Heisenberg ferromagnet

Rushbrooke and Wood have calculated the coefficients an of this series for a Heisenberg ferromagnet and have extended this treatment to an antiferromagnet29). 

The uniform interaction (UI) model assumes that the freeon, Heisenberg ferromagnetic exchange interaction is uniform for all pairs in the sample i. e.,... 

Figure 19 Log-log plot of susceptibility versus temperature for four Heisenberg ferromagnetic chains. Deviations from linearity are due to interchain interactions. (Reprinted with permission from C.P. Landee and R.D. Willett, Phys. Rev. Lett., 1979, 43, 463. 1979 by the American Physical Society)...

Similar studies have been carried out for AT (Landau et al., 1989) and Heisenberg ferromagnets with free surfaces (Binder and Hohenberg, 1974), yielding a somewhat larger value of fi (ft 0.84). This result is compatible with an experimental determination of fi for the isotropic ferromagnet Ni, fii 0.82 (Alvarado et al., 1982). 

This approximation will only be valid for 7 —> 0, as fluctuations are often visible as the sample is warmed towards 7m. Little is understood, however, about slow spin dynamics (i.e., within the iSR, but below the neutron time window) in ordered magnets. A theoretical treatment of spin lattice relaxation and its relation to jxSR for a Heisenberg ferromagnet has been given by Dalmas de Rentier and Yaouanc (1995). 

Our discussion has shown that at ultralow temperatures quantum fluctuations cause observable effects in polymers. We have calculated these effects for the lowest moments (r ) and (r" ) of the end-to-end distributiOTi for ordinary polymers as well as for polymers in which each link carries a spin S. In the latter case the polymers are flexible one-dimensional quantum Heisenberg ferromagnets. With the presently available tramps and cooling techniques, experimentalists should be able to detect these effects. 

Fig. 6.16 Definition of r, r and r" used in the derivation of the spin wave representation of the excited states of an Heisenberg ferromagnetic extended system...

Heisenberg ferromagnet reciprocal susceptibility CIX T studied versus JIkT Fig. 195... 

V = (1.30-1.40), see table 6. The critical exponents, y, are close to those predicted theoretically for a Heisenberg ferromagnet (De Jongh and Miedema 1974). 

Fig. 292. [(CH3)jNH]CuCl3-2H20sc. Magnetic susceptibility parallel to the c axis plotted as C/xTvs J/kT. The transition temperature corresponds to J/kTc =1.78. Solid curve (/) is the Curie-Weiss result with 0=2 J/kT (2) is the square Heisenberg ferromagnet and (5) is the Heisenberg ferromagnetic chain (abscissa scaled down by a factor of2)[74S51].

Plot of the powder susceptibility and the fit (solid line) to the equation of Baker et al. for a two-dimensional Heisenberg ferromagnet. C is the Curie constant for g = 2.134 and S=i, while J/k=18.7 K. The dashed line is the molecular-field prediction for a quadratic lattice, (o) data collected at 10 kG, ( ) data collected at 500 G [74L14]. 

Swendsen (1972) has shown theoretically in a Green s function analysis of a Heisenberg ferromagnet, including also dipolar interactions, that TqIO cannot be larger than 0.9. As well for EuO as for EuS the data of table 19.2 show that this ratio is 0.89. 

As a first step in the study of the Heisenberg ferromagnet, we express the dot product of two spin operators, with the help of the spin raising 5+ and lowering 5 operators (for details see Appendix B), as... 

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