Using a system for measuring magnetization under stress, we revisit the piezomagnetic effect in rutile fluorides, ${\mathrm{MnF}}_2$ and ${\mathrm{CoF}}_2$. We succeed in observing a monotonic increase in the magnetization in response to stress application. The powder-averaged piezomagnetic tensors are estimated to be $Q_{\mathrm{ave}}=\hspace{0.17em}3.7\times {10}^{-4}\mathrm{emu}\text{/}\mathrm{mol}\text{/}\mathrm{MPa}$ for ${\mathrm{MnF}}_2$ and $8.3\times {10}^{-2}$ emu/mol/MPa for ${\mathrm{CoF}}_2$, where the value for ${\mathrm{CoF}}_2$ is two orders of magnitude larger than that for ${\mathrm{MnF}}_2$. We discuss the microscopic mechanism of the piezomagnetic effect in terms of the $g$-tensor anisotropy, the single-ion anisotropy, and the Dzyaloshinskii-Moriya interaction, all of which are associated with the electronic transition via the spin-orbit interaction. The observed larger piezomagnetic tensor components in ${\mathrm{CoF}}_2$ are well interpreted in this formalism. We also observe spontaneous magnetization in ${\mathrm{CoF}}_2$, which exists even at zero stress. We argue that the observed weak ferromagnetism originates from Jahn-Teller distortions caused by orbital degeneracy in ${\mathrm{Co}}^{2+}$ ions.

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• Dzyaloshinskii-Moriya interaction
• Spin-orbit coupling
• Stress
• Fluorite structure
• Magnetization measurements