Journal of Physics C Solid State Physics

Quantum spin glasses with randomly mixed uniaxial anisotropies

G. Brieskorn, Klaus D. Usadel

Published Jun 30, 1986• 17 citations

Abstract

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.

DOI: 10.1088/0022-3719/19/18/013

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Journal of Physics C Solid State Physics

Quantum spin glasses with randomly mixed uniaxial anisotropies

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Published Jun 30, 1986• 17 citations

Publisher

Abstract

DOI: 10.1088/0022-3719/19/18/013

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\mathrm{XY}

behavior to a condensation in a nonmagnetic singlet ground state takes place for

S=1

{\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.

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.

{\mathit{T}}_{\mathit{c}}

(h)\ensuremath{\propto}

{\mathit{h}}^{2/3}

] for small fields to the Gabay-Toulouse (GT) -like behavior [

{\mathit{T}}_{\mathit{c}}

(h)\ensuremath{\propto}

{\mathit{h}}^{2}

] for large fields. For larger anisotropies (d\ensuremath{\ge}0.3) the upper critical line is essentially that of the AT type. Interestingly, the lower critical line, which persists for d0.5, exhibits the reverse type of behavior for the corresponding values of the anisotropy d. Additionally, we have analyzed transverse and longitudinal susceptibilities for different values of the field h. We found that a small amount of the anisotropy d stabilizes a plateau of the local susceptibilities in the spin-glass phase.