Weak ferromagnetism and spin reorientation in antiferroelectric BiCrO3

${\mathrm{BiCrO}}_{3}$ is an antiferroelectric perovskite known to exhibit an unconventional spin reorientation transition between antiferromagnetic structures, accompanied by a large jump in weak ferromagnetism. Using a combination of neutron powder diffraction, magnetometry, and symmetry analysis, we confirm the dominant G-type antiferromagnetic order below ${T}_{\mathrm{N}}=111$ K and identify the magnetic phase transition with a spontaneous rotation of ${\mathrm{Cr}}^{3+}$ moments from the $b$ axis to a particular direction in the $ac$ plane. We demonstrate the role of antiferroelectric displacements produced by the ${\mathrm{Bi}}^{3+}$ lone-pair electrons and octahedral rotations in establishing spin canting via the antisymmetric Dzyaloshinskii-Moriya interaction. This mechanism results in weak ferromagnetism above and below the spin-reorientation and explains the dramatic increase in net magnetization on cooling.