From kagome strip to kagome lattice: Realizations of frustrated S=12 antiferromagnets in Ti(III) fluorides

Abstract

We investigate the connection between highly frustrated kagome based Hamiltonians and a recently synthesized family of materials containing ${\mathrm{Ti}}^{3+}\phantom{\rule{4pt}{0ex}}S=\frac{1}{2}$ ions. Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets ${\mathrm{Rb}}_{2}{\mathrm{NaTi}}_{3}{\mathrm{F}}_{12},{\mathrm{Cs}}_{2}{\mathrm{NaTi}}_{3}{\mathrm{F}}_{12}$, and ${\mathrm{Cs}}_{2}{\mathrm{KTi}}_{3}{\mathrm{F}}_{12}$. We determine magnetization curves in excellent agreement with experimental observations. Our calculations successfully clarify the relationship between the experimental observations and the magnetization-plateau behavior at $\frac{1}{3}$ height of the saturation and predict characteristic behaviors under fields that are higher than the experimentally measured region. We demonstrate that the studied Ti(III) family of materials interpolates between the kagome strip and kagome lattice.