Optical study of the spontaneous magnetization at marginal dimensionality

The spontaneous magnetization in the critical region of the uniaxial, dipolar-coupled ferromagnet LiTb${\mathrm{F}}_4$ has been measured using sensitive optical techniques. The magnetic and optical properties of LiTb${\mathrm{F}}_4$ and the experimental techniques are discussed in detail. These measurements provide a quantitative comparison between the predicted logarithmic corrections to mean-field theory and the experimentally observed magnetization of a ferromagnet at marginal dimensionality. We conclude that the spontaneous magnetization in LiTb${\mathrm{F}}_4$ is described by the relation $\frac{M_c\mathrm{}\left(T\right)\mathrm{}}{M_c\mathrm{}(T=0\mathrm{})\mathrm{}}=B{\mathrm{}\left|t\right|\mathrm{}}^{\frac{1}{2}}{\left|\ln \right|\frac{t_0}{t}\mathrm{}\left|\right|\mathrm{}}^{\frac{1}{3}}$ over the range $0.002<~t<~0.09$ with $B=1.77\mathrm{}\pm 0.06$, $T_c=2.8700\mathrm{}\pm 0.002$ K and $t_0=0.53\mathrm{}\pm 0.06$.