Magnetization Transport and Quantized Spin Conductance

We analyze transport of magnetization in insulating systems described by a spin Hamiltonian. The magnetization current through a quasi-one-dimensional magnetic wire of finite length suspended between two bulk magnets is determined by the spin conductance which remains finite in the ballistic limit due to contact resistance. For ferromagnetic systems, magnetization transport can be viewed as transmission of magnons, and the spin conductance depends on the temperature [Formula presented]. For antiferromagnetic isotropic spin-[Formula presented] chains, the spin conductance is quantized in units of order [Formula presented] at [Formula presented]. Magnetization currents produce an electric field and, hence, can be measured directly. For magnetization transport in electric fields, phenomena analogous to the Hall effect emerge.