Anisotropy uniaxial

Substitution for Fe has a drastic effect on intrinsic magnetic properties. Partial substitution by or decreases J) without affecting seriously, resulting in larger and values. Substitution by Ti and Co causes a considerable decrease in K , the uniaxial anisotropy (if j > 0) may even change into planar anisotropy (if < 0). Intermediate magnetic stmctures are also possible. For example, preferred directions on a conical surface around the i -axis are observed for substitution (72). For a few substitutions the value is increased whereas the J) value is hardly affected, eg, substitution of Fe byRu (73) or by Fe compensated by at Ba-sites (65). 

In the case of Co—Cr having perpendicular anisotropy there is, in principle, a competition between the uniaxial anisotropy of a hexagonal stmcture and the demagnetizing energy of the thin film. In the case of magnetically separated Co—Cr columns (particulate morphology) then also the shape anisotropy contributes to the perpendicular anisotropy. 

Normal incidence measurements are sufficient for uniaxially oriented samples, but a third spectrum along the ND (Y) is necessary to describe the orientation in biaxially oriented samples or in the case of uniaxial anisotropy in the thickness... 

Not all the molecular symmetries are equally suited for favouring a SIM behaviour. Cubic Oh symmetry, for example, in the case of 8-coordinate complexes, does not have second-order uniaxial anisotropy, E, and this geometry does not favour a large energy barrier for magnetization reversal. 

Figures 6-9 illustrate the use of these finite size scaling relations for the square lattice gas with repulsion between both nearest and next nearest neighbors. In Fig. 6 the raw data of Fig. 5 are replotted in scaled form, as suggested by Eq. (37). Note that neither = TJcc) nor the critical exponents are known in beforehand - the phase transition of the (2x1) phase falls in the universality class of the XY model with uniaxial anisotropy which has nonuniversal exponents depending on R. Clearly, it is desirable to estimate without being biased by the choice of the critical exponents. This is possible...

With decreasing particle size, the magnetic contributions from the surface will eventually become more important than those from the bulk of the particle, and hence surface anisotropy energy will dominate over the magnetocrystalline anisotropy and magnetostatic energies. A uniaxial anisotropy energy proportional to the particle surface S... 

Hereafter, we will assume uniaxial anisotropy, of easy-axis type, given by Eq. (3.4) (if not otherwise indicated), since it is the simplest symmetry that contains the basic elements (potential minima, barriers) responsible for the important role of magnetic anisotropy in superparamagnets. Experimental evidence for uniaxial anisotropy is given in Refs. 15 and 16. 

The Hamiltonian of a noninteracting nanoparticle with uniaxial anisotropy is given by... 

All results obtained below with the thermodynamic perturbation theory are limited to the case of axially symmetric anisotropy potentials (see the Appendix, Section A.2), and all explicit calculations are done assuming uniaxial anisotropy (see the Appendix, Section B). 

There are essential differences between the systems we have presented here, even in the limit of very strong anisotropy. The RKKY spin glasses are Heisenberg systems with random unidirectional anisotropy. Ferrofluids frozen under zero field are Heisenberg systems with random uniaxial anisotropy, while an Ising system is characterized by parallel uniaxial anisotropy. 

This nanoparticle sample exhibits strong anisotropy, due to the uniaxial anisotropy of the individual particles and the anisotropic dipolar interaction. The relative timescales (f/xm) of the experiments on nanoparticle systems are shorter than for conventional spin glasses, due to the larger microscopic flip time. The nonequilibrium phenomena observed here are indeed rather similar to those observed in numerical simulations on the Ising EA model [125,126], which are made on much shorter time (length) scales than experiments on ordinary spin glasses [127]. 

The quantities Si are calculated in the case of uniaxial anisotropy in this appendix. Section B. Note finally that in the isotropic limit Si —> 0), Eqs. (A.7) and (A.8) reduce to the known moments for the isotropic distribution [134,135]... 

The thermodynamical average 5 (a) over the Legendre polynomials P occur in the expressions for the susceptibilities, the specific heat, and the dipolar fields in Section II.B. For uniaxial anisotropy these averages read... 

Co—be/Cu 1.0 nm Co9Fe/1.0 nm Cu ion-beam sputtering on MgO(llO) substrates Co-Fe/Cu grew having inplanc uniaxial anisotropy, easy axis parallel to cube direction in the MgOO 10) plane saturation field (240 kA/m) at RT for GMR = 45%... 

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