Anisotropic magnetoresistance in single electron transport

Abstract

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. 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 reports. In the case of TAMR the relevant quantity is the transmission [5], which is related to the density of states at the Fermi energy. The size of the AMR effects depends on the relative ratio of the spin orbit interaction ∆ SO , the Fermi energy ǫ F and the exchange splitting J. Not surprisingly, TAMR has been reported first in III-V ferromagnetic semiconductors, where SO coupling is the largest energy scale in the system.Motivated by recent experimental results [13], we consider a different kind of AMR effect, which takes place in a single electron transistor (SET) with ferromagnetic electrodes. Although in the experiments [13] both the electrodes and the dot are made of ferromagnetic GaMnAs, here we consider a simpler SET with

Anisotropic magnetoresistance in nanocontacts

“…Notice that crossing the conductance peak, either by gate application or magnetization rotation, implies charging the CI by one electron. 15,25 The results of Fig. 4͑b͒ assume that ⌫ is independent of , which is true as long as the resonant level is not coupled to the E 2 and E 1 bands.…”

“…From this equation, we immediately see that the charge state of the central island can be controlled both with the gate and with the orientation of the magnetization of the electrodes. 15,25 This effect is reminiscent of the so-called magneto-Coulomb effect, in which the chemical potential of the electrode is varied with the intensity of the applied field. 39 Here, the chemical potential is changed by rotating the applied field.…”

“…This situation occurs in a single electron transistor with ferromagnetic electrodes. 15,25 Resonances might also occur in the tip atoms of Ni nanocontacts in the tunneling regime. 26 This paper is organized as follows.…”

“…In the sequential regime, valid to describe systems that feature transport through resonant levels of width Γ smaller than the temperature kT 24 , we find enhanced AMR, regardless of the orbital polarization of the current, if the chemical potential ǫ F of the ferromagnetic electrode crosses a resonance as it varies due to change of the magnetization angle. This situation occurs in a sin- gle electron transistor with ferromagnetic electrodes 15,25 .…”

Huge tunnelling anisotropic magnetoresistance in (Ga,Mn)As nanoconstrictions

“…We therefore conclude that the dominant contribution to the MR arises from the CBAMR mechanism [12,24]. In an effect analogous to the application of an electric field to the Coulomb blockade nano-island, during different thermal cycles the electrostatic configuration of the constriction can change dramatically resulting in large changes in the AMR observed.…”