Thermodynamics and magnetization process of the frustrated ferromagnetic spin-1/2 chain

We report a study of the thermodynamics and magnetization curve of a $J_1$--$J_2$ spin-1/2 chain with a ferromagnetic nearest neighbor coupling $J_1$ and an antiferromagnetic next-nearest neighbor interaction $J_2$. This model has recently been suggested to describe the properties of different compounds such as LiCuVO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$. We present results for both the specific heat and the magnetic susceptibility for the whole parameter range of $J_2/4<|J_1|<0$ obtained by exact diagonalization of up to $N=24$ sites. The specific heat exhibits a two-peak structure for $J_1<0$, originating from, first, the proximity to a ferromagnetic ground state and, second, antiferromagnetic fluctuations at higher energies. Furthermore, the magnetization process at zero temperature is analyzed by means of the density matrix renormalization group technique. Particular emphasis is given to the presence (or rather absence) of magnetization plateaus and a comparison with other theoretical results for the ground-state phase diagram.