We present a Non-Equilibrium Green"s Function (NEGF)-based model for spin torque transfer (STT) devices which provides quantitative agreement with experimentally measured (1) differential resistances, (2) Magnetoresistance (MR), (3) In-plane torque and (4) out-of-plane torque over a range of bias voltages, using a single set of three adjustable parameters. We believe this is the first theoretical model that is able to cover this diverse range of experiments and a key aspect of our model is the inclusion of multiple transverse modes. We also provide a simple explanation for the asymmetric bias dependence of the in-plane torque, based on the polarization of the two contacts in energy range of transport.
DOI:PACS:Spin Torque Transfer (STT) devices that can switch the magnetization of a soft ferromagnetic layer through spin polarized electrons without any external field have generated significant interest from both basic and applied points of view (See for example Ref. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Although the concept of spin torque has been demonstrated by a number of experiments [14,15], quantitative measurement of bias dependence of spin torque has been achieved only very recently [16][17][18][19][20]. Note that these experiments show considerable dispersions in measuring the bias dependence of inplane torque [16,17,19,20]. Currently, there is no consensus as to a microscopic model that accounts for this discrepancy. Moreover, the existing theoretical models based on effective mass, tightbinding [21][22][23] and Ab-initio [24,25] band structures do not provide quantitative agreements with the experiments. Therefore, we need a model which can simultaneously explain all of the diverse aspects of STT devices namely i) differential resistances R(V), ii) TMR, iii) in-plane/spin-transfer ( ) and iv) out-ofplane/field-like ( ) components of spin torque. This paper presents a simple effective mass model with five parameters: a) equilibrium Fermi level E f , b) Spin-splitting ∆, c) Barrier height of the insulator U b , d) effective masses for electrons inside FM contacts (m FM, * = m FM, * = m FM * ) and e) effective mass for electrons inside insulator m ox * in terms of which we can understand all of the aforementioned characteristics (i-iv) of STT devices. Note that we view U b , m FM * and m ox * as parameters that account for a wide variety of factors including imperfection at ferromagnet/insulator interfaces. As such we consider these three parameters adjustable from one structure from another. On the other hand, E f and are material parameters. Although this is an effective mass model that does not include bandstructure effects explicitly, we believe that the quantitative agreement with such a diverse set of experiments shows that it captures much of the essential physics at least in the structures analyzed. One such effect our model tries to capture is the role of transverse modes on the TMR, R(V) and bias asymmetry of the in-plane torque. This last point is currently a topic of d...