Electronic structure of KTi(SO4)2·H2O: AnS=12frustrated chain antiferromagnet

Abstract

The compound KTi(SO${}_{4}$)${}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}$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 $\ensuremath{\alpha}={J}_{2}/{J}_{1}\ensuremath{\approx}$ 0.29 [G. J. Nilsen, H. M. R\o{}nnow, A. M. L\"auchli, 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 ${\ensuremath{\alpha}}_{\mathrm{DFT}}\ensuremath{\approx}0.94$---1.4, depending on the choice of ${U}_{d}$ and structural parameters. Based on transfer matrix renormalization group (TMRG) calculations we find ${\ensuremath{\alpha}}_{\mathrm{TMRG}}=1.5$. Due to an intrinsic symmetry of the ${J}_{1}$-${J}_{2}$ model, our larger frustration ratio $\ensuremath{\alpha}$ is also consistent with the previous thermodynamic data. To identify the frustration ratio $\ensuremath{\alpha}$ unambiguously, we propose performing high-field magnetization and low-temperature susceptibility measurements.