Nucleation field

Frei, E.H., Shtrikman, S. and Treves, D. (1957) Critical size and nucleation field of ideal ferromagnetic particles. Physical Review, 106 (3), 446-454. 

This coercivity is a simple example of a nucleation field. In micromagnetism, the term nucleation refers to the instability of the remanent state in a reverse magnetic field Hz = - //N. It does not necessarily imply localization effects [16, 93], although localized nucleation is frequently encountered in practice. 

To determine the nucleation field, we write the local magnetization as... 

In terms of (14), imperfections appear as a modification of the local anisotropy K r) and lead to a nucleation-field and coercivity reduction [105, 110-112], The solution of the nucleation problem is simplified by the fact that Eq. (14) has the same structure as the single-particle Schrodinger equation, J i(r) and Hc being the respective micromagnetic equivalents of V(r) and E. Consider, for example, an imperfection in form of a cubic soft inclusion of volume l) in a hard matrix. The corresponding wave functions are particle-in-a-box states, and the nucleation field is [5]... 

In the past, nucleation fields such as Eq. (15) have been obtained for several cases spherical particles in an infinitely hard matrix [110], small inclusions in a matrix of arbitrary anisotropy and exchange stiffness [105] [111], various types of multilayers [111, 113], and some core-shell and nanowire configurations [105, 114, 115], For a discussion of the unphysical limit of very small inclusions, L = 0, see e.g. [5],... 

Figure 38 shows the XRD pattern (a) and hysteresis loop (b) of FePt C double-layered nanocomposite thin-film medium. The soft underlayer FeCoNi (111) peak and the Zl0 FePt (001) and (002) peaks are shown only in the XRD pattern. This means that the preferred crystal orientation of Tl0 FePt C nanocomposite film is successfully obtained on this SUL by nonepitaxial growth. The polar-Kerr measurement shows a square loop that is only sensitive to the top layer the Kerr effect data shown in this loop give the coercivity Hc = 8.5 kOe, nucleation field Hn = 5.65 kOe, remanence ratio S = 1, and loop slope ( at Hc) a = 3.3, respectively. 

In a small applied magnetic field, the soft layer remains fully aligned along the uniaxial hard magnetization direction as a result of exchange coupling through the interfaces. The nucleation field, H , at which first departure from saturation takes place, amounts to [75] ... 

When the anisotropy energy within the hard layer cannot be considered as infinite as compared to the Zeeman energy, the nucleation field depends on the hard layer magnetic properties [122], However, as long as <7hard > 34ard ( hard and 4ard are the hard layer thickness and domain wall width respectively), Hn does not depend much on dhard. For 10 nm, the room temperature nucleation field jU()Hn is typically 1 T. 

Figure 5. Nucleation field calculated for a series of model multilayered systems.

Furthermore, as the layer thickness will become smaller, exchange interactions between the particles will favour parallel alignment of the moments throughout the whole material. In a non-textured material, this will occur at the expense of coercivity. It may be expected that large nucleation fields can only be obtained with textured materials. The development of the corresponding preparation procedures constitutes a challenge for material scientists. 

Aharoni, A., Angular dependence of nucleation field in magnetic recording media, IEEE Trans. Magn., 22, 149, 1986. 

Let us consider the condition for thermal stability of the patterned-media with perpendicular anisotropy, based on a perpendicular M-H loop [28], The net M-H loop for a dot array is the statistic result of small Stoner-Wohlfarth model like square M-H loops of each magnetic dot. The thermally stable condition for a magnetic dot array is just that of the condition for a dot, which is the easiest to reverse among the whole dots. Using the beginning field of the reversal, namely, the nucleation field of the magnetic dot array, H, the condition is expressed as. 

For these models, thermal stability conditions were first discussed as the absolute prerequisite condition. Consequently, the nucleation field of the each dot arrays... 

Durst and Kronmiiller (1985) considered the nucleation field, for the reversal of the magnetization within a planar, magnetically soft region of width 2ro, embedded within a magnetically hard region. The value is given by... 

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... 

Grossinger et al. (1986b) analysed the temperature dependence of the anisotropy field and coercivity in some commercial Nd-Fe-B magnets. A theoretical analysis predicts a correlation between and certain power of the nucleation field,... 

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