The preferred orientation of Mn3 spins in magnetic multiferroic CaMn7O12

• In CaMn7O12, the preferred orientation angle of the Mn3 spins remains controversial.
• The relative orientation angle between Mn3 and Mn2 spins should be 0.84π instead of π.
• For ϕ=π, phase transition path and polarization are inconsistent with experiments.
• The reason for observation of ϕ=π is due to Cu2+-doping in the experimental samples.

The remarkable ferroelectricity in CaMn7O12 originates from the helicoidal spin spiral, in which the Mn3 (3b Wyckoff position) spin direction remains controversial. In this paper, the total energy, phase transition path, and spontaneous polarization of CaMn7O12 are investigated by using first-principle methods. We show that, in order to account for the giant electric polarization and the correct phase transition sequence, the relative orientation between the spins of Mn3 and Mn2 (9d Wyckoff position) sites with the same coordinate along the hexagonal c-axis can not be antiparallel, i.e. their relative orientation angle should be ϕ≈0.84π instead of ϕ=π. The most likely reason for the observation of ϕ=π can be attributed to the withdrawal of spin–orbital coupling between the Mn2 and Mn3 spins, which is caused by doping Cu2+ in the samples for neutron powder diffraction measurements.