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

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