NEW MODEL OF SINGLET-GROUND-STATE MAGNET WITH EXCHANGE COUPLING : APPLICATION TO CsFeCl3

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NEW MODEL OF SINGLET-GROUND-STATE

MAGNET WITH EXCHANGE COUPLING :

APPLICATION TO CsFeCl3

M. Chiba, Y. Ajiro, K. Adachi, T. Morimoto

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Colloque C8, Suppl6ment au no 12, Tome 49, decembre 1988

NEW MODEL OF SINGLET-GROUND-STATE MAGNET WITH EXCHANGE COUPLING: APPLICATION TO CsFeCI3

M. Chiba ( I ) , Y. Ajiro (2), K. Adachi (3) and T. Morimoto (I)

(I) Institute of Atomic Energy, Kyoto University, Kyoto 611, Japan (2) Department of Chemistry, Kyoto University, Kyoto 606, Japan

(3) Kobe Tokiwa Junior College, Kobe 653, Japan

Abstract. - A model, we call "Spin-Band Modeln

,

is proposed on the exchange coupled singlet-ground-state magnet under applied magnetic field. The mechanism of nuclear spin-lattice relaxation and the applied field dependence of magnetization are discussed through this model and are compared with the experimental results of CsFeC13.

The spin state of ~ e ~ + ion in CsFeC13 is the singlet-ground-state [I, 21. Since the contribution of the single ion anisotropy energy, D, slightly overcomes

the contribution of the exchange coupling constant, J, this material is known to present no bdimensional magnetic order down to 0 K a t zero magnetic field. Under the magnetic field applied parallel to the crystal c-axis of CsFeC13 the 3-dimensional magnetic order has been reported to appear around the level crossing field, B

,

,,

of 7.5 T at temperatures below 2.5 K [2], supporting the theoretical discussion [3] on the magnetic order due to the ground-state cross-over.

As for the spin dynamics of the singlet-ground-stae magnet, the dimer system of cu2+ ion has been stud- ied through the spin-lattice relaxation time of proton

[4]. Here we measured the field induced magnetization and the spin-lattice relaxation time

TI

of 1 3 3 ~ s

under the magnetic fields applied parallel to crystal 15

c-axis (parallel configuration) and perpendicular to c-

axis (perpendicular configuration) in the paramagnetic Fig. 1. - Nuclear spin-lattice relaxation of 1 3 3 ~ ~ in

phase of CsFeCls. As shown in the insert of figure 1, the CsFeCl3. The insert shows the field induced magnetization.

magnetization in parallel configuration indicates an - - S

curve peculiar to singlet-ground-state magnet, while in perpendicular configuration the magnetization indicates a monotonous convex curve showing a tendency of saturation at high fields. The results of nuclear spin- lattice relaxation are shown in figure 1. In parallel configuration a drastic increase of 1

/

TI, independent of temperature, is observed around Bcross. As long as we know there has not been reported such a drastic field dependence. On the other hand, in perpendicular configuration 1

/ TI

decreases monotonically with increasing field depending on the temperature.

For the exchange coupled singlet-ground-state spin system with S = 1 we have proposed "Spin-Band Model" [5, 61. The Hamiltonian describing the system

.-

where (i, j) means the nearest neighbor pair; D (> 0) is the single ion anisotropy energy, g the ptensor, p~

the Bohr magneton,

Bo

the applied magnetic field,

S i a (a = s, y, z ) the component of spin at i-th site in the crystal and 2 s (> 0) the nearest neighbor ferromagnetic exchange coupling energies. In the case of CsFeCl3 the crystal c-axis corresponds to %axis in equation (1). The model starts from the single is& lated spin system by taking the coupling into account through the shift and the broadening of the energy level calculated by the moment method. An intuitive picture of the "Spin-Band" in parallel configuration is schematically drawn in figure 2, where lower two levels are concerned.

1s

On the basis of "Spin-Band Model" for the parallel

x =

(DS&

+

I.~B ~ o . g . ~ i ) configuration have been discussed the mechanisms of

the field induced magnetization and the nuclear spin-

t

lattice relaxation due t o the direct process inherent in

-'c

(J'lsizs'z + JLsixs'x + J-'-siys'y) _{the level crossing between dipole coupled nuclear and}

( i d

(3)

C8 - 1446 JOURNAL DE PHYSIQUE

Fig. 2. - An intuitive picture of "Spin-Band" in parallel configuration 161. The energy level of each site shifts to the low energy from the energy level of the isolated spin (indi- cated by dotted lines) due to the ferromagnetic exchange coupling with neighbor ions. Since the magnetic moment of each spin fluctuates paramagnetically around the average induced moment, the amount of shift changes from time to time or differs from site to site bringing the homogeneous broadening of the energy level.

electron spins 161. By applying the theory to the ferromagnetic linear chain, we have found that our model works quite well on explaining the experimental results with parameters listed in table I.

Table I. - Parameters of CsFeCls.

Present work 20 (*) 2.6 [8] 3.6 [9]

Neutron [7] 18.4 2.5 7.1 7.1

(*) assumption.

How does the "Spin-Band Model" work in perpendicular configuration ( B o l l % ) ? Fkom the anal- ogy of the "Spin-Band" in parallel configuration we assume that all the three levels have Gaussian exchange broadening with half width a t maximum slope of

6

(S,) ( J I

-

Jll

) ,

where z is the number of the nearest neighbors. The energy level diagram of "Spin- Band" is shown in figure 3 with z = 2 and parameters listed in table I. The calculated magnetization is shown in the insert of figure 1, fitting well with the experimental result. In this configuration the nuclear svin-lattice relaxation due t o AS, = f 1 transition is not dominant owing to no ground state cross-over. The

Fig. 3.

-

['Spin-Bandn in perpendicular configuration with parameters listed in table I. The Gaussian state density with half width at maximum slope of

6

( J I

-

J l l ) (S=)

with z = 2 is assumed.

mechanism due to AS, = 0 transition will be effective. The calculated relaxation rate has a strongly temperature dependent factor, exp (-j%

/

k T )

,

where Eo

is energy between the center of gravity of the lower band and the level, S, = 0 , lc tlie Boltzmann constant and T the temperature. The ratio of the factors, exp (-Eo

/

k T )

,

at T = 4.2 and 1.4 K is lo4 con- trary to that of the experimental relaxation rates of about 10. Unfortunately "Spin-Band Model" does not work in perpendicular configuration. Probably in the case of perpendicular configuratior~ the treatment has been too simplified because S, is not a good quantum

number.

[ I ] Yoshizawa, H., Kozukue, W. and Hirakawa, K.,

J. Phys. Soc. J p n 49 (1980) 144.

[2] Haseda, T., Wada, N., Hata, Ivl. and Amaya, K.,

Physica 108B (1981) 841.

[3] Tsumeto, T. and Murao, T., Physica 51 (1971) 186.

[4] Diederix, K. M., Groen, J. F'., Klaassen, T. 0.

and Poulis, N. J., Physica 9613 (1979) 41. [5] Chiba, M., Ajiro, Y., Adachi, K. and Morimoto,

T., Jpn J. Appl. Phys. Suppl. 26-3 26 (1987) 853. [6] Chiba, M., Ajiro, Y., Adachi, K. and Morimoto,

T., J. Phys. Soc. Jpn 57 (1988) 3178.

[7] Steiner, M., Kakurai, K., Knc~p, W., Dorner, B., Pynn, R., Happek, U., Day, 1'. and McLeen, G.,

Solid State Commun. 38 (1981) 1179.

[8] Chiba, M., Tsuboi, T., Hori, II., Shiozaki, I. and Date, M., Solid State Commun. 63 (1987) 427. [9] Tsuboi, T., Chiba, M., Hori, II., Shiozaki, I. and