Magnetic anisotropy and exchange interaction in Mn$_{3}$O$_{4}$ investigated by NMR

Abstract

Though the huge magnetic anisotropy in Mn$_3$O$_4$ was already reported, it was not easy to determine the type of anisotropy from macroscopic measurements due to their spin structure. Among several models, the easy axis anisotropy of Mn$^{3+}$ ion along the c axis has been widely accepted. In this study, we investigated the magnetic anisotropy and exchange interaction in single crystalline Mn$_3$O$_4$. We measured angles between magnetic moment and the magnetic field of 7 T by Nuclear Magnetic Resonance when the field was applied along the various directions. In the field applied along the c axis, Mn$^{3+}$ moments nearly lie in the ab plane while Mn$^{2+}$ moment is tilted from the ab plane by about 24$^{\circ}$. Therefore, it is clear that the Yafet-Kittel structure lies in the ab plane in zero field because of plane anisotropy of Mn$^{3+}$. When the field is applied along the ab plane, Mn$^{2+}$ moment aligns with the field when Mn$^{3+}$ moments make angles of 120$^{\circ}$ with the field. From this result, we calculated the linear relation between Mn$^{2+}$-Mn$^{3+}$ and Mn$^{3+}$-Mn$^{3+}$ exchange interaction constants. We obtained the angles between each moment and the field during the 180$^{\circ}$ rotation of the magnetic field. The experimental results of Mn$^{3+}$ is similar to the calculated curve which assumes Mn$^{3+}$ moment lying in the ab plane. This is the other proof of the easy plane anisotropy of Mn$^{3+}$. Using the method of least square, we found out the relation between the magnetic anisotropy of Mn$^{2+}$ and Mn$^{2+}$-Mn$^{3+}$ exchange interaction. This relation represents the equilibrium of three torques generated from Mn$^{2+}$-Mn$^{3+}$ exchange interaction, electron Zeeman effect of Mn$^{2+}$, and the easy axis anisotropy of Mn$^{2+}$.