Magnetoelectric effect in a single crystal of the frustrated spinel Co Al 2 O 4

The magnetic ground state of $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ has been a controversial issue because the ratio of nearest- (${J}_{1}$) to next-nearest-neighbor (${J}_{2}$) exchange interactions in the diamond lattice is close to the boundary between a spiral spin liquid and a long-range ordered antiferromagnetic ground state. Recently, Ghara et al. reported a linear magnetoelectric effect in a polycrystalline $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ and attributed it to a long-range magnetic order. However, the magnetic ground state and the easy axis anisotropy remained unsolved. Here we propose the easy magnetic axis direction by comparing the results of magnetoelectric measurements in a high-quality single crystal with phenomenological calculations. From the value of polarization ratio $P||[1\text{\ensuremath{-}}10]$ measured under magnetic field applied along $H||[1\text{\ensuremath{-}}10]$ and $H||[001]$, we determined that the magnetic easy axis is along [111]. The single ion contribution of the magnetic ions located at the noncentrosymmetric environment is responsible for the magnetoelectric effect similar to that observed in other $A$-site magnetic spinel oxides, ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$, $\mathrm{Mn}{B}_{2}{\mathrm{O}}_{4}$ ($B=\mathrm{Al},\phantom{\rule{0.16em}{0ex}}\mathrm{Ga}$).