Magnetism of HgSe:Fe

The perpendicular and parallel components of the magnetization of the mixed valence system ${\mathrm{Hg}}_{1-x}{\mathrm{Fe}}_x\mathrm{Se}$ in the strongly dilute limit ($x<\mathrm{}{10}^{-3\mathrm{}}$) have been measured in magnetic fields up to 20 T. In this interesting semimagnetic semiconductor the overall magnetization is caused simultaneously by ${\mathrm{Fe}}^{3+}$ (Brillouin paramagnet), ${\mathrm{Fe}}^{2+}$ (van Vleck paramagnet), and free electrons (diamagnetic de Haas-van Alphen effect). Using a torque magnetometer the various contributions with their anisotropy are individually determined. For very low iron content ($x<\mathrm{}2.4\mathrm{}\times {10}^{-4\mathrm{}}$) the Fe donors exclusively exhibit an isotropic Brillouin paramagnetism of noninteracting ${\mathrm{Fe}}^{3+}$ ions. For higher concentration ${\mathrm{Fe}}^{2+}$ also exists. Coexisting with the Brillouin paramagnetism of ${\mathrm{Fe}}^{3+}$ the ${\mathrm{Fe}}^{2+}$ reveal an induced van Vleck-type paramagnetism with a crystal-field-induced anisotropy. This anisotropy is analyzed by measuring the induced magnetic moment perpendicular to the magnetic field when applying the field in a nonsymmetric direction of the crystal. Using recent theoretical results on the energy-level diagram of ${\mathrm{Fe}}^{2+}$ in the $T_d$ symmetry of a HgSe host lattice we deduce a spin-orbit level splitting of 2 meV from our experimental data. In contrast to higher concentration samples, both the Brillouin paramagnetism of ${\mathrm{Fe}}^{3+}$ and the van Vleck paramagnetism of ${\mathrm{Fe}}^{2+}$ can be attributed to the sum from individual Fe donors with no obvious magnetic interaction between them. Finally, we also have measured de Haas-van Alphen oscillations of the conduction-band electrons with amplitudes of the same order as the paramagnetic background. From the measured crystal-field-induced anisotropy in the magnetic moment we deduce a Fermi-surface anisotropy of about 7%.