We develop a linear-response transport theory of diffusive spin and heat transport by magnons in magnetic insulators with metallic contacts. The magnons are described by a position dependent temperature and chemical potential that are governed by diffusion equations with characteristic relaxation lengths. Proceeding from a linearized Boltzmann equation, we derive expressions for length scales and transport coefficients. For yttrium iron garnet (YIG) at room temperature we find that long-range transport is dominated by the magnon chemical potential. We compare the model's results with recent experiments on YIG with Pt contacts [L. J. Cornelissen, et al., Nat. Phys. 11, 1022] and extract a magnon spin conductivity of σm = 5 × 10 5 S/m. Our results for the spin Seebeck coefficient in YIG agree with published experiments. We conclude that the magnon chemical potential is an essential ingredient for energy and spin transport in magnetic insulators.

Spintronic and nanomagnetic devices often derive their functionality from layers of different materials and the interfaces between them. This is especially true for synthetic antiferromagnets — two or more ferromagnetic layers that are separated by metallic spacers or tunnel barriers and which have antiparallel magnetizations. Here, we discuss the new opportunities that arise from synthetic antiferromagnets, as compared to crystal antiferromagnets or ferromagnets.

Efficient manipulation of magnon spin transport is crucial for developing magnon-based spintronic devices. In this Letter, we provide proof of principle of a method for modulating the diffusive transport of thermal magnons in an yttrium iron garnet channel between injector and detector contacts. The magnon spin conductance of the channel is altered by increasing or decreasing the magnon chemical potential via spin Hall injection of magnons by a third modulator electrode. We obtain a modulation efficiency of 1.6%/mA at T=250  K. Finite element modeling shows that this could be increased to well above 10%/mA by reducing the thickness of the channel, providing interesting prospects for the development of thermal-magnon-based logic circuits.