New metastable phases in an oxyborate compound obtained by an evolutionary algorithm and Density Functional Theory

New metastable phases in the Fe homometallic ludwigite compound are obtained and studied using an evolutionary algorithm and Density Functional Theory. Our lowest energy monoclinic structure is identified as P21/m with space group number of 11. This structure evolves towards the monoclinic structure as the result of the spin orbit coupling and a particular zigzag magnetic structure. A zigzag distortion in a class of three-leg ladders follows similar to the experimental one observed below the transition temperature of Tc = 283 K. In this distortion long and short bonds inside rungs alternating in a zigzag way along the ladder legs. Furthermore, a new type of zigzag structural ordering is observed in other two low-energy phases analyzed. In this case, the magnetic ordering behaves qualitatively similar to the experimental structure at 82 K, with antiferromagnetically coupled ferromagnetic rungs. Our calculations show that magnetic symmetry is not favorable for zigzag structural ordering. Finally, structural and magnetic properties will be discussed in comparison with the experimentally known phases.