Octahedral antiferromagnets are distinguished by crystal lattices composed of octahedra of magnetic ions. In the fully frustrated case, the Heisenberg Hamiltonian can be represented as a sum of squares of total spins for each octahedral block. We study the fully frustrated spin model for a lattice of edge-shared octahedra, which corresponds to the $J_1–J_2$ fcc antiferromagnet with $J_2/J_1=1/2$. The magnetization process at this strongly frustrated point features a remarkably rich sequence of different magnetic phases that include fractional plateaus at $m=1/3$ and $2/3$ values of the total magnetization. By performing extensive Monte Carlo simulations, we construct the $H–T$ phase diagram of the classical model with eight field-induced states, which acquire stability via the order by disorder mechanism. These antiferromagnetic states have distinct spin configurations of their octahedral blocks. The same spin configurations are also relevant for the fully frustrated corner-shared model, bringing an apparent similarity to their field-induced states.

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• Frustrated magnetism
• Antiferromagnets
• Magnetic systems
• Noncollinear magnets
• Heisenberg model
• Monte Carlo methods