Inverse Single-sided Magnet

A single-sided magnet generates a magnetic field on only one side while canceling it on the opposite side, a feature that has enabled diverse applications in both fundamental science and engineering. Here, we propose the {\it inverse} single-sided magnet: a non-ferromagnetic system that selectively attracts either the north or south pole of a ferromagnet while remaining unresponsive to the opposite pole. We demonstrate that such behavior can arise in microscopic octupolar magnets. To illustrate this, we analyze two minimal models: a coplanar magnetic structure with 120-degree ordering and a collinear magnetic structure with site-dependent anisotropy. In both cases, we find that the magnetization response is nonreciprocal with respect to the sign of the applied magnetic field. Notably, in the latter model, the system exhibits strong magnetization in one field direction and negligible response in the opposite direction. This diode-like behavior for magnetic fields suggests that inverse single-sided magnets could play a pivotal role in controlling magnetic interference, with potential impact comparable to conventional single-sided magnets.