Proposal for electrical detection of spin separation with in-plane magnetic field in mesoscopic Stern-Gerlach spin filter

In two-dimensional electron gas (2DEG), spatial gradient of effective magnetic field due to spin orbit interaction yields spin dependent force. By taking this advantage, Stern-Gerlach spin filter in 2DEG has been proposed for generating spin polarized currents without any external magnetic fields and ferromagnetic materials [Phys. Rev. B 72, 041308(R) (2005)]. In order to demonstrate the spin filtering effect, detection of spin polarized electrons becomes crucial importance. Here, we propose an electrical detection of spin filtering by introducing an in-plane magnetic field in mesoscopic Stern-Gerlach spin filter. In-plane magnetic field induces spin polarized electrons due to Zeeman splitting, generating the imbalance between up-spin and down-spin currents after the spin separation. Calculated spin separation angle becomes 20° based on experimentally accessible parameters. Time evolution of wave packet shows the spin separation as well as the charge imbalance under the in-plane magnetic field. By fabricating Y-branch shaped narrow wire structure with two split gate electrodes at the junction, spin filtering effect can be detected as the magnitude difference of each branch currents. Gate bias dependence of each branch current is measured in B_ex= ±15 T at T=4.2 K.