Microscopic origin of piezomagnetism in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Mn</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>Sn</mml:mi> </mml:mrow> </mml:math> : A dual real- and <mml:math xmlns:

We present a comprehensive first-principles study on the origin of the piezomagnetic effect in the noncollinear antiferromagnet ${\mathrm{Mn}}_{3}\mathrm{Sn}$, a material known for exhibiting a large anomalous Hall effect. We investigate stress-induced variations of electronic and magnetic states and elucidate the mechanism of the piezomagnetic effect from both real-space and wave-number space perspectives. In real space, the emergence of piezomagnetism is understood to arise from rotations of the magnetic moments at specific Mn sites, which directly couple to the strain. Through detailed electronic structure analysis, we identify the Fermi surfaces that play a crucial role in the emergence of piezomagnetism. Our results reveal that pseudodegenerate Fermi surfaces are lifted under applied stress, which significantly contributes to the induced net magnetization. By combining these complementary real-space and $k$-space pictures, our dual-space analysis provides deep insight into the microscopic origins of stress-driven magnetization in ${\mathrm{Mn}}_{3}\mathrm{Sn}$.