Magnetization, Spin Current, And Spin-transfer Torque From Su (2) Local Gauge Invariance Of The Nonrelativistic Pauli-schrödinger Theory

In this Brief Report, we consider local gauge symmetries of the nonrelativistic Pauli-Schrödinger theory. From the simplest free Lagrangian density for Pauli two-component spinors, we obtain the spin interaction with a magnetic field and define the spin-current vector without invoking relativistic theory. Applying U (1) ×SU (2) local gauge symmetry, and proceeding via the Noether's theorem, we are able to construct a covariant conserved spin-current density in a natural way. Our approach allow us to understand the main features of spin transport properties and suggests that SU (2) is a fundamental symmetry of nonrelativistic quantum mechanics. © 2008 The American Physical Society.781Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., Von Molnar, S., Roukes, M.L., Chtchelkanova, A.Y., Treger, D.M., (2001) Science, 294, p. 1488. , SCIEAS 0036-8075 10.1126/science.1065389Zutic, I., Fabian, J., Das Sarma, S., (2004) Rev. Mod. Phys., 76, p. 323. , RMPHAT 0034-6861 10.1103/RevModPhys.76.323Zhang, S., Levy, P.M., Marley, A.C., Parkin, S.S.P., (1997) Phys. Rev. Lett., 79, p. 3744. , See, for instance, PRLTAO 0031-9007 10.1103/PhysRevLett.79.3744Dartora, C.A., Cabrera, G.G., (2004) J. Appl. Phys., 95, p. 6058. , JAPIAU 0021-8979 10.1063/1.1703825Dartora, C.A., Cabrera, G.G., (2005) Phys. Rev. B, 72, p. 064456. , PRBMDO 0163-1829 10.1103/PhysRevB.72.064456Petit, S., Baraduc, C., Thirion, C., Ebels, U., Liu, Y., Li, M., Wang, P., Dieny, B., (2007) Phys. Rev. Lett., 98, p. 077203. , PRLTAO 0031-9007 10.1103/PhysRevLett.98.077203Berger, L., (1996) Phys. Rev. B, 54, p. 9353. , PRBMDO 0163-1829 10.1103/PhysRevB.54.9353Slonczewski, J., (1996) J. Magn. Magn. Mater., 159, p. 1. , JMMMDC 0304-8853 10.1016/0304-8853(96)00062-5Murakami, S., Nagaosa, N., Zhang, S.-C., (2003) Science, 301, p. 1348. , SCIEAS 0036-8075 10.1126/science.1087128Murakami, S., Nagaosa, N., Zhang, S.-C., (2004) Phys. Rev. B, 69, p. 235206. , PRBMDO 0163-1829 10.1103/PhysRevB.69.235206Jiang, Z.F., Li, R.D., Zhang, S.-C., Liu, W.M., (2005) Phys. Rev. B, 72, p. 045201. , PRBMDO 0163-1829 10.1103/PhysRevB.72.045201Sinova, J., Culcer, D., Niu, Q., Sinitsyn, N.A., Jungwirth, T., MacDonald, A.H., (2004) Phys. Rev. Lett., 92, p. 126603. , PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603Shen, S.Q., Ma, M., Xie, X.C., Zhang, F.C., (2004) Phys. Rev. Lett., 92, p. 256603. , PRLTAO 0031-9007 10.1103/PhysRevLett.92.256603Barnes, S.E., Maekawa, S., (2007) Phys. Rev. Lett., 98, p. 246601. , PRLTAO 0031-9007 10.1103/PhysRevLett.98.246601Hirsch, J.E., (1990) Phys. Rev. B, 42, p. 4774. , PRBMDO 0163-1829 10.1103/PhysRevB.42.4774Meier, F., Loss, D., (2003) Phys. Rev. Lett., 90, p. 167204. , PRLTAO 0031-9007 10.1103/PhysRevLett.90.167204Schutz, F., Kollar, M., Kopietz, P., (2003) Phys. Rev. Lett., 91, p. 017205. , PRLTAO 0031-9007 10.1103/PhysRevLett.91.017205Sun, Q.-F., Guo, H., Wang, J., (2004) Phys. Rev. B, 69, p. 054409. , PRBMDO 0163-1829 10.1103/PhysRevB.69.054409Vernes, A., Gyorffy, B.L., Weinberger, P., (2007) Phys. Rev. B, 76, p. 012408. , PRBMDO 0163-1829 10.1103/PhysRevB.76.012408Sakurai, J.J., (1994) Advanced Quantum Mechanics, , Revised ed. (Addison-Wesley, Reading, MABjorken, J.D., Drell, S.D., (1964) Relativistic Quantum Mechanics, , McGraw-Hill, New YorkGreiner, W., Reinhardt, J., (2002) Quantum Electrodynamics, , 3rd ed. (Springer-Verlag, BerlinWang, Y., Xia, K., Su, Z.B., Ma, Z., (2006) Phys. Rev. Lett., 96, p. 066601. , PRLTAO 0031-9007 10.1103/PhysRevLett.96.066601Sun, Q.F., Xie, X.C., (2005) Phys. Rev. B, 72, p. 245305. , PRBMDO 0163-1829 10.1103/PhysRevB.72.245305Fröhlich, J., Studer, U.M., (1992) Commun. Math. Phys., 148, p. 553. , CMPHAY 0010-3616 10.1007/BF02096549Fröhlich, J., Studer, U.M., (1992) Int. J. Mod. Phys. B, 6, p. 2201. , IJPBEV 0217-9792 10.1142/S0217979292001092Fröhlich, J., Studer, U.M., (1993) Rev. Mod. Phys., 65, p. 733. , RMPHAT 0034-6861 10.1103/RevModPhys.65.733Yang, C.N., Mills, R.L., (1954) Phys. Rev., 96, p. 191. , PHRVAO 0031-899X 10.1103/PhysRev.96.191Weinberg, S., (1996) The Quantum Teory of Fields, 1-2. , Cambridge University Press, CambridgeRyder, L.H., (1996) Quantum Field Theory, , 2nd ed. (Cambridge University Press, CambridgeLove, P.J., Boghosian, B.M., (2004) Physica a, 332, p. 47. , PHYADX 0378-4371 10.1016/j.physa.2003.09.055Wiese, U.-J., (2005) Nucl. Phys. B, Proc. Suppl., 141, p. 143. , 0920-5632Watts, S.M., Grollier, J., Van Der Wal, C.H., Van Wees, B.J., (2006) Phys. Rev. Lett., 96, p. 077201. , PRLTAO 0031-9007 10.1103/PhysRevLett.96.07720