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The LiHo$_x$Y$_{1-x}$F$_4$ magnetic material in a transverse magnetic field$B_{x}\hat x$ perpendicular to the Ising spin direction has long been used tostudy tunable quantum phase transitions in a random disordered system. We showthat the $B_{x}-$induced magnetization along the $\hat x$ direction, combinedwith the local random dilution-induced destruction of crystalline symmetries,generates, via the predominant dipolar interactions between Ho$^{3+}$ ions,{\it random fields} along the Ising $\hat z$ direction. This identifiesLiHo$_x$Y$_{1-x}$F$_4$ in $B_x$ as a new random field Ising system. The randomfields explain the rapid decrease of the critical temperature in the dilutedferromagnetic regime and the smearing of the nonlinear susceptibility at thespin glass transition with increasing $B_{x}$, and render the $B_{x}-$inducedquantum criticality in LiHo$_x$Y$_{1-x}$F$_4$ likely inaccessible.Comment: Version #2. Three figures. Slight modification of abstract compared  to version #1. Minor typos corrected. To appear in Physical Review Letter

physical review letters

Induced Random Fields in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>LiHo</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Y</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>Quantum Ising Magnet in a Transverse Magnetic Field

Induced Random Fields in theLiHoxY1−xF4Quantum Ising Magnet in a Transverse Magnetic Field