Scattering Theory of Current-Induced Spin Polarization arXiv:1001.1125v2 [cond-mat.mes-hall] 10 Feb 2010 I. INTRODUCTION A. Electric generation of spin polarization Ph. Jacquod 1 $^{1}$Physics Department, University of Arizona, 1118 E. 4 th Street, Tucson, AZ 85721, USA (Dated: November 13, 2018) We construct a novel scattering theory to investigate magnetoelectrically induced spin polariza- tions. Local spin polarizations generated by electric currents passing through a spin-orbit coupled mesoscopic system are measured by an external probe. The electrochemical and spin-dependent chemical potentials on the probe are controllable and tuned to values ensuring that neither charge nor spin current flow between the system and the probe, on time-average. For the relevant case of a single-channel probe, we find that the resulting potentials are exactly independent of the trans- parency of the contact between the probe and the system. Assuming that spin relaxation processes are absent in the probe, we therefore identify the local spin-dependent potentials in the sample at the probe position, and hence the local current-induced spin polarization, with the spin-dependent potentials in the probe itself. The statistics of these local chemical potentials is calculated within random matrix theory. While they vanish on spatial and mesoscopic average, they exhibit large fluctuations, and we show that single systems typically have spin polarizations exceeding all known current-induced spin polarizations by a parametrically large factor. Our theory allows to calculate quantum correlations between spin polarizations inside the sample and spin currents flowing out of it. We show that these large polarizations correlate only weakly with spin currents in external leads, and that only a fraction of them can be converted into a spin current in the linear regime of transport, which is consistent with the mesoscopic universality of spin conductance fluctuations. We numerically confirm the theory. PACS numbers: 72.25.Dc, 73.23.-b, 85.75.-d Two purely electric mechanisms have been proposed to generate spin accumulations in electronic systems with spin-orbit interaction (SOI). They are current-induced spin polarization [1, 2] and the spin Hall effect [3, 4]. Both phenomena appear when a spin-orbit coupled con- ductor is traversed by an electric current. Current- induced spin polarization manifests itself in a weak bulk polarization of the electronic spins in a direction deter- mined by the electric current and the SOI, while the spin Hall effect manifests itself in a spin accumulation at the lateral edges of the sample. Though the resulting polar- izations are usually rather weak, both effects have been demonstrated experimentally [5–9]. They offer an elegant alternative to spin injection and manipulation with fer- romagnets, Zeeman fields or by optical means, and pave the way toward spintronic devices with purely electric control of electronic spins. A dual aspect of these magnetoelectric effects is that they are accompanied by spin currents, flowing either inside the sample or leaving it. Early analytical investi- gations of these spin currents have been devoted to cal- culations of bulk spin conductivities, but it was soon re- alized that the latter are not always related to physically relevant quantities. Local approaches based on classi- cal kinetic equations have been used to investigate the conversion of magnetoelectric spin accumulations at the edge of a spin-orbit coupled sample into spin currents leaving the sample [4, 10–14]. These quasiclassical the- To that end we construct a spin-probe model , which connects local spin-dependent chemical potentials to those imposed on a nearby probe. In this way, we are able to express local current-induced spin polarizations in terms of transmission coefficients deriving from the scat- tering matrix. Focusing on chaotic ballistic mesoscopic systems, we then use random matrix theory [24, 25] to calculate the statistics of these polarizations. We find that, while the ensemble average polarization vanishes, it fluctuates from position to position (in a given sam- ple) and from sample to sample. For sufficiently large systems, the amplitude of these fluctuations by far ex- ceeds the magnitude of all current-induced polarizations investigated to date. Simultaneously, we show that this polarization is mostly uncorrelated with spin currents in ories have been quite successful, however they neglect coherent effects and, in their present form, are not appro- priate to investigate local fluctuations and spatial corre- lations of spin polarization. Coherent mesoscopic effects on spin currents have recently attracted quite some the- oretical attention, both analytically [15–20] and numeri- cally [21, 22], in both diffusive and ballistic systems, while so far only mesoscopic fluctuations of sample-integrated spin polarizations in the diffusive regime have been inves- tigated [23]. At present, little is known about local coher- ent fluctuations of spin polarizations, the scale on which they occur, how they are correlated, and how they in- fluence spin currents and their fluctuations, neither have current-induced spin polarizations in chaotic ballistic sys- tems been investigated so far. It is the purpose of this ar- ticle to start filling these gaps, by investigating the mag- netoelectric generation of spin polarizations in ballistic mesoscopic samples.