Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.