Theoretical study of isotropic ferrimagnetic chains composed of classical spins alternating with quantum systems.

Abstract

Compounds containing well-isolated complex magnetic chains are now available from inorganic and molecular chemistry. Interpreting their magnetic behavior generally requires specific models. We propose here a rather general analytical treatment: This model concerns isotropic ferrimagnetic chains, where a single moment, which may be treated classically (subsystem ${\mathrm{\ensuremath{\zeta}}}_{\mathit{i}}$), alternates with a composite subsystem ${\mathrm{\ensuremath{\Psi}}}_{\mathit{i}}$ of quantum and/or classical spins. In order to evaluate the zero-field susceptibility, it appears necessary to build up and diagonalize an appropriate Hamiltonian for each subsystem ${\mathrm{\ensuremath{\Psi}}}_{\mathit{i}}$. Moreover, one must calculate the first- and second-order derivatives of the eigenvalue ${\mathit{E}}_{\mathit{i},}$u(B) with respect to the amplitude B of the applied field. The intervening quantities depend on the angle ${\mathrm{\ensuremath{\Theta}}}_{\mathit{i}}$ between ${\mathrm{\ensuremath{\zeta}}}_{\mathit{i}}$ and ${\mathrm{\ensuremath{\zeta}}}_{\mathit{i}+1}$ and can be expanded in Legendre polynomials. Because of the properties of these functions, the various expansions only require the computation of the first and/or second coefficients. We give a general closed-form expression for the zero-field susceptibility and analyze its behavior in the low-temperature limit by the mean of the correlation length. We treat three relevant examples and describe possible extensions to random distributed classical or quantum spins in linear chains. We also recall an experimental test of this model concerning the compound ${\mathrm{MnCu}}_{2}$(bapo)(${\mathrm{H}}_{2}$O${)}_{4}$\ensuremath{\cdot}${2\mathrm{H}}_{2}$O [where bapo=N,N'-bis (oxamato 1,3-propylene) oxamido].