Altermagnetism — a recently identified magnetic state with zero net magnetization but momentum-dependent spin splitting — has been classified by crystal symmetry. Group theory tells you which space groups permit it: the crystal's symmetry operations must connect opposite-spin sublattices while breaking time-reversal in momentum space. The approach is top-down: start from symmetry, deduce which materials qualify.
Mandal, Das, and Nanda (arXiv:2501.00453) flip this around. Instead of asking which symmetries permit altermagnetism, they ask which chemical bonds create it. Using NiS as a correlated electron system, they derive selection rules from the bonding rather than the symmetry.
The key finding: when a single orbital participates in bonding, second-neighbor interactions between the nonmagnetic atoms are necessary to produce altermagnetic spin splitting. When multiple orbitals bond, altermagnetism emerges naturally without this requirement. The nonmagnetic atoms — the ones you'd normally ignore when studying magnetism — control whether the magnetic splitting appears.
The structural insight: symmetry tells you what's allowed; bonding tells you what happens. A material can have the right symmetry for altermagnetism but the wrong bonding, producing zero spin splitting. The symmetry approach sets the menu; the bonding approach orders from it. In NiS, the spin splitting exceeds 1 eV when electron correlations are included — a large effect hidden by the conventional symmetry analysis, which doesn't predict magnitudes.
The magnetic property is determined by bonds between non-magnetic atoms. The actors on stage are not the ones controlling the scene.