Spin-Wave Dispersion in Orbitally Ordered ${\mathrm{La}}_{1/2}{\mathrm{Sr}}_{3/2}{\mathrm{MnO}}_4$

The magnon dispersion in the charge, orbital, and spin ordered phase in ${\mathrm{La}}_{1/2}{\mathrm{Sr}}_{3/2}{\mathrm{MnO}}_4$ has been studied by means of inelastic neutron scattering. We find excellent agreement with a magnetic interaction model based on the CE-type superstructure. The magnetic excitations are dominated by ferromagnetic exchange parameters revealing a nearly one-dimensional character at high energies. The strong ferromagnetic interaction in the charge or orbital ordered phase appears to be essential for the capability of manganites to switch between metallic and insulating phases.

Figure 1

(a) Schematic representation of the CE-type ordering in the $ab$ plane of half-doped manganites with the three magnetic interaction parameters described in the text. Notice that the FM zigzag chains run along the [110] direction. (b) Schematic arrangement in the Zener-polaron picture [31]. (c) Dispersion of the magnetic excitations in ${\mathrm{La}}_{1/2}{\mathrm{Sr}}_{3/2}{\mathrm{MnO}}_4$ in a direction parallel to [100] ($\Gamma$ to A), perpendicular to the chains ($\Gamma$ to B), and parallel to the chains ($\Gamma$ to C). The solid and dashed lines give the spin-wave dispersion calculated with two parameter sets; see text. Inset: Sketch of the magnetic Brillouin zone, displaying the high symmetry points $\Gamma =(0,0,0)$, $A=(1/4,0,0)$, $B=(1/8,-1/8,0)$, $C=(1/8,1/8,0)$, and the path of the calculated dispersion.

Figure 2

Raw-data scans to determine the magnon dispersion in ${\mathrm{La}}_{1/2}{\mathrm{Sr}}_{3/2}{\mathrm{MnO}}_4$; symbols denote data and lines fits with Gaussians. (a)–(c) Constant $\mathbf{Q}$ scans at the antiferromagnetic zone center and zone boundaries. (b) and (c) were measured with $E_f=7.37\mathrm{meV}$ and using the copper monochromator; the different $\mathbf{Q}$ dependence separates magnetic from phononic scattering in (b) and (c). (d)–(f) Constant-energy scans for different energies across $(0.75,-0.75,0)$ in the $[1,\overline{1},0]$ direction, i.e., perpendicular to the zigzag chains (d), and in the $[1,1,0]$ direction, i.e., parallel to the zigzag chains (e). The scan is aiming at the dispersion along the $[0,1,0]$ direction, path $\mathbf{\Gamma }-\mathbf{A}$ (f).

Figure 3

Upper panel: Constant-energy cuts through the calculated spin-wave structure factor $S(\mathbf{Q},\omega )$ with a constant-energy resolution of 2 meV within each plot and with energy steps of 2 meV between adjacent plots, showing the dispersion and scattering distribution of the lowest magnon bands. Lower panel: Constant-energy scans along the direction indicated by arrows in the 29 meV cut (above) to experimentally verify the one-dimensional character of the high energy magnetic scattering. The arrows indicate the expected positions of the magnon.