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Phys560Notes-17

# Phys560Notes-17 - Ferromagnetism A simple picture...

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1 Ferromagnetism A simple picture: ferromagnetism arises from "atomic magnets" aligned in the same direction. What is the interaction to align them? Each atomic magnetic has a magnetic moment ~ 0 B g . Dipolar interaction energy between neighboring atomic magnets:  2 0 4 12 1 2 33 1 ˆˆ 3~ 1 0 B g U ra    mm mrmr eV ( a ~ 2Å) This is much less than the chemical bond energy (~1 eV) and the thermal energy (~25 meV) at room temperature. Negligible. However, dipolar interactions between magnetic domains can be significant. Most ferromagnetic materials have domains of strong magnetization. If the domains are randomly oriented, the net magnetization is zero; this is usually the lower energy state. To align the domains (to magnetize the material), one could apply a high field at high T above the Curie temperature, and allow the material to cool down in field. Exchange interaction – responsible for ferromagnetism; it depends on the spin configuration of the electrons (largely a consequence of the Pauli exclusion principle). Standard single-particle band structure treats one electron at a time. Let us consider the effective interaction between two electrons (ignore all of the other electrons for now). Assume a spin-independent Hamiltonian . 2 The total spin for the two electrons can be either S = 0 (singlet) or 1 (triplet). The total wave function = (spin part) x (spatial part) = odd under electron exchange (Pauli's exclusion principle).

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Phys560Notes-17 - Ferromagnetism A simple picture...

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