Orbital Nature of Ferromagnetic Magnons in Manganites

Magnon excitation in a ferromagnetic state of ${\mathrm{S}\mathrm{m}}_{0.55}{\mathrm{S}\mathrm{r}}_{0.45}{\mathrm{M}\mathrm{n}\mathrm{O}}_3$ located on the verge of the metal-insulator transition has been studied in terms of the neutron scattering experiment. The anomalous magnon dispersion with the zone-boundary softening is well described by the Heisenberg model with extended exchange coupling constants $J$s. In particular the fourth neighbor coupling $J_4$ is as large as 0.6 times the nearest neighbor one $J_1$. Theoretical analysis based on the local density approximation $+$ Hubbard U band calculation reveals that this one-dimensional exchange path is due to the $(3z^2-r^2)$-type orbital correlation, in sharp contrast to previous proposals.

Figure 1

Thermal evolution of (a) bulk magnetization, (b) resistivity, neutron diffractions at (c) (0,1,1) ferromagnetic Bragg reflection, and (d) off Bragg points of both $(-0.075,1,1)$ and (0.5,0.06,0.06), corresponding ferromagnetic and anti- ferromagnetic neutron diffuse scattering, respectively, from the ${}^{154}\mathrm{S}\mathrm{m}_{0.55}{\mathrm{S}\mathrm{r}}_{0.45}{\mathrm{M}\mathrm{n}\mathrm{O}}_3$ single crystal. These reflection points are shown in inserted reciprocal lattice of $(h,k,k)$.

Figure 2

Ferromagnetic magnon full dispersion curves along $[100]$, $[011]$, and $[111]$ principal axes. Filled circles indicate the observed points with the experimental uncertainty. Full lines show the best fitted dispersion relation with $J_1=0.80,J_2=J_3=0,J_4=0.49\mathrm{m}\mathrm{e}\mathrm{V}$ (also see text).

Figure 3

Scattering energy widths (filled circles) and integrated intensities (empty circles) for magnons propagating along $[100]$ in ${}^{154}\mathrm{S}\mathrm{m}_{0.55}{\mathrm{S}\mathrm{r}}_{0.45}{\mathrm{M}\mathrm{n}\mathrm{O}}_3$. Energy widths are shown in meV and integrated intensities are in arbitrary units. Experimental uncertainty is presented by vertical bars.

Figure 4

Exchange constants ratio of $J_4/J_1$ for $R{E}_{1-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{M}\mathrm{n}\mathrm{O}}_3$ as a function of $x$ with representative compounds (filled circles). Calculated results are shown by solid curves with (a) free hybridized bands, (b) ($x^2-y^2$) orbital, and (c) ($3z^2-r^2$) orbital ordered cases.