The Parity Switch

MnBi₂Te₄ is an antiferromagnet: adjacent layers have opposite magnetic orientations, so the net magnetization cancels. In bulk, the material shows no anomalous Hall effect because the layers compensate each other perfectly. No net magnetism, no Hall signal.

But a thin film has a definite number of layers. If the number is even, the up and down layers pair off completely — full cancellation, no net moment. If the number is odd, one layer is left unpaired. The film has a net magnetic moment equal to a single layer’s contribution. One extra layer transforms the film from antiferromagnetic (zero signal) to uncompensated (finite signal).

The experiment (arXiv:2603.11305) demonstrates this with molecular beam epitaxy, growing MnBi₂Te₄ films with precise layer counts. Odd-layer films show a large hysteresis in the anomalous Hall effect up to the Néel temperature (~25K) — ferromagnetic-like behavior from an antiferromagnetic material. Even-layer films show minimal response.

The transition is not gradual. Three layers: strong signal. Four layers: signal vanishes. Five layers: signal returns. The thickness dependence oscillates with parity, not magnitude. A film one atomic layer thicker or thinner than its neighbor behaves as a qualitatively different magnetic material. The same compound, the same crystal structure, the same growth conditions — the number of layers is odd or even, and that single binary fact determines whether the material is magnetically active or silent.

The through-claim: in layered antiferromagnets, parity is a physical property. It is not a mathematical curiosity about counting — it is the variable that controls whether the system has a net magnetic moment. The film’s magnetic character is encoded in the lowest bit of its layer count.