Magnetization Process in an Ising Spin System

Abstract

A method of determining the state of lowest energy of an Ising spin system under an external field is proposed. The energy of a spin arrangement is expressed in terms of the total number of negative spins and the numbers of interaction lines connecting either two negative spins or negative and positive spins. It is shown by use of topological relations among these numbers that the magnetization of an Ising spin antiferromagnet increases stepwise at absolute zero with increasing field strength. The spin arrangement at each step is determined of Oguchi and Takano's model of CoC1 2 ·2H 2 0 and the simple, body-centered, face-centered cubic and MnF 2 type lattices with nearest and next-nearest neighbor interactions. Experimental results of CoC1 2 • 2H 2 0 are discussed as well. § 1. Introduction The present study is motivated by Kobayashi~Haseda's 1) and Narath-Barham's 2) magnetization measurement of CoCl 2 • 2H20, which is an antiferromagnet with TN= 17.2°K. The crystal structure of CoC1 2 • 2H 2 0 is of monoclinic symmetry. It is inferred from a large anisotropy of the g factors (gb=7.3 and gc=2.9 2)) that a spin of Co in this substance behaves, to good approximation, like an Ising spin bound to the b axis. As is shown schematically in Fig. 1, the mag-M netization along the b axis measured at 4.2° K increases stepwise with increasing field strength; the discontinuities are located at 32 and 46 koe. The spins are in the ferro-magnetic state with the magnetization of about 3f.LB per Co above 46 koe ; between 46 and 32 koe they are in an intermediate state .._ ____________ H with the magnetization of about 1 f.LB per Co. Fig. 1. A sketch of the magnetization Similar phenomena are found in related sub-vs. field curve of CoCl2 · 2H20. stances such as CoEr 2 • 2H 2 0. 1) ' 2) This paper proposes a general method of determining the spin structure of lowest energy of an Ising spin system under an external field. It is shown that the appearance of intermediate states in the magnetization process in an Ising spin antiferromag-net is ~losely related to the topology of a given lattice. The present method is applicable to three-dimensional lattices. A method of determining the state of lowest energy of an Ising spin system under an external field is proposed. The energy of a Spin arrangement is expressed in terms of the total number of negative spins and the numbers of interaction lines connecting either two negative spins or negative and positive spins. It is shown by use of topological relations among these numbers that the magnetization of an Ising spin antiferromagnet increases stepwise at absolute zero with increasing field strength. The spin arrangement at each step is determined of Oguchi and Takano's model of CoClz-2H20 and the simple, body-centered, face-centered cubic and Man type lattices with nearest and next-nearest neighbor interactions. Experimental results of CoC12~2H20 are discussed as well. § 1. Introduction The present study is motivated by Kobayashi-'Haseda'sn and Narath-Barham'sz) magnetization measurement of CoClzv2H2O, which is an antiferromagnet with TN217.2°K. The crystal structure of CoCl2-2H2O is of monoclinic symmetry. It is inferred from a large anisotropy of the 9 factors (92»:73 and 96:22.9") that a spin of Co in this substance behaves, to good approximation, like an Ising spin bound to the [2 axis. As is shown schematically in Fig. 1, the mag-M. netization along the b axis measured at 4.2°K increases stepwise with increasing field strength; the discontinuities are located at 32 and 46 koe. The spins are in the ferro-magnetic state with the magnetization of about 3,413 per Co above 46 koe; between 46 and 32 koe they are in an intermediate state H with the magnetization of about 1 ,aB per Co. Fig. 1. A sketch of the magnetization Similar phenomena are found in related sub-VS-field curve 0f COCIZ'ZHZO-stances such. as CoBr2-2H20.1)'2) This paper proposes a general method of determining the spin structure of lowest energy of an Ising spin system under an external field. It is shown that the appearance of intermediate states in the magnetization process in an Ising spin antiferromag-net is closely related to the topology of a given lattice. The present method is applicable to three-dimensional lattices.