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arXiv:2109.01940 · Physical review. B./Physical review. B

Inverse Faraday effect in Mott insulators

Saikat Banerjee, Umesh Kumar, Shi‐Zeng Lin

Published May 31, 2022• 32 citations
arXivHTMLPDF

Abstract

The inverse Faraday effect (IFE), where a static magnetization is induced by circularly polarized light, offers a promising route to ultrafast control of spin states. Here we study the IFE in Mott insulators using the Floquet theory. We find two distinct IFE behavior governed by the inversion symmetry. In the Mott insulators with inversion symmetry, we find that the effective magnetic field induced by the IFE couples ferromagnetically to the neighboring spins. While for the Mott insulators without inversion symmetry, the effective magnetic field due to IFE couples antiferromagnetically to the neighboring spins. We apply the theory to the spin-orbit coupled single- and multiorbital Hubbard model that is relevant for the Kitaev quantum spin liquid material and demonstrate that the magnetic interactions can be tuned by light.

DOI
10.1103/physrevb.105.l180414

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The inverse Faraday effect (IFE), where a static magnetization is induced by circularly polarized light, offers a promising route to ultrafast control of spin states. Here we study the IFE in Mott insulators using the Floquet theory. We find two distinct IFE behavior governed by the inversion symmetry. In the Mott insulators with inversion symmetry, we find that the effective magnetic field induced by the IFE couples ferromagnetically to the neighboring spins. While for the Mott insulators without inversion symmetry, the effective magnetic field due to IFE couples antiferromagnetically to the neighboring spins. We apply the theory to the spin-orbit coupled single- and multiorbital Hubbard model that is relevant for the Kitaev quantum spin liquid material and demonstrate that the magnetic interactions can be tuned by light.
Hidden multipolar orders in spin-orbit-coupled Mott insulators provide a promising setting for correlated quantum matter, yet their control and detection remain major challenges. Here, we demonstrate that circularly polarized light enables both the control and detection of hidden multipolar order in 4d2/5d24d^2/5d^24d2/5d2 systems with edge-sharing octahedra. Using a Floquet Schrieffer-Wolff expansion of a driven Hubbard-Kanamori model, we derive a low-energy multipolar Hamiltonian with two qualitatively new light-driven terms. One is an effective static field that couples linearly to the magnetic octupole, realizing an octupolar inverse Faraday effect. The other is a bond-dependent anisotropic exchange interaction absent in equilibrium. These two couplings constitute the key mechanisms of this work: the first provides a direct optical handle on hidden octupolar order, while the second reorganizes the multipolar exchange landscape and introduces strong bond-dependent frustration. Together, these couplings define a nonequilibrium multipolar Hamiltonian whose phase diagram contains robust antiferro-octupolar, ferro-octupolar, and partially polarized ferro-quadrupolar phases, alongside a putative Ising-octupolar regime and a strongly frustrated, liquid-like multipolar regime whose finite-size numerical signatures are compatible with Kitaev-type behavior. We further show that the induced multipolar order couples to the lattice, generating reversible trigonal and orthorhombic or tetragonal distortions that provide symmetry-resolved structural fingerprints in pump-probe experiments. In this way, our work establishes a general mechanism for the optical generation, control, and detection of hidden multipolar quantum states.
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-filling on the honeycomb, square and triangular lattices. We derive the effective Heisenberg spin models to fourth order in perturbation theory for arbitrary fixed polarizations, and several types of unpolarized light that preserve time-reversal and lattice symmetries. Coupling these models to periodic light tunes first, second, and third neighbor exchange couplings, as well as ring exchange terms on the square and triangular lattices. Circularly polarized light induces chiral fields for the honeycomb and triangular lattices, which favors noncoplanar magnetism and potential chiral spin liquids. We discuss how to maximize the enhancement of the couplings without inducing heating.
In a Hubbard model for the Kitaev spin-liquid candidate material ααα-RuCl3_33​ with three t2gt_{2g}t2g​ orbitals per Ru site, we calculate photoinduced dynamics based on the exact diagonalization method and interpret them with the help of a high-frequency expansion in quantum Floquet theory. The high-frequency expansion shows two types of effective magnetic fields during the application of a circularly polarized light field. One of them originates from spin-orbit coupling and is within the honeycomb lattice. The other is of purely kinetic origin and perpendicular to the lattice. The former fields are antiparallel at the two sites within a unit cell and rotate in accordance with the momentum distribution of holes that follow the light field. When the light field is weak, pseudospin dynamics are governed by the former fields; thus, the average of the pseudospins almost vanishes. The latter fields are parallel at the two sites within a unit cell and produce nonzero perpendicular components of the pseudospins when the light field is strong. Numerically obtained perpendicular components are consistent with the latter fields when the frequency of the light field is well below the Mott gap. The relevance to the inverse Faraday effect recently observed in ααα-RuCl3_33​ is discussed.
Abstract In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl3 and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact that the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify protocols to drive the system to the limit of the Kitaev quantum spin model. In this work, we propose Floquet engineering of these Kitaev quantum magnets by coupling materials to a circularly polarized laser. We demonstrate that all the magnetic interactions can be tuned in situ by the amplitude and frequency of the laser, hence providing a route to stabilize the Kitaev quantum spin liquid phase.
Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling constant for scalar spin chirality can become significant for a situation in which the driving frequency and the on-site interaction are comparable. This implies that the scalar chirality can be induced by circularly polarized lights, or that it can be used conversely for probing the chirality in Mott insulators as a circular dichroism.
We study the effect of a magnetic field on the low-energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realization of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\mathrm{\ensuremath{\Gamma}}$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.