Abstract
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.
Highlights
Controlling quantum states of matter has been a longstanding subject of condensed-matter physics and other related fields
The synthesis of a compound that faithfully realizes the theoretical model does not mean realizing the quantum phase of our interest, which depends on the parameters of the compound
Microscopic DC electric-field controls, which should be theoretically simpler than AC ones, are less considered in quantum spin systems partly because these systems are usually realized in Mott insulators where the charge degree of freedom is frozen
Summary
Controlling quantum states of matter has been a longstanding subject of condensed-matter physics and other related fields. The Floquet engineering has been discussed in quantum magnetism [25,27,28,29,30,31,32,33,34,35,36] Despite these recent developments, microscopic DC electric-field controls, which should be theoretically simpler than AC ones, are less considered in quantum spin systems partly because these systems are usually realized in Mott insulators where the charge degree of freedom is frozen. The DC electric field affects the Hamiltonian of quantum spin systems, as shown, because the exchange interaction has an electronic origin. This paper develops a theory of DC electric-field controls of superexchange interactions in geometrically frustrated quantum spin systems, starting from simple electron models.
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