Uniaxial ferromagnet

We now discuss the basic features of the RG flow. This amounts to giving a physical interpretation of our general discussion of the dilatation group, and it explains qualitatively the characteristic features like universality, power laws, and scaling observed in a critical system. For a given class of systems (fluids, uniaxial ferromagnets, polymer solutions, etc.) we envisage the space of all Hamiltonians to be parameterized by a microscopic scale and dimensionless... 

There exist also systems with midticritical points in their phase diagrams and with complex crossover behaviour from one set of critical exponents to another when the range of reduced temperature is laige enough. Examples of mixed and diluted systems will be considered in the last section of this review. Here we discuss only some results of the precise experiments demonstrating the unique features of the phase transitions in dipolar uniaxial ferromagnets. 

Herzer et al. (1986) based on the so-called homogeneous rotation mode of nucleation show that in uniaxial ferromagnets, the nucleation fields are influenced by the second anisotropy constant K2 and may be expressed by the relation... 

This method is based on the Villari effect applying a uniaxial stress to a ferromagnetic substance induces a magnetoelastic anisotropy which may modify all the parameters of its magnetisation curve, e.g. magnetic susceptibility, coercive force, and so on. Some experimental techniques to measure the strain-induced anisotropy are discussed shortly below. 

Reference (261a) reports uniaxial ([100] of pseudocell) antiferromagnetisra 81.5°K < T < 88.3°K, parasitic ferromagnetism due to canted spins T < 81.5°K as a result of different single-ion anisotropies, thermal hysteresis in the canted-spin uniaxial-spin transition, and an He 9000 oe for field-induced spin canting in the intermediate temperature range. 

A single domain ferromagnetic particle with uniaxial anisotropy but excluding the effects of an external field... 

Easy axes of alignment of the magnetization, or an anisotropy, often exist within a single domain ferromagnetic particle. The simplest form of anisotropy is uniaxial anisotropy in which the magnetization favors either of two opposite directions. This may be represented in the framework of our analysis by means of an anisotropy potential of the form... 

In this section we consider the dependence of the relaxation time on the internal anisotropy of a single domain ferromagnetic particle. Thus it is applicable only to Neel relaxation. We consider the simplest form of anisotropy, namely uniaxial anisotropy described by the potential... 

Using this method it is possible to calculate the longest relaxation time of M for a single domain ferromagnetic particle with large uniaxial anisotropy. It is also possible to calculate the longest relaxation time when the particle is in the presence of an external magnetic field applied... 

The relaxation time T (o-, ) for the magnetization of a single domain ferromagnetic particle with uniaxial anisotropy in the presence of an external field from T = Mp and Eq. (3.129) is... 

The spherical harmonic analysis so far presented for uniaxial anisotropy is mainly concerned with the relaxation in a direction parallel to the easy axis of the uniaxial anisotropy. We have not considered in detail the behavior resulting from the transverse application of an external field and the relaxation in that direction for uniaxial anisotropy. Thus we have only considered potentials of the form V(r, t) = V(i, t) where the azimuthal or dependence in Brown s equation is irrelevant to the calculation of the relaxation times. This has simplified the reduction of that equation to a set of differential-difference equations. In this section we consider the reduction when the azimuthal dependence is included. This is of importance in the transition of the system from magnetic relaxation to ferromagnetic resonance. The original study [17] was made using the method of separation of variables on Brown s equation which reduced the solution to an eigenvalue problem. We reconsider the solution by casting... 

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