Theory of transport in magnetic ultrathin films

Magnetic multilayers, in which magnetic layers are separated by nonmagnetic spacer layers, exhibit several effects in which there has been significant recent interest: giant magnetoresistance (GMR), oscillatory exchange coupling, and spin-transfer torques. The GMR is the change in resistance when the relative orientation of the magnetizations in neighboring layers is switched by applying a magnetic field. When the magnetizations are parallel, there is a "short circuit" effect; electrons of one spin have a lower average resistance. They carry more of the current, lowering the total resistance of the structure compared to the total resistance for antiparallel magnetizations.

Sensitive detectors of magnetic fields can be made based on the change in resistance as a function of the magnetic field. One of the most prominent applications of such detectors are the read heads for magnetic disk storage. Read heads based on GMR are now the basis of all the heads presently on the market. There is a wide variety of additional applications for magnetic sensors. NIST has an active competence program (between the Electron Physics Group, the Magnetic Materials Group, the Magnetics Group, and the Quantum Devices Group) to develop low noise, low field magnetic sensors.

We are investigating several aspects of transport in magnetic multilayers. Spin-dependent interface reflection provides an important source of spin dependence responsible for giant magnetoresistance. Our calculations of spin-dependent interface resistances from the reflection probabilities show quantitatively how important this effect is. In addition, spin-dependent reflection plays an important role in the physics of spin transfer torques. In our calculations of those effects, we make extensive use of a variety of transport calculations, including the Boltzmann equation and the drift-diffusion approximation. Finally, we are investigating the role of the relaxation time approximation in transport calculations for these systems. We have developed a method for solving the spatially varying Boltzmann equation without the making the

We have developed a method for solving the spatially varying Boltzmann equation without the making the relaxation-time approximation. This method involves a discretization of points on the Fermi surface. The scattering terms can then be inverted by matrix methods and the spatial part of the equation can be dealt with analytically. The solution is compared with that obtained using the relaxation-time approximation for free-electron solids in the presence of boundaries. We study both a single slab of finite thickness with non-specular reflection at the surfaces and an applied electric field parallel to the surface and an infinite free-electron metal divided by a partially reflecting interface with an applied field. The relaxation-time approximation works reasonably well provided a particular relaxation time, the transport relaxation time, is used. For reasonable values of the parameters maximum differences in conductivities or resistances are of order 10% and typically the differences are considerably smaller. For non-free-electron materials, it is expected that the differences will be more complex because the transport relaxation time is exact only for an isotropic bulk material.

Online: May 1996
Last Updated: February 2008

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