The centrosymmetric tetragonal itinerant magnet ${\mathrm{EuAl}}_4$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of ${\mathrm{EuAl}}_4$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim 0.10$% and $\sim 0.03$% orthorhombic structural distortion within the $ab$ plane, respectively. We propose that the coupling between the spin system and the lattice deformation should be essential for the structural instability in ${\mathrm{EuAl}}_4$, yielding a rich variety of topological spin textures with spontaneous rotational-symmetry breaking as well as a potential controllability of the SkL phases by uniaxial stress or pressure.

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• Magnetic texture
• Helimagnets
• Thermodilatometry