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Physical review. B, Condensed matter

Crystal-field effect on the transverse susceptibility in spin-SIsing chains

Ibha Chatterjee

Published Dec 1, 1986• 4 citations
Publisher

Abstract

The crystal-field effect in the one-dimensional Ising model for spins S=1 to (5/2) has been studied in linear-response theory by considering its effect on the susceptibility in transverse directions. For S=1 analytical expressions are obtained, and for higher spins numerical calculations are performed for various values of the crystal-field parameter (D) and the exchange parameter (J). It has been found that the susceptibility maxima which appear for D<2J, do not occur for D>2J.

DOI
10.1103/physrevb.34.7969

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The crystal-field effect in the one-dimensional Ising model for spins S=1 to (5/2) has been studied in linear-response theory by considering its effect on the susceptibility in transverse directions. For S=1 analytical expressions are obtained, and for higher spins numerical calculations are performed for various values of the crystal-field parameter (D) and the exchange parameter (J). It has been found that the susceptibility maxima which appear for D<2J, do not occur for D>2J.
The crystal field effect has been studied in the linear Ising model which can be solved exactly. For spins S= 1/2 , 1, (3)/(2) it is easy to diagonalize the transfer matrix analytically, but for spins S> (3)/(2) , the transfer matrices are diagonalized numerically. The numerical results are accurate to seven decimal places and can be treated as exact for all practical purposes. Crystal field has no effect on spin- 1/2 systems, its effect has been studied in systems with spins S> (1)/(2) . The ferromagnetic as well as the antiferromagnetic sysceptibilities have been computed for the systems with and without the crystal field. It has been found that, for small crystal fields, the susceptibility behavior is not much different from that in the absence of crystal field. But for large crystal fields, not only the antiferromagnetic susceptibilities but the ferromagnetic susceptibilities also start showing maxima which appear for integer spins only.
We study the transverse susceptibility of the fully frustrated antiferromagnetic Ising Δ-chain, extending Minami's transfer-matrix method to the transverse susceptibility of general-type Ising linear-chains [J. Phys. Soc. Jpn. 67 (1998), 2255]. For the transverse fields Γ1 in tip spin sites and Γ2 in bottom spin sites, we calculate zero-field transverse susceptibilities χxtip = lim Γ1 →0Mxtip/Γ1 and χxbottom = lim Γ2 →0Mxbottom/Γ2 while keeping the ratio Γ1/Γ2 fixed, where Mxtip (bottom) denotes the magnetization for tip (bottom) spin sites. Both the transverse susceptibilities follow Curie's law at low temperatures. We also calculate χxbottom(Γ1 > 0), the transverse susceptibility of the bottom spin chain under a finite tip-spin transverse field, to understand the Curie-type behavior in zero-field susceptibility. Using the second-order perturbation theory, we also discuss the Γ1 dependence of χxbottom (Γ1) at zero temperature.
Exact expressions for the wave-number dependent longitudinal and transverse susceptibilities of the one-dimensional Ising model with competing interactions are obtained by combining the linear response theory with the transfer matrix method. The longitudinal susceptibility exhibits a characteristic wave-number dependence, while the transverse susceptibility is independent of wave-number. Special attention is paid to the condition under which the longitudinal susceptibility has a maximum value at nonzero wave-number. Furthermore, the phase diagram of a system with weakly coupled Ising chains is considered in connection with the one-dimensional susceptibility.