Paramagnetic spin correlations in colossal magnetoresistive La${}_{0.7}$Ca${}_{0.3}$MnO${}_3$

Neutron spectroscopy measurements reveal dynamic spin correlations throughout the Brillouin zone in the colossal magnetoresistive material La${}_{0.7}$Ca${}_{0.3}$MnO${}_3$ at 265 K ($\approx 1.03$ $T_C$). The long-wavelength behavior is consistent with spin diffusion, yet an additional and unexpected component of the scattering is also observed in low-energy constant-$E$ measurements, which takes the form of ridges of strong quasielastic scattering running along ($H$ 0 0) and equivalent directions. Well-defined $Q$-space correlations are observed in constant-$E$ scans at energies up to at least 28 meV, suggesting robust short-range spin correlations in the paramagnetic phase.

Figure 1

Intensity plot of $S(Q,\omega )$ measured at 265 K, with the energy integrated between $3\text{meV}⩽\hslash \omega ⩽5$ meV. (a) Scattering in the ($H$ $K$ 0) plane. (b) Scattering in the (0 $K$ $L$) plane. $Q$ perpendicular to the scattering plane has been integrated over $\pm 0.16$ Å${}^{-1}$. The black, red, purple, and orange dashed lines represent the scan directions displayed in Fig. 2. (c) Integrated intensity of transverse scans through scattering ridges, with the energy integrated between $2\text{meV}⩽\hslash \omega ⩽6$ meV. The red line is the Mn form factor squared. Uncertainties throughout this paper are statistical and refer to one standard deviation.

Figure 2

(a),(b) Differing intensities for scans in the (0 $\xi$ 0) and ($\xi$ $\xi$ 0) directions away from the (0 $-1$ 0) reflection at 265 K. The blue data points and horizontal line correspond to the background given by a scan in the ($\xi$ $\xi$ 0) direction at 100 K. (c) Scans through the (0.5 1 0) position in both directions transverse to $\vec{q}$, measured at 265 K in the $\hslash \omega \approx 3$ meV data. (d) Transverse scan through (0 0.4 0) in the elastic data, measured at 265 K. The lines in panels (c) and (d) are Gaussian fits with a HWHM of 0.16 r.l.u. (0.26 Å${}^{-1}$). For panels (a)–(c) the data have been integrated over $\pm 0.13$ Å${}^{-1}$ in both $\vec{q}$ directions transverse to the scan. For panel (d) the data have been integrated over $\pm 0.13$ Å${}^{-1}$ along $H$ and over $\pm 0.08$ Å${}^{-1}$ along $K$.

Figure 3

(a) Energy dependence of the 265 K paramagnetic scattering in constant-$Q$ scans. $Q$ values have been chosen so that $\vec{q}$ away from (0 1 0) is along either the ($\xi$ 0 0) or ($\xi$ $-\xi$ 0) directions, and with the magnitude of $q$ either 0.325 Å${}^{-1}$ or 0.812 Å${}^{-1}$. The data have been folded across the $K=0$ plane and integrated over $\pm 0.13$ Å${}^{-1}$ in all $\vec{q}$ directions. (b) The energy dependence of the ridge intensity, displayed as the difference in scattering for measurements at $\vec{Q}=(0$ 0.6 0) and (0.283 0.717 0) (both with $q=0.649$ Å${}^{-1}$). The gray line is a guide to the eye.

Figure 4

(a) Intensity plot of $S(Q,\omega )$ measured at 100 K, with the energy integrated between $24\text{meV}⩽\hslash \omega ⩽27$ meV. $Q$ perpendicular to the scattering plane has been integrated over $\pm 0.16$ Å${}^{-1}$. The black and red dashed lines represent the scan directions in the other panels. (b),(c) Differing intensities for scans in the (0 $\xi$ 0) and ($\xi$ $\xi$ 0) directions away from the (1 0 0) reflection at 100 K. The data have been integrated over $\pm 0.13$ Å${}^{-1}$ in both $\vec{q}$ directions transverse to the scan.

Figure 5

Scattering intensities with the energy integrated between $24\text{meV}⩽\hslash \omega ⩽28$ meV and $\left|L\right|=0.5$, measured at 265 K. (a) Intensity plot of the ($H$ $K$ 0.5) scattering plane. $Q$ perpendicular to the scattering plane has been integrated over $\pm 0.16$ Å${}^{-1}$. The black, red, and orange dashed lines represent the scan directions in the other panels. (b) Differing intensities for scans in the ($\xi$ 0 0) and ($\xi$ $\xi$ 0) directions away from the (1 $-1$ 0.5) reflection. (c) Scan in the ($\xi$ 0 0) direction through the (1 $-0.5$ 0.5) position. The Gaussian fit has a HWHM of 0.16 r.l.u. (0.26 Å${}^{-1}$). The data in panels (b) and (c) have been integrated over $\pm 0.13$ Å${}^{-1}$ in both $\vec{q}$ directions transverse to the scan.