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Magnetic and Mössbauer spectral properties of DyFe11Ti and DyFe11TiH
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 265 (2003) 156–166
. Magnetic and Mossbauer spectral properties of DyFe11Ti and DyFe11TiH Cristina Piquera, Olivier Isnardb,c, Fernande Grandjeana, Gary J. Longd,* a Department of Physics, B5, University of Li"ege, B-4000 Sart-Tilman, Belgium Laboratoire de Cristallographie associ!e au CNRS, Universit!e J. Fourier, BP 166X, F-38042 Grenoble Cedex, France c Institut Universitaire de France, Maison des Universite!s, 103 Boulevard Saint-Michel, F-75005 Paris Cedex, France d Department of Chemistry, University of Missouri-Rolla, Rolla, MO 65409-0010, USA
b
Received 23 January 2003
Abstract The temperature dependence of the AC magnetic susceptibility, between 4.2 and 300 K, and the magnetization, . spectral measurements between 300 and 600 K, has been measured for DyFe11Ti and DyFe11TiH. Iron-57 Mossbauer between 4.2 and 295 K have also been carried out on DyFe11Ti and DyFe11TiH and analyzed with a model which considers both the direction of the magnetization in the different magnetic phases of these compounds and the distribution of titanium atoms in the near-neighbor environment of the three crystallographically distinct iron sites. The . magnetic measurements and the Mossbauer spectra of DyFe11Ti clearly show the influence of the two spin reorientations occurring in this compound and indicate that the iron magnetic moments are oriented along the [1 0 0] . direction of the basal plane below 100 K. The magnetic measurements and the Mossbauer spectra of DyFe11TiH do not show any evidence for spin reorientations and are consistent with a basal magnetic anisotropy between 4.2 and 600 K. Hence, the hydrogen insertion into DyFe11Ti reinforces the dysprosium magnetic anisotropy. The assignment and the . temperature dependencies of the Mossbauer spectral hyperfine fields and isomer shifts are in full agreement with a Wigner–Seitz cell analysis of the three iron sites in DyFe11Ti and DyFe11TiH. r 2003 Elsevier Science B.V. All rights reserved. . Keywords: Mossbauer spectra; Rare earth compounds; Magnetic susceptibility
1. Introduction The RFe11Ti compounds, where R is a rareearth, adopt the I4/mmm ThMn12 structure [1–4] and are potential candidates for permanent magnets because they offer both a high iron content and a consequent high magnetization *Corresponding author. Tel.: +1-573-341-4420; fax: +-573341-6033. E-mail address: [email protected] (G.J. Long).
and a relatively high Curie temperature. Insertion of up to one hydrogen atom per formula unit expands the lattice, increases the Curie temperature, and increases the saturation magnetization [5,6]. In addition to these beneficial effects on the magnetic properties, hydrogen insertion also affects [7] the spin reorientations observed in the parent RFe11Ti compounds. According to Nikitin et al. [8] the insertion of hydrogen into DyFe11Ti to form DyFe11TiH ( 3 or by 0.8 increases the unit-cell volume by 2.8 A
0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00245-2
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percent and increases the Curie temperature by 27 K from 546 to 573 K. Apostolov et al. [9] report ( 3 and a Curie an increase in volume of 1.4 A temperature increase of 45 K from 530 to 575 K. The increase in volume observed herein for the hydrogenation of DyFe11Ti to form DyFe11TiH is ( 3 or an increase of 1.2 A ( 3 per hydrogen atom. 2.4 A A concomitant increase from 552 to 600 K in the Curie temperature is observed. DyFe11Ti exhibits two spin reorientations which have been studied [8–12] in detail by magnetization and magnetic susceptibility measurements. The angle, a; between the easy magnetization direction and the c-axis of the unit cell varies with temperature as is shown in Fig. 1. The temperatures at which the spin reorientations occur vary rather widely in the literature. This variation has been explained [13] by differences in the titanium content and spatial homogeneity between different samples. The temperature, TSR1 ; at which the spins rotate away from the c-axis of the unit cell varies between 200 [10–12] and 250 K [8] and the temperature, TSR2 ; at which the spins align within the basal plane of the unit cell varies from 52 [13], 60 [10,12], 100 [11] to 120 K [8]. In Fig. 1, values of 200 and 100 K have been used for TSR1 and TSR2 ; respectively, values which correspond to those observed in the AC magnetic susceptibility measurements reported in
Fig. 1. The temperature dependence of the angle, a; between the easy magnetization direction, M; and the c-axis of the tetragonal unit cell and the weighted average quadrupole shift, /eS; observed in DyFe11Ti.
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Section 3 and are in agreement with those reported by Kou et al. [11]. As stressed by Kuz’min [13], the spin reorientation at TSR2 is very sharp, whereas that at TSR1 is gradual, i.e., the transitions at ca. 100 and 200 K are first and second order, respectively. All authors agree that below TSR2 the magnetic moments are aligned within the basal plane but they disagree on the specific basal planar direction. According to Hu et al. [10] the moments are along [1 0 0] whereas, according to Algarabel et al. [12], they are along the [1 1 0] axis. The influence of hydrogen insertion on the spin reorientations found in DyFe11Ti has already been investigated but, again, there is disagreement in the literature. An early report by Zhang et al. [14] indicated that two spin reorientations occur in DyFe11TiH1.4. In contrast, according to Apostolov et al. [9] who have studied DyFe11TiHx, with 0oxo1; the two spin-reorientation temperatures, TSR1 and TSR2 ; increase with x for xo0:8 and become essentially equal to the Curie temperature for xX0:8: Hence, DyFe11TiH exhibits basal magnetic anisotropy at all temperatures below its Curie temperature of 600 K. In contrast, Nikitin et al. [8] report that DyFe11TiH exhibits a basal magnetic anisotropy below 260 K and a complex magnetic structure between 260 K and its Curie temperature. This disagreement may be related to somewhat different hydrogen and titanium contents in different DyFe11TiH samples, contents which may also explain the different unit-cell expansions reported by Nikitin et al. [8] and Apostolov et al. [9]. Our magnetic measurements, discussed in Section 3 confirm that no spin reorientation occurs in DyFe11TiH below its Curie temperature. It seems clear that, as previously observed [5,15] in several related RFe11Ti compounds, hydrogen insertion enhances the rareearth, i.e., dysprosium, magnetic anisotropy, an anisotropy which dominates over that of iron at a higher temperatures in DyFe11TiH as compared with DyFe11Ti. . Iron-57 Mossbauer spectral studies [3,7,16–19] of the R2Fe17 and RFe11Ti compounds and their hydrides have been instrumental in understanding the influence of hydrogen on the microscopic magnetic properties of the iron sublattices in these compounds. Indeed, a systematic correlation
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between the Wigner–Seitz cell volume of a site and . the Mossbauer-effect isomer shift of a given site is observed throughout most of these compounds [16]. The hydrogen insertion is accompanied by an increase in isomer shift, a reduction of the s-electron density at the iron nucleus, and an increase in hyperfine field, the latter of which is related to an increase in the iron magnetic moment [16]. Finally, the orientation of the iron magnetic moments and hyperfine fields within the unit cell of the compound influence the observed . Mossbauer spectra, spectra which are very sensitive to this orientation [20,21]. Because of these influences, we have carried out an iron-57 . Mossbauer spectral study of DyFe11Ti and DyFe11TiH with the goal of elucidating their magnetic structures.
2. Experimental DyFe11Ti has been synthesized and its hydrogenation was carried out as described earlier [15]. Gravimetric mass-gain analysis indicates that the accuracy of the hydrogen content in DyFe11TiH is 70.1 per formula unit. The thermomagnetic analyses of the samples, sealed in a silica tube under hydrogen gas to avoid oxidation and hydrogen loss, were performed on a Faraday balance. The low temperature AC magnetic susceptibilities were obtained on a computer controlled mutual inductance susceptometer [22] at an exciting field of 104 T and a frequency of 120 Hz. A lock-in amplifier was used to measure the complex susceptibility, wAC ¼ w0 jw00 ; where w0 is the initial susceptibility, a quantity which is related to the variation in the sample magnetization, and w00 is positive if magnetic energy is absorbed by the sample. The temperature dependence of the real component, w0 , and the imaginary component, w00 , of the AC susceptibility were measured in order to determine the temperatures of the magnetic phase transitions. These measurements are very sensitive to the onset of the magnetic phase transition caused by changes in the anisotropy energy. The real portion of the AC susceptibility is determined predominately by the changes in both the magnetic anisotropy energy
and the domain wall energy, whereas the imaginary AC susceptibility reflects energy absorption by the sample, an energy that mainly arises from domain wall movement. . The Mossbauer spectra were measured between 4.2 and 295 K on a constant-acceleration spectrometer which utilized a rhodium matrix cobalt-57 source and was calibrated at room temperature . with a-iron foil. The Mossbauer spectral absorbers contained 35 mg/cm2 of powdered sample which had been sieved to a 0.045 mm or smaller diameter particle size. The low temperature spectra were obtained in a Janis Super-Varitemp cryostat and the temperature was controlled with a Lakeshore Cryogenics temperature controller with an accuracy of better than 1% of the observed temperature. The resulting spectra have been fit as discussed below and the estimated errors are at most 70.2 T for the hyperfine fields and their changes per additional titanium near neighbor, 70.01 mm/s for the isomer shifts and their changes, and 70.02 mm/s for the quadrupole shifts and their changes.
3. Magnetic measurements The temperature dependence of the real part of the AC magnetic susceptibility in DyFe11Ti, shown in Fig. 2, exhibits two anomalies. The low temperature anomaly at 97 K manifests itself as a welldefined peak which is characteristic of a first-order transition. The high temperature anomaly at ca. 200 K has a step-like shape which is characteristic of a second-order transition. Two corresponding peaks are also observed in the imaginary part of the AC magnetic susceptibility. These results are in excellent agreement with those of Kou et al. [11] and suggest according to Kuz’min [13] that the two samples have a similar titanium content, which is somewhat smaller than one. Further, these anomalies and peaks correspond to the spin reorientations described above and in Fig. 1. In contrast, the real part of the AC magnetic susceptibility in DyFe11TiH, also shown in Fig. 2, increases smoothly between 4.2 and 300 K, a smooth increase which indicates the absence of any spin reorientation process over this range of temperatures.
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The temperature dependence of the magnetization in DyFe11Ti and DyFe11TiH, measured in an applied field of 0.1 T is shown in Fig. 3. The observed ordering temperatures are 552 and 600 K, respectively. The slightly larger magnetization observed in DyFe11TiH results from the different temperature dependencies of the iron and dysprosium sublattices. Further, the absence of any anomaly between 300 and 600 K definitively establishes the absence of any spin reorientation below the Curie temperature in DyFe11TiH. This result confirms the observed [9] absence of any spin reorientations in DyFe11TiHx for x > 0:8: For both compounds, the weak ferromagnetic signal observed above the ordering temperatures results from the presence of a small amount of a-iron, an . impurity that is also observed in the Mossbauer spectra, with a relative absorption area of 6 percent.
4. M.ossbauer spectral results Fig. 2. The temperature dependence of the AC magnetic susceptibility in DyFe11Ti, closed circles, and DyFe11TiH, open circles.
Fig. 3. The temperature dependence of the magnetization in DyFe11Ti, solid line, and DyFe11TiH, dotted line, measured in a field of 0.1 T.
. The Mossbauer spectra of DyFe11Ti and DyFe11TiH, obtained between 4.2 and 295 K, are shown in Figs. 4 and 5, respectively. The . Mossbauer spectra of DyFe11Ti have been obtained for the three different magnetic states of this compound shown in Fig. 1. In Fig. 4 it is obvious that the shape of the spectrum changes with the direction of the magnetic anisotropy in these different phases. In contrast, the general shape of the DyFe11TiH spectra do not change with temperature, see Fig. 5. This latter observation supports the absence in DyFe11TiH [9] of any spin reorientation between 4.2 and 295 K, in agreement with the AC magnetic susceptibility and magnetization results discussed in Section 3. Because in DyFe11Ti the iron atoms occupy three inequivalent 8f, 8i, and 8j crystallographic sites and the titanium atoms occupy only the 8i sites, at least three sextets, assigned to the 8f, 8i, and 8j sites and with relative areas in the ratio of . 8:6:8, should be used to fit the Mossbauer spectra. However, as noted earlier [3,7,23,24] for RFe11Ti where R is Ce, Er, Gd, or Ho, and their hydrides, these three sextets must be further subdivided in order to take into account the random distribution
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. Fig. 4. The Mossbauer spectra of DyFe11Ti obtained at the indicated temperatures.
. Fig. 5. The Mossbauer spectra of DyFe11TiH obtained at the indicated temperatures.
of the titanium atoms in the neighborhood of the three iron sites. If the titanium atoms randomly occupy the 8i site, the iron atoms on the 8f, 8i, and 8j sites have distribution of near-neighbor environments, distributions which are assumed to be binomial in nature. As a result, if the titanium content is one per formula unit, the 8i sextet is subdivided into three sextets with 6.47, 10.79, and 9.58 percent areas, and each of the 8f and 8j sextets are subdivided into three sextets with 11.51, 15.34,
and 9.38 percent areas. These sextets represent iron atoms with zero, one, and two or more titanium near neighbors, respectively. An analysis [25] of the point symmetry of the three iron sites in the RFe11Ti structure indicates that the principal axis of the electric field gradient tensor lies in the basal plane of the unit cell for all three sites. The point symmetry of the 8i and 8j sites is m2m and hence, the principal axis of the electric field gradient tensor is expected along either the [1 0 0] or the [0 1 0] directions. In
ARTICLE IN PRESS C. Piquer et al. / Journal of Magnetism and Magnetic Materials 265 (2003) 156–166
contrast, the point symmetry of the 8f sites is 2/m and hence, the principal axis of the electric field gradient tensor is expected to make an angle of 745 with the [1 0 0] or [0 1 0] directions. Thus, if the iron magnetic moments and, hence, hyperfine fields are oriented parallel to the c-axis of the unit cell, the angle, y; between the hyperfine field and the principal axis of the electric field gradient tensor is 90 for all three iron sites and the crystallographically equivalent iron atoms are also magnetically equivalent. Hence, in the case of the axial magnetic anisotropy of DyFe11Ti at 240 and 295 K, nine sextets are sufficient to fit the . Mossbauer spectra. In the presence of a basal or canted magnetic anisotropy, a further subdivision of the three sextets assigned to each inequivalent iron site may be necessary. Because of the orientation of the iron magnetic moments and, consequently, of the hyperfine fields away from the c-axis, multiple relative orientations of the principal axis of the electric field gradient and of the hyperfine field occur and yield different angles, y; between these two directions and hence different quadrupole . shifts in the Mossbauer spectral magnetic sextets. A close examination of the symmetry at the three iron sites indicates that, if the hyperfine field is in the basal plane along the [1 0 0] or [0 1 0] direction, there is no further subdivision of the 8f sextets, for which the angle y between the hyperfine field and the principal axis of the electric field gradient tensor is 745 . In contrast there is a further subdivision of the 8i and 8j sextets, into two magnetically inequivalent sites, with the same probability, two magnetically inequivalent sites for which the angles y between the hyperfine field and the principal axis of the electric field gradient tensor are different. Thus each sextet assigned to the 8i and 8j sites has been subdivided into two sextets of equal relative areas with identical isomer shifts but different quadrupole shifts and slightly different hyperfine fields. This sextet subdivision is well established for the R2Fe17 compounds, see for instance Ref. [20]. Hence, in their basal or canted . magnetic structure, the Mossbauer spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K have been modeled with 15 sextets. In order to check the adequacy of this fitting
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model, we have tried to analyze the spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K, assuming that the hyperfine field is along the [1 1 0] or [1–10] directions in the basal plane. In this case, the crystallographically equivalent 8f sites are subdivided into two magnetically inequivalent sites with the same population, whereas the crystallographically inequivalent 8i and 8j sites are not subdivided. The resulting fits were significantly poorer than those shown in Figs. 4 and 5. In conclusion within the assump. tions in our model, the Mossbauer spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K, in their basal or canted magnetic structure, are compatible with the iron magnetic moments oriented along the [1 0 0] direction in the basal plane in agreement with Ref. [10]. A given sextet is defined by three hyperfine parameters, the hyperfine field, H, the isomer shift, d and the quadrupole shift, e: In order to build constraints into the model and to reduce the number of adjustable parameters, we have assumed that the three hyperfine parameters for each crystallographically inequivalent iron site change linearly with the number of titanium near neighbors, n; such that Hn ¼ H0 þ nDH; dn ¼ d0 þ nDd and en ¼ e0 þ nDe; where H0 ; d0 ; and e0 are the hyperfine field, isomer shift, and quadrupole shift, respectively, for zero titanium near neighbors and DH; Dd; and De; are the changes in the hyperfine field, isomer shift, and quadrupole shift, respectively, for one additional titanium near neighbor. A similar linear dependence of the hyperfine field on the number of substitutional near-neighbor atoms has been successfully used in the analysis [17–19] of the . Mossbauer spectra of both the R2Fe17xMx solid solutions and RFe11Ti, where R is Ce, Gd, Er, and Ho, and their hydrides [3,7,23,24]. Thus the . Mossbauer spectra at 240 and 295 K of DyFe11Ti have been fit with nine sextets, which include 18 hyperfine parameters, one linewidth, and one total
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Table 1 . The Mossbauer spectral hyperfine parameters for DyFe11Ti T (K)
8i1
H0 (DH) (T)
295 240 155 85 4.2
30.2 31.9 34.1 38.3 39.1
d0 a(Dd) (mm/s)
295 240 155 85 4.2
0.006 (0.013) 0.042 (0.013) 0.127 (0.022) 0.193 (0.020) 0.210 (0.031)
0.006 (0.013) 0.042 (0.013) 0.127 (0.022) 0.193 (0.020) 0.210 (0.031)
0.126 (0.008) 0.100 (0.005) 0.020 (0.016) 0.005 (0.016) 0.010 (0.015)
0.126 (0.008) 0.100 (0.005) 0.020 (0.016) 0.005 (0.016) 0.010 (0.015)
0.142 0.100 0.028 0.017 0.017
e0 ðDeÞ (mm/s)
295 240 155 85 4.2
0.167 (0.037) 0.152 (0.023) 0.025 (0.053) 0.072 (0.035) 0.143 (0.063)
0.167 (0.037) 0.152 (0.023) 0.025 (0.053) –0.075 (0.041) 0.117 (0.011)
0.021 (0.014) 0.011 (0.000) 0.006 (0.202) 0.085 (0.025) 0.106 (0.046)
0.021 0.011 0.006 0.109 0.075
0.026 (0.063) 0.027 (0.033) 0.143 (0.110) 0.134 (0.016) 0.144 (0.014)
0.068 0.059 0.017 0.021 0.040
8f
Wt. av.
a
8i2 (1.7) (1.8) (1.8) (2.1) (2.2)
30.2 31.9 35.5 35.5 36.0
8j1 (1.7) (1.8) (2.2) (2.4) (2.5)
8j2
26.4 28.0 29.3 30.8 31.0
(2.5) (2.6) (2.6) (2.9) (2.9)
26.4 28.0 30.0 31.6 31.9
8f (2.5) (2.6) (2.4) (3.2) (3.4)
(0.014) (0.000) (0.202) (0.250) (0.279)
25.3 26.7 28.0 28.8 29.0
Wt. av. (2.6) (2.7) (2.6) (2.5) (2.6) (0.030) (0.030) (0.034) (0.034) (0.034)
24.7 26.2 28.0 29.2 29.5 0.116 0.078 0.007 0.022 0.027
Relative to room temperature a-iron foil.
Table 2 . The Mossbauer spectral hyperfine parameters for DyFe11TiH T (K)
8i1
H0 (DH) (T)
295 225 155 85 4.2
35.3 37.3 38.7 39.5 40.0
d0 a(Dd) (mm/s)
295 225 155 85 4.2
0.077 0.128 0.161 0.198 0.209
e0 ðDeÞ (mm/s)
295 225 155 85 4.2
–0.061 –0.094 –0.113 –0.147 –0.172
a
8i2 (–2.7) (–2.9) (–2.7) (–2.7) (–2.7) (–0.039) (–0.029) (–0.017) (–0.023) (–0.022) (–0.019) (–0.029) (0.002) (0.030) (0.029)
33.3 35.3 36.8 37.6 38.0
8j1 (–2.3) (–2.3) (–2.5) (–2.5) (–2.5)
0.077 0.128 0.161 0.198 0.209
(–0.039) (–0.029) (–0.017) (–0.023) (–0.022)
–0.104 –0.069 –0.118 –0.137 –0.184
(–0.019) (–0.025) (0.020) (0.010) (0.010)
28.0 29.4 30.6 31.4 31.7
8j2 (–1.7) (–1.7) (–1.9) (–1.9) (–1.9)
28.1 30.0 31.6 32.3 32.5
(–2.1) (–2.3) (–2.6) (–2.7) (–2.7)
26.4 28.1 29.5 30.2 30.4
(–2.5) (–2.7) (–2.9) (–3.0) (–3.0)
26.9 28.5 29.8 30.4 30.7
–0.103 (–0.024) –0.057 (–0.013) –0.010 (–0.010) 0.031 (–0.015) 0.040 (–0.014)
–0.103 (–0.024) –0.057 (–0.013) –0.010 (–0.010) 0.031 (–0.015) 0.040 (–0.014)
–0.122 –0.084 –0.059 –0.032 –0.017
(0.018) (–0.020) (–0.010) (–0.008) (–0.008)
0.087 –0.036 0.006 0.039 0.051
0.359 0.394 0.399 0.425 0.397
–0.225 –0.170 –0.185 –0.208 –0.183
–0.301 –0.334 –0.360 –0.351 –0.330
(0.131) (0.152) (0.147) (0.149) (0.150)
–0.047 –0.050 –0.062 –0.062 –0.065
(–0.014) (0.000) (–0.108) (–0.025) (–0.046)
(–0.105) (–0.161) (–0.144) (–0.145) (–0.145)
Relative to room temperature a-iron foil.
. absorption area. In contrast, the Mossbauer spectra below 240 K of DyFe11Ti and of DyFe11TiH have been fit with 15 sextets, which include 26 hyperfine parameters, one linewidth, and one total absorption area. As is shown in Figs. 4 and 5, all the fits are very good. The hyperfine parameters
for DyFe11Ti and DyFe11TiH are given in Tables 1 and 2, respectively. The fitted linewidths were typically 0.3970.01 mm/s and were larger than the experimental calibration linewidth of 0.26 mm/s. This broadening indicates the inability of our fitting model to adequately account both for
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changes in quadrupole shift resulting from the presence of one or more titanium atoms on given near-neighbor sites and for any possible titanium spatial inhomogeneity, an inhomogeneity which is reported [13] to be responsible for the spread in spin-reorientation temperatures. Because of the large number of parameters involved in the above fits, one would anticipate that it would be easy to obtain good spectral fits but that the fits might be far from unique. Hence, in the next section we discuss the temperature dependencies of the hyperfine parameters and indicate how they help to provide confidence for the spectral analysis, its physical basis, and the extent to which it is unique. Our past experience indicates that it is not nearly as easy as anticipated to find good fits of the observed spectra especially when, as must be the case, physically viable changes in the hyperfine parameters with temperature are imposed upon the model.
5. Discussion The assignment and temperature dependence of the three hyperfine fields with zero titanium near neighbors, and their weighted average, for
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DyFe11Ti and DyFe11TiH are shown in Fig. 6a and b, respectively. A Wigner–Seitz cell analysis [26] of the three inequivalent iron sites in RFe11Ti and RFe11TiH indicates that the 8i site has 11.75 iron near-neighbors, the largest average number of iron near neighbors, whereas the 8f and 8j iron sites have only nine iron near neighbors. Consequently, in both DyFe11Ti and DyFe11TiH, the sextets with the largest hyperfine field, H0 ; have been assigned to the 8i site, both on the basis of its percentage contribution to the spectral area and its iron near-neighbor environment. As is indicated below, this assignment is further supported by the observed isomer shift values. Because of both their identical constrained percentage areas and iron near-neighbor environments, it is not possible to unequivocally assign the 8f and 8j sextets on the basis of their fields and their assignment is based on the isomer shift, see below. Because the three H0 hyperfine fields all increase upon hydrogen insertion, the sequence of hyperfine fields, 8i>8j>8f, remains unchanged upon hydrogenation, see Fig. 6b. Indeed, a Wigner–Seitz cell analysis [26] indicates that, in addition to the lattice expansion, hydrogen insertion adds only one hydrogen to the near-neighbor environment of the 8j site; the 8f and 8i sites do not have any hydrogen near neighbors.
Fig. 6. The temperature dependence of the maximum hyperfine fields, H0 ; at the three iron sites, and their weighted average, in DyFe11Ti (a) and DyFe11TiH (b). The solid lines are the result of the fits discussed in the text. The error bars are essentially the size of the data points.
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The solid lines in Fig. 6 are the result of a leastsquares fit [27] with the equation H ¼ H0 ½1 B3=2 ðT=TC Þ3=2 C5=2 ðT=TC Þ5=2 ; where H0 and TC are the saturation field and magnetic ordering temperature, respectively. Curie temperatures of 552 and 600 K were used for DyFe11Ti and DyFe11TiH, respectively. The T 3=2 term in this equation has its origin [28] in the excitation of long-wavelength spin waves. The B3=2 coefficients are ca. 0.1 and 0.2 in DyFe11Ti and DyFe11TiH, respectively. The C5=2 coefficients are ca. 0.5 and 0.3 in DyFe11Ti and DyFe11TiH, respectively. The temperature dependence of the increase in the three hyperfine fields upon hydrogenation is shown in Fig. 7. The three hyperfine fields increase because of the lattice expansion. Similar increases in hyperfine field upon hydrogenation, deuteration, or nitrogenation of several R2Fe17 compounds have been observed [20,21,29]. The 8i site shows the most remarkable behavior. Below 100 K the hyperfine field difference is essentially small and constant within the error bars, between 100
Fig. 7. The hyperfine field difference between DyFe11Ti and DyFe11TiH for the three iron sites and their weighted average.
and 200 K, it substantially increases, and above 200 K, it is essentially constant within the error bars. This remarkable behavior follows the change in easy magnetization direction with temperature. Specifically, at 240 and 295 K, where the two compounds have different easy magnetization direction, i.e., axial for DyFe11Ti and basal for DyFe11TiH, the 8i hyperfine field difference is particularly large. In contrast, below 100 K, where the two compounds have the same basal easy magnetization direction, the hyperfine field difference is small. Such a behavior may result from the dependence of the orbital contribution to the hyperfine field upon the easy magnetization direction. A similar break [20,21] has been observed in the temperature dependence of the hyperfine fields in Tm2Fe17 and Pr2Fe17Hx, with x between 3 and 5, both of which present similar axial–basal spin reorientations. The changes in the hyperfine field per titanium near neighbor are 2.670.1 T for the 8f site, 2.270.4 T for the 8i site, and 3.070.5 T for the 8j site, in DyFe11Ti and 2.770.3 T for the 8f site, 2.670.3 T for the 8i site, and 2.270.5 T for the 8j site, in DyFe11TiH. The errors reflect the variations in the changes with temperature between 4.2 and 295 K. Hence, we can conclude, as expected, that these changes are relatively independent of temperature. The observed decreases in the hyperfine fields upon the replacement of one iron by one titanium near neighbor are very similar to those previously observed [3,7,23,24,30] in both RFe11Ti and their hydrides, where R is Y, Ce, Gd, Ho, or Er, and are within the range of 1.1 to 6 T observed in a spinel oxide [31] and in Nd2Fe16Ti [32], respectively. The assignment and the temperature dependence of the three site average isomer shifts, and their weighted average, for DyFe11Ti and DyFe11TiH are shown in Fig. 8a and b, respectively. The site average isomer shifts have been calculated from the dn values weighted with the percent contribution given by the binomial distribution. In agreement with the Wigner–Seitz cell analysis [26] of the three inequivalent iron sites, the sequence of isomer shifts, 8i>8j>8f, follows the sequence of Wigner–Seitz cell volumes, with 8f and 8j isomer shifts virtually equal in DyFe11Ti. Such a
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Fig. 8. The temperature dependence of the three site average isomer shifts, and their weighted average, in DyFe11Ti (a) and DyFe11TiH (b). The solid lines through the weighted average isomer shift is the result of a fit with a Debye model of the second-order Doppler shift. The error bars are approximately twice the size of the data points.
relationship between isomer shifts and Wigner– Seitz cell volumes has been observed [20,29] in many R2Fe17 compounds and was also found [7,23,24] to hold for RFe11Ti and RFe11TiH, where R is Er, Gd, or Ho. The temperature dependence of the weighted average isomer shifts shown in Fig. 8 has been fit [33,34] with the Debye model for the second-order Doppler shift. For both compounds the resulting effective vibrating mass is, as expected, 57 g/mol . and the effective Mossbauer temperature is 306710 and 344710 K for DyFe11Ti and DyFe11TiH, respectively. These temperatures are typical of intermetallic compounds [16,21,29]. The changes in the isomer shift per titanium near neighbor are virtually independent of temperature and are between 0.02 and 0.04 mm/s in DyFe11Ti and 0.00 and 0.02 mm/s in DyFe11TiH. Such small changes have been observed [3,7,23,24,30] in RFe11Ti and their hydrides, where R is Y, Ce, Gd, Ho, or Er. The observed quadrupole shifts in the . Mossbauer spectra of DyFe11Ti and DyFe11TiH are small and lie between 0.2 and 0.1 mm/s. Such small quadrupole shifts are expected because . Mossbauer spectral studies [35] at 295 K of some related paramagnetic RFe11Ti and RFe11Mo compounds yield quadrupole splittings of at most 0.7 mm/s. The temperature dependence of the average quadrupole shift in the DyFe11Ti spectra
interestingly reflects the two spin reorientations occurring in this compound. As indicated in Fig. 1, it is positive at 240 and 295 K, negative at 4.2 and 85 K and nearly zero at 155 K. This influence of the spin reorientations on the quadrupole shift is not unexpected as the y angle between the hyperfine field and the principal axis of the electric field gradient tensor changes at the spin reorientation.
6. Conclusions The magnetic phase diagram for DyFe11Ti has been obtained by combined AC magnetic suscept. ibility, thermomagnetic, and iron-57 Mossbauer spectral measurements. The temperature dependence of the average quadrupole shift and of the hyperfine fields follow that of the easy magnetiza. tion direction. The Mossbauer spectra at 4.2 and 85 K are consistent with the iron magnetic moments aligned along the [1 0 0] direction within the basal plane of the tetragonal unit cell. Our combined AC magnetic susceptibility, thermomag. netic, and iron-57 Mossbauer spectral measurements of DyFe11TiH show the absence of any spin reorientation below its ordering temperature and are consistent with a basal magnetic anisotropy. Hence, the insertion of hydrogen into DyFe11Ti to form DyFe11TiH enhances the dysprosium
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magnetocrystalline contribution to the magnetic anisotropy. [15]
Acknowledgements
[16] [17]
The financial support of the University of Lie" ge for grant number 2850006 is acknowledged with thanks. This work was partially supported by the US National Science Foundation through grants DMR95-21739 and INT-9815138, and the ‘‘Centre National de la Recherche Scientifique, France’’ through grant action initiative number 7418.
[18]
[19]
[20] [21]
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Journal of Magnetism and Magnetic Materials 265 (2003) 156–166
. Magnetic and Mossbauer spectral properties of DyFe11Ti and DyFe11TiH Cristina Piquera, Olivier Isnardb,c, Fernande Grandjeana, Gary J. Longd,* a Department of Physics, B5, University of Li"ege, B-4000 Sart-Tilman, Belgium Laboratoire de Cristallographie associ!e au CNRS, Universit!e J. Fourier, BP 166X, F-38042 Grenoble Cedex, France c Institut Universitaire de France, Maison des Universite!s, 103 Boulevard Saint-Michel, F-75005 Paris Cedex, France d Department of Chemistry, University of Missouri-Rolla, Rolla, MO 65409-0010, USA
b
Received 23 January 2003
Abstract The temperature dependence of the AC magnetic susceptibility, between 4.2 and 300 K, and the magnetization, . spectral measurements between 300 and 600 K, has been measured for DyFe11Ti and DyFe11TiH. Iron-57 Mossbauer between 4.2 and 295 K have also been carried out on DyFe11Ti and DyFe11TiH and analyzed with a model which considers both the direction of the magnetization in the different magnetic phases of these compounds and the distribution of titanium atoms in the near-neighbor environment of the three crystallographically distinct iron sites. The . magnetic measurements and the Mossbauer spectra of DyFe11Ti clearly show the influence of the two spin reorientations occurring in this compound and indicate that the iron magnetic moments are oriented along the [1 0 0] . direction of the basal plane below 100 K. The magnetic measurements and the Mossbauer spectra of DyFe11TiH do not show any evidence for spin reorientations and are consistent with a basal magnetic anisotropy between 4.2 and 600 K. Hence, the hydrogen insertion into DyFe11Ti reinforces the dysprosium magnetic anisotropy. The assignment and the . temperature dependencies of the Mossbauer spectral hyperfine fields and isomer shifts are in full agreement with a Wigner–Seitz cell analysis of the three iron sites in DyFe11Ti and DyFe11TiH. r 2003 Elsevier Science B.V. All rights reserved. . Keywords: Mossbauer spectra; Rare earth compounds; Magnetic susceptibility
1. Introduction The RFe11Ti compounds, where R is a rareearth, adopt the I4/mmm ThMn12 structure [1–4] and are potential candidates for permanent magnets because they offer both a high iron content and a consequent high magnetization *Corresponding author. Tel.: +1-573-341-4420; fax: +-573341-6033. E-mail address: [email protected] (G.J. Long).
and a relatively high Curie temperature. Insertion of up to one hydrogen atom per formula unit expands the lattice, increases the Curie temperature, and increases the saturation magnetization [5,6]. In addition to these beneficial effects on the magnetic properties, hydrogen insertion also affects [7] the spin reorientations observed in the parent RFe11Ti compounds. According to Nikitin et al. [8] the insertion of hydrogen into DyFe11Ti to form DyFe11TiH ( 3 or by 0.8 increases the unit-cell volume by 2.8 A
0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00245-2
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percent and increases the Curie temperature by 27 K from 546 to 573 K. Apostolov et al. [9] report ( 3 and a Curie an increase in volume of 1.4 A temperature increase of 45 K from 530 to 575 K. The increase in volume observed herein for the hydrogenation of DyFe11Ti to form DyFe11TiH is ( 3 or an increase of 1.2 A ( 3 per hydrogen atom. 2.4 A A concomitant increase from 552 to 600 K in the Curie temperature is observed. DyFe11Ti exhibits two spin reorientations which have been studied [8–12] in detail by magnetization and magnetic susceptibility measurements. The angle, a; between the easy magnetization direction and the c-axis of the unit cell varies with temperature as is shown in Fig. 1. The temperatures at which the spin reorientations occur vary rather widely in the literature. This variation has been explained [13] by differences in the titanium content and spatial homogeneity between different samples. The temperature, TSR1 ; at which the spins rotate away from the c-axis of the unit cell varies between 200 [10–12] and 250 K [8] and the temperature, TSR2 ; at which the spins align within the basal plane of the unit cell varies from 52 [13], 60 [10,12], 100 [11] to 120 K [8]. In Fig. 1, values of 200 and 100 K have been used for TSR1 and TSR2 ; respectively, values which correspond to those observed in the AC magnetic susceptibility measurements reported in
Fig. 1. The temperature dependence of the angle, a; between the easy magnetization direction, M; and the c-axis of the tetragonal unit cell and the weighted average quadrupole shift, /eS; observed in DyFe11Ti.
157
Section 3 and are in agreement with those reported by Kou et al. [11]. As stressed by Kuz’min [13], the spin reorientation at TSR2 is very sharp, whereas that at TSR1 is gradual, i.e., the transitions at ca. 100 and 200 K are first and second order, respectively. All authors agree that below TSR2 the magnetic moments are aligned within the basal plane but they disagree on the specific basal planar direction. According to Hu et al. [10] the moments are along [1 0 0] whereas, according to Algarabel et al. [12], they are along the [1 1 0] axis. The influence of hydrogen insertion on the spin reorientations found in DyFe11Ti has already been investigated but, again, there is disagreement in the literature. An early report by Zhang et al. [14] indicated that two spin reorientations occur in DyFe11TiH1.4. In contrast, according to Apostolov et al. [9] who have studied DyFe11TiHx, with 0oxo1; the two spin-reorientation temperatures, TSR1 and TSR2 ; increase with x for xo0:8 and become essentially equal to the Curie temperature for xX0:8: Hence, DyFe11TiH exhibits basal magnetic anisotropy at all temperatures below its Curie temperature of 600 K. In contrast, Nikitin et al. [8] report that DyFe11TiH exhibits a basal magnetic anisotropy below 260 K and a complex magnetic structure between 260 K and its Curie temperature. This disagreement may be related to somewhat different hydrogen and titanium contents in different DyFe11TiH samples, contents which may also explain the different unit-cell expansions reported by Nikitin et al. [8] and Apostolov et al. [9]. Our magnetic measurements, discussed in Section 3 confirm that no spin reorientation occurs in DyFe11TiH below its Curie temperature. It seems clear that, as previously observed [5,15] in several related RFe11Ti compounds, hydrogen insertion enhances the rareearth, i.e., dysprosium, magnetic anisotropy, an anisotropy which dominates over that of iron at a higher temperatures in DyFe11TiH as compared with DyFe11Ti. . Iron-57 Mossbauer spectral studies [3,7,16–19] of the R2Fe17 and RFe11Ti compounds and their hydrides have been instrumental in understanding the influence of hydrogen on the microscopic magnetic properties of the iron sublattices in these compounds. Indeed, a systematic correlation
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between the Wigner–Seitz cell volume of a site and . the Mossbauer-effect isomer shift of a given site is observed throughout most of these compounds [16]. The hydrogen insertion is accompanied by an increase in isomer shift, a reduction of the s-electron density at the iron nucleus, and an increase in hyperfine field, the latter of which is related to an increase in the iron magnetic moment [16]. Finally, the orientation of the iron magnetic moments and hyperfine fields within the unit cell of the compound influence the observed . Mossbauer spectra, spectra which are very sensitive to this orientation [20,21]. Because of these influences, we have carried out an iron-57 . Mossbauer spectral study of DyFe11Ti and DyFe11TiH with the goal of elucidating their magnetic structures.
2. Experimental DyFe11Ti has been synthesized and its hydrogenation was carried out as described earlier [15]. Gravimetric mass-gain analysis indicates that the accuracy of the hydrogen content in DyFe11TiH is 70.1 per formula unit. The thermomagnetic analyses of the samples, sealed in a silica tube under hydrogen gas to avoid oxidation and hydrogen loss, were performed on a Faraday balance. The low temperature AC magnetic susceptibilities were obtained on a computer controlled mutual inductance susceptometer [22] at an exciting field of 104 T and a frequency of 120 Hz. A lock-in amplifier was used to measure the complex susceptibility, wAC ¼ w0 jw00 ; where w0 is the initial susceptibility, a quantity which is related to the variation in the sample magnetization, and w00 is positive if magnetic energy is absorbed by the sample. The temperature dependence of the real component, w0 , and the imaginary component, w00 , of the AC susceptibility were measured in order to determine the temperatures of the magnetic phase transitions. These measurements are very sensitive to the onset of the magnetic phase transition caused by changes in the anisotropy energy. The real portion of the AC susceptibility is determined predominately by the changes in both the magnetic anisotropy energy
and the domain wall energy, whereas the imaginary AC susceptibility reflects energy absorption by the sample, an energy that mainly arises from domain wall movement. . The Mossbauer spectra were measured between 4.2 and 295 K on a constant-acceleration spectrometer which utilized a rhodium matrix cobalt-57 source and was calibrated at room temperature . with a-iron foil. The Mossbauer spectral absorbers contained 35 mg/cm2 of powdered sample which had been sieved to a 0.045 mm or smaller diameter particle size. The low temperature spectra were obtained in a Janis Super-Varitemp cryostat and the temperature was controlled with a Lakeshore Cryogenics temperature controller with an accuracy of better than 1% of the observed temperature. The resulting spectra have been fit as discussed below and the estimated errors are at most 70.2 T for the hyperfine fields and their changes per additional titanium near neighbor, 70.01 mm/s for the isomer shifts and their changes, and 70.02 mm/s for the quadrupole shifts and their changes.
3. Magnetic measurements The temperature dependence of the real part of the AC magnetic susceptibility in DyFe11Ti, shown in Fig. 2, exhibits two anomalies. The low temperature anomaly at 97 K manifests itself as a welldefined peak which is characteristic of a first-order transition. The high temperature anomaly at ca. 200 K has a step-like shape which is characteristic of a second-order transition. Two corresponding peaks are also observed in the imaginary part of the AC magnetic susceptibility. These results are in excellent agreement with those of Kou et al. [11] and suggest according to Kuz’min [13] that the two samples have a similar titanium content, which is somewhat smaller than one. Further, these anomalies and peaks correspond to the spin reorientations described above and in Fig. 1. In contrast, the real part of the AC magnetic susceptibility in DyFe11TiH, also shown in Fig. 2, increases smoothly between 4.2 and 300 K, a smooth increase which indicates the absence of any spin reorientation process over this range of temperatures.
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The temperature dependence of the magnetization in DyFe11Ti and DyFe11TiH, measured in an applied field of 0.1 T is shown in Fig. 3. The observed ordering temperatures are 552 and 600 K, respectively. The slightly larger magnetization observed in DyFe11TiH results from the different temperature dependencies of the iron and dysprosium sublattices. Further, the absence of any anomaly between 300 and 600 K definitively establishes the absence of any spin reorientation below the Curie temperature in DyFe11TiH. This result confirms the observed [9] absence of any spin reorientations in DyFe11TiHx for x > 0:8: For both compounds, the weak ferromagnetic signal observed above the ordering temperatures results from the presence of a small amount of a-iron, an . impurity that is also observed in the Mossbauer spectra, with a relative absorption area of 6 percent.
4. M.ossbauer spectral results Fig. 2. The temperature dependence of the AC magnetic susceptibility in DyFe11Ti, closed circles, and DyFe11TiH, open circles.
Fig. 3. The temperature dependence of the magnetization in DyFe11Ti, solid line, and DyFe11TiH, dotted line, measured in a field of 0.1 T.
. The Mossbauer spectra of DyFe11Ti and DyFe11TiH, obtained between 4.2 and 295 K, are shown in Figs. 4 and 5, respectively. The . Mossbauer spectra of DyFe11Ti have been obtained for the three different magnetic states of this compound shown in Fig. 1. In Fig. 4 it is obvious that the shape of the spectrum changes with the direction of the magnetic anisotropy in these different phases. In contrast, the general shape of the DyFe11TiH spectra do not change with temperature, see Fig. 5. This latter observation supports the absence in DyFe11TiH [9] of any spin reorientation between 4.2 and 295 K, in agreement with the AC magnetic susceptibility and magnetization results discussed in Section 3. Because in DyFe11Ti the iron atoms occupy three inequivalent 8f, 8i, and 8j crystallographic sites and the titanium atoms occupy only the 8i sites, at least three sextets, assigned to the 8f, 8i, and 8j sites and with relative areas in the ratio of . 8:6:8, should be used to fit the Mossbauer spectra. However, as noted earlier [3,7,23,24] for RFe11Ti where R is Ce, Er, Gd, or Ho, and their hydrides, these three sextets must be further subdivided in order to take into account the random distribution
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. Fig. 4. The Mossbauer spectra of DyFe11Ti obtained at the indicated temperatures.
. Fig. 5. The Mossbauer spectra of DyFe11TiH obtained at the indicated temperatures.
of the titanium atoms in the neighborhood of the three iron sites. If the titanium atoms randomly occupy the 8i site, the iron atoms on the 8f, 8i, and 8j sites have distribution of near-neighbor environments, distributions which are assumed to be binomial in nature. As a result, if the titanium content is one per formula unit, the 8i sextet is subdivided into three sextets with 6.47, 10.79, and 9.58 percent areas, and each of the 8f and 8j sextets are subdivided into three sextets with 11.51, 15.34,
and 9.38 percent areas. These sextets represent iron atoms with zero, one, and two or more titanium near neighbors, respectively. An analysis [25] of the point symmetry of the three iron sites in the RFe11Ti structure indicates that the principal axis of the electric field gradient tensor lies in the basal plane of the unit cell for all three sites. The point symmetry of the 8i and 8j sites is m2m and hence, the principal axis of the electric field gradient tensor is expected along either the [1 0 0] or the [0 1 0] directions. In
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contrast, the point symmetry of the 8f sites is 2/m and hence, the principal axis of the electric field gradient tensor is expected to make an angle of 745 with the [1 0 0] or [0 1 0] directions. Thus, if the iron magnetic moments and, hence, hyperfine fields are oriented parallel to the c-axis of the unit cell, the angle, y; between the hyperfine field and the principal axis of the electric field gradient tensor is 90 for all three iron sites and the crystallographically equivalent iron atoms are also magnetically equivalent. Hence, in the case of the axial magnetic anisotropy of DyFe11Ti at 240 and 295 K, nine sextets are sufficient to fit the . Mossbauer spectra. In the presence of a basal or canted magnetic anisotropy, a further subdivision of the three sextets assigned to each inequivalent iron site may be necessary. Because of the orientation of the iron magnetic moments and, consequently, of the hyperfine fields away from the c-axis, multiple relative orientations of the principal axis of the electric field gradient and of the hyperfine field occur and yield different angles, y; between these two directions and hence different quadrupole . shifts in the Mossbauer spectral magnetic sextets. A close examination of the symmetry at the three iron sites indicates that, if the hyperfine field is in the basal plane along the [1 0 0] or [0 1 0] direction, there is no further subdivision of the 8f sextets, for which the angle y between the hyperfine field and the principal axis of the electric field gradient tensor is 745 . In contrast there is a further subdivision of the 8i and 8j sextets, into two magnetically inequivalent sites, with the same probability, two magnetically inequivalent sites for which the angles y between the hyperfine field and the principal axis of the electric field gradient tensor are different. Thus each sextet assigned to the 8i and 8j sites has been subdivided into two sextets of equal relative areas with identical isomer shifts but different quadrupole shifts and slightly different hyperfine fields. This sextet subdivision is well established for the R2Fe17 compounds, see for instance Ref. [20]. Hence, in their basal or canted . magnetic structure, the Mossbauer spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K have been modeled with 15 sextets. In order to check the adequacy of this fitting
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model, we have tried to analyze the spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K, assuming that the hyperfine field is along the [1 1 0] or [1–10] directions in the basal plane. In this case, the crystallographically equivalent 8f sites are subdivided into two magnetically inequivalent sites with the same population, whereas the crystallographically inequivalent 8i and 8j sites are not subdivided. The resulting fits were significantly poorer than those shown in Figs. 4 and 5. In conclusion within the assump. tions in our model, the Mossbauer spectra of DyFe11Ti below 240 K and DyFe11TiH between 4.2 and 295 K, in their basal or canted magnetic structure, are compatible with the iron magnetic moments oriented along the [1 0 0] direction in the basal plane in agreement with Ref. [10]. A given sextet is defined by three hyperfine parameters, the hyperfine field, H, the isomer shift, d and the quadrupole shift, e: In order to build constraints into the model and to reduce the number of adjustable parameters, we have assumed that the three hyperfine parameters for each crystallographically inequivalent iron site change linearly with the number of titanium near neighbors, n; such that Hn ¼ H0 þ nDH; dn ¼ d0 þ nDd and en ¼ e0 þ nDe; where H0 ; d0 ; and e0 are the hyperfine field, isomer shift, and quadrupole shift, respectively, for zero titanium near neighbors and DH; Dd; and De; are the changes in the hyperfine field, isomer shift, and quadrupole shift, respectively, for one additional titanium near neighbor. A similar linear dependence of the hyperfine field on the number of substitutional near-neighbor atoms has been successfully used in the analysis [17–19] of the . Mossbauer spectra of both the R2Fe17xMx solid solutions and RFe11Ti, where R is Ce, Gd, Er, and Ho, and their hydrides [3,7,23,24]. Thus the . Mossbauer spectra at 240 and 295 K of DyFe11Ti have been fit with nine sextets, which include 18 hyperfine parameters, one linewidth, and one total
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Table 1 . The Mossbauer spectral hyperfine parameters for DyFe11Ti T (K)
8i1
H0 (DH) (T)
295 240 155 85 4.2
30.2 31.9 34.1 38.3 39.1
d0 a(Dd) (mm/s)
295 240 155 85 4.2
0.006 (0.013) 0.042 (0.013) 0.127 (0.022) 0.193 (0.020) 0.210 (0.031)
0.006 (0.013) 0.042 (0.013) 0.127 (0.022) 0.193 (0.020) 0.210 (0.031)
0.126 (0.008) 0.100 (0.005) 0.020 (0.016) 0.005 (0.016) 0.010 (0.015)
0.126 (0.008) 0.100 (0.005) 0.020 (0.016) 0.005 (0.016) 0.010 (0.015)
0.142 0.100 0.028 0.017 0.017
e0 ðDeÞ (mm/s)
295 240 155 85 4.2
0.167 (0.037) 0.152 (0.023) 0.025 (0.053) 0.072 (0.035) 0.143 (0.063)
0.167 (0.037) 0.152 (0.023) 0.025 (0.053) –0.075 (0.041) 0.117 (0.011)
0.021 (0.014) 0.011 (0.000) 0.006 (0.202) 0.085 (0.025) 0.106 (0.046)
0.021 0.011 0.006 0.109 0.075
0.026 (0.063) 0.027 (0.033) 0.143 (0.110) 0.134 (0.016) 0.144 (0.014)
0.068 0.059 0.017 0.021 0.040
8f
Wt. av.
a
8i2 (1.7) (1.8) (1.8) (2.1) (2.2)
30.2 31.9 35.5 35.5 36.0
8j1 (1.7) (1.8) (2.2) (2.4) (2.5)
8j2
26.4 28.0 29.3 30.8 31.0
(2.5) (2.6) (2.6) (2.9) (2.9)
26.4 28.0 30.0 31.6 31.9
8f (2.5) (2.6) (2.4) (3.2) (3.4)
(0.014) (0.000) (0.202) (0.250) (0.279)
25.3 26.7 28.0 28.8 29.0
Wt. av. (2.6) (2.7) (2.6) (2.5) (2.6) (0.030) (0.030) (0.034) (0.034) (0.034)
24.7 26.2 28.0 29.2 29.5 0.116 0.078 0.007 0.022 0.027
Relative to room temperature a-iron foil.
Table 2 . The Mossbauer spectral hyperfine parameters for DyFe11TiH T (K)
8i1
H0 (DH) (T)
295 225 155 85 4.2
35.3 37.3 38.7 39.5 40.0
d0 a(Dd) (mm/s)
295 225 155 85 4.2
0.077 0.128 0.161 0.198 0.209
e0 ðDeÞ (mm/s)
295 225 155 85 4.2
–0.061 –0.094 –0.113 –0.147 –0.172
a
8i2 (–2.7) (–2.9) (–2.7) (–2.7) (–2.7) (–0.039) (–0.029) (–0.017) (–0.023) (–0.022) (–0.019) (–0.029) (0.002) (0.030) (0.029)
33.3 35.3 36.8 37.6 38.0
8j1 (–2.3) (–2.3) (–2.5) (–2.5) (–2.5)
0.077 0.128 0.161 0.198 0.209
(–0.039) (–0.029) (–0.017) (–0.023) (–0.022)
–0.104 –0.069 –0.118 –0.137 –0.184
(–0.019) (–0.025) (0.020) (0.010) (0.010)
28.0 29.4 30.6 31.4 31.7
8j2 (–1.7) (–1.7) (–1.9) (–1.9) (–1.9)
28.1 30.0 31.6 32.3 32.5
(–2.1) (–2.3) (–2.6) (–2.7) (–2.7)
26.4 28.1 29.5 30.2 30.4
(–2.5) (–2.7) (–2.9) (–3.0) (–3.0)
26.9 28.5 29.8 30.4 30.7
–0.103 (–0.024) –0.057 (–0.013) –0.010 (–0.010) 0.031 (–0.015) 0.040 (–0.014)
–0.103 (–0.024) –0.057 (–0.013) –0.010 (–0.010) 0.031 (–0.015) 0.040 (–0.014)
–0.122 –0.084 –0.059 –0.032 –0.017
(0.018) (–0.020) (–0.010) (–0.008) (–0.008)
0.087 –0.036 0.006 0.039 0.051
0.359 0.394 0.399 0.425 0.397
–0.225 –0.170 –0.185 –0.208 –0.183
–0.301 –0.334 –0.360 –0.351 –0.330
(0.131) (0.152) (0.147) (0.149) (0.150)
–0.047 –0.050 –0.062 –0.062 –0.065
(–0.014) (0.000) (–0.108) (–0.025) (–0.046)
(–0.105) (–0.161) (–0.144) (–0.145) (–0.145)
Relative to room temperature a-iron foil.
. absorption area. In contrast, the Mossbauer spectra below 240 K of DyFe11Ti and of DyFe11TiH have been fit with 15 sextets, which include 26 hyperfine parameters, one linewidth, and one total absorption area. As is shown in Figs. 4 and 5, all the fits are very good. The hyperfine parameters
for DyFe11Ti and DyFe11TiH are given in Tables 1 and 2, respectively. The fitted linewidths were typically 0.3970.01 mm/s and were larger than the experimental calibration linewidth of 0.26 mm/s. This broadening indicates the inability of our fitting model to adequately account both for
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changes in quadrupole shift resulting from the presence of one or more titanium atoms on given near-neighbor sites and for any possible titanium spatial inhomogeneity, an inhomogeneity which is reported [13] to be responsible for the spread in spin-reorientation temperatures. Because of the large number of parameters involved in the above fits, one would anticipate that it would be easy to obtain good spectral fits but that the fits might be far from unique. Hence, in the next section we discuss the temperature dependencies of the hyperfine parameters and indicate how they help to provide confidence for the spectral analysis, its physical basis, and the extent to which it is unique. Our past experience indicates that it is not nearly as easy as anticipated to find good fits of the observed spectra especially when, as must be the case, physically viable changes in the hyperfine parameters with temperature are imposed upon the model.
5. Discussion The assignment and temperature dependence of the three hyperfine fields with zero titanium near neighbors, and their weighted average, for
163
DyFe11Ti and DyFe11TiH are shown in Fig. 6a and b, respectively. A Wigner–Seitz cell analysis [26] of the three inequivalent iron sites in RFe11Ti and RFe11TiH indicates that the 8i site has 11.75 iron near-neighbors, the largest average number of iron near neighbors, whereas the 8f and 8j iron sites have only nine iron near neighbors. Consequently, in both DyFe11Ti and DyFe11TiH, the sextets with the largest hyperfine field, H0 ; have been assigned to the 8i site, both on the basis of its percentage contribution to the spectral area and its iron near-neighbor environment. As is indicated below, this assignment is further supported by the observed isomer shift values. Because of both their identical constrained percentage areas and iron near-neighbor environments, it is not possible to unequivocally assign the 8f and 8j sextets on the basis of their fields and their assignment is based on the isomer shift, see below. Because the three H0 hyperfine fields all increase upon hydrogen insertion, the sequence of hyperfine fields, 8i>8j>8f, remains unchanged upon hydrogenation, see Fig. 6b. Indeed, a Wigner–Seitz cell analysis [26] indicates that, in addition to the lattice expansion, hydrogen insertion adds only one hydrogen to the near-neighbor environment of the 8j site; the 8f and 8i sites do not have any hydrogen near neighbors.
Fig. 6. The temperature dependence of the maximum hyperfine fields, H0 ; at the three iron sites, and their weighted average, in DyFe11Ti (a) and DyFe11TiH (b). The solid lines are the result of the fits discussed in the text. The error bars are essentially the size of the data points.
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The solid lines in Fig. 6 are the result of a leastsquares fit [27] with the equation H ¼ H0 ½1 B3=2 ðT=TC Þ3=2 C5=2 ðT=TC Þ5=2 ; where H0 and TC are the saturation field and magnetic ordering temperature, respectively. Curie temperatures of 552 and 600 K were used for DyFe11Ti and DyFe11TiH, respectively. The T 3=2 term in this equation has its origin [28] in the excitation of long-wavelength spin waves. The B3=2 coefficients are ca. 0.1 and 0.2 in DyFe11Ti and DyFe11TiH, respectively. The C5=2 coefficients are ca. 0.5 and 0.3 in DyFe11Ti and DyFe11TiH, respectively. The temperature dependence of the increase in the three hyperfine fields upon hydrogenation is shown in Fig. 7. The three hyperfine fields increase because of the lattice expansion. Similar increases in hyperfine field upon hydrogenation, deuteration, or nitrogenation of several R2Fe17 compounds have been observed [20,21,29]. The 8i site shows the most remarkable behavior. Below 100 K the hyperfine field difference is essentially small and constant within the error bars, between 100
Fig. 7. The hyperfine field difference between DyFe11Ti and DyFe11TiH for the three iron sites and their weighted average.
and 200 K, it substantially increases, and above 200 K, it is essentially constant within the error bars. This remarkable behavior follows the change in easy magnetization direction with temperature. Specifically, at 240 and 295 K, where the two compounds have different easy magnetization direction, i.e., axial for DyFe11Ti and basal for DyFe11TiH, the 8i hyperfine field difference is particularly large. In contrast, below 100 K, where the two compounds have the same basal easy magnetization direction, the hyperfine field difference is small. Such a behavior may result from the dependence of the orbital contribution to the hyperfine field upon the easy magnetization direction. A similar break [20,21] has been observed in the temperature dependence of the hyperfine fields in Tm2Fe17 and Pr2Fe17Hx, with x between 3 and 5, both of which present similar axial–basal spin reorientations. The changes in the hyperfine field per titanium near neighbor are 2.670.1 T for the 8f site, 2.270.4 T for the 8i site, and 3.070.5 T for the 8j site, in DyFe11Ti and 2.770.3 T for the 8f site, 2.670.3 T for the 8i site, and 2.270.5 T for the 8j site, in DyFe11TiH. The errors reflect the variations in the changes with temperature between 4.2 and 295 K. Hence, we can conclude, as expected, that these changes are relatively independent of temperature. The observed decreases in the hyperfine fields upon the replacement of one iron by one titanium near neighbor are very similar to those previously observed [3,7,23,24,30] in both RFe11Ti and their hydrides, where R is Y, Ce, Gd, Ho, or Er, and are within the range of 1.1 to 6 T observed in a spinel oxide [31] and in Nd2Fe16Ti [32], respectively. The assignment and the temperature dependence of the three site average isomer shifts, and their weighted average, for DyFe11Ti and DyFe11TiH are shown in Fig. 8a and b, respectively. The site average isomer shifts have been calculated from the dn values weighted with the percent contribution given by the binomial distribution. In agreement with the Wigner–Seitz cell analysis [26] of the three inequivalent iron sites, the sequence of isomer shifts, 8i>8j>8f, follows the sequence of Wigner–Seitz cell volumes, with 8f and 8j isomer shifts virtually equal in DyFe11Ti. Such a
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165
Fig. 8. The temperature dependence of the three site average isomer shifts, and their weighted average, in DyFe11Ti (a) and DyFe11TiH (b). The solid lines through the weighted average isomer shift is the result of a fit with a Debye model of the second-order Doppler shift. The error bars are approximately twice the size of the data points.
relationship between isomer shifts and Wigner– Seitz cell volumes has been observed [20,29] in many R2Fe17 compounds and was also found [7,23,24] to hold for RFe11Ti and RFe11TiH, where R is Er, Gd, or Ho. The temperature dependence of the weighted average isomer shifts shown in Fig. 8 has been fit [33,34] with the Debye model for the second-order Doppler shift. For both compounds the resulting effective vibrating mass is, as expected, 57 g/mol . and the effective Mossbauer temperature is 306710 and 344710 K for DyFe11Ti and DyFe11TiH, respectively. These temperatures are typical of intermetallic compounds [16,21,29]. The changes in the isomer shift per titanium near neighbor are virtually independent of temperature and are between 0.02 and 0.04 mm/s in DyFe11Ti and 0.00 and 0.02 mm/s in DyFe11TiH. Such small changes have been observed [3,7,23,24,30] in RFe11Ti and their hydrides, where R is Y, Ce, Gd, Ho, or Er. The observed quadrupole shifts in the . Mossbauer spectra of DyFe11Ti and DyFe11TiH are small and lie between 0.2 and 0.1 mm/s. Such small quadrupole shifts are expected because . Mossbauer spectral studies [35] at 295 K of some related paramagnetic RFe11Ti and RFe11Mo compounds yield quadrupole splittings of at most 0.7 mm/s. The temperature dependence of the average quadrupole shift in the DyFe11Ti spectra
interestingly reflects the two spin reorientations occurring in this compound. As indicated in Fig. 1, it is positive at 240 and 295 K, negative at 4.2 and 85 K and nearly zero at 155 K. This influence of the spin reorientations on the quadrupole shift is not unexpected as the y angle between the hyperfine field and the principal axis of the electric field gradient tensor changes at the spin reorientation.
6. Conclusions The magnetic phase diagram for DyFe11Ti has been obtained by combined AC magnetic suscept. ibility, thermomagnetic, and iron-57 Mossbauer spectral measurements. The temperature dependence of the average quadrupole shift and of the hyperfine fields follow that of the easy magnetiza. tion direction. The Mossbauer spectra at 4.2 and 85 K are consistent with the iron magnetic moments aligned along the [1 0 0] direction within the basal plane of the tetragonal unit cell. Our combined AC magnetic susceptibility, thermomag. netic, and iron-57 Mossbauer spectral measurements of DyFe11TiH show the absence of any spin reorientation below its ordering temperature and are consistent with a basal magnetic anisotropy. Hence, the insertion of hydrogen into DyFe11Ti to form DyFe11TiH enhances the dysprosium
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magnetocrystalline contribution to the magnetic anisotropy. [15]
Acknowledgements
[16] [17]
The financial support of the University of Lie" ge for grant number 2850006 is acknowledged with thanks. This work was partially supported by the US National Science Foundation through grants DMR95-21739 and INT-9815138, and the ‘‘Centre National de la Recherche Scientifique, France’’ through grant action initiative number 7418.
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