Determination of the magnetic order and the crystal symmetry in the multiferroic ground state of Ba 2CoGe 2O 7

Detailed structural investigation of Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ was performed in its low-temperature multiferroic state combining neutron diffraction with magnetization measurements and the optical study of lattice vibrations on single crystals. The crystal structure above (10.4 K) and the crystal and magnetic structures below (2.2 K) the antiferromagnetic transition temperature of ${T}_{N}$ $=$ 6.7 K were determined using neutron diffraction. The tetragonal space group (SG) $P$-42${}_{1}m$, corresponding to the average structure at room temperature, was found to also describe the structure at low temperatures well. Neutron diffraction data and infrared phonon mode analysis imply no structural phase transition down to 2.2 K. Orthorhombic polar SG Cmm2 is proposed as a true crystal structure. Below ${T}_{N}$, the spins of the Co${}^{2+}$ ions form a square-lattice N\'eel order within the ($a$,$b$) plane, while their alignment is ferromagnetic along the $c$ axis. The magnitude of the ordered moment, fully lying within the ($a$,$b$) plane, is found to be 2.9(1) ${\ensuremath{\mu}}_{B}$/Co${}^{2+}$ and the easy axis of the sublattice magnetizations corresponds to the [110] direction. A noncollinear spin structure due to small canting is allowed.