Phase diagrams for spin glasses with randomly mixed uniaxial anisotropies

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Abstract
Phase diagrams are derived, in the context of the infinite-range model of Sherrington and Kirkpatrick (1975) for spin glasses with single-ion uniaxial anisotropy. Special attention is given to the case where magnetic ions with competing anisotropies are dissolved in the same host. In general four distinct phases are possible: a paramagnetic phase, and three spin-glass phases in which longitudinal and/or transverse spin degrees of freedom are frozen. For mixed anisotropies, a rich variety of phase diagrams is predicted as a function of the anisotropy strengths and the concentrations of the magnetic ions. In nearly all cases where the anisotropies compete two consecutive transitions are predicted, in which first longitudinal and then transverse spin degrees of freedom freeze out (or vice versa) as the temperature is reduced. These double transitions should be observable in rare earth systems such as YEr1-yTby and YEr1-yDyy.

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