Bonner-Fisher model

The larger paramagnetism of the compounds with 5=1/2 M(mnt)j units, also vanishes at the M-I transition, indicating that there is a magnetic transition in the localised spin chains of M(mnt)J units that follows the M-I transition in the perylene chains. At temperatures well above the transition, clear antiferro-magnetic interactions are already noticed, and the susceptibility of the Pt and Pd compounds can be relatively well described by the Bonner-Fisher model... 

In real systems, the number of spin centers N is, of course, too large to deterministically solve the corresponding eigenvalue problem of a corresponding spin Hamiltonian. Thus, no exact solution exists. Several approximate expressions were developed, such as the Bonner Fisher finite-chain model for equidistant antiferro-magnetically coupled S = 1/2-based chains.20 Here, the susceptibility is calculated for finite chain segments (ca. N 10 spin centers) and extrapolated to an infinite chain (N > oo). The extrapolated expression for the susceptibility is as follows ... 

The Bonner-Fisher method has been extended to an infinite chain of S = 1 centres by Weng, valid for / < 0 and applied by Kahn to the problem of modelling the behaviour of [Ni(N02)(en)]X, where X = C104 or... 

D correlations have been detected above TN by neutron diffraction, specific heat and NMR measurements mostly by Hirakawa and coworkers64 705. Magnetic susceptibility results have also been interpreted in terms of short-range couplings of a chain model on the basis of the calculations of Bonner and Fisher and of Oguchi. The main interaction occurs along the c-axis with J/k = —190 K. 

Equation 3.25 makes the explicit assumption that it is reasonable to ignore anisotropy, that is that the zero-field splitting, IDI << l/l. It is possible to perform numerical calculations that take D into account, but these are probably of limited usefulness when trying to model real data. The Bonner and Fisher method becomes computationally difficult for S > 1 if the spin is treated as a quantum mechanical quantity. In the limit of large S, however, the spin can be treated as a classical quantity. Perhaps somewhat surprisingly, such a treatment works reasonably well for values of S as small as 5/2. Such a system can be synthetically realised with a chain of Mn, which has an isotropic ground state. Fisher has derived an expression for an infinite chain of classical spins, scaled to a quantum spin,... 

Farad antiferromagnetic linear chain magnetism fitted according to the Heisenberg model for T>10 K and according to Bonner and Fisher for T<10 K using J/k=( —3.2 0.2) K... 

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