Phase Control of Magnetic Order in (Y,Lu)BaCo$_{4}$O$_{7}$

The RBaCo$_{4}$O$_{7}$ (R=Ca, Y, Tb-Lu) provides a novel topology for studying geometric frustration, in which face-sharing tetrahedra of magnetic ions link to form trigonal bipyramids on a Kagom\'{e} lattice. Here we describe the structural and magnetic behavior of the Lu member and the solid solution joining Lu to Y as a chemical means to tune between magnetically ordered and disordered ground states. Mean-field models of the generic magnetic phase diagram of RBaCo$_{4}$O$_{7}$ determined recently by our group (D. D. Khalyavin et al. Physical Review B 82, 094401 (2010)) show a variety of magnetic states as a function of two exchange parameters: J$_{ab}$ and J$_{c}$, where J$_{ab}$ links Co ions in the Kagom\'{e} planes and J$_{c}$ links Co ions from the Kagome plane to the interleaving triangular layer. Experimentally, we find that YBaCo$_{4}$O$_{7}$ has a long-range ordered antiferromagnetic ground state, while LuBaCo$_{4}$O$_{7}$ appears to be disordered above 2 K. We use the solid solution to interpolate between these endpoints and discuss these results with respect to the mean-field phase diagram.