Antiferromagnetic Structure of CrVO4and the Anhydrous Sulfates of Divalent Fe, Ni, and Co

The antiferromagnetic structures of CrV${\mathrm{O}}_4$, FeS${\mathrm{O}}_4$, NiS${\mathrm{O}}_4$, and CoS${\mathrm{O}}_4$ have been determined from neutron diffraction data collected from polycrystalline samples. All of these compounds have the same orthorhombic crystal structure. In this structure the magnetic ions form face-centered sheets which stack at $d_{002}$ intervals in the c direction. The magnetic structure found for CrV${\mathrm{O}}_4$ consists of ferromagnetically ordered sheets which stack antiferromagnetically. The single spin direction is found to be inclined at angles ${\Phi }_a=27\mathrm{}°\pm 15°$, ${\Phi }_b=64\mathrm{}°\pm 10°$, and ${\Phi }_c=81\mathrm{}°\pm 15°$ with the crystallographic axes. A somewhat more logical spin orientation, which is close to being within experimental error, would be parallel to the a axis. The ${\mathrm{Cr}}^{3+}$ moment at 4.2°K is $(2.1\mathrm{}\pm 0.2){\mu }_B$. The magnetic structures of FeS${\mathrm{O}}_4$ and NiS${\mathrm{O}}_4$ both have antiferromagnetic sheets with ferromagnetic coupling between the sheets. In both cases the spin direction is parallel to the b axis. The moments at 4.2°K are $(4.1\mathrm{}\pm 0.4){\mu }_B$ for ${\mathrm{Fe}}^{++}$, and $(2.1\mathrm{}\pm 0.1){\mu }_B$ for ${\mathrm{Ni}}^{++}$. In CoS${\mathrm{O}}_4$ there is also antiferromagnetic ordering within each sheet, but the coupling between sheets does not lead to a collinear spin structure. Instead there are two spin directions that alternate in successive sheets. The spin vectors are found to lie in the $\mathrm{YZ}$ plane at alternately clockwise and counter-clockwise angles of 25°±2° from the b axis as translations are made along the c axis. The ${\mathrm{Co}}^{++}$ moment at 4.2°K is $(3.3\mathrm{}\pm 0.2){\mu }_B$. This magnetic structure found for CoS${\mathrm{O}}_4$ is very similar to a structure predicted recently for Cu${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O by Moriya on the basis of anisotropic superexchange calculations.