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NMR study of crystal field effect on Tb in TbNi2
Physica B 149 (1988) 319-322 North-Holland, Amsterdam
NMR STUDY OF CRYSTAL FIELD EFFECT ON Tb IN TbNi 2
Kenji S H I M I Z U , Kiyoo S A T O * and Hiroshi N A G A N O
Faculty of Education, Toyama University, 3190 Gofuku, Toyama, Japan *Faculty of Sciencd, Toyama University, 3190 Gofuku, Toyama, Japan
Spin echo NMR measurements on 159Tb have been done at 1.6 K in the magnetically ordered state of the cubic Laves phase TbNi2 compound. The magnetic hyperfine interaction and the electric quadrupole interaction parameters have been observed to be 2924 - 3 MHz and 258.3 - 3 MHz, respectively. The magnetic moment of Tb is deduced to be 7.55/x Bfrom the electric quadrupole splitting of 159Tb on the basis of a molecular field Hamiltonian.
I. Introduction
The magnetic properties of the cubic Laves phase compounds, RNi z ( R = rare earth), have been extensively studied [1,2]. In the compounds, it is known that only the rare earth atom has magnetic m o m e n t . The Curie t e m p e r a t u r e is lower than that of the other cubic Laves phase compounds RFe 2 and R C o 2. The magnetic moments of rare earth atoms in the magnetically ordered state, except for the S-state G d 3÷ ion, are signifcantly lower than the free ion value because of the crystal field effect. The T b magnetic m o m e n t in TbNi 2 has been found to be 7.7-7.8 txB by magnetization m e a s u r e m e n t s [1, 2] and to be 7.2 tzB by neutron diffraction measurements [3]. These values correspond to the crystal field quenching of 13% to 20%. The hyperfine field of rare earth due to 4f electrons, A ( J z), reflects the magnitude of the magnetic m o m e n t g/z B ( J z ) , where A is the hyperfine coupling constant and (J~) is the thermal average of the expectation value of J~ for the ion. The studies of the crystal field quenching of the rare earth magnetic m o m e n t by hyperfine field analysis have already been done [4, 5] for D y l _ x H o x N i 2 and Ho0.01(Gdl_xYx)0.99Ni2. In DyNi2, the crystal field quenching of the D y m o m e n t was found to be small from the analysis of the electric quadrupole interaction [4]. F r o m the N M R m e a s u r e m e n t s [5] on 165Ho, the quenching of
5 % was obtained for the H o magnetic m o m e n t in HoomGdo.99Ni z. In a recent N M R work [6] on HoA12, the H o magnetic m o m e n t has been evaluated from the electric quadrupole splitting of 16Silo using a molecular field Hamiltonian. It has been pointed out that the ionic ground state of H o 3+ in H o A I 2 derived f r o m the N M R analysis is inconsistent with that derived from neutron magnetic form factor experiments, but consistent with that derived from magnetization measurements. In the present work, the electric quadrupole interaction p a r a m e t e r p which is obtained by the N M R m e a s u r e m e n t s on 159Tb in TbNi 2 is compared with that calculated on the basis of a molecular field Hamiltonian. The magnetic moment of Tb in the c o m p o u n d is obtained from the calculated value of ( J z ) .
2. Experimental
The sample was p r e p a r e d by argon arc melting the appropriate quantities of the constituents. The purity of the starting materials was 99.9% for T b and 99.99% for Ni. The ingot was annealed at 800"C for about 7 days and then was crushed into powders. The powder sample was examined to have the cubic Laves phase structure (C-15 type) by X-ray diffraction.
0378-4363/88/$03.50 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
320
K , S h i m i z u et al. / N M R
The spin echo N M R measurements on 159Tb in the compound were done at 1.6 K.
study on TbNi 2
m
3. Results and discussion
For non S-state ion such as Tb +3, the hyperfine interaction is devided into a dominant intra-ionic term arising from 4f electrons and a small extraionic term. In almost all cases except for 1 6 5 H o in HoAI2, the intra-ionic hyperfine interaction is well described by the first-order perturbation treatment. In the case of HoAI z [6], the secondorder effect on the electric quadrupole hyperfine interaction has been estimated to be 6.3 MHz on the basis of the molecular field approximation. The second-order magnetic hyperfine interaction [7,81, where [g) and ]i) denote the ground state and the excited state eigenfunctions, and Eg and Ei the corresponding eigenvalues, contributes to the electric quadrupole splitting as an additional term. In the case of TbNi2, the magnitude of such a secondorder effect has been calculated to be about 1 MHz from the eigen functions and eigenvalues obtained by using the molecular field and the crystal field parameters used in the present analysis of N M R results• This value is small compared with the rather large experimental uncertainty. Therefore the second-order effects to the hyperfine interaction is neglected in the present analysis. The extra-ionic contribution to the electric quadrupole interaction would also be very small. If the deviation from the cubic crystal structure does not occur, the extra-ionic contribution due to the lattice distortion should vanish. In the case of 17SLu(I = 7/2, Q = 3.49b) N M R in Tb0.98Lu0.02Fe 2 [9] which Would have probably large magnetostriction as well as TbFe 2, no resolvable quadrupole splitting has been observed. The half-height width of the 175Lu resonance line is about 8 MHz, which suggests that the extraionic contribution to the electric quadrupole interaction is small. In GdAI 2 [10], the observed quadrupole splitting in lS7Gd N M R spectrum is at most of the order of 1 MHz. Consequently, the present analysis of the N M R results is treated within the first-order in the hyperfine
Z.,gl(ilAJ.llg)2/(Ei-Eg),
; r
,
,' i ~
,
,'
!
~
. .
2350
2400
2450
. j
2900
2950
3400
3450
MHz
Fig. 1. N M R spectrum of l~gTb in TbNi 2 taken at 1.6 K.
interactions and the extra-ionic contribution to the quadrupole interaction is also neglected. The resonance frequency, v, for the transition m ~ rn - 1 is given by v=la+p(2m-1)l, where a and p are the magnetic hyperfine and the electric quadrupole hyperfine parameters, respectively. Fig. 1 shows the 159Tb N M R spectrum observed for TbNi 2. The values of a and p are obtained to be 2924---3 MHz and 258.3-+ 3 M H z , respectively. These values are clearly smaller than the free ion values, which may be attributed to the crystal field effects. The magnetic hyperfine parameter a is decomposed into three terms: a
= a4f + a t + asp ,
where a4f is due to 4f electrons, asp is due to self-polarization of conduction electrons by their own magnetic m o m e n t and a t is the contribution from the conduction electron polarization by the neighboring rare earth spins. The electric quadrupole parameter p is equal to the intra-ionic quadrupole parameter P4f in the absence of the extra-ionic contribution to the electric quadrupole interaction. The intra-ionic hyperfine parameters a4f and P4f are related to ( J z ) and (J~) through a4f = a o ( J z ) / J and P a f = P0(3J~ J(J + 1 ) ) / J ( 2 J - 1), where a 0 = 3180 MHz, Po = 386 MHz and J = 6. Then, the magnitudes of the intra-ionic hyperfine interactions for the Tb 3+ ion in TbNi 2 are evaluated by diagonalizing the Hamiltonian consisting of the exchange and the crystal field terms. The easy axis of the magneti-
321
K . S h i m i z u et al. / N M R s t u d y on T b N i 2
zation is known [3, 11] to be (111) for TbNi 2. Then, the crystal field Hamiltonian for the z-axis lying along the ( 111 ) cubic crystallographic direction may be written as [12] Ygcf = - 2
3
B,(O
o _
20V~O] )
+--~-B 6 O 6 + T
O6+
O
,
where B 4 and B 6 a r e the crystal field parameters, O~ the Stevens operator equivalents. In the molecular field approximation, the exchange interaction may also be written with the usual notations as =
-ggsJ
Hm ,
where the molecular field H m is given by
,qm =
( g - 1)2(Jz) g/xB
The exchange constant J is related to the paramagnetic Curie temperature Op by (g - 1)2j(j + 1) 3k B Then, in order to evaluate the thermal average of the expectation values of Jz and j2, the total Hamiltonian is diagonalized for a set of three parameters B4, B 6 and H m. The thermal average of the expectation value of J~ has been taken at 1.6 K. At this temperature, only the ground state is important and the difference in (J~) between the thermal average value and that obtained only for the ground state is less than 1%. Since the molecular field H m is linear to (J~ }, H m is determined self-consistently with a given value of 0p for each set of crystal field parameters B 4 and B 6. The published values of the paramagnetic
Curie temperature 0p for TbNi 2 slightly differ from each other. In the present calculation, 0p is taken as 35 K [1]. The crystal field parameters are chosen so as to obtain a good agreement between the calculated and the experimental values of P4e. We modified the values of B 4 and B 6 obtained from the values of DyNi 2 [13] taking account of the Stevens factor of /3 and 3'. The value of 5.03 for (J~) corresponds to the magnetic moment of 7.55/x B. This value is obtained for the set of the parameters given in table I. The magnetic moment is slightly larger than that obtained by neutron diffraction and is close to values of 7.7 to 7.8/~3 obtained by magnetization measurements. We estimate the extra-ionic contribution to the magnetic hyperfine field at Tb in TbNi 2. The transferred hyperfine field, a t, is evaluated to be 69.8 MHz from the N M R result [14] of 139La in La0AGd0.9Ni2, where the difference of the spin values between Gd +3 and Tb +3 has been taken into account and the ratio of the s-electron hyperfine coupling constant [15] of Tb to that of La has been assumed to be 1.32. The value of asp is obtained to be 188.3 MHz by combining a4f and a t with the observed value of a. In TbNi2, the conduction electrons would have 5d and 6s character and would polarize parallel to the spin of 4f electrons. The positive field for asp in TbNi 2 might simply suggest the s-electron polarization to be dominant as in the case of TbFe 2 where a large and positive field due to s-electron polarization is observed [9]. If the d-electron polarization is the dominant contribution to asp in TbNi2, the self-polarization field would be caused by the d-orbital polarization which would make a positive contribution to the hyperfine field in the same manner as that of the 4f electrons. In RAI 2 [6, 16], the orbital contribution to the self-polarization field at the rare earth nucleus is relatively small compared to the spin polarization. In the
Table I The observed values of the hyperfine interaction parameters a and p (MHz), and the values of a4f , P4f (MHz) and (J~) obtained by using the crystal field parameters B4, B 6 (meV) and the paramagnetic Curie temperature 0p (K). a
p
a4f
P4f
{L)
B4
B6
0p
2924 +- 3
258.3 -+ 3
2665.9
258.3
5.03
1.70 × 10 -3
3.09 x 10 6
35
322
K . S h i m i z u et al. / N M R s t u d y o n T b N i 2
case of TbNi 2, the situation in the conduction band would differ from that of RAI 2. We cannot at the present stage draw the conclusion as to whether or not the d-orbital polarization is the dominant contribution compared to the spin polarization.
4. Conclusion
The magnetic moment of Tb in TbNi 2 has been derived to be 7.55/x B from the electric quadrupole splitting of 159Tb o n the basis of the molecular field approximation. This value for the Tb magnetic moment is in good agreement with that obtained from magnetization measurements on TbNi 2. From the hyperfine field analysis, the positive fields both for the self-polarization and the transferred field at the Tb-nucleus have been deduced using the calculated value of (J~).
Acknowledgement We are indebted to Miss. K. Horikawa, Mr. M. Katsurai and Mr. T. Ogino for their assist-
ance to the NMR measurements and the computer programming.
References [1] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973). [2] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179. [3] G.P. Felcher, L.M. Corliss and J.M. Hastings, J. Appl. Phys. 36 (1965) 1001. [4] G.J. Bowden and R.K. Day, J. Phys. F 8 (1978) 533. [5] A. Tari, Phys. Rev. B 19 (1979) 3462. [6] Om Prakash, D.St.P. Bunbury and M.A.H. McCausland, Z. Phys. B 58 (1984) 39. [7] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Oxford University Press, London, 1970). [8] P.R. Waind, I.S. Mackenzie and M.A.H. McCausland, J. Phys. F 13 (1983) 1041. [9] K. Shimizu, J. Magn. Magn. Mat. 70 (1987) 178. [10] E. Dormann, U. Dressel, H. Kropp and K.H.J. Buschow, J. Magn. Magn. Mat. 45 (1984) 207. [11] S.K. Arif, I. Sigalas and D.St.P. Bunbury, phys. star. sol. (a) 41 (1977) 585. [12] M.T. Hutchings, Solid State Phys. 16 (1964) 227. [13] D. Gignoux and F. Givord, Solid State Commun. 21 (1977) 499. [14] E. Dormann and K.H.J. Buschow, Physica 86-88B (1977) 75. [15] I.A. Campbell, J. Phys. C 2 (1969) 1338. [16] E. Belorizky and Y. Berthier, J. Phys. F 16 (1986) 637.
NMR STUDY OF CRYSTAL FIELD EFFECT ON Tb IN TbNi 2
Kenji S H I M I Z U , Kiyoo S A T O * and Hiroshi N A G A N O
Faculty of Education, Toyama University, 3190 Gofuku, Toyama, Japan *Faculty of Sciencd, Toyama University, 3190 Gofuku, Toyama, Japan
Spin echo NMR measurements on 159Tb have been done at 1.6 K in the magnetically ordered state of the cubic Laves phase TbNi2 compound. The magnetic hyperfine interaction and the electric quadrupole interaction parameters have been observed to be 2924 - 3 MHz and 258.3 - 3 MHz, respectively. The magnetic moment of Tb is deduced to be 7.55/x Bfrom the electric quadrupole splitting of 159Tb on the basis of a molecular field Hamiltonian.
I. Introduction
The magnetic properties of the cubic Laves phase compounds, RNi z ( R = rare earth), have been extensively studied [1,2]. In the compounds, it is known that only the rare earth atom has magnetic m o m e n t . The Curie t e m p e r a t u r e is lower than that of the other cubic Laves phase compounds RFe 2 and R C o 2. The magnetic moments of rare earth atoms in the magnetically ordered state, except for the S-state G d 3÷ ion, are signifcantly lower than the free ion value because of the crystal field effect. The T b magnetic m o m e n t in TbNi 2 has been found to be 7.7-7.8 txB by magnetization m e a s u r e m e n t s [1, 2] and to be 7.2 tzB by neutron diffraction measurements [3]. These values correspond to the crystal field quenching of 13% to 20%. The hyperfine field of rare earth due to 4f electrons, A ( J z), reflects the magnitude of the magnetic m o m e n t g/z B ( J z ) , where A is the hyperfine coupling constant and (J~) is the thermal average of the expectation value of J~ for the ion. The studies of the crystal field quenching of the rare earth magnetic m o m e n t by hyperfine field analysis have already been done [4, 5] for D y l _ x H o x N i 2 and Ho0.01(Gdl_xYx)0.99Ni2. In DyNi2, the crystal field quenching of the D y m o m e n t was found to be small from the analysis of the electric quadrupole interaction [4]. F r o m the N M R m e a s u r e m e n t s [5] on 165Ho, the quenching of
5 % was obtained for the H o magnetic m o m e n t in HoomGdo.99Ni z. In a recent N M R work [6] on HoA12, the H o magnetic m o m e n t has been evaluated from the electric quadrupole splitting of 16Silo using a molecular field Hamiltonian. It has been pointed out that the ionic ground state of H o 3+ in H o A I 2 derived f r o m the N M R analysis is inconsistent with that derived from neutron magnetic form factor experiments, but consistent with that derived from magnetization measurements. In the present work, the electric quadrupole interaction p a r a m e t e r p which is obtained by the N M R m e a s u r e m e n t s on 159Tb in TbNi 2 is compared with that calculated on the basis of a molecular field Hamiltonian. The magnetic moment of Tb in the c o m p o u n d is obtained from the calculated value of ( J z ) .
2. Experimental
The sample was p r e p a r e d by argon arc melting the appropriate quantities of the constituents. The purity of the starting materials was 99.9% for T b and 99.99% for Ni. The ingot was annealed at 800"C for about 7 days and then was crushed into powders. The powder sample was examined to have the cubic Laves phase structure (C-15 type) by X-ray diffraction.
0378-4363/88/$03.50 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
320
K , S h i m i z u et al. / N M R
The spin echo N M R measurements on 159Tb in the compound were done at 1.6 K.
study on TbNi 2
m
3. Results and discussion
For non S-state ion such as Tb +3, the hyperfine interaction is devided into a dominant intra-ionic term arising from 4f electrons and a small extraionic term. In almost all cases except for 1 6 5 H o in HoAI2, the intra-ionic hyperfine interaction is well described by the first-order perturbation treatment. In the case of HoAI z [6], the secondorder effect on the electric quadrupole hyperfine interaction has been estimated to be 6.3 MHz on the basis of the molecular field approximation. The second-order magnetic hyperfine interaction [7,81, where [g) and ]i) denote the ground state and the excited state eigenfunctions, and Eg and Ei the corresponding eigenvalues, contributes to the electric quadrupole splitting as an additional term. In the case of TbNi2, the magnitude of such a secondorder effect has been calculated to be about 1 MHz from the eigen functions and eigenvalues obtained by using the molecular field and the crystal field parameters used in the present analysis of N M R results• This value is small compared with the rather large experimental uncertainty. Therefore the second-order effects to the hyperfine interaction is neglected in the present analysis. The extra-ionic contribution to the electric quadrupole interaction would also be very small. If the deviation from the cubic crystal structure does not occur, the extra-ionic contribution due to the lattice distortion should vanish. In the case of 17SLu(I = 7/2, Q = 3.49b) N M R in Tb0.98Lu0.02Fe 2 [9] which Would have probably large magnetostriction as well as TbFe 2, no resolvable quadrupole splitting has been observed. The half-height width of the 175Lu resonance line is about 8 MHz, which suggests that the extraionic contribution to the electric quadrupole interaction is small. In GdAI 2 [10], the observed quadrupole splitting in lS7Gd N M R spectrum is at most of the order of 1 MHz. Consequently, the present analysis of the N M R results is treated within the first-order in the hyperfine
Z.,gl(ilAJ.llg)2/(Ei-Eg),
; r
,
,' i ~
,
,'
!
~
. .
2350
2400
2450
. j
2900
2950
3400
3450
MHz
Fig. 1. N M R spectrum of l~gTb in TbNi 2 taken at 1.6 K.
interactions and the extra-ionic contribution to the quadrupole interaction is also neglected. The resonance frequency, v, for the transition m ~ rn - 1 is given by v=la+p(2m-1)l, where a and p are the magnetic hyperfine and the electric quadrupole hyperfine parameters, respectively. Fig. 1 shows the 159Tb N M R spectrum observed for TbNi 2. The values of a and p are obtained to be 2924---3 MHz and 258.3-+ 3 M H z , respectively. These values are clearly smaller than the free ion values, which may be attributed to the crystal field effects. The magnetic hyperfine parameter a is decomposed into three terms: a
= a4f + a t + asp ,
where a4f is due to 4f electrons, asp is due to self-polarization of conduction electrons by their own magnetic m o m e n t and a t is the contribution from the conduction electron polarization by the neighboring rare earth spins. The electric quadrupole parameter p is equal to the intra-ionic quadrupole parameter P4f in the absence of the extra-ionic contribution to the electric quadrupole interaction. The intra-ionic hyperfine parameters a4f and P4f are related to ( J z ) and (J~) through a4f = a o ( J z ) / J and P a f = P0(3J~ J(J + 1 ) ) / J ( 2 J - 1), where a 0 = 3180 MHz, Po = 386 MHz and J = 6. Then, the magnitudes of the intra-ionic hyperfine interactions for the Tb 3+ ion in TbNi 2 are evaluated by diagonalizing the Hamiltonian consisting of the exchange and the crystal field terms. The easy axis of the magneti-
321
K . S h i m i z u et al. / N M R s t u d y on T b N i 2
zation is known [3, 11] to be (111) for TbNi 2. Then, the crystal field Hamiltonian for the z-axis lying along the ( 111 ) cubic crystallographic direction may be written as [12] Ygcf = - 2
3
B,(O
o _
20V~O] )
+--~-B 6 O 6 + T
O6+
O
,
where B 4 and B 6 a r e the crystal field parameters, O~ the Stevens operator equivalents. In the molecular field approximation, the exchange interaction may also be written with the usual notations as =
-ggsJ
Hm ,
where the molecular field H m is given by
,qm =
( g - 1)2(Jz) g/xB
The exchange constant J is related to the paramagnetic Curie temperature Op by (g - 1)2j(j + 1) 3k B Then, in order to evaluate the thermal average of the expectation values of Jz and j2, the total Hamiltonian is diagonalized for a set of three parameters B4, B 6 and H m. The thermal average of the expectation value of J~ has been taken at 1.6 K. At this temperature, only the ground state is important and the difference in (J~) between the thermal average value and that obtained only for the ground state is less than 1%. Since the molecular field H m is linear to (J~ }, H m is determined self-consistently with a given value of 0p for each set of crystal field parameters B 4 and B 6. The published values of the paramagnetic
Curie temperature 0p for TbNi 2 slightly differ from each other. In the present calculation, 0p is taken as 35 K [1]. The crystal field parameters are chosen so as to obtain a good agreement between the calculated and the experimental values of P4e. We modified the values of B 4 and B 6 obtained from the values of DyNi 2 [13] taking account of the Stevens factor of /3 and 3'. The value of 5.03 for (J~) corresponds to the magnetic moment of 7.55/x B. This value is obtained for the set of the parameters given in table I. The magnetic moment is slightly larger than that obtained by neutron diffraction and is close to values of 7.7 to 7.8/~3 obtained by magnetization measurements. We estimate the extra-ionic contribution to the magnetic hyperfine field at Tb in TbNi 2. The transferred hyperfine field, a t, is evaluated to be 69.8 MHz from the N M R result [14] of 139La in La0AGd0.9Ni2, where the difference of the spin values between Gd +3 and Tb +3 has been taken into account and the ratio of the s-electron hyperfine coupling constant [15] of Tb to that of La has been assumed to be 1.32. The value of asp is obtained to be 188.3 MHz by combining a4f and a t with the observed value of a. In TbNi2, the conduction electrons would have 5d and 6s character and would polarize parallel to the spin of 4f electrons. The positive field for asp in TbNi 2 might simply suggest the s-electron polarization to be dominant as in the case of TbFe 2 where a large and positive field due to s-electron polarization is observed [9]. If the d-electron polarization is the dominant contribution to asp in TbNi2, the self-polarization field would be caused by the d-orbital polarization which would make a positive contribution to the hyperfine field in the same manner as that of the 4f electrons. In RAI 2 [6, 16], the orbital contribution to the self-polarization field at the rare earth nucleus is relatively small compared to the spin polarization. In the
Table I The observed values of the hyperfine interaction parameters a and p (MHz), and the values of a4f , P4f (MHz) and (J~) obtained by using the crystal field parameters B4, B 6 (meV) and the paramagnetic Curie temperature 0p (K). a
p
a4f
P4f
{L)
B4
B6
0p
2924 +- 3
258.3 -+ 3
2665.9
258.3
5.03
1.70 × 10 -3
3.09 x 10 6
35
322
K . S h i m i z u et al. / N M R s t u d y o n T b N i 2
case of TbNi 2, the situation in the conduction band would differ from that of RAI 2. We cannot at the present stage draw the conclusion as to whether or not the d-orbital polarization is the dominant contribution compared to the spin polarization.
4. Conclusion
The magnetic moment of Tb in TbNi 2 has been derived to be 7.55/x B from the electric quadrupole splitting of 159Tb o n the basis of the molecular field approximation. This value for the Tb magnetic moment is in good agreement with that obtained from magnetization measurements on TbNi 2. From the hyperfine field analysis, the positive fields both for the self-polarization and the transferred field at the Tb-nucleus have been deduced using the calculated value of (J~).
Acknowledgement We are indebted to Miss. K. Horikawa, Mr. M. Katsurai and Mr. T. Ogino for their assist-
ance to the NMR measurements and the computer programming.
References [1] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973). [2] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179. [3] G.P. Felcher, L.M. Corliss and J.M. Hastings, J. Appl. Phys. 36 (1965) 1001. [4] G.J. Bowden and R.K. Day, J. Phys. F 8 (1978) 533. [5] A. Tari, Phys. Rev. B 19 (1979) 3462. [6] Om Prakash, D.St.P. Bunbury and M.A.H. McCausland, Z. Phys. B 58 (1984) 39. [7] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Oxford University Press, London, 1970). [8] P.R. Waind, I.S. Mackenzie and M.A.H. McCausland, J. Phys. F 13 (1983) 1041. [9] K. Shimizu, J. Magn. Magn. Mat. 70 (1987) 178. [10] E. Dormann, U. Dressel, H. Kropp and K.H.J. Buschow, J. Magn. Magn. Mat. 45 (1984) 207. [11] S.K. Arif, I. Sigalas and D.St.P. Bunbury, phys. star. sol. (a) 41 (1977) 585. [12] M.T. Hutchings, Solid State Phys. 16 (1964) 227. [13] D. Gignoux and F. Givord, Solid State Commun. 21 (1977) 499. [14] E. Dormann and K.H.J. Buschow, Physica 86-88B (1977) 75. [15] I.A. Campbell, J. Phys. C 2 (1969) 1338. [16] E. Belorizky and Y. Berthier, J. Phys. F 16 (1986) 637.