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arXiv:1803.03796 · SciPost Physics

Optical control of competing exchange interactions and coherent spin-charge coupling in two-orbital Mott insulators

Marion Barbeau, Martin Eckstein, Mikhail I. Katsnelson, Johan H. Mentink

Published Mar 5, 2019• 16 citations
arXivHTMLPDF

Abstract

In order to have a better understanding of ultrafast electrical control of exchange interactions in multi-orbital systems, we study a two-orbital Hubbard model at half filling under the action of a time-periodic electric field. Using suitable projection operators and a generalized time-dependent canonical transformation, we derive an effective Hamiltonian which describes two different regimes. First, for a wide range of non-resonant frequencies, we find a change of the bilinear Heisenberg exchange J_{\textrm{ex}} J ex that is analogous to the single-orbital case. Moreover we demonstrate that also the additional biquadratic exchange interaction B_{\textrm{ex}} B ex can be enhanced, reduced and even change sign depending on the electric field. Second, for special driving frequencies, we demonstrate a novel spin-charge coupling phenomenon enabling coherent transfer between spin and charge degrees of freedom of doubly ionized states. These results are confirmed by an exact time-evolution of the full two-orbital Mott-Hubbard Hamiltonian.

DOI
10.21468/scipostphys.6.3.027

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In order to have a better understanding of ultrafast electrical control of exchange interactions in multi-orbital systems, we study a two-orbital Hubbard model at half filling under the action of a time-periodic electric field. Using suitable projection operators and a generalized time-dependent canonical transformation, we derive an effective Hamiltonian which describes two different regimes. First, for a wide range of non-resonant frequencies, we find a change of the bilinear Heisenberg exchange J_{\textrm{ex}} J ex that is analogous to the single-orbital case. Moreover we demonstrate that also the additional biquadratic exchange interaction B_{\textrm{ex}} B ex can be enhanced, reduced and even change sign depending on the electric field. Second, for special driving frequencies, we demonstrate a novel spin-charge coupling phenomenon enabling coherent transfer between spin and charge degrees of freedom of doubly ionized states. These results are confirmed by an exact time-evolution of the full two-orbital Mott-Hubbard Hamiltonian.
The manipulation of electronic structure through periodic electric fields enables the reversible control of effective interactions in extended antiferromagnetic Mott insulators on ultrafast timescales. A careful analytical examination of the modulated effective interactions is conducted, accurately characterising it through the use of exact summation formulas and Bessel functions. As a result, time reversals are analytically determined in terms of Bessel zeroes. We discuss the half-filled Hubbard model, as well as multi-orbital models, various characteristics of the Kitaev-Heisenberg model, and the emergence of chiral spin terms.
We demonstrate how electric fields with arbitrary time profile can be used to control the time-dependent parameters of spin and orbital exchange Hamiltonians. Analytic expressions for the exchange constants are derived from a time-dependent Schrieffer-Wolff transformation, and the validity of the resulting effective Hamiltonian is verified for the case of a quarter-filled two-orbital Hubbard model, by comparing to the results of a full nonequilibrium dynamical mean-field theory simulation. The ability to manipulate Hamiltonians with arbitrary time-dependent fields, beyond the paradigm of Floquet engineering, opens the possibility to control intertwined spin and orbital order using laser or THz pulses which are tailored to minimize electronic excitations.
The strongest interaction between microscopic spins in magnetic materials is the exchange interaction Jex. Therefore, ultrafast control of Jex holds the promise to control spins on ultimately fast timescales. We demonstrate that time-periodic modulation of the electronic structure by electric fields can be used to reversibly control Jex on ultrafast timescales in extended antiferromagnetic Mott insulators. In the regime of weak driving strength, we find that Jex can be enhanced and reduced for frequencies below and above the Mott gap, respectively. Moreover, for strong driving strength, even the sign of Jex can be reversed and we show that this causes time reversal of the associated quantum spin dynamics. These results suggest wide applications, not only to control magnetism in condensed matter systems, for example, via the excitation of spin resonances, but also to assess fundamental questions concerning the reversibility of the quantum many-body dynamics in cold atom systems.
We present a scheme to control the spin-exchange interactions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, a periodic drive modifies the properties of the ligand orbitals which mediate magnetic interactions between transition-metal ions. In the other case, we consider drive-induced mixing of ddd orbitals on each magnetic ion. We first find that an AC Stark shift of orbitals induces a change comparable to that induced from photoinduced hopping schemes, but expands the applicable frequency ranges. Next, we find that radiatively induced coherent vibrations provide a realistic path for Floquet orbital engineering with short pulses of electric fields weaker than 0.5 V/\AA{} producing 55%--10%5 changes in the magnetic coupling of Mott insulators such as the rare-earth titanates.
Intense light can alter the electronic properties of materials through its oscillating electric field. The effects on magnetic excitations in insulators, however, are indirect, since these are neutral and do not see the electric field directly. This study reports on how exchange interactions in single- and multiorbital Mott insulators are modified by electromagnetic radiation, whose frequency is assumed to be on the order of the Mott-Hubbard gap. The latter condition results in a nonvanishing creation rate of doubly occupied sites (doublons), which necessitates taking into account the finite bandwidth of the doublon excitations, a feature which goes beyond the na\"{\i}ve leading order strong correlation expansion. This ultimately leads to a complex-valued exchange parameter, where the real part represents the ``Floquet'' spin-exchange interaction, while the imaginary part reflects the creation rate of doublons.
We study by dynamical mean-field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localization while the wider one being still itinerant. At quarter-filling, the physical behavior is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favor of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.