Complex antiferromagnetic order in the garnet Co 3 Al 2 Si 3 O 12

We studied the magnetic properties of the garnet $\mathrm{C}{\mathrm{o}}_{3}\mathrm{A}{\mathrm{l}}_{2}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{O}}_{12}$ synthesized under 5.5 GPa and 1250 \ifmmode^\circ\else\textdegree\fi{}C by means of dc magnetic susceptibility, neutron powder diffraction, and specific heat. Although the magnetic $\mathrm{C}{\mathrm{o}}^{2+}$ ions form a geometrically frustrated hyper-Kagome lattice, we find that $\mathrm{C}{\mathrm{o}}_{3}\mathrm{A}{\mathrm{l}}_{2}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{O}}_{12}$ exhibits a long-range antiferromagnetic order below ${T}_{\mathrm{N}}=11\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ without showing magnetic frustration, i.e., the frustration index $f\ensuremath{\equiv}|{\ensuremath{\theta}}_{\mathrm{CW}}/{T}_{N}|$ is close to unity. Refinements from neutron-diffraction data show that $\mathrm{C}{\mathrm{o}}_{3}\mathrm{A}{\mathrm{l}}_{2}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{O}}_{12}$ forms a complex antiferromagnetic structure characterized by the coexistence of collinear and commensurate spiral magnetic ordering of $\mathrm{C}{\mathrm{o}}^{2+}$ sublattices. Magnetic field induced spin-flop transition at ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}4\mathrm{T}$ was also observed below ${T}_{\mathrm{N}}$.