First-principles study on tunnel magnetoresistance effect with Cr-doped RuO$_{2}$ electrode

We investigate the functionality of the $\mathrm{Cr}$-doped $\mathrm{RuO_{2}}$ as an electrode of the magnetic tunnel junction (MTJ), motivated by the recent experiment showing that $\mathrm{Cr}$-doping into the rutile-type $\mathrm{RuO_{2}}$ will be an effective tool to control its antiferromagnetic order and the resultant magnetotransport phenomena easily. We perform first-principles calculation of the tunnel magnetoresistance (TMR) effect in the MTJ based on the $\mathrm{Cr}$-doped $\mathrm{RuO_{2}}$ electrodes. We find that a finite TMR effect appears in the MTJ originating from the momentum-dependent spin splitting in the electrodes, which suggests that $\mathrm{RuO_{2}}$ with Cr-doping will work as the electrode of the MTJ. We also show that this TMR effect can be qualitatively captured using the local density of states inside the tunnel barrier.