature range. The results presented above show that a good fitting of the experimental spectra can be achieved without assumptions of formation of two nonequivalent crystallographic positions of the Fe3þ cations, as was suggested earlier. The main reason for the observed asymmetry of hyperfine structure is the spatial modulation of the rotation angles w between adjacent moments mFe along the c axis, which induces ^ mQ(q,4) eigenvalues. Low value the modulation of the Hamiltonian H
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