Critical behavior of the magnetic susceptibility of the uniaxial ferromagnet LiHo${\mathrm{F}}_4$

The magnetic susceptibility of two LiHo${\mathrm{F}}_4$ single crystals has been measured in the range 1.2-4.2 K. Ferromagnetic order occurs at $T_c=1.527\mathrm{}$ K. Above 2.5 K, the susceptibilities parallel and perpendicular to the fourfold $c$ axis are well interpreted by the molecular-field approximation, taking into account the ground state and the first excited state of ${\mathrm{Ho}}^{3+}$ in the crystal field of $S_4$ symmetry. The experimental results are consistent with $g_{\parallel }=13.95\mathrm{}$ and $g_{\perp }=0\mathrm{}$ for the ground state. The dipolar contribution to the magnetic interaction is about three times larger than the exchange one. Near $T_c$, the parallel susceptibility is well described by the classical law with logarithmic corrections theoretically predicted by Larkin and Khmel'mitskii for the uniaxial dipolar ferromagnet or by a power law with a critical-exponent value $\gamma =1.05\mathrm{}$ rather close to 1. The upper limit of the critical region is $\frac{(T_{max}-T_c)}{T_c}=1.1\mathrm{}\times {10}^{-2\mathrm{}}$.