Influence of magnetism on vertical hopping transport in CrSBr

We investigate the c-direction conduction in CrSBr in the linear regime, not accessible in other van der Waals (vdW) magnetic semiconductors, because of the unmeasurably low current. The resistivity -- $10^8$ to $10^{11}$ times larger than in the a- and b-directions -- exhibits magnetic state dependent thermally activated and variable range hopping transport. In the spin-flip phase at 2 T, the activation energy is 20 meV lower than in the antiferromagnetic state, due to a downshift of the conduction band edge, in agreement with ab-initio calculations. In the variable range hopping regime, the average hopping length decreases from twice the interlayer distance to the interlayer distance at 2 T, because in the antiferromagnetic state the large exchange energy impedes electrons hopping between adjacent layers. Our work demonstrates that the linear transport regime provides new information about electronic processes in vdW magnetic semiconductors, and shows how magnetism influences these processes both in real and reciprocal space.