**Magnetic anisotropy**.
Magnetocrystalline anisotropy is an intrinsic property of a ferromagnet,
independent of and its shape. In can be most easily seen by measuring
magnetization curves along different crystal directions. Depending on the
crystallographic orientation of the sample in the magnetic field, the
magnetization reaches saturation in different fields. The easy axis is the
direction in which the sample could be easily magnetized, i.e. magnetized by
the smallest applied field. In a simplest case the anisotropy energy could
be described by only one angle defining the magnetization orientation with
respect to the easy axis: *E _{a}=K_{1}
sin^{2}θ+ K_{2} sin^{4}θ*, where

The **exchange energy**. The
exchange energy represents the adjacent spin-spin interaction that gives
rise to ferromagnetism. Defined in terms of the gradient of the
magnetization components, it is especially sensitive to the angle between
two neighboring spins, φ. It is usually assumed that the parallel
orientation of spins corresponds to zero of the exchange energy. The
exchange energy does not depend on orientation of spins (magnetic moments)
in the crystal. The volume density of the exchange energy is described by
*E _{ex}=A(dφ/dx)^{2}*, where A is the exchange
constant and x is a coordinate.

**Domain wall energy**. In a
domain wall the magnetization vector, ** M** gradually
turns from its direction into one domain to the direction of

(1) |

The integral should be taken over an infinite distance and minimized
under of the superimposed the boundary conditions θ(- ∞)=0 and
*θ( ∞)=π* , those correspond to the antiparallel
orientation of M in the two neighboring domains. Note, one should find a
function *θ(x)* minimizing the integral (1). Such a procedure
is called as minimization of a functional. The minimization of the
functional (Eq.1) gives the domain wall energy as*
σ=4(AK) ^{1/2}*. This is the surface density of the Bloch
wall.

**Zeeman energy** is the
energy of a magnetic body in an external field, *H*. This energy is
given by .

**Demagnetizing (or magnetostatic)
energy**. The magnetostatic energy is defined as (the integral should
be taken over all space). In a multidomain state the magnetostatic energy is
less than that in the single domain state because of a large decrease in the
intergation volume (*V _{s} *) occupied by the stray field.

**Stray field**. Stray field is
the magnetic field generated by the magnetic body itself. The sinks and
sources of the magnetization work like positive and negative "magnetic"
charges. There is analogy with an elecotrostatic field from electric
charges. The stray field energy (or magnetostatic energy ) can be avoided by
flux-closure domains (Landau and Lifshitz domain structure ).

**Magnetic poles**. The magnetic
force surrounding a magnet is not uniform. There exists a great
concentration of force at each end of the magnet and a very weak force at
the center. Proof of this fact can be obtained by dipping a magnet into iron
filings. It is found that many filings will cling to the ends of the magnet
while very few adhere to the center. The two ends, which are the regions of
concentrated lines of force, are called the* poles *of the magnet.
Magnets have two magnetic poles and both poles have equal magnetic strength.

**Ferromagnetic **materials
have a large and positive magnetic susceptibility to an external magnetic
field. They exhibit a strong attraction to magnetic fields and are able to
retain their magnetic properties after the external field has been removed.
Ferromagnetic materials have some unpaired electrons so their atoms have a
net magnetic moment.

**Magnetic lines**. Magnetic
lines of force are lines which help visually represent a magnetic field. By
convention, magnetic lines of force point from north to south outside a
magnet (and from south to north inside a magnet). Magnetic lines of force
form complete loops. They never cross.