Nontrivial temperature dependence of magnetic anisotropy in multiferroics Ba${}_2$MnGe${}_2$O${}_7$

Abstract

We measured the temperature dependences of the static magnetization and the spin excitation in a square-lattice multiferroics Ba${}_2$MnGe${}_2$O${}_7$. An anisotropy gap of the observed low energy mode is scaled by electric polarization rather than a power of sublattice moment. Spin nematic interaction in effective spin Hamiltonian, which is equivalent to interaction of electric polarization, is responsible for the easy-axis anisotropy. The nontrivial behavior of the anisotropy gap can be rationalized as change of the hybridized $d$-$p$ orbital with temperature, leading to the temperature dependence of the spin nematic interaction.

Main article: 12 pages, 4 figures. Supplementary material: 12 pages, 7 figures