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arXiv:2110.11828 · Physical review. B./Physical review. B

Magnetization dynamics fingerprints of an excitonic condensate t2g4 magnet

Nitin Kaushal, J. Herbrych, Gonzalo Álvarez, Elbio R. Dagotto

Published Dec 20, 2021• 8 citations
arXivHTMLPDF

Abstract

The competition between spin-orbit coupling (SOC) $\ensuremath{\lambda}$ and electron-electron interaction $U$ leads to a plethora of novel states of matter, extensively studied in the context of ${t}_{2g}^{4}$ and ${t}_{2g}^{5}$ materials, such as ruthenates and iridates. Excitonic magnets---the antiferromagnetic state of bounded electron-hole pairs-are prominent examples of phenomena driven by those competing energy scales. Interestingly, recent theoretical studies predicted that excitonic magnets can be found in the ground state of SOC ${t}_{2g}^{4}$ Hubbard models. Here we present a detailed computational study of the magnetic excitations in that excitonic magnet, employing one-dimensional chains (via density matrix renormalization group) and small two-dimensional clusters (via Lanczos). Specifically, first we show that the low-energy spectrum is dominated by a dispersive (acoustic) magnonic mode, with extra features arising from the $\ensuremath{\lambda}=0$ state in the phase diagram. Second, and more importantly, we found a novel magnetic excitation forming a high-energy optical mode with the highest intensity at wave-vector $q\ensuremath{\rightarrow}0$. In the excitonic condensation regime at large $U$, we also have found a novel high-energy $\ensuremath{\pi}$ mode composed solely of orbital excitations. These features do not appear all together in any of the neighboring states in the phase diagram and thus constitute unique fingerprints of the ${t}_{2g}^{4}$ excitonic magnet, of importance in the analysis of neutron and resonant inelastic x-ray scattering experiments.

DOI
10.1103/physrevb.104.235135

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The competition between spin-orbit coupling (SOC) \ensuremathλ\ensuremath{\lambda}\ensuremathλ and electron-electron interaction UUU leads to a plethora of novel states of matter, extensively studied in the context of t2g4{t}_{2g}^{4}t2g4​ and t2g5{t}_{2g}^{5}t2g5​ materials, such as ruthenates and iridates. Excitonic magnets---the antiferromagnetic state of bounded electron-hole pairs-are prominent examples of phenomena driven by those competing energy scales. Interestingly, recent theoretical studies predicted that excitonic magnets can be found in the ground state of SOC t2g4{t}_{2g}^{4}t2g4​ Hubbard models. Here we present a detailed computational study of the magnetic excitations in that excitonic magnet, employing one-dimensional chains (via density matrix renormalization group) and small two-dimensional clusters (via Lanczos). Specifically, first we show that the low-energy spectrum is dominated by a dispersive (acoustic) magnonic mode, with extra features arising from the \ensuremathλ=0\ensuremath{\lambda}=0\ensuremathλ=0 state in the phase diagram. Second, and more importantly, we found a novel magnetic excitation forming a high-energy optical mode with the highest intensity at wave-vector q\ensuremath→0q\ensuremath{\rightarrow}0q\ensuremath→0. In the excitonic condensation regime at large UUU, we also have found a novel high-energy \ensuremathπ\ensuremath{\pi}\ensuremathπ mode composed solely of orbital excitations. These features do not appear all together in any of the neighboring states in the phase diagram and thus constitute unique fingerprints of the t2g4{t}_{2g}^{4}t2g4​ excitonic magnet, of importance in the analysis of neutron and resonant inelastic x-ray scattering experiments.
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\ensuremath{\pi}$ in t2g4{t}_{2g}^{4}t2g4​ spin-orbit coupled three-orbital Hubbard models at electronic density n=4n=4n=4. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at n=3.5n=3.5n=3.5 in a one-dimensional Hubbard model with a degenerate t2g{t}_{2g}t2g​ sector, when in the presence of spin-orbit coupling. At intermediate Hubbard UUU and spin-orbit $\ensuremath{\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q=\ensuremath{\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\ifmmode\pm\else\textpm\fi{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\ifmmode\pm\else\textpm\fi{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\ensuremath{\lambda}$ vs UUU phase diagram, at a fixed and robust Hund coupling. Interestingly, this new ``block excitonic phase'' is present even at large values of $\ensuremath{\lambda}$, unlike the n=4n=4n=4 excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with d3.5{d}^{3.5}d3.5 valence and robust spin-orbit coupling.
We present a comprehensive study of the spin excitations---as measured by the dynamical spin structure factor $S(q,\ensuremath{\omega})$---of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The $2\ifmmode\times\else\texttimes\fi{}2$ particular case was already found experimentally in the ladder material BaFe2Se3\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{3}BaFe2​Se3​ that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of $S(q,\ensuremath{\omega})$ using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard UUU strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.
The condensation of spin-orbit-induced excitons in t2g4{t}_{2g}^{4}t2g4​ electronic systems is attracting considerable attention. At large Hubbard UUU, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons (Jeff=1{J}_{\text{eff}}=1Jeff​=1). Here, we show that even at intermediate UUU regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large UUU, and this BEC strong coupling regime is smoothly connected to the intermediate UUU excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ($\ensuremath{\lambda}$) in one dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $\ensuremath{\lambda}$ versus UUU phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard UUU, increasing $\ensuremath{\lambda}$ at fixed UUU the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length rcoh{r}_{\mathrm{coh}}rcoh​ of O(a)\mathcal{O}(a)O(a) and O(10a)\mathcal{O}(10a)O(10a) in 1d1d1d and 2d2d2d, respectively, with aaa being the lattice spacing. Further increasing $\ensuremath{\lambda}$, the system eventually crosses over to the BEC limit (with ${r}_{\mathrm{coh}}\ensuremath{\ll}a$).
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems, an exciton is the bound state of a double occupied and empty site. In the strong coupling limit, the exciton acts as a hard-core boson. Its physics is captured by the exciton ttt-JJJ model, containing an effective XXZXXZXXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean-field theory, we constructed the ground-state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal, and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally, we studied the collective modes and susceptibilities of the three phases. In the superfluid phase, we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).
We present a comprehensive study of a one-dimensional two-orbital model at and below quarter filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasicondense with finite center-of-mass momentum and an order parameter that changes phase with wave vector QQQ. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge- density-wave instability. When pairing dominates over the interorbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin-gapped superconductor, a genuine orbital-selective paired state. All these results are supported by both analytical and numerical calculations. By assuming a quasiclassical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from k=0k=0k=0. The full characterization of the different phases is obtained by means of extensive density-matrix renormalization-group calculations.
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