MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

46 Chapter 3
3.2.2.1.2 Conduction electron diamagnetism
The motion of conduction electrons in a metal or semiconductor will also
provide a diamagnetic response (Landau diamagnetism) to a magnetic field.
This is difficult to calculate but generally of the same order as the Pauli
paramagnetism (section 3.2.2.1.3). A superconductor, however, expels a
magnetic field completely (Meissner effect) by the motion of the
superconducting electrons. The diamagnetism of a superconductor is,
therefore, very large, χ vol = -1/4π emu/cc G in the Meissner regime. Since
superconductivity is affected by temperature and a magnetic field, the
magnetic response of a superconductor is actually quite complicated.
3.2.2.1.3 Pauli paramagnetism
Electrons in a metal can be partitioned into spin-up and spin-down bands,
parallel and antiparallel to an applied magnetic field H. The magnetic field
will lower the energy of the spin-up band compared to the spin-down band
(by 2μ B H) and spin-down electrons will flip their spins and pour over into the
spin-up band. The number of electrons (per volume) that need to flip their
spins is approximately the density of electronic states, n(E F ) times one half of
the energy splitting. This produces a net magnetization proportional to the
2
magnetic field and therefore a positive susceptibility, χvol = μB n(EF ). A more
sophisticated statistical-mechanical derivation produces the same result with
small correction proportional to T 2 . The Pauli susceptibility of a metal should
thus be nearly temperature independent and about the same magnitude as
the Larmor diamagnetism. Since the contribution of the Landau
diamagnetism is not known, it is usually not possible to get more than an
order-of-magnitude estimate of the Pauli susceptibility from magnetization
measurements. In principle, however, the Pauli susceptibility should be a
measure of the bare density of electronic states at the Fermi level, n(E F ), in the
absence of many body effects. The linear electronic specific heat term