Tilted stripes origin in ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}$ revealed by anisotropic next-nearest neighbor hopping

Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ (LSCO) is an archetype with static spin stripes at low temperatures. An intriguing, but not completely understood, phenomenon in LSCO is that the stripes are tilted away from the high-symmetry Cu-Cu directions. Using high-resolution neutron scattering on LSCO with $x=0.12$, we find two coexisting phases at low temperatures, one with static spin stripes and the other with fluctuating ones, both sharing the same tilt angle. Our numerical calculations using the doped Hubbard model elucidate the tilting's origin, attributing it to anisotropic next-nearest neighbor hopping $t^{\prime}$, consistent with the material's slight orthorhombicity. Our results underscore the model's success in describing specific details of the ground state of this real material and highlight the role of $t^\prime$ in the Hamiltonian, revealing the delicate interplay between stripes and superconductivity across theoretical and experimental contexts.