Fig. 4: Calculated TAMR and transmission.

a Calculated of the in- (y) and out-of-plane (z) TAMR^y(z) for the RuO₂[100]/MgO[110]/RuO₂[100] tunnel junction versus rigid shift of the chemical potential. The top left inset shows the calculated transmission in bulk RuO₂ along [100] versus the chemical potential for various Neel orientations; the bottom right inset shows the transmission of the tunnel junction for various configurations of the two RuO₂ Néel orientations versus chemical potential. In the parallel (antiparallel) configurations, \({\vec{n}}_{1}\) and \({\vec{n}}_{2}\) are along [010], in the orthogonal in-plane \({\vec{n}}_{1}\) and \({\vec{n}}_{2}\) are along [010] and [001] respectively, and in the orthogonal out-of-plane \({\vec{n}}_{1}\) and \({\vec{n}}_{2}\) are along [010] and [100,] respectively. b Layer resolved change in DoS, \({\delta ({LDoS})}_{i}^{{{{\rm{in}}}}-{{{\rm{plane}}}}}={{LDoS}}_{i}^{[001]}-\,{{LDoS}}_{i}^{\left[010\right]}\) of the ith layer of the top RuO₂ for two in-plane orthogonal spin configurations. At \({{{{\rm{E}}}}}_{{{{\rm{F}}}}}=-0.2\,{{{\rm{eV}}}}\) we observe a significant change of interfacial DoS which is a signature of interfacial resonant states. c Interfacial change of \({\delta {DoS}}_{{inplane}}\) of top RuO₂ versus chemical potential demonstrating a strong correlation with the calculated in-plane TAMR in (a).