Geometry induced net spin polarization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> -wave altermagnets

We show that the shape of a finite altermagnetic sample can generate a measurable spin polarization, even though these materials exhibit zero net magnetization in the large-system limit. This effect arises from the interplay between anisotropic spin-resolved band structures and the discrete set of allowed electron states in confined geometries. For rectangular samples, unequal dimensions lead to an imbalance between spin populations. We propose transport-based probes to detect this geometry-induced spin polarization, which manifests as characteristic signatures in magnetoresistance. Our results reveal a simple and robust route to controlling spin using sample geometry alone, opening new possibilities for nanoscale spintronic devices based on altermagnets.