The effect of size on spin-to-charge conversion in the magnetic Weyl semimetal

•Spin-to-Charge conversion in the Magnetic Weyl semimetal.•Use of the semi-classical Boltzmann equation which covering from the ballistic to diffusive regime.•From the ballistic to diffusive limit, the conversion efficiency increases and reaches perfect limit. A magnetic Weyl semimetal (MWSM), which only has a pair of Weyl nodes, is an ideal platform to study spin-related transport properties, such as the chiral anomaly and the magnetic chiral magnetic effect. This work investigates the sample size and impurity effects on the spin-to-charge conversion in a vertical heterostructure consisting of a ferromagnetic metal and a MWSM, where a spin bias is applied at the interface and a charge current is generated. We find that the two Weyl nodes with opposite chirality generate the same charge current in the y,z directions as a result of the spin injection but opposite in the x direction. The analytic formulas of the conductance in the ballistic and diffusive limits are given. Furthermore, we discuss that the efficiency of spin-to-charge conversion increases and becomes perfect from the ballistic to the diffusive limit. These findings provide new potentials for manipulating the interconversion between spin and charge in the topological semimetals.