Altermagnetism as a new concept in condensed matter physics is currently being thoroughly investigated. Despite the absence of macroscopic magnetization, altermagnets host a hidden spin order whose direct detection remains a challenge. Here, we report on the observation of electric-dipole forbidden optical second-harmonic generation (SHG) in the altermagnet ${\mathrm{CoF}}_2$ with a centrosymmetric lattice and spin order. We demonstrate that below the Néel temperature $T_N=38\mathrm{K}$, the SHG signal is sensitive to the ferro-type magnetic octupole ${\mathcal{O}}^M$, which is the order parameter in the antiferromagnetic phase. By combining polarization-resolved SHG experimental data and a phenomenological symmetry analysis, we show that the altermagnetic spin structure of ${\mathrm{CoF}}_2$ enables a ferroic-octupole-induced electric-quadrupolar nonlinear polarization ${\mathbf{P}}^{2\omega }=\mathrm{i}{ϵ}_0^c{\mathit{\chi }}^{(3)}({\mathcal{O}}^M):{\mathbf{E}}^{\omega }\nabla {\mathbf{E}}^{\omega }$. The temperature dependence of SHG reveals a phase transition at $T_N$, confirming the spin origin of the observed signal. The SHG response is resonantly enhanced by a coherent three-photon process caused by the electronic $d\text{−}d$ transitions of the ${\mathrm{Co}}^{2+}$ ion. Model calculations of SHG polarization rotational anisotropies and temperature dependencies give a reasonable agreement with experimental data, proving the disclosed nonlinear contribution. Our results establish SHG as a novel sensitive tool of ferroic-octupolar spin ordering and highlight the potential of ${\mathrm{CoF}}_2$ and other altermagnets for further nonlinear optical investigations and applications.

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• Electronic structure
• Magnetism
• Optical & microwave phenomena
• Optical second-harmonic generation