Magnon correlation enables spin injection, dephasing, and transport in canted antiferromagnets

Thermal and electrical injection and transport of magnon spins in magnetic insulators is conventionally understood by the nonequilibrium population of magnons. However, this view is challenged by several recent experiments in noncollinear antiferromagnets, which urge a thorough theoretical investigation at the fundamental level. We find that the magnon spin in noncollinear magnets is described by a matrix, so even when the diagonal terms---spins carried by population---vanish, the off-diagonal correlations transmit magnon spins. Our quantum theory shows that a net spin flip of electrons in adjacent conductors creates quantum coherence between magnon states, which transports magnon spins in canted antiferromagnets, even without a definite phase difference between magnon modes in the incoherent process. It reveals that the pumped magnon correlation is not conserved due to an intrinsic spin torque, which causes dephasing and strong spatial spin oscillations during transport; both are enhanced by magnetic fields. Spin transfer to proximity conductors can cause extrinsic dephasing, which suppresses spin oscillations and thereby gates spin transport.