Interdependence of Magnetism and Superconductivity in the Borocarbide ${\mathrm{TmNi}}_2{B}_{2}C$

We have discovered a new antiferromagnetic phase in ${\mathrm{TmNi}}_2{\mathrm{B}}_2\mathrm{C}$ by neutron diffraction. The ordering vector is ${\mathit{Q}}_A=(0.48,0,0)$ and the phase appears above a critical in-plane magnetic field of 0.9 T. The field was applied in order to test the assumption that the zero-field magnetic structure at ${\mathit{Q}}_F=(0.094,0.094,0)$ would change into a $c$-axis ferromagnet if superconductivity were destroyed. We present theoretical calculations which show that two effects are important: a suppression of the ferromagnetic component of the RKKY exchange interaction in the superconducting phase and a reduction of the superconducting condensation energy due to the periodic modulation of the moments at ${\mathit{Q}}_A$.