Fermion mediated state selection in the Kagome lattice and antiferromagnetism in FeCrAs

We study classical spins on a kagome lattice with weak Hund's coupling $J_{H}$ to hopping electrons. For each filling, the effective RKKY interactions at all distances are extracted both by fits of the total electronic energy to a database of random spin configurations, as well as second order perturbation theory in $J_{H}$. We apply this to model the Cr antiferromagnetic order found below 125K in FeCrAs [2], in which one Cr d band split by the crystal field plays the role of the itinerant fermions; the observed $\sqrt3 \times \sqrt3$ type order is indeed, close to half filling, the optimum state according to our model (out of the commonly considered alternatives) . In contrast, the limit of strong $J_{H}$ favors the cuboc1[1] state over the $\sqrt3 \times \sqrt3$ state[3], giving a bound on the possible value of the $J_{H}$ in FeCrAs. Additionally, for weak $J_{H}$, cuboc1[1] is selected instead of $\sqrt3 \times \sqrt3$ close to 5/12 filling. The complete phase diagram as a function of filling can be found using Monte Carlo (MC) minimization with the RKKY Hamiltonian. [1] Messio et al PRB 83, 184401 (2011) [2] W. Wu et al EPL 85, 17009 (2009) [3] Shivam Ghosh, Contributed talk, March Meeting 2013