Thermodynamics of multiferroic spin chains

The minimal model to describe many spin-chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest-neighbor coupling J(1) and antiferromagnetic next-nearest-neighbor coupling J(2). Here we study the thermodynamics of this model using a density-matrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations-crucial for the ferroelectric properties and the analog of the classical spiral pitch angle-depend not only on the ratio J(2)vertical bar J(1)vertical bar but also strongly on temperature. We study small easy-plane anisotropies which can stabilize a vector chiral order as well as the finite-temperature signatures of multipolar phases, stable at finite magnetic field. Furthermore, we fit the susceptibilities of LiCuVO4, LiCu2O2, and Li2ZrCuO4. Contrary to the literature, we find that for LiCuVO4 the best fit is obtained with J(2) similar to 90 K and J(2)vertical bar J(1)vertical bar 0.5 and show that these values are consistent with the observed spin incommensurability. Finally, we discuss our findings concerning the incommensurate spin-spin correlations and multipolar orders in relation to future experiments on these compounds.