Surface magnetoelectric (ME) coupling is conventionally attributed to strong spin-orbit coupling (SOC) or interface-induced polarization and is therefore considered strongly limited in centrosymmetric antiferromagnets. Here we show, theoretically, that rutile-type transition-metal fluorides ${M\mathrm{F}}_2$ ($M=\mathrm{V}$, Mn, Fe, Co, Ni) can exhibit a linear ME response at the (110) surface even in the absence of SOC, enabled by the interplay between bulk magnetic octupolar order and surface symmetry breaking. Our first-principles calculations reveal that ferroically ordered bulk magnetic octupoles in ${M\mathrm{F}}_2$ provide the symmetry prerequisite for a linear surface ME effect. The magnitude of this surface ME coupling is primarily governed by the magnetic exchange energy scale and the extent of interfacial electronic reconstruction. Specifically, in ${\mathrm{VF}}_2$ and ${\mathrm{CoF}}_2$, relatively weak exchange splitting generates pronounced $d$-orbital surface states near the Fermi level, yielding large displacement-induced surface magnetoelectric coefficients ${\lambda }^{\mathrm{surf}}$. In contrast, the strong exchange splitting in ${\mathrm{MnF}}_2$ and ${\mathrm{FeF}}_2$ maintains an insulating surface character and substantially suppresses ${\lambda }^{\mathrm{surf}}$. ${\mathrm{NiF}}_2$, featuring nearly degenerate $d^8$ spin configurations (i.e., an electronic configuration with eight electrons occupying the Ni $3d$ orbitals), further displays nonlinear magnetic reconstruction under small perturbations. These findings establish a general mechanism of “exchange-controlled surface magnetoelectricity” in rutile ${M\mathrm{F}}_2$ compounds, clarify that bulk octupoles act as a symmetry prerequisite rather than the primary determinant of the response amplitude, and render this ${M\mathrm{F}}_2$ family a promising platform for designing tunable, multipole-driven surface ME functionalities.

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• Electronic structure
• Magnetoelectric effect
• Magnetic thin films
• Density functional calculations