- Email: [email protected]
Nonlinear susceptibility of ferromagnetic Ga 0.6Mo2S4 spinel
Journal of Magnetism and Magnetic Materials 177 181 (1998) 263 264
~ H Journalof magnetism ~ i ~ and magnetic materials
ELSEVIER
Nonlinear susceptibility of ferromagnetic Gao.6M02S4 spinel T. Taniyama*, I. Nakatani National Research Institute Jot Metals, 1-2-1 Sengen, Tsukuba, lbaraki 305, Japan
Abstract Linear and nonlinear susceptibilities of spinel-type Gao.6Mo2S4 compound were investigated in the paramagnetic-ferromagnetic critical region to elucidate the ferromagnetic transition process. A possible sequential transition process is proposed, in which the intra-cluster magnetic moments align ferromagnetically followed by the onset of the long-range ferromagnetic ordering. ~ 1998 Elsevier Science B.V. All rights reserved. Keywords: Clustered compounds; Ferromagnetism; Nonlinear susceptibility
Ferromagnetism of molybdenum cluster compound GaxMozS4 (x = 0.5-0.67) has been reported by several authors by means of many different techniques, e.g., magnetization, resistivity, and specific heat [-1,2]. The magnetic properties are roughly interpreted in terms of the Stoner Wohlfarth model of itinerant electron magnetism. However, a visible picture of the ferromagnetic transition process has not been obtained owing to the magnetic complexity of the tetrahedral molybdenum cluster. In this work, we performed AC linear and nonlinear susceptibility measurements to elucidate the paramagnetic-ferromagnetic transition process. The results give us suggestive information on the ferromagnetic transition process. The polycrystalline compound was prepared by sintering the constituent elements in an evacuated quartz tube at 950°C for 18 h. For the homogeneity, the product was pulverized, and then further heated at 1100C for 24 h followed by quenching in cold water. Further, the powder was pressed (100 kg/cm 2) into a pellet under an argon gas atmosphere at 1100°C for 3 h. The composition of the specimen was determined to be Gaoi6MozS4 by means of chemical analysis. The powder X-ray diffraction pattern reveals a homogeneous single phase and was indexed on the basis of the lower symmetric spinel structure (space group F743m) having a = 9.737 A at room temperature. The diffraction peaks except those with indices h 0 0 were broadened below 45 K, reflecting the structural transition from space group FT~3mto R3m. The AC
*Corresponding author. Tel.: + 81 298 53 1237; fax: + 81 298 59 2601; e-mail: [email protected].
susceptibility measurements were performed using a susceptometer (PPMS, Quantum Design) at temperatures from 12 to 22 K. The first-, second-, and third-harmonic signals were simultaneously recorded in an AC modulating field ho = _+ 5 0 e at a frequency f = 91 Hz. In this paper, we concentrate on the real (in-phase) part of the linear and nonlinear susceptibilities. Fig. la shows the temperature-dependent linear 7~b and first-order nonlinear X'lho susceptibilities [3]. Z~ shows a broad maximum at around 16.4 K accompanied by a shoulder at 18.9 K. On the contrary, 7t~ho has a single sharp peak at 17.4 K which is almost independent of the excitation frequencies between 29 and 91 Hz. The divergence of Z]ho suggests the onset of the ferromagnetic ordering since zt~h0 is associated with the spontaneous magnetization. Thus, we intentionally determine the Curie temperature Tc = 17.4 K as the peak temperature, which also coincides with the temperature of the inflection point in the temperature dependent 7.5. We also note that no anomaly was observed at 18.9 K in the nonlinear susceptibilities. Shown in Fig. lb is the temperature dependence of the second-order nonlinear susceptibility 3~,t4z2,,o.~2With decreasing temperature, 3,,4z2,,o~.2shows a large negative peak followed by a positive broad maximum, which is typical of a normal ferromagnetic transition [3]. Thus, the temperature dependence ofaz2ho 3 , 2 can be analyzed on the basis of the procedure introduced in the critical phenomena. The temperature-dependent X~ is represented by the following power law in the critical region: X~ ~ (T - Tc) -~'2,
0304-8853/98/$19.00 ~C) 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 4 5 6 - 3
(l)
264
T. Tan(vama, I. Nakatani/Journal o f Magnetism and Magnetic Materials 177 181 (1998) 263 264 7
(a) .-5'" 4
[
:)
:
Z°t
_~:~
•
3/4x,2the2
-=,-
I°-~
%
%
=
~ /
~o
g-
~
10 -~
10"
/
0,01 (T-Tc)/T
(b)
E"
c
Fig. 2. Log log plot of 14z2h0[ ~'t 2 versus reduced temperature o
( T - Tc)/Tc. The straight line denotes a fitted line.
I ////j---
F~
14
16
18
20
22
T(K)
Fig. 1. Temperature-dependent linear and nonlinear susceptibilities of G a 0 . 6 M o z S 4. The dashed lines denote the schematic behavior obtained by the mean-field theory. where 72 is the critical exponent of the nonlinear susceptibility g~. Eq. (1) can be fitted to the data in the critical region (Fig. 2), which give the value of 72 = 4.8 _+ 0.3. This value is in good agreement with that of the 3D Heisenberg ferromagnet (72 = 4.887 _ 0.017) [3]. We first discuss the temperature dependence of Z~ as shown in Fig. lb. g~ shows a hyperbolic temperaturedependence in the vicinity of Tc. Such a characteristic feature was experimentally observed in a ferromagnetic Ni [3]. The obtained critical exponent 72 is in excellent agreement with the value of the 3D Heisenberg ferromagnet, indicating that the Ga0.6MozS 4 belongs to the same universality class as the isotropic Heisenberg ferromagnet. Thus, the ferromagnetic ordering would be intepreted on the basis of the localized ferromagnet picture. We should further pay attention to the critical behavior of g~ which can be analyzed in terms of the Kouvel Fisher plot. However, the temperature dependent Z{~has a shoulder in the paramagnetic region so that the usual procedure is inappropriate to the present case. Therefore, we do not discuss the critical behavior ofgb in detail in this paper. The temperature-dependent linear susceptibility g{~has two peaks at 16.4 and 18.9 K as shown in Fig. la. The similar behavior was reported previously by Rastogi et al. [1] who determined the Tc as the shoulder temperature compared with an anomaly of the specific heat at 19.5 K. However, we repeat again that the ferromagnetic long-range order should be characterized by the diver-
gence of the nonlinear susceptibility g~ (Tc = 17.4 K). No anomaly of Z] and Z~ at 18.9 K is suggestive of some local magnetic changes at the shoulder temperature rather than the long-range ordering. Thus, we propose the following picture of the ferromagnetic transition process. The shoulder would be due to spin alignment of the intra-cluster itinerant electrons, resulting in the long range ferromagnetic ordering at 17.4 K via the interaction between the local moments of the molybdenum clusters. This supports the itinerant electron magnetism [1] as well as the localized ferromagnet picture deduced from the critical exponent 72. Moreover, the picture consistently explains the frequency dependence of g~ (not shown here) in which 7.5 at 16.4 K smears with increasing excitation frequency, in contrast to the frequency-independent shoulder. Finally, we shortly comment on the ferromagnetic spin alignment in the 4d molybdenum clusters. Recent investigations on 4d transition-metal clusters have given some evidence for ferromagnetism, e.g., Mo13 cluster [-4] and Pd particles [5]. Kaiming et al. theoretically predicted 4d ferromagnetism of the high symmetrical Mo13 clusters. The ferromagnetic properties of the molybdenum cluster in the Gao.6Mo2S4 may be interpreted in this manner according to the small d-sp hybridization between molybdenum cluster and surrounding atoms.
References
[1] A.K. Rastogi, A. Berton, J. Chaussy, R. Tournier, M. Potel, R. Chevrel, M. Sergent, J. Low Temp. Phys. 52 (1983) 539. [2] K. Okuda, S. Noguchi, M. Asano, S. Endo, J. Magn. Magn. Mater. 90&91 (1990) 148. [3] T. Shirane, T. Moriya, T. Bitoh, A. Sawada, H. Aida, S. Chikazawa, J. Phys. Soc. Japan 64 (1995) 951. [4] D. Kaiming, Y. Jinlong, X. Chuanyun, W. Kelin, Phys. Rev. B 54 (1996) 11907. [5] T. Taniyama, E. Ohta, T. Sato, Europhys. Lett., to be published.
~ H Journalof magnetism ~ i ~ and magnetic materials
ELSEVIER
Nonlinear susceptibility of ferromagnetic Gao.6M02S4 spinel T. Taniyama*, I. Nakatani National Research Institute Jot Metals, 1-2-1 Sengen, Tsukuba, lbaraki 305, Japan
Abstract Linear and nonlinear susceptibilities of spinel-type Gao.6Mo2S4 compound were investigated in the paramagnetic-ferromagnetic critical region to elucidate the ferromagnetic transition process. A possible sequential transition process is proposed, in which the intra-cluster magnetic moments align ferromagnetically followed by the onset of the long-range ferromagnetic ordering. ~ 1998 Elsevier Science B.V. All rights reserved. Keywords: Clustered compounds; Ferromagnetism; Nonlinear susceptibility
Ferromagnetism of molybdenum cluster compound GaxMozS4 (x = 0.5-0.67) has been reported by several authors by means of many different techniques, e.g., magnetization, resistivity, and specific heat [-1,2]. The magnetic properties are roughly interpreted in terms of the Stoner Wohlfarth model of itinerant electron magnetism. However, a visible picture of the ferromagnetic transition process has not been obtained owing to the magnetic complexity of the tetrahedral molybdenum cluster. In this work, we performed AC linear and nonlinear susceptibility measurements to elucidate the paramagnetic-ferromagnetic transition process. The results give us suggestive information on the ferromagnetic transition process. The polycrystalline compound was prepared by sintering the constituent elements in an evacuated quartz tube at 950°C for 18 h. For the homogeneity, the product was pulverized, and then further heated at 1100C for 24 h followed by quenching in cold water. Further, the powder was pressed (100 kg/cm 2) into a pellet under an argon gas atmosphere at 1100°C for 3 h. The composition of the specimen was determined to be Gaoi6MozS4 by means of chemical analysis. The powder X-ray diffraction pattern reveals a homogeneous single phase and was indexed on the basis of the lower symmetric spinel structure (space group F743m) having a = 9.737 A at room temperature. The diffraction peaks except those with indices h 0 0 were broadened below 45 K, reflecting the structural transition from space group FT~3mto R3m. The AC
*Corresponding author. Tel.: + 81 298 53 1237; fax: + 81 298 59 2601; e-mail: [email protected].
susceptibility measurements were performed using a susceptometer (PPMS, Quantum Design) at temperatures from 12 to 22 K. The first-, second-, and third-harmonic signals were simultaneously recorded in an AC modulating field ho = _+ 5 0 e at a frequency f = 91 Hz. In this paper, we concentrate on the real (in-phase) part of the linear and nonlinear susceptibilities. Fig. la shows the temperature-dependent linear 7~b and first-order nonlinear X'lho susceptibilities [3]. Z~ shows a broad maximum at around 16.4 K accompanied by a shoulder at 18.9 K. On the contrary, 7t~ho has a single sharp peak at 17.4 K which is almost independent of the excitation frequencies between 29 and 91 Hz. The divergence of Z]ho suggests the onset of the ferromagnetic ordering since zt~h0 is associated with the spontaneous magnetization. Thus, we intentionally determine the Curie temperature Tc = 17.4 K as the peak temperature, which also coincides with the temperature of the inflection point in the temperature dependent 7.5. We also note that no anomaly was observed at 18.9 K in the nonlinear susceptibilities. Shown in Fig. lb is the temperature dependence of the second-order nonlinear susceptibility 3~,t4z2,,o.~2With decreasing temperature, 3,,4z2,,o~.2shows a large negative peak followed by a positive broad maximum, which is typical of a normal ferromagnetic transition [3]. Thus, the temperature dependence ofaz2ho 3 , 2 can be analyzed on the basis of the procedure introduced in the critical phenomena. The temperature-dependent X~ is represented by the following power law in the critical region: X~ ~ (T - Tc) -~'2,
0304-8853/98/$19.00 ~C) 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 4 5 6 - 3
(l)
264
T. Tan(vama, I. Nakatani/Journal o f Magnetism and Magnetic Materials 177 181 (1998) 263 264 7
(a) .-5'" 4
[
:)
:
Z°t
_~:~
•
3/4x,2the2
-=,-
I°-~
%
%
=
~ /
~o
g-
~
10 -~
10"
/
0,01 (T-Tc)/T
(b)
E"
c
Fig. 2. Log log plot of 14z2h0[ ~'t 2 versus reduced temperature o
( T - Tc)/Tc. The straight line denotes a fitted line.
I ////j---
F~
14
16
18
20
22
T(K)
Fig. 1. Temperature-dependent linear and nonlinear susceptibilities of G a 0 . 6 M o z S 4. The dashed lines denote the schematic behavior obtained by the mean-field theory. where 72 is the critical exponent of the nonlinear susceptibility g~. Eq. (1) can be fitted to the data in the critical region (Fig. 2), which give the value of 72 = 4.8 _+ 0.3. This value is in good agreement with that of the 3D Heisenberg ferromagnet (72 = 4.887 _ 0.017) [3]. We first discuss the temperature dependence of Z~ as shown in Fig. lb. g~ shows a hyperbolic temperaturedependence in the vicinity of Tc. Such a characteristic feature was experimentally observed in a ferromagnetic Ni [3]. The obtained critical exponent 72 is in excellent agreement with the value of the 3D Heisenberg ferromagnet, indicating that the Ga0.6MozS 4 belongs to the same universality class as the isotropic Heisenberg ferromagnet. Thus, the ferromagnetic ordering would be intepreted on the basis of the localized ferromagnet picture. We should further pay attention to the critical behavior of g~ which can be analyzed in terms of the Kouvel Fisher plot. However, the temperature dependent Z{~has a shoulder in the paramagnetic region so that the usual procedure is inappropriate to the present case. Therefore, we do not discuss the critical behavior ofgb in detail in this paper. The temperature-dependent linear susceptibility g{~has two peaks at 16.4 and 18.9 K as shown in Fig. la. The similar behavior was reported previously by Rastogi et al. [1] who determined the Tc as the shoulder temperature compared with an anomaly of the specific heat at 19.5 K. However, we repeat again that the ferromagnetic long-range order should be characterized by the diver-
gence of the nonlinear susceptibility g~ (Tc = 17.4 K). No anomaly of Z] and Z~ at 18.9 K is suggestive of some local magnetic changes at the shoulder temperature rather than the long-range ordering. Thus, we propose the following picture of the ferromagnetic transition process. The shoulder would be due to spin alignment of the intra-cluster itinerant electrons, resulting in the long range ferromagnetic ordering at 17.4 K via the interaction between the local moments of the molybdenum clusters. This supports the itinerant electron magnetism [1] as well as the localized ferromagnet picture deduced from the critical exponent 72. Moreover, the picture consistently explains the frequency dependence of g~ (not shown here) in which 7.5 at 16.4 K smears with increasing excitation frequency, in contrast to the frequency-independent shoulder. Finally, we shortly comment on the ferromagnetic spin alignment in the 4d molybdenum clusters. Recent investigations on 4d transition-metal clusters have given some evidence for ferromagnetism, e.g., Mo13 cluster [-4] and Pd particles [5]. Kaiming et al. theoretically predicted 4d ferromagnetism of the high symmetrical Mo13 clusters. The ferromagnetic properties of the molybdenum cluster in the Gao.6Mo2S4 may be interpreted in this manner according to the small d-sp hybridization between molybdenum cluster and surrounding atoms.
References
[1] A.K. Rastogi, A. Berton, J. Chaussy, R. Tournier, M. Potel, R. Chevrel, M. Sergent, J. Low Temp. Phys. 52 (1983) 539. [2] K. Okuda, S. Noguchi, M. Asano, S. Endo, J. Magn. Magn. Mater. 90&91 (1990) 148. [3] T. Shirane, T. Moriya, T. Bitoh, A. Sawada, H. Aida, S. Chikazawa, J. Phys. Soc. Japan 64 (1995) 951. [4] D. Kaiming, Y. Jinlong, X. Chuanyun, W. Kelin, Phys. Rev. B 54 (1996) 11907. [5] T. Taniyama, E. Ohta, T. Sato, Europhys. Lett., to be published.