Anisotropy transverse field

In this measurement, the hysteresis problem was solved by applying a constant transverse field. In eq. (18), this transverse field does not occur due to cancelling of terms. The same holds for the (in-plane) anisotropy and the shape anisotropy. Baril et al. (loc. cit.) claim that this is a reliable method, giving results consistent with the cantilever method and with a sensitivity better than I x 10-7. It is perhaps worthwhile, however, to consider all... 

An applied field in the xy-plane can tune the tunnel splittings Amm. via the Sx and Sy spin operators of the Zeeman terms that do not commute with the spin Hamiltonian. This effect can be demonstrated by using the Landau-Zener method (Section 3.1). Fig. 8 presents a detailed study of the tunnel splitting A 10 at the tunnel transition between m - +10, as a function of transverse fields applied at different angles (p, defined as the azimuth angle between the anisotropy hard axis and the transverse field (Fig. 4). 

Tunneling is allowed in these half-integer (S = 9/2) spin systems because of a small transverse anisotropy Htrans,i containing Sx i and S, spin operators and transverse fields (Hx and Hy). The exact form of Htrans,i is not important in this discussion. The last term in Eq. 4 is the Zeeman energy associated with an applied field. The Mn4 units within the [Mn4J2 dimer are coupled by a weak superexchange interaction via both the six C-H—Cl pathways and the Cl—Cl approach. Thus, the Hamiltonian (H) for [Ma ] 2 is... 

A systematic study by Herzer [44] on the effect of Si content on the field induced Ku in the nanocrystalline Fe-Si-B-Nb-Cu alloys indicated that Ku is mainly induced in the crystallites. By appropriate choice of alloy composition and annealing conditions, transverse field annealing of nanocrystalline Fe-Si-B-Nb-Cu alloys allows to induce anisotropies in the range of Au 5 - 100 J/m3. This corresponds to initial permeabilities of about fii 104 - 2 x 105. They perfectly cover the needs of applications like common mode chokes or earth leakage circuit breakers [45] which require high permeabilities. 

A single domain ferromagnetic particle in a transverse field excluding internal anisotropy... 

Fig. 3.10.7. Charge segregation in an applied field caused by a bend fluctuation in a nematic of positive conductivity anisotropy. The resulting transverse field is E. ...

Due to the anisotropy of conductivity, space charges will develop as indicated in fig. 3.10.7 till the transverse electric field stops the transverse current. The local transverse field in the steady state is easily seen to be... 

Because the interactions are short ranged (nearest neighbor only) in both space- and timelike directions, the anisotropy does not play a role in the critical behavior of this classical model. We thus conclude that the quantum phase transition of the d-dimensional quantum Ising model in a transverse field falls into the universality class of the (d - - l)-dimensional classical Ising model. This establishes the quantum-to-classical mapping (for a slightly different derivation based on transfer matrices see Ref. 10). 

Hereby, the branches with E - and / -symmetry are twofold degenerated. Both A - and / d-modes are polar, and split into transverse optical (TO) and longitudinal optical (LO) phonons with different frequencies wto and wlo, respectively, because of the macroscopic electric fields associated with the LO phonons. The short-range interatomic forces cause anisotropy, and A - and / d-modcs possess, therefore, different frequencies. The electrostatic forces dominate the anisotropy in the short-range forces in ZnO, such that the TO-LO splitting is larger than the A -E splitting. For the lattice vibrations with Ai- and F -symmetry, the atoms move parallel and perpendicular to the c-axis, respectively (Fig. 3.2). 

We have seen that polarizabilities are isotropic for atoms, but are anisotropic for molecules, showing different response for different directions of the field. For linear molecules we have parallel or longitudinal, [[, and transverse or perpendicular, a i, components in terms of which the isotropic polarizability a and the anisotropy factor Aa are defined (Equations 4.25 and 4.26 of Section 4.3.2). For nonlinear molecules a is... 

The exploitation of cross-correlation effects in high magnetic fields has introduced a new form of NMR spectroscopy called transverse relaxation-optimised spectroscopy or TROSY. The cross-correlation of the optimised dipole-dipole (DD) and chemical shift anisotropy (CSA) relaxation mechanisms leads to differential transverse relaxation rates for the two components of the l5N- H doublet in undecoupled spectra of l5N-labelled proteins. For one component, DD and CSA relaxation constructively add to produce very efficient relaxation, leading to a broad line, whereas for the other component, the two relaxation mechanisms constructively interfere, leading to a narrow line when the two mechanisms are nearly equal. There is no optimum field where DD and CSA relaxation are equal for all amide bonds, because DD relaxation between the amide protons and other nearby protons differs for each residue.72 Clearly, the overall effectiveness of TROSY is optimized when the non-exchangeable protons in the macromolecule... 

---