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A magnetic and Mössbauer spectral study of HoFe11Ti and HoFe11TiH
Journal of Alloys and Compounds 353 (2003) 33–41
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¨ A magnetic and Mossbauer spectral study of HoFe 11 Ti and HoFe 11 TiH a a, b c Cristina Piquer , Fernande Grandjean *, Gary J. Long , Olivier Isnard a ` , B-4000 Sart-Tilman, Belgium Department of Physics, B5, University of Liege Department of Chemistry, University of Missouri-Rolla, Rolla, MO 65409 -0010, USA c Laboratoire de Cristallographie, CNRS, Associe´ a l’ Universite´ J. Fourier, BP 166 X, F-38042 Grenoble Cedex, France b
Received 22 October 2002; accepted 29 October 2002
Abstract A.c. susceptibility measurements were carried out between 4.2 and 295 K on HoFe 11 TiH and reveal a spin-reorientation transition at ¨ |150 K. Iron-57 Mossbauer spectral measurements between 4.2 and 295 K were carried out on both HoFe 11 Ti and HoFe 11 TiH. The ¨ Mossbauer spectra were analyzed with a model which considers both the orientation of the iron magnetic moments and the distribution of titanium atoms in the near-neighbor environment of the three crystallographically distinct iron sites. The assignment and the temperature dependence of the hyperfine fields is in complete agreement with both the iron magnetic moments measured by neutron diffraction and the changes expected at the spin-reorientation. The assignment and the temperature dependence of the isomer shifts is in complete agreement both with the crystallographic changes occurring at the spin reorientation and upon hydrogen insertion. The changes in hyperfine field and isomer shift with the number of titanium near neighbors for each of the three iron sites are consistent with the values observed for related titanium–iron intermetallic compounds. 2002 Elsevier Science B.V. All rights reserved. ¨ spectroscopy; Magnetic measurements Keywords: Rare earth compounds; Hydrogen absorbing materials; Gas–solid reactions; Mossbauer
1. Introduction The magnetic behavior of HoFe 11 Ti, which crystallizes with the tetragonal I4 /mmm ThMn 12 structure [1–7], has been extensively investigated for 15 years. The Curie temperature of HoFe 11 Ti is 53364 K [3,6,7] and at room temperature its easy magnetization direction is parallel to the tetragonal axis of the unit cell. There have been several controversial reports [3–7] of a spin reorientation at |50 K, a spin reorientation which has been unquestionably ruled out [8–10]. However, the magnetic behavior of HoFe 11 Ti in an applied field is unusual and interesting. When a field of ,3 T is applied parallel to the basal plane of the tetragonal unit cell a type II first-order magnetization process occurs below 120 K, a process which exhibits a large anisotropy. Indeed, when the field is applied along the [100] direction, the first-order magnetization process occurs at a larger field than when the field is applied along the [110] direction. This unusual behavior has been attributed [10] to the coexistence of a low-field conical magnetic phase, with an angle of 78 *Corresponding author. Fax: 132-3-366-4516. E-mail address: [email protected] (F. Grandjean).
between the tetragonal axis and the magnetic easy axis, and a high-field conical magnetic phase, with an angle of 608. Because of the large anisotropy, HoFe 11 Ti has been studied [8,9] by three-dimensional magnetometry, a technique which yields the magnetization both parallel and perpendicular to the applied magnetic field. At small applied magnetic fields, the mutually and strictly antiparallel holmium and iron magnetic moments of HoFe 11 Ti rotate within the plane defined by the tetragonal axis, i.e. the easy magnetization direction, and the applied field direction. For applied fields .3.5 T, the first-order magnetization process induces a rotation of the magnetization vector both towards the applied magnetic field and out of the plane defined by the tetragonal axis and the applied field direction, presumably towards the [110] direction within the basal plane of the unit cell. Because of the controversial existence of a spin reorientation in HoFe 11 Ti, the magnetic properties of the hydrides, HoFe 11 TiH x , have been investigated [1,2] by both neutron diffraction and magnetic measurements. The neutron diffraction studies indicate that hydrogen occupies the octahedral 2b site in the ThMn 12 structure and that the unit cell expands anisotropically upon hydrogenation. The Curie temperatures of the hydrides, HoFe 11 TiH x , increase
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01204-5
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Table 1 Lattice parameters and magnetic properties of HoFe 11 Ti and HoFe 11 TiH Compound
˚ a (A)
˚ c (A)
T C (K)
T sr (K)
HoFe 11 Ti HoFe 11 TiH
8.491 (1) 8.525 (1)
4.784 (1) 4.794 (1)
533 590
– 150
from 533 to 590 K as x increases from 0 to 1. The magnetic measurements indicate that, above a critical hydrogen content of 0.4, the magnetic moments deviate slightly from the tetragonal c axis at all temperatures below the Curie temperature. In addition, a spin reorientation, a change in the tilt angle of the magnetic moments, occurs at a temperature which increases from 100 to 150 K as x increases from 0.65 to 1. Above and below the spin reorientation, the tilt angles of the magnetic moment [1] are 30 and 708, respectively. This spin reorientation, which is accompanied by substantial and abrupt variations in the lattice parameters [1], results from a change in the magnetocrystalline anisotropy, a change which is induced by the insertion of hydrogen. The neutron diffraction measurements also show substantial changes in the iron magnetic moments on two, the 8i and 8j sites, of the three iron sites. This spin reorientation was further confirmed [11] by torque measurements performed on single crystals of HoFe 11 Ti and HoFe 11 TiH. Because HoFe 11 Ti and its hydrides, HoFe 11 TiH x , exhibit such unusual and interesting magnetic properties, we have carried out a.c. magnetic susceptibility and iron-57 ¨ Mossbauer spectral studies with the goal of investigating in
detail the behavior of the iron sublattices in the different magnetic phases.
2. Experimental HoFe 11 Ti and its hydride, HoFe 11 TiH x , were synthesized as described [12] previously. The hydrogen content was determined to be one through the gravimetric massgain method. The lattice parameters and some of the magnetic properties are summarized in Table 1. The temperature dependence of the magnetization, shown in Fig. 1a, has been used to determine the Curie temperatures. The low temperature a.c. magnetic susceptibilities have been obtained on a computer controlled mutual inductance susceptometer [13] with an exciting field of 10 24 T and a frequency of 120 Hz. A lock-in amplifier was used to measure the complex susceptibility, xac 5 x 9 2 ix 0 where x 9 is the initial susceptibility, a quantity which is related to the variation in the sample magnetization, and x 0 is non zero if magnetic energy is absorbed by the sample. ¨ 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 / cm 2 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 Supervaritemp cryostat and the temperature was controlled with a Lakeshore Cryogenics temperature controller with an accuracy of better than 1%
Fig. 1. Temperature dependence of (a) the magnetization of HoFe 11 Ti, solid line, and HoFe 11 TiH, dashed line, and (b) the a.c. magnetic susceptibility of HoFe 11 TiH.
C. Piquer et al. / Journal of Alloys and Compounds 353 (2003) 33–41
35
of the observed temperature. The resulting spectra have been fit as discussed below and the estimated errors are at most 60.2 T for the hyperfine fields and their changes upon hydrogenation, 60.01 mm / s for the isomer shifts and their changes, and 60.02 mm / s for the quadrupole shifts and their changes. The observed linewidths were typically 0.4060.01 mm / s.
3. A.c. magnetic susceptibility results The a.c. magnetic susceptibility of HoFe 11 Ti has been measured [5,15] previously between 4 and 300 K. These investigations confirmed [4,16,17] the absence of any magnetic transition and the alignment of the magnetization along the c axis of the tetragonal unit cell in this temperature range. The temperature dependence of the real component of the a.c. susceptibility of HoFe 11 TiH, as is shown in Fig. 1b, exhibits an anomaly at |150 K. This maximum in the a.c. susceptibility is similar to that observed for ErFe 11 Ti, a maximum that has been associated [5] with a second-order spin-reorientation transition. The occurrence of such a spin-reorientation transition in HoFe 11 TiH has been confirmed [1,2] through a powder neutron diffraction study. Hydrogen insertion in the lattice induces a significant modification in the crystal electric field parameters at the rare-earth site and hence modifies the axial magnetic anisotropy observed in HoFe 11 Ti. The change in the crystal field gradient at the gadolinium site in both GdFe 11 Ti and GdFe 11 TiH has been demonstrated by ¨ gadolinium-155 Mossbauer spectroscopy [14]. More recently, a comparative study of HoFe 11 Ti and HoFe 11 TiH has shown that not only the crystal electric field gradient but also the higher order terms in the crystal electric field coefficients are modified by hydrogen insertion [11]. This modification arises from the changes produced by the inserted hydrogen atom in the rare-earth near-neighbor environment.
¨ 4. Mossbauer spectral measurements ¨ The Mossbauer spectra of HoFe 11 Ti and HoFe 11 TiH obtained between 4.2 and 295 K are shown in Figs. 2 and 3, respectively. Because the iron atoms occupy the 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, with relative areas in the ratio of 8:6:8 are required to fit the spectra. However, as already noted [18–20] in our studies of other RFe 11 Ti compounds and their hydrides, these three sextets must be further subdivided in order to take into account the distribution of the titanium atoms in the neighborhood of the three iron sites. The random occupation of the 8i sites by titanium
¨ Fig. 2. Mossbauer spectra of HoFe 11 Ti obtained at the indicated temperatures.
results in a binomial distribution of the titanium near neighbors of the three iron sites. Hence, the 8i sextet is subdivided into three sextets with 6.47, 10.79 and 9.98 percent areas, and each of the 8f and 8j sextets is subdivided into three sextets with 11.51, 15.34, and 9.52 percent areas, sextets which represent the iron with zero, one, and two or more titanium near neighbors, respectively. Hence, at least nine sextets, with their areas fixed to the
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crystallographically inequivalent iron site vary linearly with the number, n, of titanium near neighbors, as given by the equations Hn 5 H0 1 nDH
dn 5 d0 1 nDd and
en 5 e0 1 nDe
¨ Fig. 3. Mossbauer spectra of HoFe 11 TiH obtained at the indicated temperatures.
above relative values, are required to accurately model the ¨ Mossbauer spectra of HoFe 11 Ti obtained at all temperatures in its uniaxial magnetic phase. For HoFe 11 TiH in its conical magnetic phases, even more sextets are required, see below. Three hyperfine parameters define each sextet, the hyperfine field, H, the isomer shift, d, and the quadrupole shift, e. In order to both build in constraints into the model and to reduce the number of adjustable parameters, we assume that the three hyperfine parameters for each
where H0 , d0 , and e0 are the hyperfine field, isomer shift, and quadrupole shift, respectively, for zero titanium near neighbor 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 [21–24] in the analysis of the Mossbauer spectra of ¨ the R 2 Fe 172x M x solid solutions. Hence, the Mossbauer spectra of HoFe 11 Ti have been fit with nine sextets, which include 18 hyperfine parameters, one linewidth, and one total absorption area. As is shown in Fig. 2, all the fits are very good; the resulting hyperfine parameters are given in Table 2. The conical magnetic structure [1] of HoFe 11 TiH further subdivides the three sextets assigned to each inequivalent iron site. Because of the canting 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 the hyperfine field occur and yield different angles, u, between these two directions and hence different quadrupole shifts and hyperfine fields. A close examination of the symmetry at the three iron sites indicates that, if the easy magnetization direction lies in the plane defined by the [001] and [100] or [010] directions, there is no further subdivision of the sextet representing the 8f site, whereas there is a further subdivision of those representing the 8i and 8j sites. Each sextet assigned to the 8i and 8j sites is subdivided into two sextets 8i 1 , 8i 2 , 8j 1 , and 8j 2 of equal relative areas with identical isomer shifts but different quadrupole shifts and slightly different hyperfine fields. The subdivision of the sextets is different if the easy magnetization direction lies in the plane defined by the [001] and [110] directions. In this case, the 8f sextet is subdivided into two, 8f1 and 8f2 , sextets of equal relative areas and with identical isomer shifts but with different quadrupole shifts and slightly different hyperfine fields; there is no further subdivision of the 8i and 8j sextets. This sextet subdivision is well established for the R 2 Fe 17 compounds, see for instance Ref. [25]. In the former case, ¨ the Mossbauer spectra of the HoFe 11 TiH compound should be modelled with 15 sextets, which involve 26 hyperfine parameters, one linewidth and one total absorption area. In the latter case 12 sextets, involving 22 hyperfine parameters, one linewidth and one total absorption area would be
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Table 2 ¨ Mossbauer spectral hyperfine parameters for HoFe 11 Ti Parameter
T (K)
H0 (DH ) (T)
4.2 85 155 225 295
d0 a (Dd ) (mm / s)
4.2 85 155 225 295
20.085 (0.051) 20.108 (0.060) 20.149 (0.064) 20.205 (0.090) 20.247 (0.094)
0.139 (0.000) 0.137 (0.008) 0.117 (0.007) 0.083 (0.007) 0.010 (0.006)
20.047 (0.016) 20.061 (0.020) 20.087 (0.014) 20.125 (0.025) 20.150 (0.019)
0.013 0.006 20.025 20.056 20.101
e0 (De ) (mm / s)
4.2 85 155 225 295
0.017 (0.047) 0.009 (0.035) 0.007 (0.054) 0.019 (0.047) 0.013 (0.069)
0.147(0.048) 0.150 (0.037) 0.119 (0.046) 0.112 (0.052) 0.075 (0.092)
20.078 (0.074) 20.062 (0.052) 20.078 (0.062) 20.096 (0.069) 20.122 (0.069)
0.074 0.063 0.061 0.058 0.056
a
8f
8i
28.0 27.6 27.0 26.0 24.4
(22.4) (22.6) (22.6) (22.5) (22.5)
34.0 33.6 32.9 31.9 29.9
8j (21.9) (22.0) (22.1) (22.3) (22.1)
31.6 31.2 30.3 29.0 27.0
Wt. av. (22.3) (22.3) (22.3) (22.1) (21.9)
28.7 28.2 27.5 26.4 24.7
Relative to a-iron at 295 K.
required. Actually, above the spin reorientation in HoFe 11 TiH, when the canting angle of the moments from the c axis is small, i.e. 08 [11] or 308 [1,2], it was found that the further subdivision of the sextets was not required to obtain good fits. However, below the spin-reorientation temperature, at 4.2 and 85 K, the further subdivision of the 8i and 8j sextets was required to obtain good fits. As may be observed in Fig. 3, the fits are very good; the resulting hyperfine parameters are given in Table 3. The alternative fits with a subdivision of the 8f sextets were not satisfactory. Because of the number of parameters mentioned above, it would seem that it should be easy to obtain good fits but that the fits may be far from unique. Hence, in the next section we discuss the temperature dependencies of the hyperfine parameters and indicate how they help to give confidence to the spectral analysis, its physical basis, and the extent of its uniqueness. Our experience indicates that
it is not as easy as might be expected to obtain good fits of the observed spectra, especially when physically viable changes in the hyperfine parameters with temperature are imposed upon the fits. Indeed, we have not been able to find an alternative model that both provided good fits and viable changes in the hyperfine parameters with temperature, but such an undiscovered model may, of course, exist.
5. Discussion
5.1. Hyperfine fields The assignment and temperature dependence of the three hyperfine fields for zero titanium near neighbor and their weighted average for HoFe 11 Ti and HoFe 11 TiH are shown in Fig. 4a and b, respectively. A Wigner–Seitz cell analysis [26] of the three inequivalent iron sites in HoFe 11 Ti and
Table 3 ¨ Mossbauer spectral hyperfine parameters for HoFe 11 TiH Parameter
T (K)
H0 (DH ) (T)
4.2 85 155 225 295
d0 a (Dd ) (mm / s)
4.2 85 155 225 295
e0 (De ) (mm / s)
4.2 85 155 225 295
a
8f
8i 1
29.5 28.6 27.5 26.7 25.3
(22.2) (22.5) (22.2) (22.4) (22.2)
0.010 20.036 20.056 20.130 20.190
Relative to a-iron at 295 K.
(0.027) (0.027) (0.020) (0.042) (0.040)
0.015 (0.042) 0.020 (0.032) 0.110 (20.019) 0.135 (20.038) 0.100 (0.016)
38.1 36.3 34.1 33.3 31.8
8i 2 (22.2) (21.7) (21.9) (21.7) (21.8)
37.7 (22.3) 35.3 (22.9) – – –
0.200 (20.036) 0.166 (20.042) 0.105 (20.034) 0.032 (20.013) 20.014 (20.002)
– – – –
20.054 20.143 0.017 0.002 0.004
20.069 (0.027) 20.040 (0.069) – – –
(0.017) (0.068) (0.090) (0.102) (0.079)
8j 1 33.4 32.6 31.0 29.6 28.3
8j 2 (22.1) (22.4) (21.9) (21.9) (21.9)
0.080 (20.027) 0.026 (20.001) 0.028 (20.025) 20.025 (0.001) –0.075 (0.001) 0.015 (0.007) 0.088 (20.041) 0.006 (20.020) 0.028 (20.017) 0.003 (0.012)
32.9 (22.1) 31.7 (21.9) – – – – – – – – 20.091 (0.049) 20.059 (0.020) – – –
Wt. av. 30.9 29.5 28.6 27.5 26.2 0.076 0.037 0.006 20.037 20.087 0.006 0.022 0.061 0.072 0.072
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Fig. 4. Temperature dependence of the maximum hyperfine fields, H 0 , at the three iron sites and their average in HoFe 11 Ti (a) and HoFe 11 TiH (b). The solid lines in (a) are the result of the fits discussed in the text.
HoFe 11 TiH indicates that the 8i site has 11.75 iron near neighbors, the largest average number of iron near neighbors, whereas both the 8f and 8j iron sites have only nine iron near neighbors. Consequently, the sextets with the largest hyperfine field, H0 , have been assigned to the 8i site, both on the basis of its percent contribution and its iron near-neighbor environment. As is indicated below, this assignment is further supported by the observed isomer shift values and the large iron magnetic moment that has been observed [1,2] by neutron diffraction for this site. Because of both their identical constrained percentage areas and their identical 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 their isomer shifts, see below. If the three H0 hyperfine fields increase upon hydrogen insertion, the sequence of hyperfine fields, 8i . 8j . 8f, remains unchanged as is shown in Fig. 4b. 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. The solid lines in Fig. 4a are the result of a least-squares fit [27] with the equation H 5 H0 [1–B3 / 2 (T /T C )3 / 2 –C5 / 2 (T /T C )5 / 2 ] where H0 and T C are the saturation field and Curie temperature, 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 between 0.08 and 0.15
and the C5 / 2 coefficients are |0.35; similar values have been obtained [20] for GdFe 11 Ti and GdFe 11 TiD. The temperature dependence of the hyperfine fields in HoFe 11 TiH, see Fig. 4b, is quite different from that shown in Fig. 4a for HoFe 11 Ti and the difference is clearly related to the spin reorientation occurring at |150 K. The hyperfine fields observed at 4.2 and 85 K are substantially larger than those expected from a Brillouin extrapolation of the fields observed above 150 K. The increase in the hyperfine fields below 150 K is clearly related to the increase in the iron magnetic moments observed [1,2] by neutron diffraction. Specifically, the large increase in the 8i hyperfine field corresponds to an increase in the site magnetic moment of |15%. From the 8i hyperfine fields at 155, 225 and 295 K, a 4.2 K Brillouin extrapolated value of 35 T may be estimated whereas a field of 38 T is observed, i.e. 9% more than would be expected. Hence, the temperature dependence of the maximum hyperfine fields in HoFe 11 TiH reflects the temperature dependence [1,2] of the iron magnetic moments. In addition, the discontinuity in the temperature dependence of the 8i hyperfine field is similar to that observed [29] in the temperature dependence of the 4f hyperfine field in Tm 2 Fe 17 , a compound which also exhibits a spin-reorientation transition at 90 K. The temperature dependence of the increase in the three hyperfine fields upon hydrogenation is shown in Fig. 5. Similar increases in the hyperfine fields upon hydrogenation or nitrogenation of several R 2 Fe 17 and RFe 11 Ti compounds have been observed [19–21,29,30]. The very large increase in the 8i hyperfine field at 4.2 and 85 K is related to the spin reorientation occurring below 150 K and
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Hence, we can conclude that, as expected, these changes are relatively independent of temperature below 295 K. The observed decreases in the hyperfine fields upon the replacement of one iron by one titanium near neighbor are very similar to those observed [18,19,31] in the RFe 11 Ti and their hydrides and are within the range of 21.1 to 26 T observed [32,33] in a spinel oxide and in Nd 2 Fe 16 Ti, respectively. Finally, the hyperfine fields observed in the subdivided pairs of sextets, 8i 1 and 8i 2 or 8j 1 and 8j 2 , are very similar, see Table 3. Their differences range between 0.4 and 1 T and are very similar to the differences found in ErFe 11 TiH [19], and somewhat smaller than the differences found for the Pr 2 Fe 17 H x hydrides [25], for x between 1 and 5.
5.2. Isomer shifts
Fig. 5. Hyperfine field difference between HoFe 11 Ti and HoFe 11 TiH for the three iron sites and their average.
the large increase in the 8i iron magnetic moment discussed above. The changes in the hyperfine field per titanium near neighbor are between 22.060.2 T and 22.560.2 T for the three sites, where the errors reflect the variations in the difference with temperature between 4.2 and 295 K.
The assignment and the temperature dependence of the three site average isomer shifts, and their weighted average, for HoFe 11 Ti and HoFe 11 TiH are shown in Fig. 6a 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. Such a relationship between isomer shifts and Wigner–Seitz cell volumes has been observed [21,30] in many R 2 Fe 17 compounds. The overall increase in unit-cell volume accounts for the increase in the weighted average isomer shift upon hydrogenation. All the 295 K isomer
Fig. 6. Temperature dependence of the three site average isomer shifts and their average in HoFe 11 Ti (a) and HoFe 11 TiH (b). The solid line in (a) for the average value is the result of the second-order Doppler shift fit discussed in the text.
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shifts are negative relative to a-iron as has been observed [34,35] in other iron–titanium compounds. The temperature dependence of the weighted average isomer shift in HoFe 11 Ti shown in Fig. 6a has been fit [36,37] with the Debye model for the second order Doppler shift. The resulting effective vibrating mass [37] ¨ of 5962 g / mol and the effective Mossbauer temperature of 447610 K are typical [30,38] of an intermetallic compound. The temperature dependence of the weighted average isomer shifts in HoFe 11 TiH shown in Fig. 6b is somewhat unusual because the three isomer shifts and their weighted average increase almost linearly from 295 to 4.2 K. We believe that this unexpected temperature dependence is related to the unusual temperature dependence [1,2] of the lattice parameters observed for HoFe 11 TiH between 100 and 150 K. Further, a similar increase in isomer shift below the spin reorientation has been observed [29] in Tm 2 Fe 17 . The changes in the isomer shift per titanium near neighbor are virtually independent of temperature and are between 20.04 and 0.10 mm / s, as has already been observed [18,31] for YFe 11 Ti and CeFe 11 Ti and their hydrides. However, it seems difficult to rationalize the sign of these changes for the three inequivalent iron sites.
5.3. Quadrupole shifts ¨ The quadrupole shifts observed in the Mossbauer spectra of HoFe 11 Ti and their changes per titanium near neighbor are small and lie between 20.10 and 0.15 mm / s and 0.03 and 0.09 mm / s, respectively. Small quadrupole shifts are ¨ expected because Mossbauer spectral studies [39] at 295 K of some related paramagnetic RFe 11 Ti and RFe 11 Mo compounds yield quadrupole splittings of at most 0.6 ¨ mm / s. The observed quadrupole shifts in the Mossbauer spectra of HoFe 11 TiH are equally small and the temperature dependence of the maximum quadrupole shift, e0 , see Fig. 7, clearly reveals the spin reorientation between 85 and 155 K. Indeed, first, the observation of two different quadrupole shifts for the 8i and 8j sites indicates that the iron magnetic moments are contained in the plane defined by the [001] and [100] axes of the tetragonal unit cell, in agreement with the angle of 708 between the iron moments and the c axis, obtained [1,2] by powder neutron diffraction. Second, a change in the sign of the quadrupole shift is observed for at least one of the subcomponents of the 8i and 8j sites, as would be expected for a change in sign of (3 cos 2u 21) when u changes from 30 to 708. Because no ¨ satisfactory fits of the Mossbauer spectra of HoFe 11 TiH with a model subdividing the 8f sextets could be obtained, we exclude the possibility that the iron magnetic moments lie in the plane defined by the [001] and [110] directions in the tetragonal unit cell. This conclusion seems to disagree with the easy magnetization direction along [110] observed by Nikitin et al. [11] on a single crystal of HoFe 11 TiH in a large applied field of 2 T. The magnetic torque measure-
Fig. 7. Temperature dependence of the quadrupole shifts in HoFe 11 TiH. The vertical line separates the small cone angle and the large cone angle regions of the magnetic phase diagram.
ments carried out by Nikitin et al. [11] suggest that the magnetic moments are in the plane defined by the [001] and [110] directions in an applied field of 1.2 T. Our ¨ present Mossbauer measurements are carried out in the absence of an applied field and the direction of the iron magnetic moments is different. In view of the sensitivity [8,9] of the magnetic structure of HoFe 11 Ti to the applied magnetic field, it is not surprising that the magnetic structure of HoFe 11 TiH shows a similar sensitivity.
6. Conclusions From a macroscopic point of view the insertion of hydrogen into HoFe 11 Ti to form HoFe 11 TiH expands the lattice, increases the Curie temperature, and induces a spin reorientation between 100 and 150 K. From a microscopic point of view, the insertion of hydrogen increases the 8i and 8j iron magnetic moments and hyperfine fields, whereas it does not change substantially the 8f iron magnetic moment and hyperfine field. In agreement with the observed lattice expansion, the iron-57 weighted ¨ average Mossbauer spectral isomer shift increases. In HoFe 11 TiH, the temperature dependence of the three iron isomer shifts, hyperfine fields, and quadrupole shifts are clearly indicative of the spin reorientation between 100 and 150 K and are related to the peculiar temperature dependence of the lattice parameters. Further, the fitting model with a subdivision of the 8i and 8j sites reveals that the iron magnetic moments lie in the plane defined by the [001] and [100] axes of the tetragonal unit cell. The presence of one titanium near neighbor in the environment of an iron site decreases the hyperfine field by |2 T.
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Acknowledgements ` through The financial support of the University of Liege grant number 2850006 is acknowledged with thanks. This work was partially supported by the US National Science Foundation through grants DMR95-21739 and INT9815138, and the Centre National de la Recherche Scientifique, France through grant action initiative number 7418.
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[16] B.P. Hu, Ph. D. Thesis, Trinity College, Dublin, 1990. [17] Y.C. Yang, L.S. Kong, Y.B. Zha, H. Sun, X.D. Pei, J. Phys. Coll. C8 49 (1988) 543. [18] G.J. Long, D. Hautot, F. Grandjean, O. Isnard, S. Miraglia, J. Magn. Magn. Mater. 202 (1999) 100. [19] C. Piquer, R.P. Hermann, F. Grandjean, G.J. Long, O. Isnard, J. Appl. Phys. (2002) submitted for publication. [20] C. Piquer, F. Grandjean, G.J. Long, O. Isnard, J. Magn. Magn. Mater. (2002) submitted for publication. [21] D. Hautot, G.J. Long, P.C. Ezekwenna, F. Grandjean, D.P. Middleton, K.H.J. Buschow, J. Appl. Phys. 83 (1998) 6736. [22] G.J. Long, G.K. Marasinghe, S. Mishra, O.A. Pringle, Z. Hu, W.B. Yelon, D.P. Middleton, K.H.J. Buschow, F. Grandjean, J. Appl. Phys. 76 (1994) 5383. [23] D.P. Middleton, S.R. Mishra, G.J. Long, O.A. Pringle, Z. Hu, W.B. Yelon, F. Grandjean, K.H.J. Buschow, J. Appl. Phys. 78 (1995) 5568. [24] S.R. Mishra, G.J. Long, O.A. Pringle, D.P. Middleton, Z. Hu, W.B. Yelon, F. Grandjean, K.H.J. Buschow, J. Appl. Phys. 79 (1996) 3145. [25] D. Hautot, G.J. Long, F. Grandjean, O. Isnard, S. Miraglia, J. Appl. Phys. 86 (1999) 2200. [26] L. Gelato, J. Appl. Crystallogr. 14 (1981) 141. [27] H.N. Ok, K.S. Baek, C.S. Kim, Phys. Rev. B 24 (1981) 6600. [28] C. Herring, C. Kittel, Phys. Rev. 81 (1951) 869. [29] F. Grandjean, O. Isnard, G.J. Long, Phys. Rev. B 65 (2002) 64429. [30] D. Hautot, G.J. Long, F. Grandjean, O. Isnard, Phys. Rev. B 62 (2000) 11731. [31] I.S. Tereshina, P. Gaczynsku, V.S. Rusakov, H. Drulis, S.A. Nikitin, W. Suski, N.V. Tristan, T. Palewski, J. Phys.: Condens. Matter 13 (2001) 8161. [32] J.L. Dormann, Rev. Phys. Appl. 15 (1980) 1113. [33] F. Grandjean, P.C. Ezekwenna, G.J. Long, O.A. Pringle, Ph. ´ L’Heritier, M. Ellouze, H.P. Luo, W.B. Yelon, J. Appl. Phys. 84 (1998) 1893. [34] E.V. Mielczarek, W.P. Winfree, Phys. Rev. B 11 (1975) 1026. [35] J. Lu, H.J. Hesse, J. Zukrowski, J. Przewoznik, G. Wortmann, in: I. Ortalli (Ed.), Conference Proceedings, 50, International Conference ¨ of the Applications of the Mossbauer Effect, Italian Physical Society, Bologna, 1996, p. 243. [36] G.J. Long, D. Hautot, F. Grandjean, D.T. Morelli, G.P. Meisner, Phys. Rev. B 60 (1999) 7410; G.J. Long, D. Hautot, F. Grandjean, D.T. Morelli, G.P. Meisner, Phys. Rev. B 62 (2000) 6829. ¨ [37] R.H. Herber, in: R.H. Herber (Ed.), Chemical Mossbauer Spectroscopy, Plenum Press, New York, 1984, p. 199. [38] G.J. Long, O. Isnard, F. Grandjean, J. Appl. Phys. 91 (2002) 1423. [39] F. Grandjean, R.P. Hermann, G.J. Long, unpublished results.
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¨ A magnetic and Mossbauer spectral study of HoFe 11 Ti and HoFe 11 TiH a a, b c Cristina Piquer , Fernande Grandjean *, Gary J. Long , Olivier Isnard a ` , B-4000 Sart-Tilman, Belgium Department of Physics, B5, University of Liege Department of Chemistry, University of Missouri-Rolla, Rolla, MO 65409 -0010, USA c Laboratoire de Cristallographie, CNRS, Associe´ a l’ Universite´ J. Fourier, BP 166 X, F-38042 Grenoble Cedex, France b
Received 22 October 2002; accepted 29 October 2002
Abstract A.c. susceptibility measurements were carried out between 4.2 and 295 K on HoFe 11 TiH and reveal a spin-reorientation transition at ¨ |150 K. Iron-57 Mossbauer spectral measurements between 4.2 and 295 K were carried out on both HoFe 11 Ti and HoFe 11 TiH. The ¨ Mossbauer spectra were analyzed with a model which considers both the orientation of the iron magnetic moments and the distribution of titanium atoms in the near-neighbor environment of the three crystallographically distinct iron sites. The assignment and the temperature dependence of the hyperfine fields is in complete agreement with both the iron magnetic moments measured by neutron diffraction and the changes expected at the spin-reorientation. The assignment and the temperature dependence of the isomer shifts is in complete agreement both with the crystallographic changes occurring at the spin reorientation and upon hydrogen insertion. The changes in hyperfine field and isomer shift with the number of titanium near neighbors for each of the three iron sites are consistent with the values observed for related titanium–iron intermetallic compounds. 2002 Elsevier Science B.V. All rights reserved. ¨ spectroscopy; Magnetic measurements Keywords: Rare earth compounds; Hydrogen absorbing materials; Gas–solid reactions; Mossbauer
1. Introduction The magnetic behavior of HoFe 11 Ti, which crystallizes with the tetragonal I4 /mmm ThMn 12 structure [1–7], has been extensively investigated for 15 years. The Curie temperature of HoFe 11 Ti is 53364 K [3,6,7] and at room temperature its easy magnetization direction is parallel to the tetragonal axis of the unit cell. There have been several controversial reports [3–7] of a spin reorientation at |50 K, a spin reorientation which has been unquestionably ruled out [8–10]. However, the magnetic behavior of HoFe 11 Ti in an applied field is unusual and interesting. When a field of ,3 T is applied parallel to the basal plane of the tetragonal unit cell a type II first-order magnetization process occurs below 120 K, a process which exhibits a large anisotropy. Indeed, when the field is applied along the [100] direction, the first-order magnetization process occurs at a larger field than when the field is applied along the [110] direction. This unusual behavior has been attributed [10] to the coexistence of a low-field conical magnetic phase, with an angle of 78 *Corresponding author. Fax: 132-3-366-4516. E-mail address: [email protected] (F. Grandjean).
between the tetragonal axis and the magnetic easy axis, and a high-field conical magnetic phase, with an angle of 608. Because of the large anisotropy, HoFe 11 Ti has been studied [8,9] by three-dimensional magnetometry, a technique which yields the magnetization both parallel and perpendicular to the applied magnetic field. At small applied magnetic fields, the mutually and strictly antiparallel holmium and iron magnetic moments of HoFe 11 Ti rotate within the plane defined by the tetragonal axis, i.e. the easy magnetization direction, and the applied field direction. For applied fields .3.5 T, the first-order magnetization process induces a rotation of the magnetization vector both towards the applied magnetic field and out of the plane defined by the tetragonal axis and the applied field direction, presumably towards the [110] direction within the basal plane of the unit cell. Because of the controversial existence of a spin reorientation in HoFe 11 Ti, the magnetic properties of the hydrides, HoFe 11 TiH x , have been investigated [1,2] by both neutron diffraction and magnetic measurements. The neutron diffraction studies indicate that hydrogen occupies the octahedral 2b site in the ThMn 12 structure and that the unit cell expands anisotropically upon hydrogenation. The Curie temperatures of the hydrides, HoFe 11 TiH x , increase
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01204-5
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Table 1 Lattice parameters and magnetic properties of HoFe 11 Ti and HoFe 11 TiH Compound
˚ a (A)
˚ c (A)
T C (K)
T sr (K)
HoFe 11 Ti HoFe 11 TiH
8.491 (1) 8.525 (1)
4.784 (1) 4.794 (1)
533 590
– 150
from 533 to 590 K as x increases from 0 to 1. The magnetic measurements indicate that, above a critical hydrogen content of 0.4, the magnetic moments deviate slightly from the tetragonal c axis at all temperatures below the Curie temperature. In addition, a spin reorientation, a change in the tilt angle of the magnetic moments, occurs at a temperature which increases from 100 to 150 K as x increases from 0.65 to 1. Above and below the spin reorientation, the tilt angles of the magnetic moment [1] are 30 and 708, respectively. This spin reorientation, which is accompanied by substantial and abrupt variations in the lattice parameters [1], results from a change in the magnetocrystalline anisotropy, a change which is induced by the insertion of hydrogen. The neutron diffraction measurements also show substantial changes in the iron magnetic moments on two, the 8i and 8j sites, of the three iron sites. This spin reorientation was further confirmed [11] by torque measurements performed on single crystals of HoFe 11 Ti and HoFe 11 TiH. Because HoFe 11 Ti and its hydrides, HoFe 11 TiH x , exhibit such unusual and interesting magnetic properties, we have carried out a.c. magnetic susceptibility and iron-57 ¨ Mossbauer spectral studies with the goal of investigating in
detail the behavior of the iron sublattices in the different magnetic phases.
2. Experimental HoFe 11 Ti and its hydride, HoFe 11 TiH x , were synthesized as described [12] previously. The hydrogen content was determined to be one through the gravimetric massgain method. The lattice parameters and some of the magnetic properties are summarized in Table 1. The temperature dependence of the magnetization, shown in Fig. 1a, has been used to determine the Curie temperatures. The low temperature a.c. magnetic susceptibilities have been obtained on a computer controlled mutual inductance susceptometer [13] with an exciting field of 10 24 T and a frequency of 120 Hz. A lock-in amplifier was used to measure the complex susceptibility, xac 5 x 9 2 ix 0 where x 9 is the initial susceptibility, a quantity which is related to the variation in the sample magnetization, and x 0 is non zero if magnetic energy is absorbed by the sample. ¨ 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 / cm 2 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 Supervaritemp cryostat and the temperature was controlled with a Lakeshore Cryogenics temperature controller with an accuracy of better than 1%
Fig. 1. Temperature dependence of (a) the magnetization of HoFe 11 Ti, solid line, and HoFe 11 TiH, dashed line, and (b) the a.c. magnetic susceptibility of HoFe 11 TiH.
C. Piquer et al. / Journal of Alloys and Compounds 353 (2003) 33–41
35
of the observed temperature. The resulting spectra have been fit as discussed below and the estimated errors are at most 60.2 T for the hyperfine fields and their changes upon hydrogenation, 60.01 mm / s for the isomer shifts and their changes, and 60.02 mm / s for the quadrupole shifts and their changes. The observed linewidths were typically 0.4060.01 mm / s.
3. A.c. magnetic susceptibility results The a.c. magnetic susceptibility of HoFe 11 Ti has been measured [5,15] previously between 4 and 300 K. These investigations confirmed [4,16,17] the absence of any magnetic transition and the alignment of the magnetization along the c axis of the tetragonal unit cell in this temperature range. The temperature dependence of the real component of the a.c. susceptibility of HoFe 11 TiH, as is shown in Fig. 1b, exhibits an anomaly at |150 K. This maximum in the a.c. susceptibility is similar to that observed for ErFe 11 Ti, a maximum that has been associated [5] with a second-order spin-reorientation transition. The occurrence of such a spin-reorientation transition in HoFe 11 TiH has been confirmed [1,2] through a powder neutron diffraction study. Hydrogen insertion in the lattice induces a significant modification in the crystal electric field parameters at the rare-earth site and hence modifies the axial magnetic anisotropy observed in HoFe 11 Ti. The change in the crystal field gradient at the gadolinium site in both GdFe 11 Ti and GdFe 11 TiH has been demonstrated by ¨ gadolinium-155 Mossbauer spectroscopy [14]. More recently, a comparative study of HoFe 11 Ti and HoFe 11 TiH has shown that not only the crystal electric field gradient but also the higher order terms in the crystal electric field coefficients are modified by hydrogen insertion [11]. This modification arises from the changes produced by the inserted hydrogen atom in the rare-earth near-neighbor environment.
¨ 4. Mossbauer spectral measurements ¨ The Mossbauer spectra of HoFe 11 Ti and HoFe 11 TiH obtained between 4.2 and 295 K are shown in Figs. 2 and 3, respectively. Because the iron atoms occupy the 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, with relative areas in the ratio of 8:6:8 are required to fit the spectra. However, as already noted [18–20] in our studies of other RFe 11 Ti compounds and their hydrides, these three sextets must be further subdivided in order to take into account the distribution of the titanium atoms in the neighborhood of the three iron sites. The random occupation of the 8i sites by titanium
¨ Fig. 2. Mossbauer spectra of HoFe 11 Ti obtained at the indicated temperatures.
results in a binomial distribution of the titanium near neighbors of the three iron sites. Hence, the 8i sextet is subdivided into three sextets with 6.47, 10.79 and 9.98 percent areas, and each of the 8f and 8j sextets is subdivided into three sextets with 11.51, 15.34, and 9.52 percent areas, sextets which represent the iron with zero, one, and two or more titanium near neighbors, respectively. Hence, at least nine sextets, with their areas fixed to the
36
C. Piquer et al. / Journal of Alloys and Compounds 353 (2003) 33–41
crystallographically inequivalent iron site vary linearly with the number, n, of titanium near neighbors, as given by the equations Hn 5 H0 1 nDH
dn 5 d0 1 nDd and
en 5 e0 1 nDe
¨ Fig. 3. Mossbauer spectra of HoFe 11 TiH obtained at the indicated temperatures.
above relative values, are required to accurately model the ¨ Mossbauer spectra of HoFe 11 Ti obtained at all temperatures in its uniaxial magnetic phase. For HoFe 11 TiH in its conical magnetic phases, even more sextets are required, see below. Three hyperfine parameters define each sextet, the hyperfine field, H, the isomer shift, d, and the quadrupole shift, e. In order to both build in constraints into the model and to reduce the number of adjustable parameters, we assume that the three hyperfine parameters for each
where H0 , d0 , and e0 are the hyperfine field, isomer shift, and quadrupole shift, respectively, for zero titanium near neighbor 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 [21–24] in the analysis of the Mossbauer spectra of ¨ the R 2 Fe 172x M x solid solutions. Hence, the Mossbauer spectra of HoFe 11 Ti have been fit with nine sextets, which include 18 hyperfine parameters, one linewidth, and one total absorption area. As is shown in Fig. 2, all the fits are very good; the resulting hyperfine parameters are given in Table 2. The conical magnetic structure [1] of HoFe 11 TiH further subdivides the three sextets assigned to each inequivalent iron site. Because of the canting 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 the hyperfine field occur and yield different angles, u, between these two directions and hence different quadrupole shifts and hyperfine fields. A close examination of the symmetry at the three iron sites indicates that, if the easy magnetization direction lies in the plane defined by the [001] and [100] or [010] directions, there is no further subdivision of the sextet representing the 8f site, whereas there is a further subdivision of those representing the 8i and 8j sites. Each sextet assigned to the 8i and 8j sites is subdivided into two sextets 8i 1 , 8i 2 , 8j 1 , and 8j 2 of equal relative areas with identical isomer shifts but different quadrupole shifts and slightly different hyperfine fields. The subdivision of the sextets is different if the easy magnetization direction lies in the plane defined by the [001] and [110] directions. In this case, the 8f sextet is subdivided into two, 8f1 and 8f2 , sextets of equal relative areas and with identical isomer shifts but with different quadrupole shifts and slightly different hyperfine fields; there is no further subdivision of the 8i and 8j sextets. This sextet subdivision is well established for the R 2 Fe 17 compounds, see for instance Ref. [25]. In the former case, ¨ the Mossbauer spectra of the HoFe 11 TiH compound should be modelled with 15 sextets, which involve 26 hyperfine parameters, one linewidth and one total absorption area. In the latter case 12 sextets, involving 22 hyperfine parameters, one linewidth and one total absorption area would be
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Table 2 ¨ Mossbauer spectral hyperfine parameters for HoFe 11 Ti Parameter
T (K)
H0 (DH ) (T)
4.2 85 155 225 295
d0 a (Dd ) (mm / s)
4.2 85 155 225 295
20.085 (0.051) 20.108 (0.060) 20.149 (0.064) 20.205 (0.090) 20.247 (0.094)
0.139 (0.000) 0.137 (0.008) 0.117 (0.007) 0.083 (0.007) 0.010 (0.006)
20.047 (0.016) 20.061 (0.020) 20.087 (0.014) 20.125 (0.025) 20.150 (0.019)
0.013 0.006 20.025 20.056 20.101
e0 (De ) (mm / s)
4.2 85 155 225 295
0.017 (0.047) 0.009 (0.035) 0.007 (0.054) 0.019 (0.047) 0.013 (0.069)
0.147(0.048) 0.150 (0.037) 0.119 (0.046) 0.112 (0.052) 0.075 (0.092)
20.078 (0.074) 20.062 (0.052) 20.078 (0.062) 20.096 (0.069) 20.122 (0.069)
0.074 0.063 0.061 0.058 0.056
a
8f
8i
28.0 27.6 27.0 26.0 24.4
(22.4) (22.6) (22.6) (22.5) (22.5)
34.0 33.6 32.9 31.9 29.9
8j (21.9) (22.0) (22.1) (22.3) (22.1)
31.6 31.2 30.3 29.0 27.0
Wt. av. (22.3) (22.3) (22.3) (22.1) (21.9)
28.7 28.2 27.5 26.4 24.7
Relative to a-iron at 295 K.
required. Actually, above the spin reorientation in HoFe 11 TiH, when the canting angle of the moments from the c axis is small, i.e. 08 [11] or 308 [1,2], it was found that the further subdivision of the sextets was not required to obtain good fits. However, below the spin-reorientation temperature, at 4.2 and 85 K, the further subdivision of the 8i and 8j sextets was required to obtain good fits. As may be observed in Fig. 3, the fits are very good; the resulting hyperfine parameters are given in Table 3. The alternative fits with a subdivision of the 8f sextets were not satisfactory. Because of the number of parameters mentioned above, it would seem that it should be easy to obtain good fits but that the fits may be far from unique. Hence, in the next section we discuss the temperature dependencies of the hyperfine parameters and indicate how they help to give confidence to the spectral analysis, its physical basis, and the extent of its uniqueness. Our experience indicates that
it is not as easy as might be expected to obtain good fits of the observed spectra, especially when physically viable changes in the hyperfine parameters with temperature are imposed upon the fits. Indeed, we have not been able to find an alternative model that both provided good fits and viable changes in the hyperfine parameters with temperature, but such an undiscovered model may, of course, exist.
5. Discussion
5.1. Hyperfine fields The assignment and temperature dependence of the three hyperfine fields for zero titanium near neighbor and their weighted average for HoFe 11 Ti and HoFe 11 TiH are shown in Fig. 4a and b, respectively. A Wigner–Seitz cell analysis [26] of the three inequivalent iron sites in HoFe 11 Ti and
Table 3 ¨ Mossbauer spectral hyperfine parameters for HoFe 11 TiH Parameter
T (K)
H0 (DH ) (T)
4.2 85 155 225 295
d0 a (Dd ) (mm / s)
4.2 85 155 225 295
e0 (De ) (mm / s)
4.2 85 155 225 295
a
8f
8i 1
29.5 28.6 27.5 26.7 25.3
(22.2) (22.5) (22.2) (22.4) (22.2)
0.010 20.036 20.056 20.130 20.190
Relative to a-iron at 295 K.
(0.027) (0.027) (0.020) (0.042) (0.040)
0.015 (0.042) 0.020 (0.032) 0.110 (20.019) 0.135 (20.038) 0.100 (0.016)
38.1 36.3 34.1 33.3 31.8
8i 2 (22.2) (21.7) (21.9) (21.7) (21.8)
37.7 (22.3) 35.3 (22.9) – – –
0.200 (20.036) 0.166 (20.042) 0.105 (20.034) 0.032 (20.013) 20.014 (20.002)
– – – –
20.054 20.143 0.017 0.002 0.004
20.069 (0.027) 20.040 (0.069) – – –
(0.017) (0.068) (0.090) (0.102) (0.079)
8j 1 33.4 32.6 31.0 29.6 28.3
8j 2 (22.1) (22.4) (21.9) (21.9) (21.9)
0.080 (20.027) 0.026 (20.001) 0.028 (20.025) 20.025 (0.001) –0.075 (0.001) 0.015 (0.007) 0.088 (20.041) 0.006 (20.020) 0.028 (20.017) 0.003 (0.012)
32.9 (22.1) 31.7 (21.9) – – – – – – – – 20.091 (0.049) 20.059 (0.020) – – –
Wt. av. 30.9 29.5 28.6 27.5 26.2 0.076 0.037 0.006 20.037 20.087 0.006 0.022 0.061 0.072 0.072
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Fig. 4. Temperature dependence of the maximum hyperfine fields, H 0 , at the three iron sites and their average in HoFe 11 Ti (a) and HoFe 11 TiH (b). The solid lines in (a) are the result of the fits discussed in the text.
HoFe 11 TiH indicates that the 8i site has 11.75 iron near neighbors, the largest average number of iron near neighbors, whereas both the 8f and 8j iron sites have only nine iron near neighbors. Consequently, the sextets with the largest hyperfine field, H0 , have been assigned to the 8i site, both on the basis of its percent contribution and its iron near-neighbor environment. As is indicated below, this assignment is further supported by the observed isomer shift values and the large iron magnetic moment that has been observed [1,2] by neutron diffraction for this site. Because of both their identical constrained percentage areas and their identical 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 their isomer shifts, see below. If the three H0 hyperfine fields increase upon hydrogen insertion, the sequence of hyperfine fields, 8i . 8j . 8f, remains unchanged as is shown in Fig. 4b. 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. The solid lines in Fig. 4a are the result of a least-squares fit [27] with the equation H 5 H0 [1–B3 / 2 (T /T C )3 / 2 –C5 / 2 (T /T C )5 / 2 ] where H0 and T C are the saturation field and Curie temperature, 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 between 0.08 and 0.15
and the C5 / 2 coefficients are |0.35; similar values have been obtained [20] for GdFe 11 Ti and GdFe 11 TiD. The temperature dependence of the hyperfine fields in HoFe 11 TiH, see Fig. 4b, is quite different from that shown in Fig. 4a for HoFe 11 Ti and the difference is clearly related to the spin reorientation occurring at |150 K. The hyperfine fields observed at 4.2 and 85 K are substantially larger than those expected from a Brillouin extrapolation of the fields observed above 150 K. The increase in the hyperfine fields below 150 K is clearly related to the increase in the iron magnetic moments observed [1,2] by neutron diffraction. Specifically, the large increase in the 8i hyperfine field corresponds to an increase in the site magnetic moment of |15%. From the 8i hyperfine fields at 155, 225 and 295 K, a 4.2 K Brillouin extrapolated value of 35 T may be estimated whereas a field of 38 T is observed, i.e. 9% more than would be expected. Hence, the temperature dependence of the maximum hyperfine fields in HoFe 11 TiH reflects the temperature dependence [1,2] of the iron magnetic moments. In addition, the discontinuity in the temperature dependence of the 8i hyperfine field is similar to that observed [29] in the temperature dependence of the 4f hyperfine field in Tm 2 Fe 17 , a compound which also exhibits a spin-reorientation transition at 90 K. The temperature dependence of the increase in the three hyperfine fields upon hydrogenation is shown in Fig. 5. Similar increases in the hyperfine fields upon hydrogenation or nitrogenation of several R 2 Fe 17 and RFe 11 Ti compounds have been observed [19–21,29,30]. The very large increase in the 8i hyperfine field at 4.2 and 85 K is related to the spin reorientation occurring below 150 K and
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Hence, we can conclude that, as expected, these changes are relatively independent of temperature below 295 K. The observed decreases in the hyperfine fields upon the replacement of one iron by one titanium near neighbor are very similar to those observed [18,19,31] in the RFe 11 Ti and their hydrides and are within the range of 21.1 to 26 T observed [32,33] in a spinel oxide and in Nd 2 Fe 16 Ti, respectively. Finally, the hyperfine fields observed in the subdivided pairs of sextets, 8i 1 and 8i 2 or 8j 1 and 8j 2 , are very similar, see Table 3. Their differences range between 0.4 and 1 T and are very similar to the differences found in ErFe 11 TiH [19], and somewhat smaller than the differences found for the Pr 2 Fe 17 H x hydrides [25], for x between 1 and 5.
5.2. Isomer shifts
Fig. 5. Hyperfine field difference between HoFe 11 Ti and HoFe 11 TiH for the three iron sites and their average.
the large increase in the 8i iron magnetic moment discussed above. The changes in the hyperfine field per titanium near neighbor are between 22.060.2 T and 22.560.2 T for the three sites, where the errors reflect the variations in the difference with temperature between 4.2 and 295 K.
The assignment and the temperature dependence of the three site average isomer shifts, and their weighted average, for HoFe 11 Ti and HoFe 11 TiH are shown in Fig. 6a 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. Such a relationship between isomer shifts and Wigner–Seitz cell volumes has been observed [21,30] in many R 2 Fe 17 compounds. The overall increase in unit-cell volume accounts for the increase in the weighted average isomer shift upon hydrogenation. All the 295 K isomer
Fig. 6. Temperature dependence of the three site average isomer shifts and their average in HoFe 11 Ti (a) and HoFe 11 TiH (b). The solid line in (a) for the average value is the result of the second-order Doppler shift fit discussed in the text.
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shifts are negative relative to a-iron as has been observed [34,35] in other iron–titanium compounds. The temperature dependence of the weighted average isomer shift in HoFe 11 Ti shown in Fig. 6a has been fit [36,37] with the Debye model for the second order Doppler shift. The resulting effective vibrating mass [37] ¨ of 5962 g / mol and the effective Mossbauer temperature of 447610 K are typical [30,38] of an intermetallic compound. The temperature dependence of the weighted average isomer shifts in HoFe 11 TiH shown in Fig. 6b is somewhat unusual because the three isomer shifts and their weighted average increase almost linearly from 295 to 4.2 K. We believe that this unexpected temperature dependence is related to the unusual temperature dependence [1,2] of the lattice parameters observed for HoFe 11 TiH between 100 and 150 K. Further, a similar increase in isomer shift below the spin reorientation has been observed [29] in Tm 2 Fe 17 . The changes in the isomer shift per titanium near neighbor are virtually independent of temperature and are between 20.04 and 0.10 mm / s, as has already been observed [18,31] for YFe 11 Ti and CeFe 11 Ti and their hydrides. However, it seems difficult to rationalize the sign of these changes for the three inequivalent iron sites.
5.3. Quadrupole shifts ¨ The quadrupole shifts observed in the Mossbauer spectra of HoFe 11 Ti and their changes per titanium near neighbor are small and lie between 20.10 and 0.15 mm / s and 0.03 and 0.09 mm / s, respectively. Small quadrupole shifts are ¨ expected because Mossbauer spectral studies [39] at 295 K of some related paramagnetic RFe 11 Ti and RFe 11 Mo compounds yield quadrupole splittings of at most 0.6 ¨ mm / s. The observed quadrupole shifts in the Mossbauer spectra of HoFe 11 TiH are equally small and the temperature dependence of the maximum quadrupole shift, e0 , see Fig. 7, clearly reveals the spin reorientation between 85 and 155 K. Indeed, first, the observation of two different quadrupole shifts for the 8i and 8j sites indicates that the iron magnetic moments are contained in the plane defined by the [001] and [100] axes of the tetragonal unit cell, in agreement with the angle of 708 between the iron moments and the c axis, obtained [1,2] by powder neutron diffraction. Second, a change in the sign of the quadrupole shift is observed for at least one of the subcomponents of the 8i and 8j sites, as would be expected for a change in sign of (3 cos 2u 21) when u changes from 30 to 708. Because no ¨ satisfactory fits of the Mossbauer spectra of HoFe 11 TiH with a model subdividing the 8f sextets could be obtained, we exclude the possibility that the iron magnetic moments lie in the plane defined by the [001] and [110] directions in the tetragonal unit cell. This conclusion seems to disagree with the easy magnetization direction along [110] observed by Nikitin et al. [11] on a single crystal of HoFe 11 TiH in a large applied field of 2 T. The magnetic torque measure-
Fig. 7. Temperature dependence of the quadrupole shifts in HoFe 11 TiH. The vertical line separates the small cone angle and the large cone angle regions of the magnetic phase diagram.
ments carried out by Nikitin et al. [11] suggest that the magnetic moments are in the plane defined by the [001] and [110] directions in an applied field of 1.2 T. Our ¨ present Mossbauer measurements are carried out in the absence of an applied field and the direction of the iron magnetic moments is different. In view of the sensitivity [8,9] of the magnetic structure of HoFe 11 Ti to the applied magnetic field, it is not surprising that the magnetic structure of HoFe 11 TiH shows a similar sensitivity.
6. Conclusions From a macroscopic point of view the insertion of hydrogen into HoFe 11 Ti to form HoFe 11 TiH expands the lattice, increases the Curie temperature, and induces a spin reorientation between 100 and 150 K. From a microscopic point of view, the insertion of hydrogen increases the 8i and 8j iron magnetic moments and hyperfine fields, whereas it does not change substantially the 8f iron magnetic moment and hyperfine field. In agreement with the observed lattice expansion, the iron-57 weighted ¨ average Mossbauer spectral isomer shift increases. In HoFe 11 TiH, the temperature dependence of the three iron isomer shifts, hyperfine fields, and quadrupole shifts are clearly indicative of the spin reorientation between 100 and 150 K and are related to the peculiar temperature dependence of the lattice parameters. Further, the fitting model with a subdivision of the 8i and 8j sites reveals that the iron magnetic moments lie in the plane defined by the [001] and [100] axes of the tetragonal unit cell. The presence of one titanium near neighbor in the environment of an iron site decreases the hyperfine field by |2 T.
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Acknowledgements ` through The financial support of the University of Liege grant number 2850006 is acknowledged with thanks. This work was partially supported by the US National Science Foundation through grants DMR95-21739 and INT9815138, and the Centre National de la Recherche Scientifique, France through grant action initiative number 7418.
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