  We investigate phonon spin transport in an insulating
ferromagnet-nonmagnet-ferromagnet heterostructure. We show that the
magnetoelastic interaction between the spins and the phonons leads to nonlocal
spin transfer between the magnets. This transfer is mediated by a local phonon
spin current and accompanied by a phonon spin accumulation. The spin
conductance depends nontrivially on the system size, and decays over millimeter
length scales for realistic material parameters, far exceeding the decay
lengths of magnonic spin currents.
