Electrical detection of unconventional transverse spin-currents in obliquely magnetized thin films

In a typical experiment in magnonics, thin films are magnetized in-plane and spin waves only carry angular momentum along their spatial propagation direction. Motivated by the experiments of Bozhko et al. [Phys. Rev. Research 2, 023324 (2020)], we show theoretically that for obliquely magnetized thin films, exchange-dipolar spin waves are accompanied by a transverse spin-current. We propose an experiment to electrically detect this transverse spin-current with Pt strips on top of a YIG film, by comparing the induced spin-current for spin waves with opposite momenta. We predict the relative difference to be of the order $10^{-4}$, for magnetic fields tilted at least $30^{\circ}$ out of plane. This transverse spin-current is the result of the long range dipole-dipole interaction and the inversion symmetry breaking of the interface.