Anisotropic magnetoresistance in single electron transport

We study the effect of magnetic anisotropy in a single electron transistor with ferromagnetic electrodes and a non-magnetic island. We identify the variation δµ of the chemical potential of the electrodes as a function of the magnetization orientation as a key quantity that permits to tune the electrical properties of the device. Different effects occur depending on the relative size of δµ and the charging energy. We provide preliminary quantitative estimates of δµ using a very simple toy model for the electrodes. Introduction Spin polarized transport through carefully designed ferromagnet-non magnetic-ferromagnet (FM 1-NM-FM 2) nanostructures can be very sensitive to the relative orientation of their magnetic moments[1], Ω 1 and Ω 2. The latter are controlled by external magnetic fields that result in the so called tunnel magnetoresistance[2] (TMR), Giant magnetoresistance[3] (GMR) and Ballistic magnetoresistance[4] (BMR) when the NM layer is a tunnel barrier, a metal and a geometrical nanoconstriction respectively. In bulk ferromagnets, the dependence of resistance on the angle between the magnetization Ω and the current j gives rise to the so called anisotropic magneto-resistance (AMR). The microscopic origin of this phenomenon is the spin orbit interaction, which also accounts for the stability of the magnetization orientation (magnetic anisotropy). Recently, the concept of Tunneling Anisotropic Magnetoresistance (TAMR) has been proposed theoretically [5] and independently verified in experiments [6, 7, 8] in tunnel junctions with GaAsMn electrodes. The related concept of Ballistic Anisotropic Magneto Resistance (BAMR) has been proposed theoretically [9] and observed in atomic sized Nickel [10] and Iron nanocontacts [11]. As opposed to TMR and BMR, where the high and low resistance states are related to variations in Ω 1 · Ω 2 , TAMR and BAMR effects occur for Ω 1 = Ω 2 ≡ Ω and depend on the angle between the transport direction and Ω, which is controlled by an external field. The microscopic origin of BAMR and TAMR can be traced back to the dependence of the electronic structure on the angle between Ω and the crystal lattice, originated by the spin orbit (SO) coupling. In ideal 1-dimensional chains, BAMR occurs if the number of bands at the Fermi energy is different for the magnetization parallel and perpendicular to current flow [9]. In real metallic nanocontacts, the transmission of the different channels is not perfect and an ab-initio approach [12] extended to include SO interaction would be necessary to account for the experimental …