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Evolution of magnetic layers stacking sequence within the magnetic structure of Ho(CoxNi1−x)2B2C
Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Evolution of magnetic layers stacking sequence within the magnetic structure of Ho(CoxNi1 x)2B2C M. ElMassalami a,n, H. Takeya b, B. Ouladdiaf c, A.M. Gomes a, T. Paiva a, R.R. dos Santos a a
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro RJ, Brazil National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan c Institut Laue-Langevin, B.P. 156, F-38042 Grenoble Cedex 9, France b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2014 Received in revised form 18 June 2014 Available online 31 July 2014
We evaluated the influence of Co substitution on the magnetic structure of Ho(CoxNi1 x)2B2C (x ¼ 0.2, 0.4, 0.6, 0.8) using neutron diffraction, magnetization and specific heat studies. Different modes are !x ¼ 0:2 !x ¼ 0:4 stabilized: an AFM k ¼ ð0; 0; 1Þ mode for x ¼0.2, a spiral k ¼ ð0; 0; 0:49Þ mode for x ¼0.4, a !x ¼ 0:8 !x ¼ 0:6 ¼ ð0; 0; 0:26Þ mode for x ¼0.6, and a FM k ¼ ð0; 0; 0Þ mode for x ¼0.8. Recalling that spiral k !x ¼ 1:0 !x ¼ 0 ¼ ð0; 0; 1Þ while for x ¼ 1.0, k ¼ ð0; 0; 0Þ, then all these magnetic structures can be for x ¼0.0, k visualized as a variation in the stacking sequence, along the z-axis, of the intra-planar FM-coupled Ho !x sheets as such Co substitution controls the z-component of the k ¼ ð0; 0; ux Þ vector where ux ¼ 0; 0:26; 0:49, or 1. We discuss this inference and the observation that in spite of such a diversity of magnetic structures, the critical temperatures and the saturated moments are only weakly influenced by substitution. & 2014 Elsevier B.V. All rights reserved.
Keywords: Quaternary borocarbides Magnetic structure Ferromagnetism Antiferromagnetism Local moment in compounds and alloys
1. Introduction HoNi2B2C is a model system wherein magnetism, superconductivity and their interplay are manifested [1–10]: it superconducts at T c 8:5 K and it exhibits two incommensurate AFM !x ¼ 0 modes around T m 6 K oT c , namely a c-axis modulated k 2 ¼ !x ¼ 0 ¼ ð0:58; 0; 0Þ ð0; 0; 0:92Þ mode and an a-axis modulated k 3 mode. Below T N 5 K, both modes are replaced by an AFM state !x ¼ 0 with k ¼ ð0; 0; 1Þ and a saturated local moment of μxsat¼ 0 8:6 μB . Within T N o T o T m , a reentrant behavior of Hc2 ðTÞ emerges, testifying to the strong coupling between magnetism and superconductivity. Such a coupling as well as the magnetic and electronic structure are known to be strongly influenced by a variation of some control parameters such as temperature T, field H, pressure P, and chemical substitution. The influence of chemical substitution, in particular, on such a rich manifestation of magnetism, superconductivity and their interplay has been extensively probed [11,12] through rare earth (R) or
n
Corresponding author. Tel.: þ 55 2139387320. E-mail address: [email protected] (M. ElMassalami).
http://dx.doi.org/10.1016/j.jmmm.2014.07.026 0304-8853/& 2014 Elsevier B.V. All rights reserved.
transition metal (M) substitution. The M-substitution with its exposed outer d-electrons (in contrast to the isovalent R-substitution with its deep-shielded f-electrons) is expected to have a stronger impact on the electronic structure [see e.g. Refs. [13,14]]. A best illustration is encountered in Ho(CoxNi1 x)2B2C (lower x): thermodynamic studies [6] showed that (i) the superconductivity is steeply suppressed within 0:005 o x o 0:008, reaching reentrance at 5 o T o 6 K, and finally quenched to below 2 K for x 4 0:03 [Fig. 1(b)]. (ii) In spite of such a drastic suppression of superconductivity, the magnetic mode [4,15,16] is hardly influenced within the same limited 0 r x r 0:015 range. Such a robust stability of the magnetic modes is an indication that low substitution of the almost-samesized Co into the Ni2B2 layers (that are sandwiched between the magnetic HoC sheets) does not modify, at least not sufficiently, the exchange couplings. Obviously, such a stability is not expected for higher Co substitution: it is recalled that the magnetic structure of !x ¼ 1 HoCo2B2C is a FM k ¼ ð0; 0; 0Þ mode [17] while that of HoNi2B2C !x ¼ 0 exhibits the modes with k i ¼ ð0; 0; uxi ¼ 0 Þ, uxi ¼ 0 ¼ 0:92; 1. The question is how does the magnetic structure evolve with substitution, going from AFM mode at x¼0 to FM at x¼ 1. This work investigated the evolution of the magnetism (in parti!x cular the magnetic structure with their distinct k , μxsat, Txcr) of Ho
M. ElMassalami et al. / Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
(CoxNi1 x)2B2C (0 ox o1). Our main findings are that Co-substitution in Ho(CoxNi1 x)2B2C modifies mainly the stacking sequence along the z-axis of the strongly intra-planar FM-coupled Ho sheets: only the !x z-component of k is varied. In all concentrations, it is observed that Co substitution, though strongly influences the magnetic structures, has only a weak influence on
μxsat and Txcr.
2. Experimental Polycrystalline samples were prepared by conventional arcmelting procedures. Room-temperature X-ray diffraction analysis confirms their single-phase character with a structure being the same as the that of HoNi2B2C [Refs. [18,19]] and HoCo2B2C [17]: space group I4=mmm with atomic positions of Ho at 2a (0, 0, 0), Ni/Co at 4d (12 ; 0; 14 ), B at 4e (0; 0; 0:35), and C at 2b (0; 0; 12 ). Magnetization and dc susceptibility (M, χ dc ¼ M=H, 2 o T o20 K, H r 90 kOe) were measured on an extraction-type magnetometer, while the specific heat (C; 2 o T o40 K) was measured on a relaxation-type calorimeter. AC susceptibilities (χ ac ¼ ∂M=∂H, f ¼500 Hz, 2 r T r 20 K, hac ¼ 5 Oe) were measured on a mutualinduction susceptometer. Powder neutron-diffractograms were collected at the high resolution powder diffractometer D2B of the Institut Laue-Langevin (ILL), France (λ ¼1.6 Å, T¼ 1.5 K and 30 K).
3. Results and analyses 3.1. Magnetization and specific heat Thermal and x-dependent evolution of magnetization and specific heat of Ho(CoxNi1 x)2B2C are shown in Figs. 3–5 and summarized in Fig. 1: similar to end members, long-range magnetic order occurs at T xcr liquid helium temperature but such an event is widely spread and accompanied by hysteresis effects: this
Fig. 1. Some properties of Ho(Ni1 xCox)2B2C are plotted as function of x. The lines are guide to the eye. The x-axis break at the lower range emphasizes the region wherein the interplay of superconductivity and magnetism is evident. (a) Magnetic moment as obtained from neutron diffraction (stars), μð2 K; 90 kOeÞ (open squares), and μð2 K; 1=H-0Þ (filled squares). (b) Magnetic transition temperatures as determined from the magnetic susceptibility and specific heat (data of x ¼0 are taken from Refs. [1,2,6,7,10] while that of x ¼1 from Ref. [17]). The solid line represents the superconducting transition temperature as reported in Ref. [6]. (c) Unit-cell volume measured at 2 K (open circles) and 30 K (solid circles); (d) measured unit-cell a parameter at 2 K (open stars) and 30 K (solid stars); c=3 parameter at 2 K (open circle) and 30 K (solid circle).
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is partially attributed to the disorder influence which is introduced by the random distribution of Co on the Ni sites (see below). Moreover, evidence of some type of relaxation-dependent features can be deduced from the distinct differences between the static χ dc ¼ MðT; HÞ=H and dynamic χ ac ¼ ∂MðT; H; 500 HzÞ=∂H susceptibilities. For each composition, the entropy (insets of Fig. 4) evolves smoothly with T, exhibits a shoulder at Txcr and saturates to R lnð2S þ1Þ ¼ 11:52 J=mol K at 15 K. The fact that S-32 at 15 K (a quadruplet level occupation [20] for all compositions) is a clear evidence that the substitution of Co at the 4d site does not modify the high-symmetry (point group 4=mmm) environment of Ho3 þ site; accordingly, the single-ion properties of Ho ions are not modified, nevertheless, the collective magnetism of Ho sublattice are evidently modified (see below). The isotherms of Fig. 5 show that Mðx; H; 2 KÞ tends to saturate at a relatively lower field (10–20 kOe), which is indicative of moderate exchange couplings as well as moderate magnetic anisotropies. The saturated magnetic moments at 2 K, as reflected in the μð2 K; 90 kOeÞ or μð2 K; 1=H-0Þ, are around 8:3–9 μB , which is close to the values obtained for the end members but 10–17% lower than μsat of the free Ho3 þ (10 μB ). As these Mð0 o x o 1; H; 2 KÞ curves were measured on polycrystalline samples, then neither metamagnetic transitions nor easy axis anisotropy can be unambiguously evaluated; nevertheless, as Mðx ¼ 0; HÞ of HoNi2B2C indicated an easy axis along the ð1; 1; 0Þ direction [7], it is reasonable to assume the easy orientation for all x compositions to be confined within the ab plane, most probably along ð1; 1; 0Þ. Finally, the initial shape of the Mðx ¼ 0:2; H; 2 KÞ curve is reminiscent of the field response of the AF mode of HoNi2B2C [20], while that of Mðx ¼ 0:8; H; 2 KÞ resembles the field response of the FM mode of HoCo2B2C [17]: these resemblances will be confirmed below by neutron diffraction analysis. Once again, hysteresis effects can be clearly identified. 3.2. Neutron diffraction Rietveld analysis of the neutron diffractograms taken above Txcr [see Fig. 6(a–d)] indicates a single-phase tetragonal I4=mmm crystal structure. The lattice parameters, Fig. 1(c) and (d), evolve smoothly but non-monotonically with the Co concentration, just as exhibited by our room-temperature XRD analysis (not shown): such a breakdown of the Vegard's law (but still maintaining the tetragonal unit-cell) is attributed to a feature common among these quaternary RM2B2C series [18,19]: Co substitution modifies the angle (but only weakly the length) of the B–T–B (T ¼Co, Ni) bonds. On lowering the temperature down to 1.5 K, the same tetragonal crystal structure is maintained for all studied compositions (i.e. no orthorhombic distortion within available accuracy). Evidently, anisotropic magnetoelastic forces are much weaker than the ones observed in, say, isomorphous Tb(CoxNi1 x)2B2C [21–23]. The magnetic modes which are evident in the diffractograms of Fig. 6 (T ¼ 1:5 K o T xcr ) can be readily identified and analyzed (see Table 1 and Fig. 2). (a) Ho(Co0.2Ni0.8)2B2C: The main magnetic mode of Fig. 6(e) is a !x ¼ 0:2 commensurate AF structure with k1 ¼ ð0; 0; 1Þ and x ¼ 0:2 μND ¼ 8:7ð1Þ μB . This mode is the same as the one observed in the x¼ 0 case and as such the easy axis is assumed to be along ð1; 1; 0Þ [3,5,8]. A careful look at Fig. 6(e) reveals additional (but weak) magnetic peaks; the most evident ones are shown in the inset of Fig. 6(e). These pertain to an incommensurate c-axis spiral !x ¼ 0:2 k2 ¼ ð0; 0; 0:85Þ mode with μx1 ¼ 0:2 ¼ 4:8ð2Þ μB (each consecutive FM plane is rotated by 153.71).
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M. ElMassalami et al. / Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
Table 1 Selected magnetic properties of Ho(CoxNi1 x)2B2C. For studied samples, μND is the moment as obtained from neutron diffraction while μM is the saturated, 1=H-0, moment as obtained from magnetization isotherms. Moments are confined to the ab planes (see text). For completeness, the spiral modes at x¼ 0.2 and 0.4 are also included (see text). x
0a
Structure
AFM
Spiral
AFM
Spiral
Spiral
!x
(0; 0; 1)
(0,0,0.92)
(0; 0; 1)
(0; 0; 0:85)
j! μ jND (μB ) j! μ j (μ )
8.6
6.7
8.7
4.8(2)
k
M
a b c
B
8.6c
0.2
0.6
0.8
1.0b
Spiral
Spiral
FM
FM
(0; 0; 0:49)
(0; 0; 0:89)
(0; 0; 26)
(0; 0; 0)
(0; 0; 0)
5.3
5.2
7.4(2)
8.3
7.2
8.3
8.3
7.2
0.4
9.0
8.8
Reference [5]. Reference [17]. Reference [7].
x ¼ 0;0:2
Fig. 2. The 1.5 K magnetic structures of the studied Ho(CoxNi1 x)2B2C compositions: (a) commensurate AF for x ¼ 0 [Ref. [3]] and 0.2 with k1 ¼ ð0; 0; 1Þ; (b) c-axis spiral x with k2 ¼ ð0; 0; ux Þ where ux ¼ 0.92, 0.85, and 0.89 for x ¼ 0, 0.2, and 0.4, respectively. For completeness, we also include the spiral modes of x¼ 0.2 and 0.4 (see text); (c) c-axis x ¼ 0:4 x ¼ 0:6 x ¼ 0:8;1 spiral with k1 ¼ ð0; 0; 0:49Þ for x ¼ 0.4; (d) c-axis spiral with k1 ¼ ð0; 0; 0:26Þ for x¼ 0.6; (e) FM mode for x¼ 0.8 and 1 [Ref. [17]] with k1 ¼ ð0; 0; 0Þ. In each composition, Ho moments are perpendicular to the c-axis and their magnitudes are given in Table 1.
Fig. 3. Magnetic susceptibilities (χ dc ¼ M=H) of Ho(CoxNi1 x)2B2C: (a) x ¼ 0.2, (b) 0.4, (c) 0.6, and (d) 0.8. Zero-field-cooled and field-cooled cycles (H¼ 1.0 Oe) were carried out on warming and cooling branch, respectively. The insets exhibit the thermal evolution of the real ac susceptibility component (χ 0ac ) taken at hac ¼ 5 Oe and f ¼500 Hz.
Fig. 4. Magnetization isotherms of Ho(CoxNi1 x)2B2C measured at T ¼ 2 K. The inset of each panel illustrates the extrapolation used to estimate the high-field value of the saturated moment, μxsat ð2 K, 1=H-0).
M. ElMassalami et al. / Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
(b) Ho(Co0.4Ni0.6)2B2C: Fig. 6(f) indicates that the main magnetic contribution is an incommensurate c-axis spiral modes with
Fig. 5. Specific heat of Ho(CoxNi1 x)2B2C: (a) x ¼ 0.2, (b) 0.4, (c) 0.6, and (d) 0.8. The insets show the thermal evolution of the corresponding entropy. With the exception of panel (a), all curves exhibit a wide shoulder around the critical temperatures: an indicative of the influence of the Co/Ni disorder. The horizontal arrows indicate the entropy value for a doublet, triplet, and quadruplet occupations.
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!x ¼ 0:4 ¼ ð0; 0; 0:49Þ and μx1 ¼ 0:4 ¼ 5:3 μB (the FM planes along the k1 c-axis are rotated by almost 901). There is an additional weak !x ¼ 0:4 ¼ ð0; 0; 0:89Þ mode with μx1 ¼ 0:4 ¼ 5:2 μB (the spiral rotation k2 angle is 1611) (c) Ho(Co0.6Ni0.4)2B2C: The magnetic order, shown in Fig. 6 (g), !x ¼ 0:6 consists of a single incommensurate mode with k 1 ¼ ð0; 0; 0:26Þ (the FM planes are rotated by 46.81) and μxsat¼ 0:6 ¼ 7:4ð2Þ μB . (d) Ho(Co0.8Ni0.2)2B2C: The magnetic structure, Fig. 6(h), consists !x ¼ 0:8 of a single FM k 1 ¼ ð0; 0; 0Þ mode with μxsat¼ 0:8 ¼ 8:3ð2Þ μB : this structure is similar to the one observed in HoCo2B2C wherein x¼1 μsat ¼ 7:6ð2Þ μB [17]. !x The additional magnetic k 2 mode observed only for !x ¼ 0 ¼ ð0; 0; 0:92Þ mode of x ¼ 0:2; 0:4 is reminiscent of the k 2 HoNi2B2C (Refs. [3,5,8]) and Ho(CoxNi1 x)2B2C (x r 0:015) [4,15,16]: in fact the origin of this mode is still an unsettled question. It is worth emphasizing two points: (i) this relatively weak mode [see inset of Fig. 6(e)] is not due to a chemical contamination, rather it belongs to the very same tetragonal main phase. (ii) It proved difficult to get an improved fit because of the lower experimental resolution: as such we did not allow for any variation in many of the fit parameters of this mode. In spite of this restriction, we managed to identify correctly the main magnetic mode. This serves the main objective of this work: the evolution of magnetic layers stacking sequence within these compositions.
Fig. 6. Neutron diffractograms of Ho(NixCo1 x)2B2C, measured at (a–d) T ¼30 K showing the tetragonal crystal structure, and (e–h) at T ¼ 1.5 K showing additional magnetic contribution. Symbols: measured intensities; vertical short bars: Bragg positions of the nuclear and magnetic peaks; solid line: Rietveld refined fit. Insets (a–c): difference plots showing the thermal evolution of the magnetic contribution: I(1.5 K)–I(30 K) (black, upper curve), I(3 K)–I(30 K) (red, mid curve), and I(6 K)–I(30 K) (green, lower curve). Insets (e–g): an expansion showing the lower peaks of the involved magnetic modes. Space groups, positions, and occupations are given in text; thermal parameters are the !x same as those reported by Lynn et al. [5]. ! μ ND and lattice parameters are given in Fig. 1, while k in Fig. 2 and Table 1. (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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4. Discussion and conclusions It is remarkable that even though all studied Ho(CoxNi1 x)2B2C compositions order at T xcr 5 K with μxsat 8–9 μB , nonetheless, there is a wide variation in their magnetic structures: for the !x ¼ 0 Ni-rich side, the k 1 ¼ ð0; 0; 1Þ structure (similar to x ¼0) is maintained while that of the Co rich side consists of the FM mode (similar to that of x ¼1). For intermediate compositions, the !x magnetic structures consist of distinct k ¼ ð0; 0; ux Þ modes wherein ux depends critically on x. It is recalled that a similar !x influence of the Co substitution on k is manifested in Tb !x ¼ 0 (CoxNi1 x)2B2C [22]: on varying x, the k ð0:55; 0; 0Þ mode is !x ¼ 0:2;0:4 ¼ ð12 ; 0; 12 Þ mode, afterwards transformed into a collinear k !x ¼ 0:6 ¼ ð0; 0; 13 Þ mode, and finally into a transverse c-axis spiral k into a simple FM mode at x¼ 0.8 and 1. It is expected that a variation in Co substitution (or temperature) would modify the details of the electronic structure [13] which in turn influences the generalized susceptibilities, χ ðqÞ, and as such leads to the observed cascade of magnetic modes. These arguments can best be visualized by recalling the expression for RKKY interaction (all symbols have their usual meaning) [24]: HRKKY ¼
! ! I2 1 ∑χ ðqÞeiqr S α S β g 2 μ2B V q
Evidently the energetically favorable magnetic mode is the one wherein χ ðqÞ [or J(q) since JðqÞ p I 2 χ ðqÞ] reaches a maxima. For borocarbides, the calculated normal-state χ ðqÞ function, along the !0 cn-axis, does reveal local maxima at k cal ¼ ð0; 0; 0:3Þ and !″ k cal ¼ ð0; 0; 0:9Þ [25]. Assuringly, each of these vectors have been observed before [5,22]. Here, we show, once again, that such a wave vector, at which χ ðqÞ is maximum, can be controlled by Co substitution: variation in x of Ho(CoxNi1 x)2B2C modifies ux of !x k ¼ ð0; 0; ux Þ.
μxsat of all compositions are hardly modified by Co substitution. The weak variation in μxsat (and as expected in μxeff, not shown) confirms the earlier conclusion Fig. 1 indicates that both Txcr, and
regarding the single-ion properties. These features also confirm the earlier observation that Co/Ni sublattice is nonmagnetic [11,26]: neither Co nor the Ni atoms in these structures are endowed with a magnetic moment and that their d subbands are not polarized. On the other hand the observation that T xcr 5 K can be understood in terms of a simplified molecular field approach: as that T cr p JðqÞ, then the position of J(q) (or χ ðqÞ) shifts with x but its value (thus Txcr) is hardly modified. It is worth adding that Co doping introduces disordering effect which, in turn, influences both the long range as well as short range order: indeed there is a distribution of TxN as manifested in the thermodynamic measurements as well as a broadening in the neutron diffractograms. The ease with which these wave vectors (whose manifestation are supported by group theory arguments [27]) can be modified by temperature or electron count suggests that the exchange couplings are much stronger than the CEF forces (otherwise, if dominant, would tend to pin the Ho moments along the equivalent easy axes). As that the nearest-neighbor intra-planar Ho–Ho separations are much shorter than the inter-planar ones, then the intra-planar couplings would be much stronger than the inter-
planar ones. The experiments on Ho(CoxNi1 x)2B2C (0 r x r 1) and Tb(CoxNi1 x)2B2C (0:4 o x r 1) indicate that these intra-planar couplings are FM and, most importantly, that all these widely different magnetic modes are nothing but a variation on the stacking sequence of the individual FM Ho sheets: the latter statement, elegantly confirmed by Fig. 2, suggests a 1-D model [28] wherein the moments orientation along the z-axis is gov!x ! !x ! ! erned by S n ¼ S ð cos ð k : r n Þ; sin ð k r n Þ; 0Þ (for more details see Ref. [28]). In summary, our investigations xon Ho(CoxNi1 x)2B2C indicate ! that a variation in x modifies the k ¼ ð0; 0; ux Þ mode leading to a variation in the stacking sequence of the FM Ho sheets. This is taken to be a manifestation of the influence of Co substitution on the detail of the electronic structure: a variation in x shifts the maxima in the generalized susceptibility function, thus controlling !x k . Similar features are evident also in the isomorphous Tb (CoxNi1 x)2B2C) [22].
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Evolution of magnetic layers stacking sequence within the magnetic structure of Ho(CoxNi1 x)2B2C M. ElMassalami a,n, H. Takeya b, B. Ouladdiaf c, A.M. Gomes a, T. Paiva a, R.R. dos Santos a a
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro RJ, Brazil National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan c Institut Laue-Langevin, B.P. 156, F-38042 Grenoble Cedex 9, France b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2014 Received in revised form 18 June 2014 Available online 31 July 2014
We evaluated the influence of Co substitution on the magnetic structure of Ho(CoxNi1 x)2B2C (x ¼ 0.2, 0.4, 0.6, 0.8) using neutron diffraction, magnetization and specific heat studies. Different modes are !x ¼ 0:2 !x ¼ 0:4 stabilized: an AFM k ¼ ð0; 0; 1Þ mode for x ¼0.2, a spiral k ¼ ð0; 0; 0:49Þ mode for x ¼0.4, a !x ¼ 0:8 !x ¼ 0:6 ¼ ð0; 0; 0:26Þ mode for x ¼0.6, and a FM k ¼ ð0; 0; 0Þ mode for x ¼0.8. Recalling that spiral k !x ¼ 1:0 !x ¼ 0 ¼ ð0; 0; 1Þ while for x ¼ 1.0, k ¼ ð0; 0; 0Þ, then all these magnetic structures can be for x ¼0.0, k visualized as a variation in the stacking sequence, along the z-axis, of the intra-planar FM-coupled Ho !x sheets as such Co substitution controls the z-component of the k ¼ ð0; 0; ux Þ vector where ux ¼ 0; 0:26; 0:49, or 1. We discuss this inference and the observation that in spite of such a diversity of magnetic structures, the critical temperatures and the saturated moments are only weakly influenced by substitution. & 2014 Elsevier B.V. All rights reserved.
Keywords: Quaternary borocarbides Magnetic structure Ferromagnetism Antiferromagnetism Local moment in compounds and alloys
1. Introduction HoNi2B2C is a model system wherein magnetism, superconductivity and their interplay are manifested [1–10]: it superconducts at T c 8:5 K and it exhibits two incommensurate AFM !x ¼ 0 modes around T m 6 K oT c , namely a c-axis modulated k 2 ¼ !x ¼ 0 ¼ ð0:58; 0; 0Þ ð0; 0; 0:92Þ mode and an a-axis modulated k 3 mode. Below T N 5 K, both modes are replaced by an AFM state !x ¼ 0 with k ¼ ð0; 0; 1Þ and a saturated local moment of μxsat¼ 0 8:6 μB . Within T N o T o T m , a reentrant behavior of Hc2 ðTÞ emerges, testifying to the strong coupling between magnetism and superconductivity. Such a coupling as well as the magnetic and electronic structure are known to be strongly influenced by a variation of some control parameters such as temperature T, field H, pressure P, and chemical substitution. The influence of chemical substitution, in particular, on such a rich manifestation of magnetism, superconductivity and their interplay has been extensively probed [11,12] through rare earth (R) or
n
Corresponding author. Tel.: þ 55 2139387320. E-mail address: [email protected] (M. ElMassalami).
http://dx.doi.org/10.1016/j.jmmm.2014.07.026 0304-8853/& 2014 Elsevier B.V. All rights reserved.
transition metal (M) substitution. The M-substitution with its exposed outer d-electrons (in contrast to the isovalent R-substitution with its deep-shielded f-electrons) is expected to have a stronger impact on the electronic structure [see e.g. Refs. [13,14]]. A best illustration is encountered in Ho(CoxNi1 x)2B2C (lower x): thermodynamic studies [6] showed that (i) the superconductivity is steeply suppressed within 0:005 o x o 0:008, reaching reentrance at 5 o T o 6 K, and finally quenched to below 2 K for x 4 0:03 [Fig. 1(b)]. (ii) In spite of such a drastic suppression of superconductivity, the magnetic mode [4,15,16] is hardly influenced within the same limited 0 r x r 0:015 range. Such a robust stability of the magnetic modes is an indication that low substitution of the almost-samesized Co into the Ni2B2 layers (that are sandwiched between the magnetic HoC sheets) does not modify, at least not sufficiently, the exchange couplings. Obviously, such a stability is not expected for higher Co substitution: it is recalled that the magnetic structure of !x ¼ 1 HoCo2B2C is a FM k ¼ ð0; 0; 0Þ mode [17] while that of HoNi2B2C !x ¼ 0 exhibits the modes with k i ¼ ð0; 0; uxi ¼ 0 Þ, uxi ¼ 0 ¼ 0:92; 1. The question is how does the magnetic structure evolve with substitution, going from AFM mode at x¼0 to FM at x¼ 1. This work investigated the evolution of the magnetism (in parti!x cular the magnetic structure with their distinct k , μxsat, Txcr) of Ho
M. ElMassalami et al. / Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
(CoxNi1 x)2B2C (0 ox o1). Our main findings are that Co-substitution in Ho(CoxNi1 x)2B2C modifies mainly the stacking sequence along the z-axis of the strongly intra-planar FM-coupled Ho sheets: only the !x z-component of k is varied. In all concentrations, it is observed that Co substitution, though strongly influences the magnetic structures, has only a weak influence on
μxsat and Txcr.
2. Experimental Polycrystalline samples were prepared by conventional arcmelting procedures. Room-temperature X-ray diffraction analysis confirms their single-phase character with a structure being the same as the that of HoNi2B2C [Refs. [18,19]] and HoCo2B2C [17]: space group I4=mmm with atomic positions of Ho at 2a (0, 0, 0), Ni/Co at 4d (12 ; 0; 14 ), B at 4e (0; 0; 0:35), and C at 2b (0; 0; 12 ). Magnetization and dc susceptibility (M, χ dc ¼ M=H, 2 o T o20 K, H r 90 kOe) were measured on an extraction-type magnetometer, while the specific heat (C; 2 o T o40 K) was measured on a relaxation-type calorimeter. AC susceptibilities (χ ac ¼ ∂M=∂H, f ¼500 Hz, 2 r T r 20 K, hac ¼ 5 Oe) were measured on a mutualinduction susceptometer. Powder neutron-diffractograms were collected at the high resolution powder diffractometer D2B of the Institut Laue-Langevin (ILL), France (λ ¼1.6 Å, T¼ 1.5 K and 30 K).
3. Results and analyses 3.1. Magnetization and specific heat Thermal and x-dependent evolution of magnetization and specific heat of Ho(CoxNi1 x)2B2C are shown in Figs. 3–5 and summarized in Fig. 1: similar to end members, long-range magnetic order occurs at T xcr liquid helium temperature but such an event is widely spread and accompanied by hysteresis effects: this
Fig. 1. Some properties of Ho(Ni1 xCox)2B2C are plotted as function of x. The lines are guide to the eye. The x-axis break at the lower range emphasizes the region wherein the interplay of superconductivity and magnetism is evident. (a) Magnetic moment as obtained from neutron diffraction (stars), μð2 K; 90 kOeÞ (open squares), and μð2 K; 1=H-0Þ (filled squares). (b) Magnetic transition temperatures as determined from the magnetic susceptibility and specific heat (data of x ¼0 are taken from Refs. [1,2,6,7,10] while that of x ¼1 from Ref. [17]). The solid line represents the superconducting transition temperature as reported in Ref. [6]. (c) Unit-cell volume measured at 2 K (open circles) and 30 K (solid circles); (d) measured unit-cell a parameter at 2 K (open stars) and 30 K (solid stars); c=3 parameter at 2 K (open circle) and 30 K (solid circle).
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is partially attributed to the disorder influence which is introduced by the random distribution of Co on the Ni sites (see below). Moreover, evidence of some type of relaxation-dependent features can be deduced from the distinct differences between the static χ dc ¼ MðT; HÞ=H and dynamic χ ac ¼ ∂MðT; H; 500 HzÞ=∂H susceptibilities. For each composition, the entropy (insets of Fig. 4) evolves smoothly with T, exhibits a shoulder at Txcr and saturates to R lnð2S þ1Þ ¼ 11:52 J=mol K at 15 K. The fact that S-32 at 15 K (a quadruplet level occupation [20] for all compositions) is a clear evidence that the substitution of Co at the 4d site does not modify the high-symmetry (point group 4=mmm) environment of Ho3 þ site; accordingly, the single-ion properties of Ho ions are not modified, nevertheless, the collective magnetism of Ho sublattice are evidently modified (see below). The isotherms of Fig. 5 show that Mðx; H; 2 KÞ tends to saturate at a relatively lower field (10–20 kOe), which is indicative of moderate exchange couplings as well as moderate magnetic anisotropies. The saturated magnetic moments at 2 K, as reflected in the μð2 K; 90 kOeÞ or μð2 K; 1=H-0Þ, are around 8:3–9 μB , which is close to the values obtained for the end members but 10–17% lower than μsat of the free Ho3 þ (10 μB ). As these Mð0 o x o 1; H; 2 KÞ curves were measured on polycrystalline samples, then neither metamagnetic transitions nor easy axis anisotropy can be unambiguously evaluated; nevertheless, as Mðx ¼ 0; HÞ of HoNi2B2C indicated an easy axis along the ð1; 1; 0Þ direction [7], it is reasonable to assume the easy orientation for all x compositions to be confined within the ab plane, most probably along ð1; 1; 0Þ. Finally, the initial shape of the Mðx ¼ 0:2; H; 2 KÞ curve is reminiscent of the field response of the AF mode of HoNi2B2C [20], while that of Mðx ¼ 0:8; H; 2 KÞ resembles the field response of the FM mode of HoCo2B2C [17]: these resemblances will be confirmed below by neutron diffraction analysis. Once again, hysteresis effects can be clearly identified. 3.2. Neutron diffraction Rietveld analysis of the neutron diffractograms taken above Txcr [see Fig. 6(a–d)] indicates a single-phase tetragonal I4=mmm crystal structure. The lattice parameters, Fig. 1(c) and (d), evolve smoothly but non-monotonically with the Co concentration, just as exhibited by our room-temperature XRD analysis (not shown): such a breakdown of the Vegard's law (but still maintaining the tetragonal unit-cell) is attributed to a feature common among these quaternary RM2B2C series [18,19]: Co substitution modifies the angle (but only weakly the length) of the B–T–B (T ¼Co, Ni) bonds. On lowering the temperature down to 1.5 K, the same tetragonal crystal structure is maintained for all studied compositions (i.e. no orthorhombic distortion within available accuracy). Evidently, anisotropic magnetoelastic forces are much weaker than the ones observed in, say, isomorphous Tb(CoxNi1 x)2B2C [21–23]. The magnetic modes which are evident in the diffractograms of Fig. 6 (T ¼ 1:5 K o T xcr ) can be readily identified and analyzed (see Table 1 and Fig. 2). (a) Ho(Co0.2Ni0.8)2B2C: The main magnetic mode of Fig. 6(e) is a !x ¼ 0:2 commensurate AF structure with k1 ¼ ð0; 0; 1Þ and x ¼ 0:2 μND ¼ 8:7ð1Þ μB . This mode is the same as the one observed in the x¼ 0 case and as such the easy axis is assumed to be along ð1; 1; 0Þ [3,5,8]. A careful look at Fig. 6(e) reveals additional (but weak) magnetic peaks; the most evident ones are shown in the inset of Fig. 6(e). These pertain to an incommensurate c-axis spiral !x ¼ 0:2 k2 ¼ ð0; 0; 0:85Þ mode with μx1 ¼ 0:2 ¼ 4:8ð2Þ μB (each consecutive FM plane is rotated by 153.71).
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Table 1 Selected magnetic properties of Ho(CoxNi1 x)2B2C. For studied samples, μND is the moment as obtained from neutron diffraction while μM is the saturated, 1=H-0, moment as obtained from magnetization isotherms. Moments are confined to the ab planes (see text). For completeness, the spiral modes at x¼ 0.2 and 0.4 are also included (see text). x
0a
Structure
AFM
Spiral
AFM
Spiral
Spiral
!x
(0; 0; 1)
(0,0,0.92)
(0; 0; 1)
(0; 0; 0:85)
j! μ jND (μB ) j! μ j (μ )
8.6
6.7
8.7
4.8(2)
k
M
a b c
B
8.6c
0.2
0.6
0.8
1.0b
Spiral
Spiral
FM
FM
(0; 0; 0:49)
(0; 0; 0:89)
(0; 0; 26)
(0; 0; 0)
(0; 0; 0)
5.3
5.2
7.4(2)
8.3
7.2
8.3
8.3
7.2
0.4
9.0
8.8
Reference [5]. Reference [17]. Reference [7].
x ¼ 0;0:2
Fig. 2. The 1.5 K magnetic structures of the studied Ho(CoxNi1 x)2B2C compositions: (a) commensurate AF for x ¼ 0 [Ref. [3]] and 0.2 with k1 ¼ ð0; 0; 1Þ; (b) c-axis spiral x with k2 ¼ ð0; 0; ux Þ where ux ¼ 0.92, 0.85, and 0.89 for x ¼ 0, 0.2, and 0.4, respectively. For completeness, we also include the spiral modes of x¼ 0.2 and 0.4 (see text); (c) c-axis x ¼ 0:4 x ¼ 0:6 x ¼ 0:8;1 spiral with k1 ¼ ð0; 0; 0:49Þ for x ¼ 0.4; (d) c-axis spiral with k1 ¼ ð0; 0; 0:26Þ for x¼ 0.6; (e) FM mode for x¼ 0.8 and 1 [Ref. [17]] with k1 ¼ ð0; 0; 0Þ. In each composition, Ho moments are perpendicular to the c-axis and their magnitudes are given in Table 1.
Fig. 3. Magnetic susceptibilities (χ dc ¼ M=H) of Ho(CoxNi1 x)2B2C: (a) x ¼ 0.2, (b) 0.4, (c) 0.6, and (d) 0.8. Zero-field-cooled and field-cooled cycles (H¼ 1.0 Oe) were carried out on warming and cooling branch, respectively. The insets exhibit the thermal evolution of the real ac susceptibility component (χ 0ac ) taken at hac ¼ 5 Oe and f ¼500 Hz.
Fig. 4. Magnetization isotherms of Ho(CoxNi1 x)2B2C measured at T ¼ 2 K. The inset of each panel illustrates the extrapolation used to estimate the high-field value of the saturated moment, μxsat ð2 K, 1=H-0).
M. ElMassalami et al. / Journal of Magnetism and Magnetic Materials 372 (2014) 74–78
(b) Ho(Co0.4Ni0.6)2B2C: Fig. 6(f) indicates that the main magnetic contribution is an incommensurate c-axis spiral modes with
Fig. 5. Specific heat of Ho(CoxNi1 x)2B2C: (a) x ¼ 0.2, (b) 0.4, (c) 0.6, and (d) 0.8. The insets show the thermal evolution of the corresponding entropy. With the exception of panel (a), all curves exhibit a wide shoulder around the critical temperatures: an indicative of the influence of the Co/Ni disorder. The horizontal arrows indicate the entropy value for a doublet, triplet, and quadruplet occupations.
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!x ¼ 0:4 ¼ ð0; 0; 0:49Þ and μx1 ¼ 0:4 ¼ 5:3 μB (the FM planes along the k1 c-axis are rotated by almost 901). There is an additional weak !x ¼ 0:4 ¼ ð0; 0; 0:89Þ mode with μx1 ¼ 0:4 ¼ 5:2 μB (the spiral rotation k2 angle is 1611) (c) Ho(Co0.6Ni0.4)2B2C: The magnetic order, shown in Fig. 6 (g), !x ¼ 0:6 consists of a single incommensurate mode with k 1 ¼ ð0; 0; 0:26Þ (the FM planes are rotated by 46.81) and μxsat¼ 0:6 ¼ 7:4ð2Þ μB . (d) Ho(Co0.8Ni0.2)2B2C: The magnetic structure, Fig. 6(h), consists !x ¼ 0:8 of a single FM k 1 ¼ ð0; 0; 0Þ mode with μxsat¼ 0:8 ¼ 8:3ð2Þ μB : this structure is similar to the one observed in HoCo2B2C wherein x¼1 μsat ¼ 7:6ð2Þ μB [17]. !x The additional magnetic k 2 mode observed only for !x ¼ 0 ¼ ð0; 0; 0:92Þ mode of x ¼ 0:2; 0:4 is reminiscent of the k 2 HoNi2B2C (Refs. [3,5,8]) and Ho(CoxNi1 x)2B2C (x r 0:015) [4,15,16]: in fact the origin of this mode is still an unsettled question. It is worth emphasizing two points: (i) this relatively weak mode [see inset of Fig. 6(e)] is not due to a chemical contamination, rather it belongs to the very same tetragonal main phase. (ii) It proved difficult to get an improved fit because of the lower experimental resolution: as such we did not allow for any variation in many of the fit parameters of this mode. In spite of this restriction, we managed to identify correctly the main magnetic mode. This serves the main objective of this work: the evolution of magnetic layers stacking sequence within these compositions.
Fig. 6. Neutron diffractograms of Ho(NixCo1 x)2B2C, measured at (a–d) T ¼30 K showing the tetragonal crystal structure, and (e–h) at T ¼ 1.5 K showing additional magnetic contribution. Symbols: measured intensities; vertical short bars: Bragg positions of the nuclear and magnetic peaks; solid line: Rietveld refined fit. Insets (a–c): difference plots showing the thermal evolution of the magnetic contribution: I(1.5 K)–I(30 K) (black, upper curve), I(3 K)–I(30 K) (red, mid curve), and I(6 K)–I(30 K) (green, lower curve). Insets (e–g): an expansion showing the lower peaks of the involved magnetic modes. Space groups, positions, and occupations are given in text; thermal parameters are the !x same as those reported by Lynn et al. [5]. ! μ ND and lattice parameters are given in Fig. 1, while k in Fig. 2 and Table 1. (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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4. Discussion and conclusions It is remarkable that even though all studied Ho(CoxNi1 x)2B2C compositions order at T xcr 5 K with μxsat 8–9 μB , nonetheless, there is a wide variation in their magnetic structures: for the !x ¼ 0 Ni-rich side, the k 1 ¼ ð0; 0; 1Þ structure (similar to x ¼0) is maintained while that of the Co rich side consists of the FM mode (similar to that of x ¼1). For intermediate compositions, the !x magnetic structures consist of distinct k ¼ ð0; 0; ux Þ modes wherein ux depends critically on x. It is recalled that a similar !x influence of the Co substitution on k is manifested in Tb !x ¼ 0 (CoxNi1 x)2B2C [22]: on varying x, the k ð0:55; 0; 0Þ mode is !x ¼ 0:2;0:4 ¼ ð12 ; 0; 12 Þ mode, afterwards transformed into a collinear k !x ¼ 0:6 ¼ ð0; 0; 13 Þ mode, and finally into a transverse c-axis spiral k into a simple FM mode at x¼ 0.8 and 1. It is expected that a variation in Co substitution (or temperature) would modify the details of the electronic structure [13] which in turn influences the generalized susceptibilities, χ ðqÞ, and as such leads to the observed cascade of magnetic modes. These arguments can best be visualized by recalling the expression for RKKY interaction (all symbols have their usual meaning) [24]: HRKKY ¼
! ! I2 1 ∑χ ðqÞeiqr S α S β g 2 μ2B V q
Evidently the energetically favorable magnetic mode is the one wherein χ ðqÞ [or J(q) since JðqÞ p I 2 χ ðqÞ] reaches a maxima. For borocarbides, the calculated normal-state χ ðqÞ function, along the !0 cn-axis, does reveal local maxima at k cal ¼ ð0; 0; 0:3Þ and !″ k cal ¼ ð0; 0; 0:9Þ [25]. Assuringly, each of these vectors have been observed before [5,22]. Here, we show, once again, that such a wave vector, at which χ ðqÞ is maximum, can be controlled by Co substitution: variation in x of Ho(CoxNi1 x)2B2C modifies ux of !x k ¼ ð0; 0; ux Þ.
μxsat of all compositions are hardly modified by Co substitution. The weak variation in μxsat (and as expected in μxeff, not shown) confirms the earlier conclusion Fig. 1 indicates that both Txcr, and
regarding the single-ion properties. These features also confirm the earlier observation that Co/Ni sublattice is nonmagnetic [11,26]: neither Co nor the Ni atoms in these structures are endowed with a magnetic moment and that their d subbands are not polarized. On the other hand the observation that T xcr 5 K can be understood in terms of a simplified molecular field approach: as that T cr p JðqÞ, then the position of J(q) (or χ ðqÞ) shifts with x but its value (thus Txcr) is hardly modified. It is worth adding that Co doping introduces disordering effect which, in turn, influences both the long range as well as short range order: indeed there is a distribution of TxN as manifested in the thermodynamic measurements as well as a broadening in the neutron diffractograms. The ease with which these wave vectors (whose manifestation are supported by group theory arguments [27]) can be modified by temperature or electron count suggests that the exchange couplings are much stronger than the CEF forces (otherwise, if dominant, would tend to pin the Ho moments along the equivalent easy axes). As that the nearest-neighbor intra-planar Ho–Ho separations are much shorter than the inter-planar ones, then the intra-planar couplings would be much stronger than the inter-
planar ones. The experiments on Ho(CoxNi1 x)2B2C (0 r x r 1) and Tb(CoxNi1 x)2B2C (0:4 o x r 1) indicate that these intra-planar couplings are FM and, most importantly, that all these widely different magnetic modes are nothing but a variation on the stacking sequence of the individual FM Ho sheets: the latter statement, elegantly confirmed by Fig. 2, suggests a 1-D model [28] wherein the moments orientation along the z-axis is gov!x ! !x ! ! erned by S n ¼ S ð cos ð k : r n Þ; sin ð k r n Þ; 0Þ (for more details see Ref. [28]). In summary, our investigations xon Ho(CoxNi1 x)2B2C indicate ! that a variation in x modifies the k ¼ ð0; 0; ux Þ mode leading to a variation in the stacking sequence of the FM Ho sheets. This is taken to be a manifestation of the influence of Co substitution on the detail of the electronic structure: a variation in x shifts the maxima in the generalized susceptibility function, thus controlling !x k . Similar features are evident also in the isomorphous Tb (CoxNi1 x)2B2C) [22].
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