Structure, magnetic, and ferroelectric properties of multiferroic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>GdCrO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math>

We investigate the structure, magnetic, and ferroelectric properties of orthochromite ${\mathrm{GdCrO}}_{3}$ using density functional theory simulations. Structure relaxation with the experimental lattice found centrosymmetric Pbnm and $P{2}_{1}/c$ phases together with noncentrosymmetric $Pna{2}_{1}$ and $\mathit{Pc}$ phases, and corresponding atom coordinates were calculated. The $Pna{2}_{1}$ phase was found to be the ground state structure responsible for a 0.12 $\textmu{}{\mathrm{C}/\mathrm{cm}}^{2}$ spontaneous polarization. We found that both the Cr and Gd moments are antiferromagnetic aligned with G-type antiferromagnetism for Cr, while, intriguingly, the Gd sublattice was found to be C type antiferromagnetic. The antiferromagnetic N\'eel temperature was estimated to be 170.10 K for Cr and 4.74 K for Gd; spin moments calculated with spin-orbit coupling remained C type antiferromagnetic for the Gd sublattice with the spins canting in other directions. Our results not only agree well with recent experimental results and Bertaut's spin transformation theory but also reveal the fundamental relations of magnetic and ferroelectric properties of multiferroic ${\mathrm{GdCrO}}_{3}$.