Effects of spin relaxation on trap-assisted tunneling through ferromagnetic metal-oxide-semiconductor structures

A signal measured within a three-terminal setup at room temperature [1,2] is attributed to the spin injection from a ferromagnetic electrode into n-silicon; however, its amplitude is orders of magnitude larger than predicted by theory [3]. The reasons for this discrepancy are heavily debated [3-6], with trap-assisted resonant tunneling [4] and spin-dependent magnetoresistance gaining recognition. However, effects of spin relaxation important at room temperature were not considered in [4]. To elucidate the role of spin relaxation and coherence, corresponding Lindblad terms are added to the equation for the density matrix evolution of spin on a trap coupled to ferromagnetic contacts. Fast spin relaxation suppresses the magnetoresistance modulation. Interestingly, strong decoherence at fixed spin lifetime results in a more pronounced magnetoresistance modulation and in a narrower magnetoresistance linewidth as a function of the perpendicular magnetic field. 1.S.P.Dash {\it et al.}, Nature {\bf 462},491 (2009). 2.C.Li {\it et al.}, Nature Commun.{\bf 2}, 245 (2011). 3.R.Jansen, Nature Mater.{\bf 11}, 400 (2012). 4.Y.Song and H.Dery, PRL {\bf 113}, 047205 (2014). 5.A.Spiesser {\it et al.}, PRB {\bf 90}, 205213 (2014). 6.K.-R.Jeon {\it et al.}, PRB {\bf 91}, 155305 (2015).