Pressure Dependence of Magnetism in KCuF$_3$

The perovskite KCuF$_3$ is a prototypical compound for studying both orbital ordering and 1-D Heisenberg antiferromagnetism. In the conventional Kugel-Khomskii picture, this material undergoes a Jahn-Teller distortion at T$_{JT}$=800~K causing long-range ordering of 3d Cu$^{2+}$ orbitals, effectively driving the spin interactions 1-D. A second magnetic transition to 3-D antiferromagnetism is observed at the N\'{e}el temperature, T$_N$=39~K. Recent data by Lee \emph{et al}. suggests a new interpretation where Cu$^{2+}$ orbitals do not order until a glassy structural transition at T$_s$=50~K, and this transition is a necessary precursor to 3-D ordering of spins. It was later shown that the glassy transition can be suppressed to zero temperature with pressures as low as P=7~kbar, implying that spin order should follow suit. Contrary to this prediction, single crystal neutron scattering measurements by our group demonstrated a moderate increase in T$_N$ with pressure, opposite of predictions. However, some evidence for uniaxial strain complicated interpretation. In an attempt to resolve this issue, we performed neutron powder diffraction measurements in helium gas and clamp pressure cells. We will present these data and discuss them in the context of the Lee \emph{et al}. model.