Exchange energies of kapellasite from high-temperature series analysis of the kagome latticeJ1−J2−Jd-Heisenberg model

Abstract

We present a method to build magnetic models of insulators based on high-temperature expansions by fitting both the magnetic susceptibility and the low-temperature specific heat data. It is applied to the frustrated magnet kapellasite [Cu${}_{3}$Zn(OH)${}_{6}$Cl${}_{2}$] with the ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{d}$-Heisenberg model on the kagome lattice. Experimental data are reproduced with a set of competing exchange energies centered at ${J}_{1}=\ensuremath{-}12,\phantom{\rule{0.28em}{0ex}}{J}_{2}=\ensuremath{-}4$, and ${J}_{d}=15.6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, where ${J}_{d}$ is the third-neighbor exchange energy across the hexagon. Strong constraints between these exchange energies are established. These values confirm the results of F\aa{}k et al. [Phys. Rev. Lett. 109, 037208 (2012)] regarding the location of kapellasite in the cuboc2 phase of the Heisenberg model. The quality and limits of this modeling are discussed.