Magnetic field induced anisotropy of ${}^{139}\mathrm{L}\mathrm{a}$ spin-lattice relaxation rates in stripe ordered ${\mathrm{L}\mathrm{a}}_{1.875}{\mathrm{B}\mathrm{a}}_{0.125}{\mathrm{C}\mathrm{u}\mathrm{O}}_4$

We report ${}^{139}$La nuclear magnetic resonance studies performed on a La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ single crystal. The data show that the structural phase transitions (high-temperature tetragonal $\to$ low-temperature orthorhombic $\to$ low-temperature tetragonal phase) are of the displacive type in this material. The ${}^{139}$La spin-lattice relaxation rate $T_1^{-1}$ sharply upturns at the charge-ordering temperature $T_{\text{CO}}$ = 54 K, indicating that charge order triggers the slowing down of spin fluctuations. Detailed temperature and field dependencies of the $T_1^{-1}$ below the spin-ordering temperature $T_{\text{SO}}$ = 40 K reveal the development of enhanced spin fluctuations in the spin-ordered state for $H \parallel [001]$, which are completely suppressed for large fields along the CuO${}_2$ planes. Our results shed light on the unusual spin fluctuations in the charge and spin stripe ordered lanthanum cuprates.