Uniaxial stress study of spin and charge stripes in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ by ${}^{139}\mathrm{La}$ NMR and ${}^{63}\mathrm{Cu}$ NQR

We study the response of spin and charge order in single crystals of ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ to uniaxial stress through ${}^{139}\mathrm{La}$ nuclear magnetic resonance and ${}^{63}\mathrm{Cu}$ nuclear quadrupole resonance, respectively. In unstressed ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$, the low-temperature tetragonal structure sets in below $T_{\text{LTT}}=57\mathrm{K}$, while the charge order and the spin order transition temperatures are $T_{\text{CO}}=54\mathrm{K}$ and $T_{\text{SO}}=37\mathrm{K}$, respectively. We find that uniaxial stress along the [110] lattice direction strongly suppresses $T_{\text{CO}}$ and $T_{\text{SO}}$, but has little effect on $T_{\text{LTT}}$. In other words, under stress along [110] a large splitting ($\approx 21\mathrm{K}$) opens between $T_{\text{CO}}$ and $T_{\text{LTT}}$, showing that these transitions are not tightly linked. On the other hand, stress along [100] causes a slight suppression of $T_{\text{LTT}}$ but has essentially no effect on $T_{\text{CO}}$ and $T_{\text{SO}}$. Magnetic field $H$ along [110] stabilizes the spin order: the suppression of $T_{\text{SO}}$ under stress along [110] is slower under $H\parallel \left[110\right]$ than $H\parallel \left[001\right]$. We develop a Landau free-energy model, and we interpret our findings as an interplay of symmetry-breaking terms driven by the orientation of spins.

Figure 1

Schematic of characteristic in-plane symmetry-breaking strains (a) $B_{\text{1g}}$ (orthorhombic) and (b) $B_{\text{2g}}$ (rhombic), and (c) symmetric, $A_{\text{1g,1}}$ and $A_{\text{1g,2}}$. The unstrained lattice in the foreground illustrates how the strain is applied with respect to the CO and SO parameter ${\mathrm{\Psi }}_{B_{\text{2g}}}$, structural symmetry-breaking order parameter ${\mathrm{\Phi }}_{B_{\text{2g}}}$ (octahedral tilts). $B_{\text{1g}}$ and $B_{\text{2g}}$ denote the irreducible representations of $D_{\text{4h}}$ point group. Strain directions are expressed in the principal axes of the HTT phase (see the text).

Figure 2

(a) Temperature dependence of ${}^{139}\mathrm{La}$ spin-lattice relaxation rate ${}^{139}T_1^{-1}$ for $H\parallel \left[001\right]$ and stress applied in [110]. Maximum in $T_1^{-1}$ coincides with $T_{\text{SO}}$. Lines are guides to the eyes. (b) Normalized intensity of ${}^{63}\mathrm{Cu}$ B-line measured by NQR under ${\varepsilon }_{\text{[110]}}$ strain. The lines are fitted to a phenomenological function $I\left(T\right)$ (see the text). (c) $T_1^{-1}$ measurement at uniaxial strain ${\varepsilon }_{\text{[110]}}=0.4\%$ in a wide temperature range shows an anomaly at $T_{\text{LTT}}\approx 56\mathrm{K}$. In the inset, stretch exponent $s$ drops slightly at $T_{\text{LTT}}$, then to $s=0.5$ close to $T_{\text{SO}}$. The legend shows the values of measured ${\varepsilon }_{\text{[110]}}$ and ${\varepsilon }_{\text{[100]}}$ strain.

Figure 3

Temperature dependence of ${}^{139}T_1^{-1}$ measured with stress applied along [100] and $H\parallel \left[001\right]$. Lines are guides to the eyes. The inset shows the NQR measurements of copper B-line at ${\sigma }_{\left[100\right]}$. Lines are fits to the phenomenological function $I\left(T\right)$ (see the text). The legend shows the values of induced strain.

Figure 4

Strain-temperature phase diagram for $H\parallel c$ and stress applied (a) along the [110] direction, and (b) along the [100] direction. The data points are extracted from the data of Figs. 2 and 3 and show that ${\sigma }_{\left[110\right]}$ reduces $T_{\text{SO}}$ (blue) and $T_{\text{CO}}$ (green), even though the onset of LTT structural phase remains the same (red). However, ${\sigma }_{\left[100\right]}$ does not change $T_{\text{SO}}$ at all, while $T_{\text{LTT}}$ shows a mild drop. Lines are guides to the eyes.

Figure 5

Temperature dependence of ${}^{139}T_1^{-1}$ measured with stress ${\sigma }_{\left[110\right]}$ and $H\parallel \left[1\overline{1}0\right]$. Lines are guides to the eyes. The suppression of $T_{\text{SO}}$ is greatly reduced. The legend shows the values of measured strain.

Figure 6

$T_{\text{SO}}$ and $T_{\text{CO}}$ suppression induced by different strains (lower axis) and hydrostatic pressure $p$ (top axis). The points are experimental data showing either strain dependence from this work, or hydrostatic pressure dependence from Ref. [4] ($p>1.2\mathrm{GPa}$ data are omitted for clarity) and Ref. [5]. Full thick lines mark curves fitted to the LFE model (see the text), while dashed lines are predictions of $T_{\text{CO,SO}}\left(p\right)$ calculated from the model. Curvy arrows indicate hydrostatic pressure data (measured and calculated) should be read on the top axis.

Figure 7

NMR coil with the sample in the uniaxial cell.

Figure 8

${}^{139}\mathrm{La}$ NMR spectra (central transition) under different [110] uniaxial strains, at chosen temperatures above and below $T_{\text{SO}}$.

Figure 9

Stretching exponent $s$ fitted to our measurements. For clarity, we show only a subset of measured [110] strains with interpolated cubic splines as guides to the eye. Change in $s$ close to the transition temperature $T_{\text{SO}}$ is undoubtedly visible, and the strain dependence of the observed dip follows the same pattern as the $T_1$ data. The color-coded arrows mark $T_{\text{SO}}$ at respective strain.

Figure 10

Stretching exponent $s$ fitted to our measurements. For clarity, we show only a subset of measured [110] strains with interpolated cubic splines as guides to the eye. Change in $s$ close to the transition temperature $T_{\text{SO}}$ is undoubtedly visible, and the strain dependence of the observed dip follows the same pattern as the $T_1$ data. The color-coded arrows mark $T_{\text{SO}}$ at respective strain.

Figure 11

The anomaly in displacement change ($\mathrm{\Delta }L/\mathrm{\Delta }T$) of the strain cell measured in cooling ($r=1\mathrm{K}/\min$) for different applied stresses along the [100] direction. The anomaly temperature coincides with the structural transition temperature $T_{\text{LTT}}=57.5\mathrm{K}$ at zero applied stress. For increased strain values shown in the legend, the anomaly shifts to a lower temperature of 55.5 K.