Magnetic field effects first-order

In 1962 the first implicit prediction appeared of a cross-effect between natural and magnetic optical activity, which discriminates between the two enantiomers of chiral molecules [7]. This was followed independently by a prediction of magnetospatial dispersion in noncentrosymmetrical crystalline materials [8]. This cross-effect has been called magnetochiral anisotropy and has since been predicted independently several times more [9-12]. Its existence can be appreciated by expanding the dielectric tensor of a chiral medium subject to a magnetic field to first order in the wave vector k and magnetic field B [8] ... 

Lelievre-Bema, E., Rouchy, J. and Ballou, R. (1994) Field induced first order magnetic transition and associated volume effect in TbMn2, J. Mag. Mag. Mar., 137, L6-L10. 

While all contributions to the spin Hamiltonian so far involve the electron spin and cause first-order energy shifts or splittings in the FPR spectmm, there are also tenns that involve only nuclear spms. Aside from their importance for the calculation of FNDOR spectra, these tenns may influence the FPR spectnim significantly in situations where the high-field approximation breaks down and second-order effects become important. The first of these interactions is the coupling of the nuclear spin to the external magnetic field, called the... 

According to the classical theory, the effect of a magnetic field on a system composed of electrons in motion about a fixed nucleus is equivalent to the first order of approximation to the imposition on the system of a uniform rotation... 

First-order means that we consider nothing beyond that described here. In second-order , we would include the effects of mixing between ground and excited states brought about by the magnetic field. This is briefly discussed under second-order Zeeman effects later. 

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

The quadrupolar effects of order higher than two (7) are usually assumed to be negligible, especially at high magnetic fields. However, once the first- and second-order effects are removed, the measurement of third-order contributions becomes realistic. It can be easily shown that, similar to the first-order case, the CT and all symmetric MQ transitions (q = 0) are free of the third-order contribution, which thus can be safely ignored in DAS, DOR, and MQMAS experiments [161,162]. This is not the case for transitions between non-symmetric spin states, such as the STs. Indeed, numerical simulations of the third-order effect have explained the spectral features that have been observed in 27A1 STMAS spectra of andalusite mineral [161]. 

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