__ f !!I
cQ%
AA journal of lla magi netlsm 1 and M I maonetic A mate trials
ELSEVIER
Journal of Magnetism and Magnetic Materials 150 (199.5)25-29
Anomalous temperature dependence of the electric field gradient at the Gd nuclear site in intermetallic compounds F.M. Mulder a, R.C. Thiel a, L.J. de Jongh a, K.H.J. Buschow a7b, * a Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9506, 2300 R4 Leiden, The Netherlands b Van der Waals-Zeeman Institute, University of Amsterdam,
1081 XE Amsterdam,
The Netherlands
Received 21 December 1994
Abstract We have in a variety assumed but experimental corresponding the hyperfine
used “‘Gd Mikbauer spectroscopy to study the behavior of the electric field gradient (V,,) at the nuclear site as is commonly of Gd intermetallic compounds. We found that V’, is not always temperature-independent can exhibit strong temperature dependences when the Gd moments become magnetically ordered. Examples of results are presented, where V,, either decreases (GdGa,) or increases (Gd,Zn,,) with temperature below the magnetic ordering temperature. In both cases the temperature variation of V,, appears to correlate with that of field. Possible explanations are briefly discussed.
1. Introduction Using the quadrucole splitting from “‘Gd MGssbauer spectroscopy, the electric-field gradient at the Gd nuclear site can be determined (EFG, with the principal component V,,). In several previous papers we have studied the behavior of V,, in a variety of different Gd compounds [1,2]. By means of band structure calculations for several of these compounds it was shown that the EFG is primarily determined by the asphericity of the on-site valence electron charge cloud of the Gd atoms [3]. The contribution of the Gd 4f shell to the EFG is zero, since it is half filled and spherical symmetric. These results made it also clear that the commonly assumed proportionality between V,, and the second order crystal field
* Corresponding author. Fax: + 31-20-525-5788. 0304-8853/95/$09.50
coefficient Ai lacks a fundamental basis [3]. The latter coefficient reflects the EFG felt by the 4f electrons, and mainly determines the macroscopic magnetic anisotropy constant in compounds of uniaxial symmetry. It therefore does not seem to be straightforward to obtain direct information of the magnetic anisotropy from measurements of V,,. In view of the importance to obtain experimental information on the magnetic anisotropy we have investigated whether there is a semi-empirical relation between V,, and A;. In the course of these investigations we discovered that there is an additional complication in the form of a temperature dependence of V,, [4] in particular in case of magnetic order. Since V,, is commonly considered as temperature independent in Gd intermetallic compounds, we have studied more closely in series of comthis phenomenon pounds of widely different composition and crystal structures.
0 1995 Elsevier Science B.V. All rights reserved
.SsDI 0304-8853(95)00103-4
2. Experiment All spectra have been analyzed by means of a least-squares fitting procedure involving diagonalization of the full nuclear Hamiltonian and use of a transmission integral. The independently refined variables consisted of the isomer shift (IS), the effective hyperfine field (B,,), and the quadrupole splitting (QS). From the last quantity, the EFG tensor element V,, was obtained via the relation QS = feQV,,(3 cos20 - 1). Q is the ground state nuclear quadrupole moment. The angle 8 between B,, and the c-axis was kept as an adjustable parameter. The 86.5 keV resonance of “‘Gd that was used limits the choice of the compounds to ones with a TC,N below 70 K. Above about 60 K the Miissbauer recoil free fractions are very low and measuring times can exceed one week per spectrum (lo* counts for one velocity point).
Fig.
The results displayed in Table 1, and Fig. 3 can be summarized as follows: 0 A strong temperature dependence of the EFG is
T>
ordering
temperatures
Mijssbauer spectra of GdGa,
at the temperatures
Tc,N of several Gd intermetallic
compounds,
with the relative change of V,,
between 4.2 K, and
TC,N
Compound
Structure
Q(4.2 K) [lOzlV m-2]
GdGa, GdGaAl GdCuSi GdAgGe GdAl,Ga, GdRu,Ge, GdCu,Sb,
A&
TN = 15
A”32
ThCr,Si, ThCr,Si, ThCr, Si,
TN =50 TN = 14 TN = 14 TN = 42 T, =32 TN = 16
GdaZnr, GdZn, GdCo,B, GdCo,B,C
Th,Zn,, C&u, CeCo,B, YNi,B,C
TN = TN = Tc = TN =
GdNi, GdRh, GdPd,Al, GdCo,Ga, GdRu,Si,
CaCu, CaCu, CeCo,B, Ce.Co,B, ThCr,Si,
Tc = 29 Tc = 25 Tc = 30 T, = 90 TN = 48
A”32 A%
10 68 58 5.5
indicated.
not generally observed, but occurs incidentally, a correlation with composition being absent 0 The temperature dependence of the EFG is strongly correlated with the occurrence of antiferromagnetic ordering, and the associated temperature dependence of the hyperfine field.
3. Results and discussion
Table 1 The magnetic
1.
5.9 -4.6 - 3.2 8.0 2.9 - 18.1 2.9 - 0.44 - 7.4 31.2 - 7.4 10.4 7.6 12.6 13.4 - 18.9
UT> ~(4.2
Tc,,> RI
/ 4,,(4.2 K) / 61
0.41 0.87 0.91 0.95 0.66 0.86 0.83
33.3 26.1 30.5 27.3 29.2 28.6 27.3
2.73 1.09 1.04 1.30
24.7 28.5 15.0 45.6
1.00 1.00 1.00 1.01 1.00
24.6 23.5 26.0 23.2 29.0
F.M. Mulder et al. /Journal
of Magnetism and Magnetic Materials 150 (1995) 25-29
27
mula os = np2, where II is the magneto elastic coupling constant and p the temperature dependent Gd moment. In general one may take the hyperfine field as being proportional to (J,), and hence proportional to p. From the discussion given above, one may expect therefore that the increase of the EFG below T, is proportional to the squared hyperfine field: V,,(T)
-2
-1
0
Velocity
Fig. 2. MGssbauer cated.
2
1
3
(mm/s)
spectra of Gd,Zn,,
at the temperatures
indi-
0 The values of the EFG may decrease as well as increase with temperature. Basically one does not expect any correlation between the hyperfine field and the EFG, because the former samples magnetic interactions while the latter samples electrostatic interactions. A possible connection between both quantities may be offered by the magneto elastic interaction, which leads to a lattice distortion upon magnetic ordering. Another possible connection may exist in the form of a difference in the EFG associated with the two spin directions of the 6p and 5d electronic states. These mechanisms do not explain, however, why only antiferromagnets seem to show the effect. A third connection may result from the increased dimensions of the unit cell in the antiferromagnetic state. We will discuss these possibilities below. Since in these compounds only Gd carries a magnetic moment, the spontaneous volume magnetostriction ( os) may be of mainly itinerant nature and results from the exchange splitting of the narrow 5d band upon magnetic order. Another source of its origin might involve a strongly volume dependent anisotropic exchange interaction between the 4f moments. Whatever its origin, ws can generally be expressed by means of the phenomenological for-
= V,,( T > T,) + constant X B&.
(1)
The full curves displayed in Fig. 3 have been calculated on the basis of Eq. (1). Given the experimental inaccuracies at temperatures close to TN, one might state that this curve accounts fairly well for the anomalous temperature dependence of the EFG observed. The spontaneous volume magnetostriction os is generally a fairly small effect. In Gd metal ws = 10e4, [6] whereas in the compounds Gd,Ni, Gd,Co, and GdCu,, it is about 2 X 10e3 [7,8,9]. A marked effect on the EFG can be expected only if ws is anisotropic and involves lattice expansions almost exclusively in the c direction or in the a direction (as in the first two Gd compounds mentioned). The latter requirement may be fulfilled in GdGa,: a comparison of preliminary results of measurements of the lattice constants of GdGa, at 10, 77 and 293 K suggests that the situation is similar as in GdCu, [9], where disordering from the antiferromagnetic state is accompanied by a significant volume expansion. We also found that the volume expansion is mainly in the a direction (As/a = 2 X 10-3). In the system GdGa,_,Al, with 0
10
T
W
20
30
40
T (0
parameters V,,(T)/ V,,(2 K) and Fig. 3. The hyperfine , . , . , . B,,U)/B,,~:! KJ of GdGa, plotted against T (left), and of GdzZn,, (right). The full lines represent the ‘fits’ discussed in the text.
GdGa, could rherefore lead to an increase of the EFG of the order of magnitude observed experimentally. Unfortunately, no thermal expansion data are available for the other compounds studied in the present investigation. The second mechanism that would be able to account for the anomalous temperature dependence of the EFG involves a difference between the contributions produced by electrons of different spin directions. From several previous investigations and band-structure calculations [3,10] it is known that the EFG is caused by the asymmetry of the on-site 6p, 5d valence electron charge distributions at the nuclear site. As one may expect, the spatial distribution of the majority electrons differs often from that of the minority electrons, which leads to different EFG contributions for these electrons When the exchange interaction with the polarized 4f electron system is sufficiently large, the spin up and spin down subbands may shift relative to each other. The amount of charge transferred from the spin down band to the spin up band will also depend on the band widths. The spin induced changes of the electric field gradient can have different signs and magnitudes for 6p and 5d electrons and hence may not always add constructively. For this reason it is difficult to predict sign and magnitude of the net spin induced field gradient changes in the different compounds. But these changes should increase in a given compound along with the spin polarization of the valence electron bands, and hence increase along with the hyperfine field upon magnetic ordering. Unfortunately, it is not possible to give a quantitative expression for the dependence of the EFG on spin polarization or on hyperfine field, as in the case of the spontaneous volume magnetostriction. This does not mean that we consider this mechanism less likely. A third mechanism that may be of importance makes use of the antiferromagnetic spin arrangement in the compounds, although at present we cannot exclude that also ferromagnetic compounds may show anomalous temperature dependences of the EFG. The exchange interaction with the localized 4f moments causes the electronic unit cell to increase due to the additional periodicity of the antiferromagnetic spin arrangement. It is well known that this increase of the unit cell causes additional energy gaps in reciprocal space [lI]. Examples of rare earth
compounds are imown where these so-called snperzone gaps wipe out substantial portions of Fermi surface areas in particular crystallographic directions (see e.g. [6]). These gaps increase with increasing subla magnetization below the MeI temperature. A large influence of this can be seen in e.g. electrical transport measnrgm~nts [IZ]. though the G measures the anisotropy in the tal charge sities around the nucleus, and not only of the charge at tbe Fermi level, it may also be influenced. This may be because the anisotropy may res mainly from the charge near the Fermi level. The parameter, which measures just the total electron density at the nucleus (mainly 6s), shows no change upon magnetic ordering indeed. It should be noted that, depending on the exact spin-structure, inequivalent magnetic Gd sites may occur. This may result in different B,, or 0 values. Therefore the low temperature spectra have also been analyzed with up to five different magnetic sites. When the VZ/,, values were kept at the high temperature value, this resulted in m-r-physically large f values (e.g. GdGa,). Since the best multi-comnent fits were not significantly better than the fits listed in Table 1, they were discarded as irrelevant. Concluding, we have shown that the EFG a%the (nuclear) rare earth site in intermetallic compounds cannot be taken as almost temperature-i~de~e~d~~t~ as is commonIy assumed. We have presented exam. ples where the EFG strongly decreases or strongly increases with temperature. From the corres~~~de~ce in behavior between the EFG and the hy~e~i~e field we conclude that this anomalous temperature dependence of the EFG depends on the spin polarization of the valence electron bands. We have proposed different mechanisms which may be held responsible for this phenomenon. The experimental data are at present not sufficient to reach a conclusion as to which mechanism causes the strong temperature dependence of the EFG below the magnetic ordering temperature. Further investigations are in progress to trace the origin of this interesting effect.
We acknowledge IA. Mydosh, G.J. Mieuwenhuys, and R. Coehoorn for valuable discussions. This
F.M. Mulder et al. /Journal
of Magnetism and Magnetic Materials 150 (1995) 25-29
work is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM), which is financially supported by the ‘‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek” (NWO). The investigations are sponsored by the Leiden Materials Science Centre (Werkgroep Fundamenteel Materialen Onderzoek).
References [l] M.W. Dirken, R.C. Thiel, K.H.J. Buschow, Met. 146 (1989) L 15. [2] M.W. Dirken, R.C. Thiel, K.H.J. Buschow, Met. 147 (1989) 97.
J. Less-Common J. Less-Common
29
[3] R. Coehoorn, K.H.J. Buschow, M.W. Dirken, R.C. Thiel, Phys. Rev. B 42 (1990) 4645. [4] F.M. Mulder, R.C. Thiel, K.H.J. Buschow, J. Alloys Compds. 203 (1994) 97. [5] H. de Graaf, Thesis, University of Leiden, 1982. [6] S. Legvold, in: Ferromagnetic Materials, E.P. Wohlfarth, Ed., Vol 1 North Holland, Amsterdam, (1980). [7] E. Talic and A. Slebarski, J. Alloys Compds. (in press). [8] A.V. Andreev, in: Magnetic Materials Vol. 8, K.H.J. Buschow, Ed. (North-Holland, Amsterdam, 1994). [9] N.H. Luong and J.J.M. Frame, Phys. Stat. Sol. A 66 (1981) 399. [lo] K.H.J. Buschow, R. Coehoom, F.M. Mulder, R.C. Thiel, J. Magn. Magn. Mater. 118 (1993) 347. [ll] A.R. Mackintosh, Phys. Rev. Lett. 9 (1962) 90. [12] e.g. K.A. McEwen, in: Handbook on the Physics and Chemistry of Rare Earths Vol. 1, K.A. Gschneider, L. Eyring, Eds. (North-Holland, Amsterdam, 1978).