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Physical review. B, Condensed matter

Spin-glasses with uniaxial anisotropy

Klaus D. Usadel, K. Bien, H.-J. Sommers

Published Jun 1, 1983• 38 citations
Publisher

Abstract

We study a long-range quantum spin-glass model with uniaxial anisotropy. A calculation of the phase diagram as well as the susceptibilities above the freezing temperature is presented. For easy-axis systems Ising-like behavior is found, while for easy-plane systems with increasing anisotropy a change from $\mathrm{XY}$ behavior to a condensation in a nonmagnetic singlet ground state takes place for $S=1$.

DOI
10.1103/physrevb.27.6957

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We study a long-range quantum spin-glass model with uniaxial anisotropy. A calculation of the phase diagram as well as the susceptibilities above the freezing temperature is presented. For easy-axis systems Ising-like behavior is found, while for easy-plane systems with increasing anisotropy a change from XY\mathrm{XY}XY behavior to a condensation in a nonmagnetic singlet ground state takes place for S=1S=1S=1.
The authors study a long-range quantum spin glass model with randomly mixed local uniaxial anisotropies. Two types of magnetic impurities are considered, and the case of competing anisotropies will be discussed in particular. They calculate the phase diagrams of these systems as a function of impurity concentrations and strengths of the anisotropies. Depending on the parameters of the system, interesting transitions from longitudinal to transverse freezing and/or condensation in a non-magnetic state are observed.
An infinite-range quantum Heisenberg spin glass with uniaxial (D) and cubic (K) anisotropies is studied using the thermo-field-dynamic method. Mean-field theory phase diagrams in the temperature-anisotropy plane (T,D) for quantum spins S=2 and S=5/2 are presented for different values of K. Generally, for integer spin values and large anisotropy D a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value Dc{\mathrm{D}}_{\mathrm{c}}Dc​(T=0). For half-integer S and sufficiently low temperature, the spin-glass phase persists for arbitrary D and K. In both cases the presence of a cubic term induces complicated crossovers from longitudinal to transverse freezing of spins.
An infinite-range quantum Ising spin glass with cubic anisotropy (K) is studied using the imaginary-time representation with the n-replica approach and the thermofield dynamic method. Mean-field-theory phase diagrams in the temperature-anisotropy plane (T,K) for quantum spins S ranging from 2 to 9/2 are presented. For integer-spin values and large cubic anisotropy (positive or negative, depending on S) a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value Kc{\mathit{K}}_{\mathit{c}}Kc​(T=0). For half-integer S and sufficiently low temperature the spin-glass phase persists for arbitrary K.
The infinite-range quantum spin glasses with cubic anisotropy (K) are studied using a combination of the imaginary-time representation with the n-replica approach and the thermofield dynamic method. Mean-field theory phase diagrams in the temperature-anisotropy plane (T,K) are presented for quantum spin numbers S ranging from 2 to 9/2. At T=0, the ground state is nonmagnetic and the spin-glass order is absent for integer spin and large cubic anisotropy, the sign of which depends on S. For half-integer S and sufficiently low temperatures the spin-glass phase persists for arbitrary K.
In the replica symmetric approximation and the static limit in Matsubara ``imaginary time,'' we have investigated a quantum XY spin-glass system with the ferromagnetic coupling and the uniaxial anisotropy numerically. We found that, for S=1,S=1,S=1, under the uniaxial anisotropy, the spin-glass phase breaks into two phases: a longitudinal spin-glass phase, and a spin-glass phase; the mixed phase of the spin glass and the ferromagnet breaks into two phases: a mixed phase of the longitudinal spin glass and the longitudinal ferromagnet, a mixed phase of the spin glass and the ferromagnet; the peak in the curve of the specific heat versus temperature is split into two peaks: the peak of uniaxial anisotropy and the peak of the ferromagnetic coupling. The system will be dominated by the random exchange interaction if the probability of the random exchange interaction taking negative value is greater than 15.87%. In the absence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase and the paramagnetic phase. In the presence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase, the longitudinal spin-glass phase and the paramagnetic phase. In these phases, the entropy, the specific heat and the susceptibility do not depend on the mean-interaction.
The infinite-range quantum Heisenberg spin glass with uniaxial anisotropy (D) and coaxial external magnetic field (h) is studied by means of the thermo-field-dynamics as a substitute for the n-replica trick. Within the mean-field theory a multiplicity of spin-glass phases has been found for the spin values S=1 and S=3/2, respectively, including: longitudinal, transverse, and mixed phases. The stability of the mean-field-type solution against the action of fluctuations has been investigated and the existence of a crossover from the longitudinal-to-transverse freezing is demonstrated explicitly in the temperature-field (T-h) phase diagram for various values of the constant D.