Fig. 1: CrPS4 structure and anisotropic magnon transport measurement geometry.

a Crystal and spin structures of anti-ferromagnetic insulator CrPS4. b In-plane atom arrangement indicating anisotropic magnetic exchange energies along the <100> and <010> direction, as well as the preferred cleavage crystallographic direction <110>. c Artistic schematics of the anisotropic magnon valve devices with external circuits and direction of the applied in-plane magnetic field. Specifically, \({I}_{{in}}\): AC injection current; \({I}_{{gate}}\): DC gate current; \({V}_{2\omega }\): the second harmonic thermal magnon inverse spin Hall signal; θ: the angle of the in-plane magnetic field with respect to the direction perpendicular to the Pt electrodes. d Optical micrograph of the devices, in which the Pt electrodes of Device-S (Device-W) are perpendicular to the <010>(<100>) direction, respectively. The injectors, gates and detectors are colored with yellow, red and green, respectively.