  While the dominant magnetic interaction in La$_2$CuO$_4$ is superexchange
between nearest-neighbor Cu moments, the pinning of the spin direction depends
on weak anisotropic effects associated with spin-orbit coupling. The symmetry
of the octahedral tilt pattern allows an out-of-plane canting of the Cu spins,
which is compensated by an opposite canting in nearest-neighbor layers. A
strong magnetic field applied perpendicular to the planes can alter the spin
canting pattern to induce a weak ferromagnetic phase. In light of recent
evidence that the lattice symmetry is lower than originally assumed, we take a
new look at the nature of the field-induced spin-rotation transition. Comparing
low-temperature neutron diffraction intensities for several magnetic Bragg
peaks measured in fields of 0 and 14 T, we find that a better fit is provided
by a model in which spins rotate within both neighboring planes but by
different amounts, resulting in a noncollinear configuration. This model allows
a more consistent relationship between lattice symmetry and spin orientation at
all Cu sites.
