Exact magnetic properties for classical delta-chains with ferromagnetic and antiferromagnetic interactions in applied magnetic field

We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe₁₀Gd₁₀, which is nearly quantum critical, as well as for the new kagome fluoride Cs₂LiTi₃F₁₂. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The s-spin quantum model is studied using exact diagonalization and finite-temperature Lanczos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number s at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe₁₀Gd₁₀ is discussed.