Reinvestigation of crystal symmetry and fluctuations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$

New surprises continue to be revealed about ${\mathrm{La}}_2{\mathrm{CuO}}_4$, the parent compound of the original cuprate superconductor. Here we present neutron scattering evidence that the structural symmetry is lower than commonly assumed. The static distortion results in anisotropic Cu-O bonds within the ${\mathrm{CuO}}_2$ planes; such anisotropy is relevant to pinning charge stripes in hole-doped samples. Associated with the extra structural modulation is a soft phonon mode. If this phonon were to soften completely, the resulting change in ${\mathrm{CuO}}_6$ octahedral tilts would lead to weak ferromagnetism. Hence, we suggest that this mode may be the “chiral” phonon inferred from recent studies of the thermal Hall effect. We also note the absence of interaction between the antiferromagnetic spin waves and low-energy optical phonons, in contrast to what is observed in hole-doped samples.

Figure 1

(a) Temperature dependence of magnetic susceptibility ($\chi =M/H$) measured with a field of ${\mu }_{\mathrm{o}}H=0.1$ T along a random direction. The peak in the figure corresponds to Néel temperature $T_{\mathrm{N}}$. (b) Temperature dependence of the integrated intensity of $(1,0,0)$ magnetic and (0,1,0) nuclear Bragg peaks (in close proximity due to twinning, but not resolved), illustrating the evolution of the antiferromagnetic order and the structural transition temperature, $T_{\mathrm{s}}=555\pm 5$ K, to the HTT phase.

Figure 2

Slices of elastic scattering (integrated over $\pm 0.3$ r.l.u. in $L$) at temperatures (a) 35 K and (b) 500 K. (c) Transverse cuts through $(3,-3,0)$ [inset: $(2,-3,0)$] at $T=35$, 332, and 500 K; dashed lines are Gaussian fits. (d) Temperature dependence of the integrated intensity for $(3,-3,0)$ and $(2,-3,0)$ peaks, normalized at 332 K; dotted lines are shape-preserving interpolations. The continuous rings are diffraction from the Al sample holder.

Figure 3

Elastic scattering along $(H,-3,0)$. Diffraction peaks from the Al sample holder are faded; the red line indicates the background level.

Figure 4

(a) Inelastic neutron scattering spectra at 332 K illustrating dispersion along $[H,0,0]$ at $K=-3$ (integrated over $\pm 0.1$ in $K$ and $\pm 0.3$ in $L$). One can see soft-mode phonons at $H=1$ and 3, but only spin waves at $H=0$ and 2, with the acoustic phonons from the corresponding monoclinic peaks being too weak to detect. (b) Calculated phonons for the same range, assuming LTT structure.

Figure 5

Comparisons of phonons in the vicinity of $(3,-3,0)$. Constant-energy slices at $E=5$ meV, integrated over $\pm 2$ meV in $E$ and $\pm 0.5$ r.l.u. in $L$ for (a) 35 K and (b) 332 K. Transverse dispersion for (c) 35 K and (d) 332 K. Longitudinal dispersion for (e) 35 K and (f) 332 K. The latter four plots were integrated over $\pm 0.5$ r.l.u. in $L$ and $\pm 0.1$ r.l.u. in the in-plane direction transverse to each plot.

Figure 6

Calculated phonons in the vicinity of $(3,-3,0)$ for comparison with data in Fig. 5. Transverse dispersion for (a) 35 K and (b) 332 K. Longitudinal dispersion for (c) 35 K and (d) 332 K.

Figure 7

Intensity of phonon scattering for several temperatures in the vicinity of (a) $(3,-3,0)$ and (b) $(4-\xi ,-2-\xi ,0)$ with $\xi =0.225$. In each case, the intensities average over windows of $\pm 0.1$ r.l.u. in the $[1,-1,0]$ direction, $\pm 0.05$ in the [1,1,0] direction, and $\pm 0.5$ in $L$. The corresponding results for ${\chi }^{″}$ are plotted in (c) and (d), respectively.

Figure 8

(a) and (b) Inelastic neutron scattering spectra showing spin fluctuation dispersion in two magnetic Brillouin zones for temperatures below and above $T_{\mathrm{N}}$, respectively. Slices are created after averaging along $[0,K,0]$ and $[0,0,L]$ by $\pm 0.08$ and $\pm 0.3$ r.l.u., respectively. (c) and (d) 1D energy cuts at $(0,-1,0)$ showing the energy dependence of the spin fluctuations, blue circles, for $T_{\mathrm{N}}$, respectively. Energy cuts for the spin fluctuations are obtained after integrating the data in $H$ by $\pm 0.05$. Black open squares are the background obtained at the wave vectors ($0.15\pm 0.05,-1,0$). (e) Energy cuts are obtained from (c) after subtracting the background and Gaussian line-shape fits to the zero-energy signal, and they highlight the presence of the spin gap at 35 $\mathrm{K}<T_{\mathrm{N}}$. The solid orange line is fit to the spin-gap equation in Ref. [66]. (f) Energy cuts obtained after subtracting the background in (d).

Figure 9

(a) and (b) Inelastic neutron scattering spectra for 35 and 332 K, respectively, illustrating the energy dependence of spin fluctuation dispersions along $[0,K,0]$. Data were averaged over $\pm 0.05$ r.l.u. in $H$ and $\pm 0.3$ r.l.u. in $L$. (c) and (d) ${\chi }^{″}\left(E\right)$ for 35 and 332 K, respectively, obtained after subtracting the background from intensity vs $E$ plot for spin fluctuations and then applying the Bose-factor correction. Intensity vs $E$ plot is a 1D cut at the magnetic zone center $(2,-1,0)$ and the background is a similar plot taken away from the magnetic zone center.

Figure 10

Schematic diagram of the LA eigenvector with $\mathbf{q}=[0.1,-0.1,0]$, where $E\left(\mathbf{q}\right)\approx 5$ meV. Atomic structure of 1.5 unit cells is indicated in the middle, with La in green, O red, and Cu with antiparallel spins in blue and magenta. Left panels indicate displacements of atoms in the middle layer for the top La-O layer, Cu-O layer, and bottom La-O layer. Right panels show the same for the bottom layer.