Formation of a simple cubic antiferromagnet through charge ordering in a double Dirac material

The appearance of spontaneous charge order in chemical systems is often associated with the emergence of novel, and useful, properties. Here we show through single crystal diffraction that the Eu ions in the mixed valent metal EuPd$_3$S$_4$ undergo long-range charge ordering at $T_{\mathrm{CO}} = 340 \mathrm{~K}$ resulting in simple cubic lattices of Eu$^{2+}$ ($J = 7/2$) and Eu$^{3+}$ ($J = 0$) ions. As only one of the two sublattices has a non-magnetic ground state, the charge order results in the emergence of remarkably simple G-type antiferromagnetic order at $T_{\mathrm{N}} = 2.85(6) \mathrm{~K}$, observed in magnetization, specific heat, and neutron diffraction. Application of a $0.3 \mathrm{~T}$ field is sufficient to induce a spin flop transition to a magnetically polarized, but still charge ordered, state. Density functional theory calculations show that this charge order also modifies the electronic degeneracies present in the material: without charge order, EuPd$_3$S$_4$ is an example of a double Dirac material containing 8-fold degenerate electronic states, greater than the maximum degeneracy of six possible in molecular systems. The symmetry reduction from charge order transmutes 8-fold double Dirac states into 4-fold Dirac states, a degeneracy that can be preserved even in the presence of the magnetic order. Our results show not only how charge order can be used to produce interesting magnetic lattices, but also how it can be used to engineer controlled degeneracies in electronic states.