Altermagnetism, characterized by pronounced momentum-space spin splitting without net magnetization, provides an emerging platform for spintronics. Yet nonvolatile control of its spin states remains a key challenge for device application. Here, we demonstrate that antiferroelastic lattice distortions offer a universal structural mechanism for controlling altermagnetism by directly locking the momentum-space spin texture to the antiferroelastic structural order parameter $\eta$. In contrast to ferroelastic distortions, which involve uniform strain, antiferroelasticity consists of oppositely staggered lattice distortions with zero macroscopic strain, analogous to antiferroelectricity (zero net polarization) or antiferromagneticity (zero net magnetization), thereby introducing a hidden structural degree of freedom. Reversal of $\eta$ ($+\eta \to -\eta$) enforces inversion of the altermagnetic spin splitting without Néel vector reversal or net magnetization, providing a low-energy pathway for nonvolatile control. Guided by this principle, we identify a family of antiferroelastic altermagnets, spanning from two-dimensional monolayers (e.g., $\mathrm{Cr}{\mathrm{S}}_3$) to three-dimensional compounds (e.g., $\mathrm{N}{\mathrm{a}}_3\mathrm{Mn}{\mathrm{S}}_4$). Both $\mathrm{Cr}{\mathrm{S}}_3$ and $\mathrm{N}{\mathrm{a}}_3\mathrm{Mn}{\mathrm{S}}_4$ exhibit robust lattice-spin coupling, where biaxial strain triggers antiferroelastic phase transitions accompanied by an inversion of spin-splitting energy (about 396 meV for $\mathrm{Fe}{\mathrm{S}}_2$). Our results establish antiferroelasticity as a general materials design paradigm for strain-driven switchable altermagnets and open avenues for nonvolatile-control spintronic devices.

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• Magnetism
• Spintronics
• Altermagnets
• Multiferroics
• Density functional theory
• First-principles calculations