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Physical review. B, Condensed matter

Competition between axial and cubic anisotropies in Heisenberg spin glasses

Zbigniew Domański

Published Mar 1, 1997• 1 citation
Publisher

Abstract

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 ${\mathrm{D}}_{\mathrm{c}}$(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.

DOI
10.1103/physrevb.55.5827

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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 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.
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.
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.
We study the anisotropic Heisenberg spin-glass model in a three-dimensional hierarchical lattice (designed to approximate the cubic lattice), within a real-space renormalization-group approach. Two different initial probability distributions for the exchange interaction (JijJ_{ij}Jij​), Gaussian and uniform, are used, with zero mean and width Jˉ\bar{J}Jˉ. The (kT/Jˉ)×Δ0(kT/\bar{J}) \times \Delta_0(kT/Jˉ)×Δ0​ phase diagram is obtained, where TTT is the temperature, Δ0\Delta_0Δ0​ is the first moment of the probability distribution for the uniaxial anisotropy, and kkk is the Boltzmann constant. For the Ising model (Δ0=1\Delta_0=1Δ0​=1), there is a spin-glass phase at low temperatures (high Jˉ\bar{J}Jˉ) and a paramagnetic phase at high temperatures (low Jˉ\bar{J}Jˉ). For the isotropic Heisenberg model (Δ0=0\Delta_0=0Δ0​=0), our results indicate no spin-glass phase at finite temperatures. The transition temperature between the spin-glass and paramagnetic phase decreases with Δ0\Delta_0Δ0​, as expected, but goes to zero at a finite value of the anisotropy parameter, namely Δ0=Δc∼0.59\Delta_0 = \Delta_c \sim 0.59Δ0​=Δc​∼0.59. Our results indicate that the whole transition line, between the paramagnetic and the spin-glass phases, for Δc≤Δ0<1\Delta_c \leq \Delta_0 < 1Δc​≤Δ0​<1, belongs to the same universality class as the transition for the Ising spin glass.
The infinite-range quantum Heisenberg spin-glass model with random-anisotropy axes and external magnetic field (h) is studied by means of the thermofield dynamics for the spin value S=1/2. The stability of the mean-field-type solution against the action of fluctuations has been evaluated in the presence of h leading to the upper and lower critical lines in the field-temperature (h-T) plane. For small values of the anisotropy variance we find a crossover of the upper critical line from the de Almeida--Thouless-type behavior for small fields to the Gabay-Toulouse-like behavior for large fields and a reversed type of behavior at the lower critical line for corresponding values of the random anisotropy---in close analogy to the recently analyzed quantum vector spin glass with random Dzyaloshinsky-Moriya interactions.