We study the response of spin and charge order in single crystals of La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ to uniaxial stress, through $^{139}$La nuclear magnetic resonance (NMR) and $^{63}$Cu nuclear quadrupole resonance (NQR), respectively. In unstressed La$_{1.875}$Ba$_{0.125}$CuO$_{4}$, the low-temperature tetragonal structure onsets below $T_{\text{LTT}} = 57$K, while the charge order and the spin order transition temperatures are $T_\text{CO} = 54$K and $T_\text{SO} = 37$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 ($\approx 21$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 $H \parallel [110]$ than $H \parallel [001]$. We develop a Landau free energy model and interpret our findings as an interplay of symmetry breaking terms driven by the orientation of spins.
Comment: 14 pages, 17 figures