Origin of Higher Order Magnetic Exchange: Evidence for Local Dimer Exchange Striction in ${\mathrm{CsMn}}_{0.28}{\mathrm{Mg}}_{0.72}{\mathrm{Br}}_3$ Probed by Inelastic Neutron Scattering

The origin of higher-order exchange interactions in localized $S$-state systems has been the subject of intensive investigations in the past. In particular, it has been suggested that a biquadratic exchange term may arise from the magnetoelastic energy. Here we report on the pressure and temperature dependence of the excitation spectra of magnetic ${\mathrm{Mn}}^{2+}$ dimers in ${\mathrm{CsMn}}_{0.28}{\mathrm{Mg}}_{0.72}{\mathrm{Br}}_3$ probed by inelastic neutron scattering. Biquadratic exchange and a strong distance dependence of the bilinear exchange are observed. It is shown that the mechanism of local exchange striction may explain the occurrence of biquadratic exchange in accordance with the elastic properties of the compound.

Figure 1

Crystal structure of ${\mathrm{CsMn}}_x{\mathrm{Mg}}_{1-x}{\mathrm{Br}}_3$: the $[(\mathrm{Mn},\mathrm{Mg}){\mathrm{Br}}_{6/2}]$ octahedra form chains along the $c$ axis well separated by ${\mathrm{Cs}}^{+}$ ions.

Figure 2

Inelastic neutron spectra of the three first dimer excitations $|\mathbf{S}-1⟩\to |\mathbf{S}⟩$ in ${\mathrm{CsMn}}_{0.28}{\mathrm{Mg}}_{0.72}{\mathrm{Br}}_3$: ($a$)–($d$) measurements without pressure cell, $P=0$, $T=200,150,100,50\mathrm{K}$; ($e$) and ($f$) measurements in the pressure cell at $T=50\mathrm{K}$ and $P=0,0.52(5)\mathrm{GPa}$. The intensity at around 4 meV is due to excitations from $n$-mers with $n>2$. Lines refer to Gaussian peak fits.

Figure 3

Dependences of the bilinear and biquadratic exchange parameter ($J$ and $K$) on the intradimer distance $r$ (crossed circles: $P=0,0.52(5)\mathrm{GPa}$ at $T=50\mathrm{K}$, in pressure cell; empty circles: ambient pressure at $T=50,100,150,200\mathrm{K}$). Solid lines refer to polynomial fits (see the text) with the dashed lines their respective confidence bands (95%). Stars represent results from earlier measurements under pressure [$P=0.56(2),0.73(2)\mathrm{GPa}$ at $T=4.2\mathrm{K}$] not considered for the fit (see the text and Table ).