How Demagnetizing field affects magnetic behavior of a thin film of magnetic material and up to what thickness ?
I would say, this is basically a problem of model versus reality, i.e. how good matches the real thin film the idealized model.
Generally, the main question is, what kind of domains can be built ? This depends on the kind of material and its thickness as well. If only in-plain domains are built, this influences the demagnatizing field. Have a look at "Magnetic anisotropy and domains", this may help.
Demagnetizing field is directly linked with the shape of a ferromagnetic body and the magnetization distribution within it. For the case of uniformly magnetized ellipsoid shaped FM body the demagnetization field will be uniform and can be easily calculated using the demagnetization tensor. The above-written, however, can fail if the number of elementary magnetic dipoles becomes countable. The film's shape is typically approximated by an oblate spheroid with infinitely big lateral dimensions, that gives that the demagnetization field exist only for the normal component of the magnetization. For the films with the thickness much lower than the exchange length Bloch domain walls are typically replaced by Neel domain walls which can influence on magnetization reversal mechanism. Neel domain walls are sensitive to the demagnetization field.
O' Handley's book "Modern magnetic materials" treats the demagnetizing field and tensor early on. Recommended reading.
Shape anisotropy results from the demagnetizing field.
Whatever exactly you mean by "volume anisotropy", i would guess it is unrelated to the demagnetizing field.
Demagnetizing field is well defined only in ellipsoidal forms. I will be strongly nonuniform for other shapes. You need include full micro-magnetic calculation in either cases
The demagnetizing field in a direction perpendicular to the film plane 4piM. In a direction normal to the film it is zero. Shape anisotropy for instance in a recrtangular film would be such it is higher along the shorter edge. In a circular film plane it is just isotropic and the field would be 4piM. I do not understand what is volume anisotropy.
The demagnetizing field or dipolar field is the field created by the magnetic moments inside the material.It is complex to calculate it, but in the case of ellipsoids uniformly magnetized the demagnetizing field is defined as a certain demagnetizing tensor N time the magnetization vector. The diagonal terms (Nx, Ny, Nz) of the demagnetizing tensor are nonzero. These components of the demagnetizing tensor, called the demagnetizing coefficient depend on the dimension of the ellipsoid.For example for the particularly case of an ellipsoid as the sphere Nx=Ny=Nz=1/3. Another particularly case is a flattened cylinder. Considering the normal to its surface is parallel to z-axis Nx=Ny=0 Nz=0. Thin films magnetic materials are treated as flattened cylinder because the thickness of the film is very small relative to lateral dimensions
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