Internal spin field

D. Antisymmetric Stresses, Internal Spin Fields, and Vortex Viscosity in Magnetic Fluids... 

Accompanying the impeded particle rotation is the (kinematical) existence of an internal spin field 12 within the suspension, which is different from one-half the vorticity to = ( )V x v of the suspension. The disparity to — 2 between the latter two fields serves as a reference-frame invariant pseudovector in the constitutive relation T = ((to — 12), which defines the so-called vortex viscosity ( of the suspension. Expressions for (( ) as a function of the volume of suspended spheres are available (Brenner, 1984) over the entire particle concentration range and are derived from the prior calculations of Zuzovsky et ai (1983) for cubic, spatially-periodic suspension models. 

The mixed derivative of an external and an internal magnetic field (nuclear spin) is the NMR shielding eonstant, [Pg.239]

Powder spectra of paramagnetic compounds measured with applied fields are generally more complicated than those shown in Fig. 4.14. Large internal fields at the Mossbauer nucleus that are temperature- and field-dependent give rise to this complication. If, however, the measurement is performed at sufficiently high temperature, which is above ca. 150 K, the internal magnetic fields usually collapse due to fast relaxation of the electronic spin system (vide infra, Chap. 6). Under... 

The essence of the DDIF method is to first establish a spin magnetization modulation that follows the spatial variation of the internal magnetic field within the individual pore. Such modulation is created by allowing spins to precess in the internal magnetic field. Then the diffusion-driven time-evolution (often decay) of such a modulation is monitored through a series of signal measurements at various evolution times tD. The time constant of this decay corresponds to the diffusion time of a molecule (or spin) across the pore and thus is a direct measure of the pore size. 

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

Fig. 1. Schematic for /zSR and fiLCR experiments. For pSR the muon spin polarization vector starts off in the x direction (open arrow). It then precesses about an effective field (the vector sum of the external field and the internal hyperfine field), which is normally approximately the z direction. The muons are detected in the M counter, and positrons from muon decay are detected in the L or R counters. For pLCR, the muon spin polarization is initially along the external field or t axis (solid arrow). The positron rates in the F and B counters are measured as a function of external field. A sharp decrease in the asymmetry of the F and B counting rates signifies a level crossing.

In the case of iron, magnetism is due to the unpaired electrons in the 3d-orbitals, which have all parallel spin. These electrons interact with all other electrons of the atom, also the s-electrons that have overlap with the nucleus. As the interaction between electrons with parallel spins is slightly less repulsive than between electrons with anti parallel spins, the s-electron cloud is polarized, which causes the large but also highly localized magnetic field at the nucleus. The field of any externally applied magnet adds vectorially to the internal magnetic field at the nucleus. 

These spectra, taken at variable temperatures and a small polarizing applied magnetic field, show a temperature-dependent transition for spinach ferredoxin. As the temperature is lowered, the effects of an internal magnetic field on the Mossbauer spectra become more distinct until they result at around 30 °K, in a spectrum which is characteristic of the low temperature data of the plant-type ferredoxins (Fig. 11). We attribute this transition in the spectra to spin-lattice relaxation effects. This conclusion is preferred over a spin-spin mechanism as the transition was identical for both the lyophilized and 10 mM aqueous solution samples. Thus, the variable temperature data for reduced spinach ferredoxin indicate that the electron-spin relaxation time is around 10-7 seconds at 50 °K. The temperature at which this transition in the Mossbauer spectra is half-complete is estimated to be the following spinach ferredoxin, 50 K parsley ferredoxin, 60 °K adrenodoxin, putidaredoxin, Clostridium. and Axotobacter iron-sulfur proteins, 100 °K. 

The Mossbauer spectra (between 4.2 K and 298 K) show two overlapping doublets with temperature dependent relative intensities. In conjunction with the data from magnetic susceptibility measurements (between 83 and 313 K) the Mossbauer spectra were interpreted in terms of a singlet triplet spin transition of the central iron(II) ion. No internal magnetic field was observed in a Mossbauer experiment under applied field at 4.2 K. The authors consider this complex the first authentic example of a singlet < triplet spin transition in the 3 d6 configuration of iron(II). Support has been received from UV-vis spectra and IR vibrational spectra201). 

Fig. 8. Induced, spin-originated atomic moment in the presence of a magnetic field // at T = 0°K. At higher temperatures electrons near Fermi level spread out. Internal magnetic fields induce spontaneous magnetization. External fields induce weak (Pauli) paramagnetism. If Ef(0) < EQ null or Ef(P) > Et — hbH, atomic moments are saturated.

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