Neutron scattering study of the magnetic transition in $\left({\mathrm{Ho}}_{1-x}{\mathrm{Er}}_x\right){\mathrm{Rh}}_4{\mathrm{B}}_4$ alloys

Using neutron scattering techniques we have examined the magnetic transitions for compounds in the $\left({\mathrm{Ho}}_{1-x}{\mathrm{Er}}_x\right){\mathrm{Rh}}_4{\mathrm{B}}_4$ pseudoternary system. We find a wide variety of behavior ranging from mean-field behavior for Ho${\mathrm{Rh}}_4$ ${\mathrm{B}}_4$ to complicated behavior with more than one type of ordering for ${\mathrm{Ho}}_{0.3}$ ${\mathrm{Er}}_{0.7}$ ${\mathrm{Rh}}_4$ ${\mathrm{B}}_4$. Our results for the pseudoternary compounds are consistent with a model in which Ho orders along the $c$ axis with nearly its free-ion moment, while ER orders in the basal plane, but with a moment reduced from the free-ion value. Ordering along the $c$ axis results in the destruction of superconductivity in a sharp transition at the same temperature that a sharp spike appears in the heat capacity. Because Ho and Er have competing orthogonal magnetic anisotropies, pseudoternary compounds near the composition ${\mathrm{Ho}}_{0.3}$ ${\mathrm{Er}}_{0.7}$ ${\mathrm{Rh}}_4$ ${\mathrm{B}}_4$ are near a multicritical point in the magnetic phase diagram.