The cubic perovskite ${\mathrm{SrFeO}}_3$ is a prototypical centrosymmetric itinerant magnet that hosts a quadruple-$\mathbf{Q}$ hedgehog-antihedgehog lattice and exhibits a complex magnetic-field–temperature phase diagram. Yet, the microscopic mechanism underlying the emergence of its versatile multiple-$\mathbf{Q}$ phases remains unresolved. Here, we reveal the field-orientation dependence of the magnetic phase diagram and establish an effective spin Hamiltonian for ${\mathrm{SrFeO}}_3$ that incorporates a cubic single-ion anisotropy together with bilinear and biquadratic interactions in momentum space, which originate from the spin-charge coupling. In addition, we observe magnetoelastic signatures of a redistribution of the ligand-hole density upon entering the forced ferromagnetic phase. These findings are consistent with an important role of electronic itinerancy associated with the formation of a ligand-hole band in stabilizing multiple-$\mathbf{Q}$ phases.

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• High magnetic fields
• Magnetic phase transitions
• Magnetic texture
• Strongly correlated systems
• Monte Carlo methods
• Ultrasound techniques