Electronic and magnetic properties of the chain compounds K$_3$T$_2$O$_4$ (T=Ni, Pd, Pt)

Recent susceptibility measurements on the chain compound K$_3$Pd$_2$O$_4$ were interpreted in terms of localized spin 1/2 Pd moments on one of the two crystallographically different Pd sites, only [{\it R.V. Panin et al., J. Solid St. Chem. {\bf 180}, 1566 (2007)}]. The main exchange interaction was reported to be antiferromagnetic from the negative Curie-Weiss temperature $\Theta$=$-$80K. Earlier measurements for the isostructural and isovalent Ni and Pt compounds suggest an antiferromagnetic coupling for T=Ni whereas it is ferromagnetic for T=Pt. [{\it H. Zentgraf et al., Z. Aanorg. allg. Chem., {\bf 462}, 92 (1980)}] Here, we report an electronic structure study focusing on the interplay of covalency, spin-orbit coupling and correlation to describe the behavior of this compound family. The inclusion of strong Coulomb repulsion at the transition-metal sites is necessary to obtain the correct insulating ground state observed in recent measurements for the Pd system. The origin of the different magnetic behavior will be discussed.