1
Magnetoresistance – Giant MagnetoResistance (GMR) and Tunnelling MagnetoResistance (TMR) (http://www.almaden.ibm.com/st/ gives more information)
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2
Fundamentals of ferromagnets
Pair-interaction between atomic magnetic moments J ij
Eex = −2∑ J ij s i ⋅ s j , Jij [J] i, j
with the magnetic moments given by the relation mi = gµ B s i . Short-range interaction, often enough to consider nearest-neighbour (nn) interactions. For ferromagnetic 3d elements, the magnitude of the pair- interaction can be estimated from mean-field theory (z = number of nn's,
J ij = J if nn-interaction, J ij = 0 otherwise)
zJ k T ≈ if T ≈ 1000 K , this implies an energy ~ 0.1 eV B c 2 c
The Density Of States (DOS), N (E), in a ferromagnet is split into majority and minority bands due to the exchange interaction.
N (E)
majority 3d N↑ ()E 4s E F
E
N E ↓ () minority