Abstract
Two-dimensional (2D) van der Waals (vdW) magnetic semiconductors have attracted wide interest for their promising application in next-generation spintronic devices. We investigate the scaling behavior of the tunnel magnetoresistance (TMR) of the $\mathrm{Ag}/$n-layer ${\mathrm{Cr}\mathrm{I}}_{3}/\mathrm{Ag}$ and graphite/n-layer ${\mathrm{Cr}\mathrm{I}}_{3}$/graphite magnetic tunnel junctions (MTJs) by using ab initio quantum-transport simulations. The calculated monotonic increasing TMR of the graphite/n-layer ${\mathrm{Cr}\mathrm{I}}_{3}$/graphite MTJ with n = 2--4 at zero bias agrees with the experimental value. The TMR of the $\mathrm{Ag}/$n-layer ${\mathrm{Cr}\mathrm{I}}_{3}/\mathrm{Ag}$ MTJ generally increases with the tunnel-barrier layer number, n, that is, from 200% (2-layer ${\mathrm{Cr}\mathrm{I}}_{3}$) to a record ${10}^{9}$% value (12-layer ${\mathrm{Cr}\mathrm{I}}_{3}$) at zero bias but has an odd-even oscillation when n 7. When we apply a bias voltage to the $\mathrm{Ag}/$2-layer ${\mathrm{Cr}\mathrm{I}}_{3}/\mathrm{Ag}$ MTJ, the TMR first decreases slightly and then increases, followed by a monotonic decrease. The noncollinear magnetization direction of the ${\mathrm{Cr}\mathrm{I}}_{3}$ layers also changes the TMR value of the graphite/n-layer ${\mathrm{Cr}\mathrm{I}}_{3}$/graphite MTJ relative to the collinear case, a result in agreement with experiments.
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