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: $\ensuremath{\sim}1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ for inorganic Mott insulators such as transition-metal oxides and $\ensuremath{\sim}0.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ 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 $\ensuremath{\propto}{|\mathbit{E}|}^{2/3}$ in the Heisenberg antiferromagnetic chain will reach $\ensuremath{\sim}10%$ of the dominant superexchange interaction in the case of a spin-chain compound ${\mathrm{KCuMoO}}_{4}(\mathrm{OH})$ when the DC electric field of $\ensuremath{\sim}1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ is applied.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: $\ensuremath{\sim}1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ for inorganic Mott insulators such as transition-metal oxides and $\ensuremath{\sim}0.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ 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 $\ensuremath{\propto}{|\mathbit{E}|}^{2/3}$ in the Heisenberg antiferromagnetic chain will reach $\ensuremath{\sim}10%$ of the dominant superexchange interaction in the case of a spin-chain compound ${\mathrm{KCuMoO}}_{4}(\mathrm{OH})$ when the DC electric field of $\ensuremath{\sim}1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ is applied.

arXiv:2102.04607Physical Review ResearchJul 19, 20218 citations

Total control over ultracold interactions via electric and magnetic fields

S. J. J. M. F. Kokkelmans, Bout Marcelis, BOUDEWIJN J. VERHAAR

Bulletin of the American Physical SocietyMay 29, 20080 citations

Control of magnetic and topological orders with a DC electric field

Kazuaki Takasan, Masahiro Sato

We theoretically propose a route to control magnetic and topological orders in a broad class of insulating magnets with a DC electric field. We show from the strong-coupling expansion that magnetic exchange interactions along the electric field direction are generally enhanced in Mott insulators. Employing this DC field effect, we demonstrate that several magnetic or topological ordered phases such as quantum spin liquids and Haldane-gap states can be induced if we apply a strong enough DC electric field to typical frustrated or low-dimensional magnets. Our proposal is effective especially for magnets in the vicinity of magnetic phase transition points, and would also be applicable for magnets under low-frequency AC electric fields such as terahertz laser pulses. A similar strategy of controlling exchange interactions can also be utilized in cold atomic systems.We theoretically propose a route to control magnetic and topological orders in a broad class of insulating magnets with a DC electric field. We show from the strong-coupling expansion that magnetic exchange interactions along the electric field direction are generally enhanced in Mott insulators. Employing this DC field effect, we demonstrate that several magnetic or topological ordered phases such as quantum spin liquids and Haldane-gap states can be induced if we apply a strong enough DC electric field to typical frustrated or low-dimensional magnets. Our proposal is effective especially for magnets in the vicinity of magnetic phase transition points, and would also be applicable for magnets under low-frequency AC electric fields such as terahertz laser pulses. A similar strategy of controlling exchange interactions can also be utilized in cold atomic systems.

arXiv:1802.04311Physical review. B./Physical review. BAug 21, 201918 citations

Atom–Field Interactions

André Xuereb

Springer thesesJan 1, 20120 citations

Electric field control of a quantum spin liquid in weak Mott insulators

Daniel J. Schultz, Alexandre Khoury, Félix Desrochers +3 more

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to on-site Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$ , which is difficult to tune with external stimuli. One approach to address this problem is applying a dc electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$ . Through density matrix renormalization group calculations, we compute the ground-state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$ . Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to on-site Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$, which is difficult to tune with external stimuli. One approach to address this problem is applying a dc electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$. Through density matrix renormalization group calculations, we compute the ground-state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.

arXiv:2309.00037Physical review. B./Physical review. BJun 17, 20246 citations

Atom–Field Interactions

Stephen Colby Rand

Oxford University Press eBooksJun 9, 20160 citations

{\mathrm{KCuMoO}}_{4}(\mathrm{OH})

when the DC electric field of $\ensuremath{\sim}1\phantom{\rule{3.33333pt}{0ex}}\mathrm{MV}/\mathrm{cm}$ is applied.

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping

t

to on-site Coulomb repulsion

U

is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of

t/U

, which is difficult to tune with external stimuli. One approach to address this problem is applying a dc electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small

t/U

expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant

t/U

. Through density matrix renormalization group calculations, we compute the ground-state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of

t/U

. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field.