A. Vedyayev

Quantum Theory of Giant Magnetoresistance of Spin-Valve Sandwiches

Using Kubo formalism, we develop a quantum-statistical theory of the magneto-resistance properties of spin-valve sandwiches of the form: substrate |F1|Cu|F2|FeMn. F1 and F2 are ferromagnetic transition metals or their alloys, the magnetization of F2 is constrained by exchange anisotropy. The model is based on the coherent interplay between F1 and F2 of spin-dependent scattering phenomena occurring in the bulk of the ferromagnetic layers. We first study the case of F1|Cu|F2 sandwiches with specular reflexion on outer boundaries (which is equivalent to the case of infinite multilayers). Scattering at the substrate |F1 interface is then considered also taking into account the highly resistive FeMn layer. Within these conditions, we obtain good quantitative agreement with experimental data. The results of this quantum-theoretical interpretation are then compared to those obtained by a classical approach based on the Fuchs-Sondheimer theory.

Quantum effects in the giant magnetoresistance of magnetic multilayered structures

We present an analytical quantum statistical theory of giant magnetoresistance in magnetic multilayers (current flowing in the plane of the layers) which takes into account both spin-dependent scattering of conduction electrons (s, d or hybridized sd electrons) and spin-dependent potential barriers between successive layers. The model also includes quantization of the momentum of conduction electrons in the direction perpendicular to the plane of the layers (kz). The influence of the following parameters is discussed: ratio of spin-up to spin-down mean free paths, height of potential barriers between adjacent materials and thicknesses of the various layers. It is shown that the main contribution to the giant magnetoresistance is spin-dependent scattering rather than spin-dependent potential barriers. In fact, if the mean free paths of spin-up and spin-down electrons in the magnetic material are significantly different, the presence of potential barriers (spin-dependent or not) can only decrease the magnetoresistance amplitude. Furthermore, the quantization of component momentum kz leads to well-defined oscillations of magnetoresistance with respect to thicknesses of the various layers. It should be possible to observe these quantum oscillations experimentally.

Angular Dependence of Giant Magnetoresistance in Magnetic Multilayered Structures

We present an analytical quantum-statistical theory of the angular variation of the giant magnetoresistance (GMR) in magnetic multilayers (current flowing in the plane of the layers) which takes into account both spin-dependent scattering of conduction electrons and spin-dependent potential barriers between successive layers. We show that the widely accepted linear variation of the GMR with the cosine of the angle between the magnetizations in the successive ferromagnetic layers is valid when the GMR originates from a spin-dependent scattering mechanism without potential barriers between layers. In the presence of potential barriers, the angular variation of the GMR can be much more complex.

Resonant spin-dependent tunneling in spin-valve junctions in the presence of paramagnetic impurities

The tunnel magnetoresistance (TMR) of F/O/F magnetic junctions, (Fs are ferromagnetic layers and O is an oxide spacer) in the presence of magnetic impurities within the barrier, is investigated. We assume that magnetic couplings exist both between the spin of impurity and the bulk magnetization of the neighboring magnetic electrode, and between the spin of impurity and the spin of tunneling electron. Consequently, the resonance levels of the system formed by a tunneling electron and a paramagnetic impurity with spin S=1, are a sextet. As a result the resonant tunneling depends on the direction of the tunneling electron spin. At low temperatures and zero bias voltage the TMR of the considered system may be larger than TMR of the same structure without paramagnetic impurities. It is calculated that an increase in temperature leads to a decrease in the TMR amplitude due to excitation of spin-flip processes resulting in mixing of spin up and down channels. It is also shown that asymmetry in the location of the impurities within the barrier can lead to asymmetry in

Magnetic diode effect in double-barrier tunnel junctions

I(V)

Extraordinary Hall effect (EHE) of ferromagnetic composites in the effective medium approximation

characteristics of impurity assisted current and two mechanisms responsible for the origin of this effect are established. The first one is due to the excitation of spin-flip processes at low voltages and the second one arises from the shift of resonant levels inside the insulator layer under high applied voltages.

Modelling spin transfer torque and magnetoresistance in magnetic multilayers

A quantum-statistical theory of spin-dependent tunneling through asymmetric magnetic double-barrier junctions is presented which describes both ballistic and diffuse tunneling by a single analytical expression. It is evidenced that the key parameter for the transition between these two tunneling regimes is the electron scattering. For these junctions a strong asymmetric behaviour in the I-V characteristics and the tunnel magnetoresistance (TMR) is predicted which can be controlled by an applied magnetic field. This phenomenon relates to the quantum well states in the middle metallic layer. The corresponding resonances in the current and the TMR are drastically phase-shifted under positive and negative voltage.

A unified theory of CIP and CPP giant magnetoresistance in magnetic sandwiches

Abstract The expression for the EHE coefficient R s of ferromagnetic composites is derived in the framework of the effective medium approximation. In the case of a composite ferromagnetic metal-dielectric, R s increases monotonically as the concentration of the magnetic component c decreases and in the dielectric region (c ≤ 1 3 ) R s = 9R s 1 (1 − c) , where R s 1 is the EHE coefficient of the ferromagnetic component. The dependences of R s on composition are calculated for composites ferromagnetic-paramagnetic metals, ferromagnet-ferromagnet. The typical relation R s ∼ρ 2 for uniform ferromagnets, where ρ is electroresistivity, is not fulfilled in all the cases considered.

Crossover from Easy-Plane to Perpendicular Anisotropy in Magnetic Thin Films: Canted Anisotropy Due to Partial Coverage or Interfacial Roughness

Theoretical models of spin-dependent transport in magnetic spin-valves and tunnel junctions are presented. A general definition of current-induced spin transfer torque (STT) and interlayer exchange coupling (IEC) based on the spin density continuity principle is given. We then present an extension of the Valet and Fert model, based on the Boltzmann description of spin-dependent transport in metallic structures. This model describes STT and IEC in any kind of magnetic metallic multilayer, for any orientation of the magnetization of the ferromagnetic layers. Simulation results show that spin torque and magnetoresistance originate from the same physical effect. In a second step, we model STT and IEC in magnetic tunnel junctions with an amorphous insulator, using the non-equilibrium Keldysh technique. The general features of STT and IEC are described, showing an important asymmetry in STT bias dependence. Moreover, the influence of a layer of impurities in the barrier is investigated and shows an important enhancement of STT and IEC at resonance. Finally, we apply this model to double magnetic tunnel junctions and show that a dramatic enhancement of spin torque can be obtained when the conditions of resonance in the free layer are fulfilled.

Description of current-driven torques in magnetic tunnel junctions

A theory of giant magnetoresistance (GMR) in magnetic sandwiches F/P/F for current in plane (CIP) and current perpendicular to plane (CPP) geometries is developed. We adopted the free electron model described by four parameters: mean free paths and scattering amplitudes (coherent potentials) at the interfaces for spin-up and spin-down electrons. For both CIP and CPP geometries, we calculated the conductivities and GMR using Kubo formalism and the Green function technique in mixed real space-momentum representation. The final expressions for GMR in both geometries were obtained using the same microscopic parameters. Main attention was paid to the relative role of spin-dependent bulk and interfacial scattering. It was shown that increasing of surface scattering for fixed spin asymmetry leads to non-monotonic behaviour of CIP GMR due to renormalization of the scattering amplitude. In the case of CPP geometry the dependence of GMR on interfacial scattering amplitude is monotonic.