Magnetic structure of the magnetoelectric material Ca$_{2}$CoSi$_{2}$O$_{7}$

Detailed investigation of Ca$_{2}$CoSi$_{2}$O$_{7}$ was performed in its low-temperature magnetoelectric state combining neutron diffraction with magnetization measurements on single crystals. The crystal and magnetic structures well below the antiferromagnetic transition temperature of TN≈5.7 K were determined using neutron diffraction. Neutron diffraction data imply no structural phase transition from 10 K down to 2.5 K and are well described within the orthorhombic space group P21212 with a 3×3×1 supercell compared with the high-temperature unmodulated state (tetragonal space group P¯421m). We found that in zero magnetic field the magnetic space group is P212′12′ with antiferromagnetic order along the [100] or [010] axes for two types of 90∘ twin domains, while neighboring spins along the [001] axis are ordered ferromagnetically. A noncollinear spin arrangement due to small canting within the ab plane is allowed by symmetry and leads to the existence of the tiny spontaneous magnetization below TN. The ordered moment with a magnitude of about 2.8 μB/Co$_{2}$+ at 2.5 K lies in the ab plane. Distinct differences between the magnetic structure of Ca$_{2}$CoSi$_{2}$O$_{7}$ as compared to those of Ba$_{2}$CoGe$_{2}$O$_{7}$ and Sr$_{2}$CoSi$_{2}$O$_{7}$ are discussed.