Magnetic anomalies associated with slowly cooled igneous and metamorphic rocks are commonly attributed to the presence of the mineral magnetite. Although the intermediate members of the ilmenite-haematite mineral series can also carry a strong ferrimagnetic remanence, it is preserved only in rapidly cooled volcanic rocks, where formation of intergrowths of weakly magnetic haematite and paramagnetic ilmenite is suppressed. But the occurrence of unusually large and stable magnetic remanence in rocks containing such intergrowths has been known for decades, and has recently been the subject of intense investigation. These unmixed oxide phases have been shown to contain pervasive exsolution lamellae with thickness from 100 μm down to about 1 nm (one unit cell). These rocks, many of which contain only a few per cent of such oxides, show natural remanent magnetizations up to 30Am−1 - too strong to be explained even by pure haematite in an unsaturated state. Here we propose a new ferrimagnetic substructure created by ferrous-ferric 'contact layers' that reduce charge imbalance along lamellar contacts between antiferromagnetic haematite and paramagnetic ilmenite. We estimate that such a lamellar magnetic material can have a saturation magnetization up to 55 kA m−1 - 22 times stronger than pure haematite-while retaining the high coercivity and thermal properties of single-domain haematite.