  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
which has static spin density wave (SDW) order at low temperatures. An
intriguing, but not completely understood, phenomenon in LSCO is that the
stripes are not perfectly aligned with the high-symmetry Cu-Cu directions, but
are tilted. Using high-resolution neutron scattering, we find that the model
material LSCO with $x=0.12$ has two coexisting phases at low temperatures, one
with static spin stripes and one with fluctuating spin stripes, where both
phases have the same tilt angle. For the static SDW, we accurately determined
the spin direction as well as the interlayer correlations. Moreover, we
performed numerical calculations using the doped Hubbard model to explain the
origin of the tilting of the stripes. The tilting is quantitatively accounted
for with a next-nearest neighbor hopping $t^{\prime}$ that is anisotropic,
consistent with the slight orthorhombicity of the sample. Our results highlight
the success of the doped Hubbard model to describe specific details of the
ground state of a real material, as well as the importance of $t^\prime$ in the
Hamiltonian. These results further reveal how the stripes and superconductivity
are sensitively intertwined at the level of model calculations as well as in
experimental observations.
