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 ${\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}$, which is nearly quantum critical, as well as for the new kagome fluoride ${\mathrm{Cs}}_2{\mathrm{LiTi}}_3{\mathrm{F}}_{12}$. 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 ${\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}$ is discussed.

• Received 11 November 2019
• Revised 9 January 2020
• Accepted 5 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.054427