Ferromagnetic crystal

Zener appears to have been the first to consider this problem to some depth in his theoretical work on ferromagnetic crystals of the type l.a. Ca.MnO, (Zener 1951). For x = 0 one has LainMnin03 but for x > 0 some of the Mn will be 4+, and so we have the structure I. a " / a " Mn "(Mn CL in which some Mn-Mn pairs will be mixed valence, that is, MiF Mnj) or MnJ) Mn . Mnm is 3d4 (S = 2) and MnIV is 3d3 (S = 3/2), and Zener proposed that the excess electron (also called itinerant electron or Zener electron) on Mn111 can travel to the MnIV via a doubly-occupied p-orbital of... 

Figure 3.30 Magnetic domains in a ferromagnetic crystal (schematic). The magnetic dipoles, represented by arrows, are aligned parallel in each domain. The domain walls constitute (approximately) planar defects in the structure.

Figure 3.32 Hysteresis behavior of the magnetization of a ferromagnetic crystal or polarization of a ferroelectric crystal with respect to the applied magnetic or electric switching field.

Figure 9.4 Schematic representation of Weiss domains in a ferromagnetic crystal. The arrows represent the direction of alignment of the magnetic moments in each domain.

BITTER PATTERNS. A method for detecting domain boundaries at the surface of ferromagnetic crystals. If a drop of a colloidal suspension of ferromagnetic particles is placed on the surface of the crystals, the particles will collect along the domain boundaries where the field is strongest,... 

CP = JT312 + aT3 ferromagnetic crystals below the magnetic transition temperature... 

Black, ferromagnetic crystals rutile structure, d 4.89. Metastable in air various temperatures (250-500") reported for decompu to Cr303. 

Figure 15.4 (a) Temperature dependence of x ag for a ferromagnetic solid that undergoes a transition at the Curie temperature Tc- (h) Spontaneous magnetization H = 0) of a ferromagnetic crystal as a function of temperature. 

IXq is the permeability of free space. The relation between the magnetic induction B and the magnetic field H is exactly analogous to that which relates the electric displacement D and the electric field E (Section 4.4.1). With the exception of ferromagnetic crystals (which are only rarely transparent), the eigenvalues of i are close to 1 ... 

Figure 11.17 Hysteresis behaviour of the polarisation, P, in relation to the apphed electric field, E, for a ferromagnetic crystal. As the field takes values between +E and —E, the polarisation, P, takes values between +P and —P...

Notc . Isotopes w-naiuraJly radioactive isotopes, <7-isotopes capable of being rendered artificially radioactive. Valency principal valency is shown in bold type. Magnetic properties (at ordinary temperatures) diamagnetic, p—paramagnetic. /- ferromagnetic. Crystal-structure classification ... 

Fig. 30. Proton resonance frequencies in the TbES ferromagnetic crystal and their dependence on the external magnetic field.

If the applied field is directed along the c-axis of a sphere-shaped axial ferromagnetic crystal, and its value does not exceed the Lorentz field Hi, the resonance frequent Vj Hoz differ from eq. (255). At Hoz>Ht, NMR frequencies are calculated according to the formula... 

Fig. 31. Molecular field directions at H5A protons in the TbES and DyES ferromagnetic crystals.

The experimental spectra, as mentioned above, can be distorted due to the inaccurate settlement of crystals in the magnetic field Hq splittings and additional line shifts appear when the crystal c-axis deviates from the direction of the field Hq. Therefore it will be most proper to compare the measured and calculated NMR frequencies in ferromagnetic crystals in the absence of an external field. The resonance of the H5A protons in both crystals have been observed at temperatures T < 0.8 7c the frequencies of these resonances,... 

Using the data of table 26, one can estimate the molecular fields in ferromagnetic crystals ... 

As mentioned above, the molecular fields in ferromagnetic crystals are extremely inhomogeneous, and therefore the nuclei in different crystallographic positions are affected by fields with different magnitudes and directions. So the nuclei have different resonance frequencies, which form a broad NMR spectrum. In the present subsection we shall consider the separate line width of the proton resonance spectrum in ethylsulfates. 

The resonance of the H5A protons in ferromagnetic crystals can be observed even without an external field. In the TbES crystal at temperatures 0.20 K < T < 0.22 K, which are adjacent from below to the phase transition point, an anomalous behaviour of the relaxation is observed its rate falls somewhat when the temperature approaches 7c = 0.24 K. Too short times Ti prevent the measurements of the H5A proton relaxation in the DyES crystal in the immediate proximity to 7c = 0.118 K. 

Domain. In a ferroelectric or ferromagnetic crystal, e.g. barium titanate, a domain is a small area within which the polarization is uniform. If the crystal is exposed to a high electric or magnetic field, those domains in which the polarization is in a favourable direction will grow at the expense of other domains. A domain structure gives rise to hysteresis (q.v.). 

The question arises as to the critical crystal size at which the destruction of the antiferromagnetic ordering of the spin system occurs. If the dimensional criterion is used, as was previously applied to ferromagnetic crystals by Vonsovsky (77), then a rough estimate gives a value about 3 nm. Thus, Cr-containing PAN after thermolysis in air contains Cr203 particles with a size less than 3 nm. 

Van Hove L (1954) Time-dependent correlations between spins and ferromagnetic crystals. Phys Rev 95(6) 1374-1384... 

Van Hove, L. (1954). Hme-dependent correlations between spins and neutron scattering in ferromagnetic crystals. Phys. Rev., 95,1374-1384. 

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