Abstract
Non-negligible higher-order exchange terms are ubiquitous in the spin Hamiltonians of a large variety of magnetic compounds. Yet the origin of higher-order exchange has not been satisfactorily established. This question was addressed by performing inelastic neutron scattering experiments for the magnetically diluted compound $\mathrm{K}{\mathrm{Mn}}_{0.1}{\mathrm{Zn}}_{0.9}{\mathrm{F}}_{3}$. The observed excitations can be associated with transitions between the low-lying electronic states of ${\mathrm{Mn}}^{2+}$ multimers which are well described by a spin Hamiltonian including bilinear and biquadratic exchange interactions. The bilinear exchange parameter $J$ derived from the dimer spectra exhibits a strong temperature dependence, whereas the biquadratic exchange parameter $K$ is independent of temperature. By minimizing the total elastic and magnetic energy of the dimer, we can express the parameter $K$ in terms of lattice, elastic, and magnetic properties. The good agreement between the calculated and observed values of $K$ indicates that the mechanism of exchange striction is the likely origin of the biquadratic interaction in the title compound.
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