The 2$^{1/3}$ rule for magnetic susceptibility of gadolinium

The dependences of the magnetization $M$ and the magnetic susceptibility $\chi=\partial M/\partial H$ of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt%) on the temperature $T$ and the magnetic field $H$ have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature $T_C$) over the volume of the sample. The obtained dependences of $M$ and $\chi$ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2$^{1/3}$ rule is fulfilled. The rule relates the portions of the dependence $\chi(T,H)$ which at the temperature $T= T_C$ and at the maximum in the curve $\chi(T)$ $(T = T_m)$ depend on $H$ in accordance with the $H^{2/3}$ law. It has been shown that the portions separated from the experimental curves $\chi(T_C,H)$ and $\chi(T_m,H)$ obey the 2$^{1/3}$ rule.