ALBERTO BOLLERO REAL

2.2 Magnetic properties
often fairly strong. Then, a crystal anisotropy energy is stored in a crystal when J s points
into a non-easy direction. The crystal anisotropy is not only based on crystal fields but also
on the spin-orbit coupling because the magnetisation is dominated by the spin (of 3d and 4f
electrons) and the crystal fields act on the orbital part of the wave functions, only. The
anisotropy energy can be defined as the energy required to rotate the magnetisation away
from the easy direction. In a material with uniaxial symmetry (e.g., hexagonal cobalt) it
may be described by:
E a = K 1 sin 2 θ + K 2 sin 4 θ + σ(θ 6 ) (2.5)
where K 1 and K 2 are the anisotropy constants (in first approximation, they can be
associated with the work necessary to rotate the direction of magnetisation from the easy
direction to that perpendicular to it); θ is the angle formed by the magnetisation and the
easy direction; σ(θ 6 ) includes all the terms in θ with power ≥ 6. The anisotropy energy can
be represented by a ficticious magnetic field H a (anisotropy field), which is parallel to the
easy direction and reproduces the energy increase due to small deviations from the easy
axis [1]:
H a
2 K1 + 4K
2
= (2.6)
J
In structures with one preferred crystallographic direction (c direction), i.e. hexagonal,
rhombohedral or tetragonal, K 1 usually dominates over the other anisotropy constants. If K 2
is neglected in (2.6), K 1 > 0 means that c is the magnetically easy direction. This type of
anisotropy is called easy-axis or uniaxial anisotropy. In the case of K 1 < 0 the anisotropy is
said to be of easy-plane type. The anisotropy constants differ for different materials and
almost always decrease as the temperature increases and become essentially zero even
before the Curie temperature is reached. In R-T intermetallics the contribution of the R
sublattice to K 1 usually is an order of magnitude larger than that of the T sublattice. Only at
high temperatures the T sublattice is dominant because of the rapid decrease of the R
sublattice anisotropy with increasing temperature.
s
2.2.4 Magnetic domains
In thermal equilibrium, a ferromagnetic material consists of magnetic domains [6],
and these find their origin in the lower magnetostatic energy, in comparison to a state
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