Magnetic inhomogeneity

Deuterated PB networks filled with carbon black have been investigated recently [74]. The 2H NMR lineshape is different from that in unfilled elastomers an asymmetric doublet is observed as the sample is uniaxially stretched (A,=1.8)). This asymmetry is related to the presence of carbon black fillers, which induce magnetic inhomogeneities. 

In a polycrystalline material each crystallite experiences its own effective field, which is determined in part by magnetic anisotropy. Therefore, because of the different orientations of the crystallites, there will be a distribution of resonant frequencies in consequence, narrow linewidths are associated with low anisotropies. Magnetic inhomogeneities - inclusions and pores - also disturb the local effective fields and so lead to line broadening. The effect of porosity on resonance linewidth can be expressed by the relationship... 

Figure 3. Exchange energy as a function of the wave vector of the magnetization inhomogenity Lindhard function (solid line) and exchange-stiffness or continuum approximation (dashed line). For late 3d elements (Cu), k/2kf = 1 corresponds to modulation wavelength of 0.23 nm...

Doskocilova D, Tao DD, Schneider B, Effects of macroscopic spinning upon line width of NMR signals of liquid in magnetically inhomogeneous systems, Czech. J. Phys. B, 25 202-209, 1975. 

Edmonds DT, Wormald MR, Theory of resonance in magnetically inhomogeneous specimens and some useful calculations, J. Magn. Reson., 77 223-232, 1988. 

Fig. 3. Fourier transform of the current induced by the cyclotron motion of 6 ions. The magnetic inhomogeneity causes the frequency to decrease with increasing cyclotron energy...

Fig. 9. This Larmor spectrum was measured in the analysis trap by resonant excitation (at 104 GHz) of the transition between the two spin states (spin up and down) of the bound electron. The asymmetric line shape of the resonance curve is due to the strong magnetic inhomogeneity in the analysis trap in combination with the thermal Boltzmann distribution of the ion s axial oscillation amplitude...

The difficulty with this approach to separation of orders is that the effect of magnet inhomogeneity is proportional to q. The sample volume at position r with offset Aco(r) contributes a term pjj, ty, r) = exp (i Acu(r)ri)/7g(T + rj and integration over r leads to damping of the coherence with a time inversely proportional to q. ... 

The physics of appearance of long range proximity effect in SF systems can be understood in terms of Andreev reflection. In the absence of spin active scattering or magnetization inhomogeneity Cooper pairs composed of minority or majority electrons do not mix with each other and there is no long range... 

T.,a is the spin-spin relaxation time in site A, and rA is the lifetime in site A. The line is thus Lorentzian in shape with a width (Acj)yZ = (2/T2a)- The value of T2A may be obtained at lower temperatures or in many cases, since the actual line width is limited by magnet inhomogeneities, a sharp signal from an included standard peak as in tetramethylsiiane may be used. The method of measuring small line widths by fast passage techniques has been adequately dealt with before (Pople et al., 1959). 

Fig. 47. Schematic representation of hysteresis loops (a) the coercive force is determined by wall nucleation (b) the coercive force is determined by inhomogeneous nucleation and pinning of walls at grain boundaries (c) the coercive force is determined by magnetic inhomogeneities distributed more or...

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