MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

44 Chapter 3
substances. Otherwise, M = M 0 + χH + χ 3 H 3 + É can be used where χ is now a
second rank tensor describing the linear response, M 0 is the spontaneous
magnetization, and χ n describe the higher order nonlinear terms.
The magnetic field H can be produced either by electric currents or by the
magnetization. If a sample is magnetized, an H field is produced in the
sample to oppose the magnetization and therefore demagnetize the sample.
This demagnetization field H d is for an ellipsoidal sample directly
proportional to the magnetization H d = N d M, where 0 ≤ N d ≤ 4π is the
demagnetization factor. Since the demagnetization field depends on the
shape of the sample, it is the internal field H i = H a - H d the applied field minus
the demagnetization field which affects the magnetic response. Since the
correction for the demagnetization fields is often ignored, one should be wary
of the effects of demagnetization. Ferromagnets in small applied fields for
example may have reduced bulk magnetization due to demagnetization.
3. 2. 2. 1 Diamagnetism and Paramagnetism
Since atoms are made up of charged particles which undergo orbital
motion and have magnetic moments, there are many ways a materials can
have a magnetic response. A diamagnetic response is that for which the
susceptibility is negative while a positive contribution to the susceptibility is
paramagnetic.
3.2.2.1.1 Larmor diamagnetism
Since the electrons in an atom are essentially free charges orbiting a
nucleus, the application of a magnetic field, by LenzÕs law, induces an
opposing magnetic moment. The resulting magnetic susceptibility is
therefore negative and known as Larmor or core-electron diamagnetism.
Both the classical and quantum mechanical analyses yield the same result,
namely that the diamagnetic susceptibility of an atom or ion is proportional
to the number of electrons it contains, Z and its cross sectional area