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Enhanced Seebeck coefficient through the magnetic fluctuations in Sr$_2$Ru$_{1-x}M_x$O$_4$ ($M = $ Co, Mn)

The layered perovskite Sr$_2$RuO$_4$ is a most intensively studied superconductor, but its pairing mechanism, which is often coupled intimately with magnetic fluctuations in correlated materials, is still an open question. Here we present a systematic evolution of the Seebeck coefficient in Co- and Mn-substituted Sr$_2$RuO$_4$ single crystals, in which ferromagnetic and antiferromagnetic glassy states respectively emerge in proximity to the superconducting phase of the parent compound. We find that the Seebeck coefficient $S$ divided by temperature $T$, $S/T$, shows a maximum near characteristic temperatures seen in the irreversible magnetization $M_{\rm ir}$ in both of the Co- and Mn-substituted crystals, demonstrating both of the ferromagnetic and antiferromagnetic fluctuations to enhance the Seebeck coefficient. Interestingly, $S/T$ increases with lowering temperature in the parent compound, reminiscent of non-Fermi-liquid behavior, indicating an essential role of coexisting ferromagnetic and antiferromagnetic fluctuations for the itinerant electrons in Sr$_2$RuO$_4$.