The compound KTi(SO${}_4$)${}_2·$H${}_2$O was recently reported as a quasi-one-dimensional spin-1/2 compound with competing antiferromagnetic nearest-neighbor exchange $J_1$ and next-nearest-neighbor exchange $J_2$ along the chain with a frustration ratio $\alpha =J_2/J_1\approx$ 0.29 [G. J. Nilsen, H. M. Rønnow, A. M. Läuchli, F. P. A. Fabbiani, J. Sanchez-Benitez, K. V. Kamenev, and A. Harrison, Chem. Mater. 20, 8 (2008)]. Here, we report a microscopically based magnetic model for this compound derived from density functional theory (DFT) based electronic structure calculations along with respective tight-binding models. Our (LSDA+$U_d$) calculations confirm the quasi-one-dimensional nature of the system with antiferromagnetic $J_1$ and $J_2$, but suggest a significantly larger frustration ratio ${\alpha }_{\mathrm{DFT}}\approx 0.94$—1.4, depending on the choice of $U_d$ and structural parameters. Based on transfer matrix renormalization group (TMRG) calculations we find ${\alpha }_{\mathrm{TMRG}}=1.5$. Due to an intrinsic symmetry of the $J_1$-$J_2$ model, our larger frustration ratio $\alpha$ is also consistent with the previous thermodynamic data. To identify the frustration ratio $\alpha$ unambiguously, we propose performing high-field magnetization and low-temperature susceptibility measurements.

• Received 11 April 2013

DOI:https://doi.org/10.1103/PhysRevB.88.224410