Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy

TL;DR

This paper demonstrates that an effective spin-1/2 model accurately describes the generation of random fields in dipolar spin glasses with strong anisotropy under a transverse magnetic field, validated through analytical and numerical methods.

Contribution

The study introduces an effective S=1/2 framework for modeling random fields in S≥1 dipolar spin glasses, especially in the presence of weak transverse fields, aligning with experimental observations.

Findings

Effective S=1/2 model captures qualitative physics at small Bx.

Results agree with second-order perturbation theory.

Explicit Bx-dependent random fields emerge in the low-energy description.

Abstract

We present analytical and numerical evidence for the validity of an effective S=1/2 approach to the description of random field generation in S>=1, and especially in an S=1, dipolar spin glass models with strong uniaxial Ising anisotropy and subject to weak external magnetic field Bx transverse to the Ising direction. Explicitely Bx-dependent random fields are shown to naturally emerge in the effective low-energy description of a microscopic S=1 toy model. We discuss our results in relation to recent theoretical studies pertaining to the topic of Bx-induced random fields in the LiHo$_x$Y$_{1-x}$F$_4$ magnetic materials with the Ho$^{3+}$ Ising moments subject to a transverse field. We show that the S_{eff}=1/2 approach is able to capture both the qualitative and quantitative aspects of the physics at small Bx, giving results that agree with those obtained using conventional second order perturbation theory.