PROPERTIES OF ISING MAGNETIC SYSTEM FexTiS2

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PROPERTIES OF ISING MAGNETIC SYSTEM

FexTiS2

Y. Tazuke, T. Saitoh, F. Matsukura, T. Satoh, T. Miyadai, K. Hoshi

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplbment au no 12, Tome 49, dbcembre 1988

PROPERTIES OF ISING MAGNETIC SYSTEM FesTiS2

Y. Tazuke (I), T. Saitoh ( I ) , F. Matsukura (I), T. Satoh (I), T. Miyadai (I) and K. Hoshi (2)

(I) Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060, Japan

(') Muroran Institute of Technology, Muroran 050, fapan

Abstract. - Analysis of frequency dependence of spin glass transition temperatures of an Ising spin glass Feo.lTiS2 shows that power law with a finite transition temperature is the most probable formula describing the experimental data. Magnetization measurement on FellaTiS2 suggests that atomically ordered FellsTiSz is an antiferrornagnet with

TN = 33 K .

Various transition metals are intercalated in the van der Waals gap between the neighboring sulfur lay- ers of hexagonal TiSz. Iron atoms in Fe,TiSz are distributed in ordered manners for x = 1/4, 1/3 and 1/2, forming ordered magnetic compounds; they are ran- domly distributed for other values of x, forming random magnetic compounds. The magnetic properties of random compound Fe,TiSz have been studied by several authors [I]. The compound with 0

<

x

5

0.35 is an Ising spin glass and that with 0.35

<

a:

5

0.43 is an Ising ferromagnet. Transition to spin glass state is suggested at low temperature for 0.35

<

a:

<

0.4. On the other hand, few studies have been made about the magnetic properties of ordered compounds [2]. Here we report two new results: result of ac-susceptibility measurements in the spin glass phase x = 0.1, and magnetic property of ordered compound x = 1/3.

There are many exampl'es about the frequency (f) dependence of the paramagnetic-to-spin-glass transition temperature Tg (f) of a spin glass defined by the cusp in ac-susceptibility

x,.

Several functions are proposed to explain the frequency dependence of T,. The Fulcher law

f

= foexp [-Eo/k (T,

-

To)] (1) was phenomenologically proposed 131, although its sig- nificance is not clear. Short-range Ising model [4] lead to a power law with a zero-temperature transition,

with

zv N 4.

Assumption of a finite transition temperature T* lead to another power law

f = f * [(Tg

-

T*) /Tglzv

.

₍₃₎ This relation was theoretically supported by a recent simulation study about short-range Ising model [5], which gave zv = 7.9.

Polycrystalline sample of Feo.lTiSz was prepared a t 900 OC. The sample was quenched to room temperature by dropping the quartz tube containing the sam-

Fig. 1. - Temperature dependences of ac-susceptibility at various frequencies on Feo.lTiS2. The frequencies are 8,17, 80, 480, 1710 and 3 410 Hz from top to bottom. Various lines are used only for sivual convenience.

ple into water. X-ray diffraction shows that the sample is the random compound. Figure 1 shows

x,,

of Feo.lTiS2 a t various frequencies. The parameters in the above three equations are determined by the following method. First, by seeting fo,

f'

or f * to a value other two parameters are calculated by the least squares method. Secondly, most probable value of fo, f' or f * which gives the minimum of the mean square error is determined. Figure 2 shows that the data are fitted to the three equations similarly well [6]. In or- der to determine which of the three is the best equation to describe the data, we examine the values of the parameters in the following. The fitting to equation (1) gives fo = 8.5 x 10' Hz, To = 25.6 K and Eo/k = 60.6 K. fo is too small, because it should be the highest of the characteristic frequencies of the spin system, 1 0 ' ~ - 1 0 ~ ~ HZ [16]. TO is very low compared with the lowest value of T, (29.2 K at 8 Hz). The fitting to equation (2) gives f' = 2.5

x

lo6

Hz, E'/k = 39.2 K and zv = 8.7.

Again f ' is too small. zv is about twice the theoretical value [4]. Finally, the fitting t o equation (3) gives f * = 8.1 x 1012 Hz, T* = 26.4 K and zv = 11.9. The value of f * is reasonable. As many experimental values of zv

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JOURNAL DE PHYSIQUE

Fig. 2.

-

Fitting of the Tg

-

f data of Feo.lTiS2 to equations (1-3) from top to bottom. The solid lines show the calculated values.

are located in 5-10, the value of zv is not unreasonable. However, T* is unreasonably small. If f * is adjusted t o 2.3 x 101° Hz, reasonable parameters are obtained (T* = 27.7 K and zv = 7.0). The mean square error in the latter set of parameters is not much larger than that in the former set. This means that equation (3) can explain the experimental results. On the other hand, the adjusting of fo or

f'

in equations (1) or (2) cannot give reasonable sets of parameters. Therefore equation (3) is the most probable equation.

Polycrystalline sample of Fel/sTiS2 was prepared at 900 OC. The sample was cooled to room temperature at a rate of 1 "C/hour. X-ray diffraction pattern shows that the sample is a mixture of the ordered phase

x

= 1/3, whose structure was presented by Takahashi and Yamada [7], and the random phase x

-

1/3. Fig- ure 3 shows temperature dependence of magnetization at 5.6 kOe. The temperature dependence consists of two parts: a broad maximum around 35 K and a sharp peak at 33 K. By the following reasons the broad maximum is assigned to the spin glass transition of the random phase detected previously at Tg = 44 K by

xac

measurement [I]. i) The temperature dependence rounds off compared with the X , cusp. ii) The temperature of the maximum is shifted to lower tempera- ture compared with the temperature of the X , cusp.

Fig. 3. - Temperature dependence of the magnetization of FeilsTiS2 at 5.6 kOe.

iii) Below 35 K a time dependence 'of the magnetization is observed. The facts i-iii) art? characteristic of a spin glass at a finite field. Then, ithe sharp peak at 33 K is associated with the magnetic transition to long- range-ordered state of the atomicalily ordered phase Fel/sTiSa. This ordered state is probably an antifer- romagnetic state because no ferromagnetic moment is observed. Mossbauer spectrum similar t o the previous one for x = 1/4 at 4.2 K [2] is obtained at 19 K. It is a future theme to study about pure simples of ordered Fel13TiS2 prepared by other metliod, for example, by CVT method.

[l] Yoshioka, T. and Tazuke, Y., J Phys. Soc. Jpn

54 (1985) 2088;

Satoh, T., Tazuke, Y., Miyadai, T. and Hoshi, K.,

J. Phys. SOC. Jpn 57 (1988) 1743;

Negishi, H., Takahashi, T. and Inoue, M., J. Magn. Magn. Muter. 68 (1987) 271.

[2] Katada, M. and Herber, R. H., J. Solid State Phys. 33 (1980) 361.

[3] Tholence, J. L., Solid State C o ~ o m u n . 35 (1980) 113.

[4] Binder, K; and Young, A. P., l'hys. Rev. B 29

(1984) 2864.

[5] Ogielski, A. T., Phys. Rev. B 32 (1985) 7384. [6] Souletie, J. and Tholence, J. L., Phys. Rev. B 32

(1985) 516;

Aruga, H., Tokoro, T. and ito, A., J. Phys. Soc.

Jpn 57 (1988) 261.