Spin Circuit Model for 2D Channels with Spin-Orbit Coupling

In this paper we present a general theory for an arbitrary 2D channel with “spin momentum locking” due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, −). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U−, and D−. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green’s function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.

[1]  Kang L. Wang,et al.  Switching of perpendicular magnetization by spin-orbit torques in the absence of external magnetic fields. , 2013, Nature nanotechnology.

[2]  R. H. Silsbee,et al.  TOPICAL REVIEW: Spin orbit induced coupling of charge current and spin polarization , 2004 .

[3]  M. Stiles,et al.  Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling , 2013, 1301.4513.

[4]  Kang L. Wang,et al.  Electrical detection of spin-polarized surface states conduction in (Bi(0.53)Sb(0.47))2Te3 topological insulator. , 2014, Nano letters.

[5]  A. Hoffmann.  Spin Hall Effects in Metals , 2013, IEEE Transactions on Magnetics.

[6]  Markus Buttiker,et al.  Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way , 2012, 1207.1629.

[7]  Avik W. Ghosh,et al.  Chiral tunneling of topological states: towards the efficient generation of spin current using spin-momentum locking. , 2014, Physical review letters.

[8]  Eiji Saitoh,et al.  Theory of spin Hall magnetoresistance , 2013, 1302.1352.

[9]  Electrical injection and detection of spin-polarized currents in topological insulator Bi2Te2Se , 2015, Scientific reports.

[10]  A. Fert,et al.  Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films. , 2016, Physical review letters.

[11]  Jianping Wang,et al.  Giant Spin Pumping and Inverse Spin Hall Effect in the Presence of Surface and Bulk Spin-Orbit Coupling of Topological Insulator Bi2Se3. , 2015, Nano letters.

[12]  R. Gross,et al.  Spin Hall magnetoresistance induced by a nonequilibrium proximity effect. , 2012, Physical review letters.

[13]  Yoichi Ando,et al.  Spin-electricity conversion induced by spin injection into topological insulators. , 2014, Physical review letters.

[14]  Matthew Brahlek,et al.  Observation of inverse spin hall effect in bismuth selenide , 2014 .

[15]  J. Robinson,et al.  Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3. , 2014, Nature nanotechnology.

[16]  A. Fert,et al.  Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials , 2013, Nature Communications.

[17]  N. Samarth,et al.  Mapping the chemical potential dependence of current-induced spin polarization in a topological insulator , 2015, 1507.07063.

[18]  T. Yokoyama,et al.  Spin diffusion and magnetoresistance in ferromagnet/topological-insulator junctions , 2013, 1310.3354.

[19]  S. Datta,et al.  Modeling potentiometric measurements in topological insulators including parallel channels , 2012 .

[20]  Y. Tserkovnyak,et al.  Spin Hall phenomenology of magnetic dynamics , 2014, 1405.6354.

[21]  Albert Fert,et al.  Theory of the perpendicular magnetoresistance in magnetic multilayers. , 1993, Physical review. B, Condensed matter.

[22]  M. Kamalakar,et al.  Room Temperature Electrical Detection of Spin Polarized Currents in Topological Insulators. , 2014, Nano letters.

[23]  T. Yokoyama.  Current-induced magnetization reversal on the surface of a topological insulator , 2011, 1107.0116.

[24]  Nitin Samarth,et al.  Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator , 2012, Nature Physics.

[25]  S. G. Tan,et al.  Current-Induced Spin Torque on Magnetization Textures Coupled to the Topological Surface States of Three-Dimensional Topological Insulators , 2014 .

[26]  S. Datta.  Electronic transport in mesoscopic systems , 1995 .

[27]  E. Rashba.  Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents , 2003 .

[28]  K. Kim,et al.  Prohibition of equilibrium spin currents in multiterminal ballistic devices , 2004, cond-mat/0411070.

[29]  Supriyo Datta,et al.  Modular Approach to Spintronics , 2015, Scientific Reports.

[30]  J. S. Lee,et al.  Spin-transfer torque generated by a topological insulator , 2014, Nature.