Biquadratic exchange from susceptibility data in classical one-dimensional Heisenberg systems

We have investigated the magnetic susceptibility of three quasiclassical one-dimensional magnetic systems, ${\mathrm{CsMnBr}}_3$, (${\mathrm{CH}}_3$ ${)}_4$ ${\mathrm{NMnCl}}_3$ (TMMC), and ${\mathrm{CH}}_3$ ${\mathrm{NH}}_3$ ${\mathrm{MnCl}}_3$⋅2${\mathrm{H}}_2$O (MMC), in their paramagnetic regimes. We find that a previous analysis in terms of a classical Heisenberg Hamiltonian does not provide an adequate description of the data at low temperatures where short-range correlations are high. We show that approximate quantum-mechanical corrections to this exact treatment do not account for the discrepancies systematically. A classical treatment which includes exchange interactions biquadratic in the spins is applied to this problem, resulting in a marked improvement of the description of experiments by theory at all temperatures. We include weak dipolar terms in the Hamiltonian, in addition to both bilinear and biquadratic exchange terms, for the case of ${\mathrm{CsMnBr}}_3$ by means of a Monte Carlo simulation. To within the quoted accuracy, the simulation describes the susceptibility completely for the temperature range considered. Our results show that the strength of the biquadratic exchange interactions, relative to the strength of the bilinear interactions, is strongest in MMC and weakest in TMMC, but that the absolute magnitude is greatest for ${\mathrm{CsMnBr}}_3$. Quantitatively, we find that our calculations produce a biquadratic exchange strength for ${\mathrm{CsMnBr}}_3$ which is in agreement with neutron spectroscopic measurements of transition energies in ${\mathrm{Mn}}^{2+}$ linear triads.