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Why do spinel ferrites have a permanent magnetic moment?

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Spinel ferrites exhibit a permanent magnetic moment due to a phenomenon known as ferrimagnetism. Unlike ferromagnetic materials, where atomic magnetic moments align in the same direction, ferrites contain multiple sublattices of magnetic ions that align in opposite, or antiparallel, directions.12

In spinel ferrites, which follow the general formula $M F e_{2} O_{4}$ , the magnetic moments of the constituent metal ions do not cancel each other out completely because the moments on the different sublattices are unequal in size. This asymmetry—often caused by the presence of different types of magnetic ions or the specific spinel crystalline structure—results in a net spontaneous magnetization.324

For example, in magnetite ( $F e_{3} O_{4}$ ), the trivalent iron ions align in opposite directions and cancel each other out, leaving the divalent iron ions to account for the material's overall magnetic field. Because this alignment is spontaneous below the Curie point, these materials maintain a permanent magnetic moment despite the partial cancellation of their internal fields.132