Antisymmetric exchange in the $\mathrm{CuB_2O_4}$ $\mathrm{А}$ subsystem

The space distribution of the components of the microscopic Hamiltonian of the antisymmetric Dzyaloshinskii-Moriya exchange with respect to the exchange bond pairs of the A subsystem of Cu²⁺ ions in the crystallographic 4b positions of CuB₂O₄ has been obtained using symmetry analysis. The possibility of the coexistence of two different types of the exchange spatial distribution is demonstrated. The component of the antisymmetric exchange vector D parallel to the tetragonal axis has a weakly ferromagnetic distribution for all of the directions of the bonds between the nearest magnetic neighbors. Each exchange bond has an additional component of the antisymmetric exchange parallel to the bond projection on the tetragonal plane. The spatial distribution of these components is helicoidal with the modulation vector in the tetragonal crystal plane.