Analysis of equations like (11) in physically meaningful limiting cases of small anisotropy energy
as compared to the exchange energy (k [much less than] 1) and small deviations of the vectors [M.sub.1] and [M.sub.2] from the easy axis allows one to describe the antiferromagnetic resonance [19, 20] and ferromagnetic resonance  on a phenomenological level.
The magnetic anisotropy energy
([K.sub.u]V; V: volume of an isolated magnetic grain or dot) becomes lower relative to the thermal fluctuation energy ([k.sub.B]T; [k.sub.B]: Boltzmann constant, T: temperature) when the grain and/or dot size is reduced for increasing storage density.
It has reported  that grains dimensions and anisotropy energy
influence the magnetic properties like coercivity.
Heat generation through Neel-relaxation is due to rapid changes in the direction of magnetic moments, hindered by anisotropy energy
that tends to turn the magnetic domain of the magnetic nanoparticle in a given direction according to their crystal lattice structure.
Therefore, these single domain magnetic nanoparticles are called "superspins" or "macrospins." Usually, an ellipsoidal shape of the particles is assumed, where the magnetic moments have the tendency to align along the longest axis, which defines the direction of lowest "shape" anisotropy energy
The higher the anisotropy energy
, the higher the magnetic field induced stress.
The microwave property of M-type doped Ba-ferrites is dependent on their magnetocrystalline anisotropy energy
, and that is dependent on the atomic lattice anisotropy of these ferrites.
In Fe-Si grain oriented strips, the first magnetocrystalline anisotropy constant [K.sub.1] is high and positive (3.5x[10.sup.4] J/[m.sup.3]) and therefore <100> is an easy direction, since the magnetocrystalline anisotropy energy
is equal to zero.
Specifically, they studied the energy required to reverse the direction of an island's magnetization--a quantity that scientists technically call magnetic anisotropy energy
. Brune and his coworkers deposited atoms of cobalt on a platinum surface, forming islands of various sizes.
where [E.sub.ani], [E.sub.ms], [E.sub.exch], and [E.sub.external] are magnetocrystalline anisotropy energy
, magnetostatic energy, exchange energy, and Zeeman energy, respectively.
where [h.sub.c] is the reduced coercive field ([H.sub.c]/[H.sub.c(T=0)]), D is the nanoparticle size, and [D.sub.p] is the critical nanoparticle size in which the anisotropy energy
(KV) dominates the thermal energy ([k.sub.b]T) and the magnetic properties change from superparamagnetic to ferromagnetic.
Recent developments in ultrahigh-density magnetic storage technology rely on novel recording media with high magnetocrystalline anisotropy energy
(MAE) together with high-performance giant magnetoresistive (GMR) heads [1-4].