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We perform magnetic susceptibility and magnetic torque measurements on theorganic $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Br, which is recently suggested tohost an exotic quantum dipole-liquid in its low-temperature insulating phase.Below the metal-insulator transition temperature, the magnetic susceptibilityfollows a Curie-Weiss law with a positive Curie-Weiss temperature, and aparticular $M\propto \sqrt{H}$ curve is observed. The emergentferromagnetically interacting spins amount to about 1/6 of the full spin momentof localized charges. Taking account of the possible inhomogeneousquasi-charge-order that forms a dipole-liquid, we construct a model ofantiferromagnetically interacting spin chains in two adjacent charge-ordereddomains, which are coupled via fluctuating charges on a Mott-dimer at theboundary. We find that the charge fluctuations can draw a weak ferromagneticmoment out of the spin singlet domains.

Ferromagnetism out of charge fluctuation of strongly correlated electrons in $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Br