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Spin- and charge- stripe order has been extensively studied in thesuperconducting cuprates, among which underdoped${\mathrm{La}}_{2-x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ (LSCO) is an archetypewhich has static spin density wave (SDW) order at low temperatures. Anintriguing, but not completely understood, phenomenon in LSCO is that thestripes are not perfectly aligned with the high-symmetry Cu-Cu directions, butare tilted. Using high-resolution neutron scattering, we find that the modelmaterial LSCO with $x=0.12$ has two coexisting phases at low temperatures, onewith static spin stripes and one with fluctuating spin stripes, where bothphases have the same tilt angle. For the static SDW, we accurately determinedthe spin direction as well as the interlayer correlations. Moreover, weperformed numerical calculations using the doped Hubbard model to explain theorigin of the tilting of the stripes. The tilting is quantitatively accountedfor with a next-nearest neighbor hopping $t^{\prime}$ that is anisotropic,consistent with the slight orthorhombicity of the sample. Our results highlightthe success of the doped Hubbard model to describe specific details of theground state of a real material, as well as the importance of $t^\prime$ in theHamiltonian. These results further reveal how the stripes and superconductivityare sensitively intertwined at the level of model calculations as well as inexperimental observations.

Prevalence of tilted stripes in ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}$ and the importance of $t^{\prime}$ in the Hamiltonian