Control of superexchange interactions with DC electric fields

We discuss DC electric-field controls of superexchange interactions. We first present generic results about antiferromagnetic and ferromagnetic superexchange interactions valid in a broad class of Mott insulators, where we also estimate typical field strength to observe DC electric-field effects: $\sim 1~\mathrm{MV/cm}$ for inorganic Mott insulators such as transition-metal oxides and $\sim 0.1~\mathrm{MV/cm}$ for organic ones. Next, we apply these results to geometrically frustrated quantum spin systems. Our theory widely applies to (quasi-)two-dimensional and thin-film systems and one-dimensional quantum spin systems on various lattices such as square, honeycomb, triangular, and kagome ones. In this paper, we give our attention to those on the square lattice and on the chain. For the square lattice, we show that DC electric fields can control a ratio of the nearest-neighbor and next-nearest-neighbor exchange interactions. In some realistic cases, DC electric fields make the two next-nearest-neighbor interactions nonequivalent and eventually turns the square-lattice quantum spin system into a deformed triangular-lattice one. For the chain, DC electric fields can induce singlet-dimer and Haldane-dimer orders. We show that the DC electric-field-induced spin gap $\propto |\boldsymbol E|^{2/3}$ in the Heisenberg antiferromagnetic chain will reach $\sim 10~\%$ of the dominant superexchange interaction in the case of a spin-chain compound $\mathrm{KCuMoO_4(OH)}$ when the DC electric field of $\sim 1~\mathrm{MV/cm}$ is applied.