Significance of the hyperfine interactions in the phase diagram of LiHoxY1-xF4

We consider the quantum magnet at LiHo(x)Y(1-x)F(4) at x = 0.167. Experimentally the spin glass to paramagnet transition in this system was studied as a function of the transverse magnetic field and temperature, showing peculiar features: for example, (i) the spin glass order is destroyed much faster by thermal fluctuations than by the transverse field; and (ii) the cusp in the nonlinear susceptibility signaling the glass state decreases in size at lower temperature. Here we show that the hyperfine interactions of the Ho atom must dominate in this system, and that along with the transverse inter-Ho dipolar interactions they dictate the structure of the phase diagram. The experimental observations are shown to be natural consequences of this.