MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

72 Chapter 3
with temperature and field much like a ferromagnet. When this is due to a
canting of neighboring moments from truly parallel or antiparallel, this is
called a canted antiferromagnet. If the ferromagnetic moment is not due
entirely to canting but arises from the different strengths of the sublattice
magnetizations, the material is called a ferrimagnet.
Most commercial insulating “ferromagnets” are actually ferrimagnets.
Common examples are ferrites and garnets such as YIG. The multiple
magnetic interactions inherent to a ferrimagnet provide a variety a magnetic
behavior. For example, when the magnetizations of the opposing sublattices
exactly cancel, the net moment is zero like it is in an antiferromagnet. The
temperature where this occurs is called the compensation temperature T Comp .
3.2.2.4.1 Mean field model for Gd 0.67Ca 0.33MnO 3
The gross features of a ferrimagnet can be explained using the molecular
field model of section 3.2.2.2.5. For a ferrimagnet with two sublattices, the
total magnetization M is the sum of the two sublattice magnetizations M A and
M B . The molecular field acting on each sublattice can then arise from
interactions with atoms in the other sublattice as well as atoms in the same
sublattice. For example on the A sublattice H mA = λ AA M A + λ AB M B . The
molecular field constants λ ij can be either positive for ferromagnetic coupling
between sublattices or negative for antiferromagnetic coupling. For a
ferrimagnet or antiferromagnet, there must be strong antiferromagnetic
coupling. Similarly, on the B sublattice H mB = λ BB M B + λ AB M A . Once the
molecular field constants are known, the magnetization of each sublattice can
be calculated iteratively as described in section 3.2.2.2.5 until self consistency is
reached.