N. Ryzhanova

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.

Recent results on the giant magnetoresistance in magnetic multilayers (anisotropy, thermal variation and CCP-GMR)

Abstract We present some recent results obtained on the electrical transport properties in magnetic multilayers. Three points are addressed. The first one is an experimental demonstration of the existence of an intrinsic anisotropy of the giant magnetoresistance (GMR). The experiments have been carried out on spin-valve samples for which there is no contribution of the usual anisotropic magnetoresistance to the observed magnetoresistance. The GMR amplitude is found to be larger (lower) in the direction perpendicular (parallel) to the sensing current. The second point concerns a quantitative analysis of the thermal variation of the CIP (current-in-plane) GMR in magnetic multilayers. This analysis is based on a semi-classical theory including the spin-intermixing due to spin-flip scattering by magnons. This approach allows quantitatively evaluation of the respective weights of the various contributions to the thermal decrease in GMR: (i) scattering by magnons in the bulk of the ferromagnetic layers; (ii) phonon scattering in the non-magnetic spacer layer; and (iii) interfacial scattering by paramagnetic interfacial layers which may form as the temperature is increased. The third point is a theoretical investigation of the CPP (current perpendicular to the plane) electrical transport through an interface between two semi-infinite metallic materials. It is shown that when a potential step U exists at such an interface, this step gives rise to an interfacial resistance proportional to U 2 . It also leads to the existence of large oscillations in the electric fields on both sides of the interface.

Modelling spin transfer torque and magnetoresistance in magnetic multilayers

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.

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

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.

Description of current-driven torques in magnetic tunnel junctions

A free electron description of spin-dependent transport in magnetic tunnel junctions with non-collinear magnetizations is presented. We investigate the origin of transverse spin density in tunneling transport and the quantum interferences which give rise to oscillatory torques on the local magnetization. Spin transfer torque is also analyzed and an important bias asymmetry is found as well as a damped oscillatory behavior. Furthermore, we investigate the influence of the s?d exchange coupling on torque, in particular in the case of half-metallic MTJs, in which the spin transfer torque is due to interfacial spin-dependent reflections.

Quantum statistical theory of giant magnetoresistance in magnetic heterogeneous alloys

Abstract We present a quantum-statistical theory of giant magnetoresistance in magnetic heterogeneous alloys, consisting of small particles of ferromagnetic metal embedded in a nonmagnetic conducting matrix. The paper focuses on the spin-dependent size-effect on the conductivity of the system, i.e. the influence of the relative orientation of the magnetization in neighboring particles on their conductivity as a function of the size and distance between the particles. It is shown that the conductivity of heterogeneous alloys is not self-averaging when the particle sizes and/or distances are comparable to the mean-free paths. As for current in-plane giant magnetoresistance, the electron mean-free paths are the relevant length scale parameters. When the size-effects due to the bulk and interfacial spin-dependent electron scattering are taken into account, the giant magnetoresistance amplitude exhibits a maximum as a function of the average radius of the particles. The optimum radius value is determined by a balance between the interfacial and bulk scattering.

Quantum singularities in the angular dependence of giant magnetoresistance in ultrathin ferromagnetic sandwiches

Abstract We present an analytical quantum statistical theory of the angular variation of the giant magnetoresistance (GMR) in thin ferromagnetic sandwiches (current flowing in the plane of the layers). Both spin-dependent scattering of conduction electrons and the existence of spin-dependent potential barriers between the successive layers are taken into account. We show that quantum singularities can arise in the variation of the electrical resistivity of the structure with the angle between the magnetizations in the ferromagnetic layers. These singularities result from the quantization of the momentum of electrons in the direction perpendicular to the plane of the layers.

QUANTUM OSCILLATIONS IN THE ELECTRIC FIELD FOR PERPENDICULAR TRANSPORT THROUGH AN INTERFACE BETWEEN TWO METALLIC LAYERS

Abstract We present a quantum statistical theory of the electronic transport through an interface between two metallic layers. It is shown that when an electric current flows in the direction perpendicular to the interfaces, spatial oscillations in the charge density and electric field exist on both sides of the interface. These oscillations are due to quantum interference effects between the incident and reflected electrons. They arise when the electrons have different Fermi wave vectors k F in the two adjacent metallic layers. The dominant term in these oscillations has period π k F and its amplitude decreases as a hyperbolic function of the distance from the interface at short distances (relative to the elastic mean-free paths) and exponentially with a characteristic damping length equal to the mean-free paths at large distances. Furthermore, the presence of a potential barrier of height U at the interface gives rise to a new interfacial resistance proportional to U 2 . For the case of an interface between two ferromagnetic transition metal layers, a discussion of the relative role of s and d electrons in the in-plane and perpendicular transport is presented.