Stripeless incommensurate magnetism in strongly correlated oxide ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_4$

We studied the nanoscale structure of the short-range incommensurate magnetic order in ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_4$ by elastic neutron scattering. We find that magnetic diffuse scattering is isotropic in the $a\text{−}b$ plane, in contrast with the naive expectation based on the popular stripe model. Indeed, charge segregation into lines favoring certain lattice direction(s) would facilitate linear stacking faults in an otherwise robust antiferromagnetism of undoped material, leading to anisotropic disorder with a characteristic symmetry pattern present in the neutron scattering data.

Figure 1

(Color online) (a) Checkerboard charge and spin order at half-doping. (b) Stacking fault giving rise to short-range correlation and magnetic incommensurability in ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_4$ in stripe picture. (c), (d) LTO superlattice of weakly doped cuprates. $a^{\ast }$, $b^{\ast }$ are reciprocal lattice vectors of the HTT phase; arrows show tilts of O octahedra. Stacking faults separating structural domains with opposite tilts (broken lines) running along “stripes” (perpendicular to $Q_c$), (c), and perpendicular to stripes (parallel to $Q_c$), (d), have the same energy, implying isotropic disorder.

Figure 2

(Color online) Contour map of the measured neutron elastic scattering intensity in $\left(h,k,0\right)$ (a) and $\left(h,h,l\right)$ (b) zones at $T=3.5\text{K}$ and 10 K, respectively. Ellipses show the calculated full width at half maximum (FWHM) instrument resolution (Ref. 23). Magnetic peaks are at $h,k\approx 0.25,0.75\text{r}\text{.l}\text{.u}\text{.}$ Charge order scattering is seen at $h=k=0.5\text{r}\text{.l}\text{.u}\text{.}$ Intensity in the map around (1,1,0) Bragg peak shown in the top right corner was scaled down by a factor of 100.

Figure 3

(Color online) Resolution and sample size effects for (1,1,0) Bragg reflection. (a) Contour map of the measured neutron scattering intensity in the $\left(h,k,0\right)$ zone at $T=3.5\text{K}$. (b) Calculated intensity for the pointlike sample, corresponding to the resolution-broadened $\delta$ function (Ref. 23). (c) Same as in (b), but with sample size effects included. Small extra intensity extended along a diagonal corresponds to a small $\left(\sim 0.3\%\right)$ oriented powder component with angular distribution of $\approx 0.8°$, much broader than sample mosaic spread $\eta \approx 0.3°$.

Figure 4

(Color online) Elastic neutron scattering from ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_4$. (a) $\left(h,k,0\right)$ reciprocal lattice zone, (b) $\left(h,h,l\right)$ zone. The lines show the global fit of the data to Eq. (5) describing coupled anisotropic 3D correlations.

Figure 5

(Color online) Simulated magnetic scattering intensity for ${\text{La}}_{1.5}{\text{Sr}}_{0.5}{\text{CoO}}_4$ in the $\left(h,k,0\right)$ reciprocal lattice zone with anisotropic correlation lengths in the $a\text{−}b$ plane ${\xi }_{1,1,0}=9.2$ and ${\xi }_{1,-1,0}=18.4$ LTO (HTT diagonal) lattice units (l.u.). 2:1 ratio of the correlation lengths corresponds to findings of Ref. 26. (a) factorized 1D lattice Lorentzian cross section (b) Lorentzian-squared corresponding to anisotropic 3D disorder.

Figure 6

(Color online) (a) Typical scan through magnetic peak with fits to cross sections for completely independent linear disclinations $\left[{\left(1\text{D}\right)}^3\right]$, isotropic disorder in $a\text{−}b$ plane with stacking faults along $c$ $\left(2\text{D}\times 1\text{D}\right)$, or disorder coupled in all three directions (3D). (b) and (c) “correlation length” for scans offset by $\delta q$ from the magnetic peak position, $Q\approx \left(0.744+\delta h,0.256-\delta h,0\right)$ for (b) and $Q\approx \left(0.256+\delta h,0.256+\delta h,1\right)$ for (c). The solid/dashed lines are single-parameter fits to Eq. (6), $\delta q=\delta h\sqrt{2}$.

Figure 7

(Color online) Fit results of neutron scattering intensity in $\left(h,k,0\right)$ (a), (c), (e) and $\left(h,h,l\right)$ (b), (d), (f) zones at $T=3.5\text{K}$ and 10 K. $1\text{D}\times 1\text{D}\times 1\text{D}$ correlation (stripelike) are in (a) and (b). (c) and (d) show results for $2\text{D}\times 1\text{D}$ correlations. (e) and (f) are fitted intensity patterns for coupled isotropic correlations (superlattice).