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Constraints on exotic dipole-dipole couplings between electrons at the micrometer scale

New constraints on exotic dipole-dipole interactions between electrons at the micrometer scale are established, based on a recent measurement of the magnetic interaction between two trapped $^{88}$Sr$^+$ ions. For light bosons (mass $\le$ 0.1 eV) we obtain a $90\%$ confidence interval on axial-vector mediated interaction strength of $\left|g_A^eg_A^e/4π\hbar c\right|\le 1.2\times 10^{-17}$. Assuming CPT invariance, this constraint is compared to that on anomalous electron-positron interactions, derived from positronium hyperfine spectroscopy. We find that the electron-electron constraint is six orders of magnitude more stringent than the electron-positron counterpart. Bounds on pseudo-scalar mediated interaction as well as on torsion gravity are also derived and compared with previous work performed at different length scales. Our constraints benefit from the high controllability of the experimental system which contained only two trapped particles. It therefore suggests a useful new platform for exotic particle searches, complementing other experimental efforts.