Induced Random Fields in the LiHo_xY_1-xF₄ Quantum Ising Magnet in a Transverse Magnetic Field

The LiHo_xY_1-xF₄ magnetic material in a transverse magnetic field B_xx̂ perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the B_x-induced magnetization along the x̂ direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho³⁺ ions, random fields along the Ising ẑ direction. This identifies LiHo_xY_1-xF₄ in B_x as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing B_x and render the B_x-induced quantum criticality in LiHo_xY_1-xF₄ likely inaccessible.