Temperature and magnetic field dependent Raman scattering study of magnetically frustrated Mn$_{3}$O$_{4}$

The coupling between spin and lattice degrees of freedom is presumed to be responsible for many of the novel phenomena observed in the magnetically frustrated spinel Mn$_{3}$O$_{4}$. While the lattice excitations have previously been investigated by Kim $\textit{et al.}$,* the dependences of the spin excitations in Mn$_{3}$O$_{4}$ with magnetic field and temperature have not yet been reported. We perform inelastic light (Raman) scattering to study the spin excitations in Mn$_{3}$O$_{4}$ as functions of temperature and magnetic field. We observe both one- and two-magnon excitations below the magnetic transition temperature of Mn$_{3}$O$_{4}$. In this presentation, we will discuss the temperature and magnetic field dependent evolutions of these excitations. Interestingly, we conclude that some of the magnon excitations are likely associated with the frustrated B-site sublattice of the spinel (AB$_{2}$O$_{4}$) structure. These results set the stage for future studies of the coupling between spin and lattice degrees of freedom in Mn$_{3}$O$_{4}$ as functions of pressure, temperature, and magnetic field. *M. Kim, X. M. Chen, X.Wang, C. S. Nelson, R. Budakian, P. Abbamonte, and S. L. Cooper, Phys. Rev. B 84, 74424 (2011).