Quantized Spin Waves in the Metallic State of Magnetoresistive Manganites

Spin wave measurements have been carried out in ferromagnetic ($F$) ${\mathrm{La}}_{1-x}(\mathrm{Sr},\mathrm{Ca}{)}_x{\mathrm{MnO}}_3$ with $x(\mathrm{Sr})=0.15$, 0.175, 0.2, 0.3, and $x(\mathrm{Ca})=0.3$. In all $q$ directions, close to the zone boundary, the spin wave spectra consist of several energy levels, with the same values in the metallic and the $x\approx 1/8$ doping ranges. For $x(\mathrm{Sr})=0.15$, the data are quantitatively interpreted in terms of quantized spin waves within 2D ordered $F$ domains or clusters of $4a$ size. The same picture holds in the metallic state with, however, disordered clusters embedded in a 3D $F$ matrix.

Figure 1

Schematic phase diagram of ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$. Zone 1: insulating canted antiferromagnetic state. Zone 2: ferromagnetic quasimetallic state. Zone 3: insulating ferromagnetic state. Zone 4: metallic ferromagnetic state.

Figure 2

Spin waves determination in ${\mathrm{La}}_{0.85}{\mathrm{Sr}}_{0.15}{\mathrm{MnO}}_3$ at 14 K. (a) and (b) are examples of energy spectra at $Q=(1.25,0,0)$ and (1.5,0,0) respectively, (c) and (d) are spin wave spectra along $[100]+[010]+[001]$ and [111] respectively, with, in (c’), a zoom of the low energy part of (c). The full (empty) color of the symbols indicates large (weak) intensity. In (d), triangles (squares) indicate measurements in second (third) Brillouin zones. The black squares are phonons measured with magnons in the third Brillouin zone.

Figure 3

(a) schematic drawing of two units of the 2D stripe model with red or solid gray (blue or open gray and green or solid dark gray) circles for Mn (O and $\mathrm{O}+\mathrm{\text{hole}}$). (b),(c),(d) calculated spin wave spectra (see the text). (b) zone 3, along [100], (c) zone 3, along [111], (d) zone 4, along [100] using $44\times 44$ spins in (a),(b) plane and 5 planes with cyclic boundary conditions.

Figure 4

Left panel: spin wave dispersion for $x(\mathrm{Sr})=0.3$. The full (empty) circles correspond to large (weak) intensity. The dashed line points out the softening effect. Right panel: raw data for $Q=(0,0,1.5)$ at five $T$ values. Solid lines are fits from which $\Gamma$ values ($\Gamma \approx 0.5$) are determined. Full arrows point modes typical of the $x\approx 1/8$ range and empty ones, the new ones observed in the metallic state.

Figure 5

Left panel: spin wave dispersions for $x(\mathrm{Sr})=0.2$ (top) and $x(\mathrm{Ca})=0.3$ (bottom) at $T=14\mathrm{K}$. The full (empty) circles correspond to large (weak) intensity. The dashed lines point out the softening effect. Right panel: corresponding data at several $T$ for $q=0.45$ [$x(\mathrm{Sr})=0.2$] and $q=0.5$ [$x(\mathrm{Ca})=0.3$] using $E_f=14.7\mathrm{meV}$ (b),(d) and $E_f=35\mathrm{meV}$ (a),(b). Solid lines are fits from which $\Gamma \approx 0.7$ and $\approx 6\mathrm{meV}$ are determined for the modes in $x(\mathrm{Sr})=0.2$ and $x(\mathrm{Ca})=0.3$, respectively. Full and empty arrows have the same meaning as in Fig. 4.