Anisotropy constants

Fig. 4. The effect of temperature for Mng 6 Zng 3 Fe Fe on (a) initial magnetic permeabiUty, )J., measured on a polycrystalline toroid appHed as a core for a coil driven by a low (B <0.1 mT) ampHtude, low (10 kHz) frequency sinusoidal signal and (b) magnetocrystalline anisotropy constant, measured on a monocrystalline sphere showing the anisotropy/compensation temperature Tq and the Curie temperature, T. To convert joules to calories, divide by...

If there is a crystal anisotropy, with the easy axis parallel to the shape-anisotropy axis of the particle, the total anisotropy is = shape + crystal and the total switchHig field is = (A — Aj,)Af + 2Aj = crystal anisotropy constant). In the case of practical... 

Here iC is the intrinsic anisotropy constant due to the crystalline anisotropy. After the demagnetization in the longest direction, k is the shape-dependent constant (for an infinite cylinder k = 1.38), M is the exchange constant, and R the particle radius. An infinite cylinder with only shape anisotropy gives... 

Fig. 3. Effect of siHcon on properties of iron (10). = Curie temperature = magnetocrystaUine anisotropy constant. To convert T to G, multiply by...

Optimum permeability is achieved by choosing the composition where the anisotropy constants X are near zero, by using high purity raw... 

The results of these modeling studies are shown in Figures 2 and 3> The value of ic (anisotropy constant) was chosen so that the average particle radius determined from the reduction in the average hyperfine field splitting due to collective magnetic excitations... 

The temperature dependence of the magnetic hyperfine splitting in spectra of interacting nanoparticles may be described by a mean field model [75-77]. In this model it is assumed that the magnetic energy of a particle, p, with volume V and magnetic anisotropy constant K, and which interacts with its neighbor particles, q, can be written... 

Magnetocrystalline anisotropy constant, of M-type ferrites, 11 67, 68 Magnetohydrodynamic (MHD) convection, in microfluidic mixers, 26 967 Magnetohydrodynamic power generation, cesium application, 5 704 Magnetometers, SQUID, 23 871... 

The first one is the bulk magneto crystalline anisotropy field. It depends on the chemical composition and crystallographic structure of the material. For instance, the anisotropy constant is 30 times larger in cobalt ferrite particles than in magnetite particles. 

The anisotropy constant depends also on the surface structure of the crystal. 

For large super-paramagnetic crystals or for crystals with a very high anisotropy constant (12), the anisotropy energy is larger than the thermal energy, which maintains the direction of the crystal magnetic moment very... 

The height of the energy barrier between the forward and reverse states is the product of the particle volume, V, and the anisotropy constant Kefr (which is, to some extent, a function of particle size). Superparamagnetic relaxation occurs when the thermal energy of the particles exceeds the activation energy barrier between the spin states and so allows rapid, spontaneous fluctuations between these states. The effect of these spin reversals is that the observed magnetic field is reduced or even absent. 

Because the appearance of the superparamagnetic effect depends on the particle size and on the anisotropy constant, it is often displayed at room temperature by iron oxides <10 nm in size, for example, soil iron oxides. Superparamagnetic relaxation may be counteracted by lowering the temperature and thereby increasing x. Superparamagnetic particles will usually be ordered below a blocking temperature,Tb, which is ... 

The magnetic properties of iron oxides can be determined using Mossbauer spectroscopy, neutron powder diffraction and magnetometry (see Chap. 7). The characteristic parameters are the magnetic moment, the permeability, the saturation magnetization, the magnetic anisotropy constants and the Bhf (Tab. 6.2). 

Oxide Temperature K Magnetic structure Saturation Magnetization <7s at 300 K Ptrr kg" Anisotropy Constant Jm- Magneto- Restriction Constant Jl Magnetic hypeifine field Bhf 295 K 4 K ... 

An alternative way of identifying the domain state of magnetite utilizes the dependence of both the crystal and strain anisotropy constants on temperature. Kj of eq. (7.2) is negative at RTand becomes positive at -118 K, which is the so-called Ver-wey transition at which the crystal anisotropy vanishes and any original remanence, which is controlled by this anisotropy, is lost. This provides an easy test for the do-... 

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