Spin Valve Systems for Angle Sensor Applications - tuprints

2Theory
2.1 Electrical Resistance and Magnetoresistance
The source of the electrical resistance R or specific electric resistivity ρ of metals stems
from the scattering of conduction electrons during electron transport. The dominant scattering
sites in polycrystalline metals are from grain boundaries, but also include interstitial defects,
vacancies, impurity atoms or dislocations. Phonons lead to additional scattering of the
conduction electrons and to a temperature dependence of electrical resistance.
Magneto-Resistance (MR) is the resistance change in a material induced by the application
of a magnetic field. This is defined by the following expression:
MR
R
− R
R
max min
= =
(2.1)
min
where Rmax is the maximum measured resistance, Rmin is the minimum measured resistance
and ∆R the amount of resistance change. MR is commonly expressed as a percent value.
This convention will be used throughout this dissertation.
The MR effect has been observed in nonmagnetic metals upon application of an applied
magnetic field more than half a century ago [Koh49] [Jan57]. This resistance change stems
from the Lorentz force of magnetic field acting on the conduction electrons. The Lorentz
force changes the trajectory of the conducting electron, therefore increasing its scattering
potential. The MR effect, due to the Lorentz force, is two orders of magnitude smaller in
comparison to the AMR and GMR effects, and its contribution to the overall MR effect is
typically ignored.
∆R
R
2.2 Anisotropic Magneto Resistance (AMR)
The AMR effect is a current-induced MR that exists in ferromagnetic metals such as Ni,
Co or Fe upon application of an applied field H. The physical origin of the AMR effect is
spin-orbital coupling on the 3d orbitals caused by an applied magnetic field [Smi51]. This
increases the scattering potential of the electrons during conduction in ferromagnetic
materials. The magnitude of the AMR effect is dependent on the angle between the current
flow I and the angle of the magnetization M in the ferromagnetic metal as shown in Figure
2.1. θM is usually the same as the angle of the applied field θH, but can be influenced by other
factors such as a form or crystalline anisotropy in the ferromagnetic thin film [McG75]. θj is
the direction of the current flow.
min
5