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arXiv:2401.02532 · Physical review. B./Physical review. B

Emergent transverse-field Ising model in d4 spin-orbit Mott insulators

Jiří Chaloupka

Published Jan 16, 2024• 3 citations
arXivHTMLPDF

Abstract

Mott-insulating transition metal oxides containing ${t}_{2g}^{4}$ ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-$\frac{1}{2}$. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using ${\mathrm{Ru}}^{4+}$ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.

DOI
10.1103/physrevb.109.l020403

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Mott-insulating transition metal oxides containing t2g4{t}_{2g}^{4}t2g4​ ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-12\frac{1}{2}21​. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using Ru4+{\mathrm{Ru}}^{4+}Ru4+ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with t2g4{t}_{2g}^{4}t2g4​ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor ``triplon'' operators describing the transitions between spin-orbit entangled J=0J=0J=0 ionic ground state and excited J=1J=1J=1 levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find close analogies with the Kitaev spin model---an infinite number of conserved quantities, no magnetic condensation, and spin correlations being strictly short-ranged. However, due to the bosonic nature of triplons, there are no emergent gapless excitations within the spin gap, and the ground state is a strongly correlated paramagnet of dense triplon pairs with no long-range entanglement. Using exact diagonalization, we study the bosonic Kitaev model and its various extensions, which break exact symmetries of the model and allow magnetic condensation of triplons. Possible implications for magnetism of ruthenium oxides are discussed.
The Ising model in transverse magnetic field is perhaps the simplest quantum spin model, yet the elements of site disorder, random magnetic fields, and tunable quantum fluctuations permit a rich array of ground states, and the rare ability to emphasize their classical or quantum character. We briefly review in this chapter experimental results from chains to crystals of spins, with magnetic, glassy, and spin liquid ground states. Singlet Ground State Magnets In a crystalline lattice, the crystal fields often take a form such that the ground states of magnetic ions are singlets separated from the higher lying spin multiplets. Sufficiently strong magnetic dipolar or exchange couplings between different sites can mix the singlets with the multiplets enough so as to induce non-zero expectation values for the magnetic dipoles at individual sites. Examples of this phenomenon are generally found among metals and insulators based on rare earths. Such metals were a subject of extensive research in the 1960's and 1970's, and the book by MacKintosh and Jensen [408] gives an excellent account of both the data as well as mean field approaches. With respect to insulating materials, LiTbF 4 emerged as a model system in the 1970's. It is an example of an ideal Ising dipolar coupled ferromagnet; here the long-range nature of the dipolar interactions leads to an upper critical dimension [149] (at which mean field theory with logarithmic corrections calculable using RG methods becomes an exact description of thermal phase transitions) of three rather than four. LiTbF 4 belongs to the LiREF 4 isostructural series of ionic salts. Li and F carry valences +1 and −1 respectively, leaving RE, which can be any rare earth atom or the nonmagnetic element Y, with a valence of +3. Figure 14.1 shows the body-centered tetragonal crystal structure for the family.
The physics of spin-orbital entanglement in effective j=12j=\frac{1}{2}j=21​ Mott insulators, which have been experimentally observed for various 5d5d5d transition-metal oxides, has sparked an interest in Heisenberg-Kitaev (HK) models thought to capture their essential microscopic interactions. Here, we argue that the recently synthesized Ba3IrTi2O9{\mathrm{Ba}}_{3}{\mathrm{IrTi}}_{2}{\mathrm{O}}_{9}Ba3​IrTi2​O9​ is a prime candidate for a microscopic realization of the triangular HK model, a conceptually interesting model for its interplay of geometric and exchange frustration. We establish that an infinitesimal Kitaev exchange destabilizes the ${120}^{\ensuremath{\circ}}$ order of the quantum Heisenberg model. This results in the formation of an extended Z2{\mathbb{Z}}_{2}Z2​-vortex crystal phase in the parameter regime most likely relevant to the real material, which can be experimentally identified with spherical neutron polarimetry. Moreover, using a combination of analytical and numerical techniques, we map out the entire phase diagram of the model, which further includes various ordered phases as well as an extended nematic phase around the antiferromagnetic Kitaev point.
The rare-earth magnet TmMgGaO 4 is proposed to be an intrinsic quantum Ising magnet described by the antiferromagnetic transverse field Ising model (TFIM) on a triangular lattice, where the relevant degrees of freedom are the nondegenerate dipole-multipole doublets of the Tm 3+ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet.We compare this special doublet of Tm 3+ with the dipole-octupole Kramers doublet.We study the proposed effective model for the Tm-based triangular lattice and consider the effects of external magnetic fields and finite temperatures.From the orthogonal operator approach, we show that the TFIM with the three-sublattice intertwined ordered state agrees with the experiments and further clarify the discrepancy in the numbers of the magnetic sublattices and the measured magnon branches.We make specific predictions for the evolution of the magnetic properties with the external magnetic field.Furthermore, we demonstrate that an emergent U(1) symmetry emerges in thermal melting of the underlying orders and at the criticality, and summarize the previously known signatures related to the finite-temperature Berezinskii-Kosterlitz-Thouless physics.We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially Tm-based materials.
We study the interplay of strong electron correlations and intratriangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-1 Mott insulator, a metal, and a spin-0 Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intratriangle multiorbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenough-Kanamori rules, may occur in coordination polymers from kinetic exchange via the ligands. We characterize the magnetism in the regime where spin triplets dominate. For small UUU a spin-1 Slater insulator occurs with antiferromagnetic order between triangles. Magnetism in the spin-1 Mott insulator is described by a spin-1 Heisenberg model on a honeycomb lattice, whose ground state is N\'eel ordered.
We study the photoinduced ultrafast dynamics in relativistic Mott insulators, i.e., Mott insulators with strong spin-orbit coupling. For this purpose, we consider a minimal one-band Hubbard model on lattices with square and triangular symmetries, as relevant for layered transition metal compounds such as Sr2_22​IrO4_44​. Depending on the lattice and the spin-orbit coupling, the systems have canted antiferromagnetic or 120∘120^\circ120∘ order. They are excited by simulating a short laser pulse, and the dynamics is solved using nonequilibrium dynamical mean-field theory. The pulse generates hot carriers, which subsequently perturb the magnetic order due to the coupling between the collective order and photocarriers. We find that this dynamics, which is known form regular antiferromagnets, depends sensitively on the spatial structure of the spin-orbit coupling. On the triangular lattice, in particular, relaxation times are influenced by the spin-orbit coupling for the chiral 120∘120^\circ120∘ order, while on the square lattice with canted antiferromagnetic order the spin-orbit induced canting angle remains unchanged after the excitation. Our study opens up new possibilities of controlling magnetism and exotic spin states on the ultrafast timescales.