Relieving the frustration through Mn$^{3+}$ substitution in Holmium Gallium Garnet

We present a study on the impact of Mn$^{3+}$ substitution in the geometrically frustrated Ising garnet Ho$_3$Ga$_5$O$_{12}$ using bulk magnetic measurements and low temperature powder neutron diffraction. We find that the transition temperature, $T_N$ = 5.8 K, for Ho$_3$MnGa$_4$O$_{12}$ is raised by almost 20 when compared to Ho$_3$Ga$_5$O$_{12}$. Powder neutron diffraction on Ho$_3$Mn$_x$Ga$_{5-x}$O$_{12}$ ($x$ = 0.5, 1) below $T_N$ shows the formation of a long range ordered ordered state with $\mathbf{k}$ = (0,0,0). Ho$^{3+}$ spins are aligned antiferromagnetically along the six crystallographic axes with no resultant moment while the Mn$^{3+}$ spins are oriented along the body diagonals, such that there is a net moment along [111]. The magnetic structure can be visualised as ten-membered rings of corner-sharing triangles of Ho$^{3+}$ spins with the Mn$^{3+}$ spins ferromagnetically coupled to each individual Ho$^{3+}$ spin in the triangle. Substitution of Mn$^{3+}$ completely relieves the magnetic frustration with $f = \theta_{CW}/T_N \approx 1.1$ for Ho$_3$MnGa$_4$O$_{12}$.