"From Giant Magneto Resistance in nano-pillars to spin torque in domain Wall (an unified approach)"

For a long time, spintronic has been synonymous of giant magnetoresistance (GMR), however many interesting physical effect can be observed in non collinear magnetic system. Most notably the reverse phenomenon of GMR the so called Spin Transfer Torque effect (STT) has raised very important expectation in the industry (ST-MRAM, tunable current high-frequency oscillators,.....).
There exist various approaches to describe the transport properties of such magnetic structures, but most of them are in practice limited to an oversimplified (1D) descriptions of the real systems. We will show how this limitation can be overcome and present a simple theoretical framework that permit to describe spin transport properties for real 3D samples with complex magnetic texture.
After a brief description of the formalism we will illustrate its capability by addressing two problems. Firstly we investigate the GMR in the current in plane geometry (CIP) and show a new mechanism leading to a mesoscopic GMR effect. Secondly we study the Spin Transfer Torque in two non uniform magnetic system : a multilayer nano-pillars and a domain wall. In particular we address the so called "field like torque", also known as the "non-adiabatic torque" and relate the latter to the microscopic length scale of the problem (experimentally accessible).