Orientation, single-domain magnetic

Kinetics of establishing of orientational equilibrium of a magnetic moment of a single-domain particle in the presence of thermal fluctuations is described by FPE (4.27). We express it in spherical coordinates at the surface of a unit sphere. Assuming that all the functions depend only on the meridional angle H, we obtain, [47]... 

In conclusion, let us estimate the dimensional values of particle parameters and held amplitudes at which the orientational effects discussed would be most pronounced and, hence, observable. For a magnetic colloid (single-domain particles of linear size 10 nm, volume Vm 5 x 10 19 cm3, and magnetization Is 500 G) at room temperature, one hnds p = IsVm 2.5 10 16 erg/G. The magnetic held amplitude that can cause a distinctive orientational nonlinearity is determined by the condition 2,0 > 1> which yields Hq > V i 160 Oe. According to Ref. 152, the actual values and were 500 and 683 Oe, respectively. 

A total of 1500 crystallites and 500 particles was assumed for the calculations. The particles were randomly oriented. The anisotropy constant of the crystallites was Kt = 5.6 106 J/m3, Js = 1.31 [28]. The exchange constant was varied in the range of A = 0.1 10 11 J/m to A = 2.2 10 uJ/m. Five percent of all crystallites are assumed to remain in the disordered fee phase. To represent the fee phase we simply set Ki = 0. For the chosen parameters the critical size for magnetization reversal by uniform rotation, dcrit, is in the range from 7.8 to 36 nm which is greater than the assumed particle diameter of 5 nm. For comparison, the critical single domain diameter, D, is in the range from 130 to 590 nm. 

A ferromagnetic material consists of magnetically ordered domains separated by transition zones, the so-called Bloch walls (ca 30 nm). In finely divided ferromagnetic compounds, with size less than this critical value, particles consist of magnetic single domains, At temperature T, they may exhibit a kind of Brownian movement, affecting the orientation of the magnetic moment p of the particle considered as a whole (p = NpD N,... 

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