Spin-orbit excitations and electronic structure of the putative Kitaev magnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>RuCl</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

Sandilands, Luke J.; Tian, Yao; Reijnders, Anjan; Kim, Heung Sik; Plumb, K. W.; Kim, Yong Baek; Kee, Hae‐Young; Burch, Kenneth S.

doi:10.1103/physrevb.93.075144

Cited by 186 publications

(191 citation statements)

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“…The recent optical absorption experiments for α-RuCl 3 have found a dominant peak around 1.2 eV as well as a small additional peak near 0.3 eV [32,57]. The photoemission spectroscopy measurement has also observed a large gap about 1.2 eV [58].…”

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confidence: 84%

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t2g5 Systems with a Honeycomb Lattice Structure

2016

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The t2g orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin et al. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for t 5 2g systems. However, with help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against not only the spin-orbit coupling (SOC) but also the Coulomb repulsion. We show that the electronic phase of t 5 2g systems can vary from a quasimolecular band insulator to a relativistic J eff = 1/2 Mott insulator with increasing the SOC as well as the Coulomb repulsion. The different electronic phases manifest themselves in electronic excitations observed in optical conductivity and resonant inelastic x-ray scattering. Based on our calculations, we assert that the currently known Ru 3+ -and Ir 4+ -based honeycomb systems are far from the quasimolecular band insulator but rather the relativistic Mott insulator. Introduction -Physical properties of 4d and 5d transition metal (TM) compounds with nominally less than six d electrons are determined by the t 2g manifold because of a strong cubic crystal field. A strong spin-orbit coupling (SOC) causes t 2g orbitals split into effective total angular momenta j eff = 1/2 and 3/2. The relativistic electronic feature in these TM compounds has drawn much attraction recently as exotic electronic, magnetic, and topological phases have been expected, including J eff = 1/2 Mott insulator [1-5], superconductivity [6,7], topological insulator [8,9], Weyl semimetal [10,11], and spin liquid [12,13]. Among them, the research on t 5 2g systems forming a honeycomb lattice structure with edge-sharing ligands has been triggered by the possibility of a nontrivial topological phase [14,15]

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confidence: 84%

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t2g5 Systems with a Honeycomb Lattice Structure

2016

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“…All of the configurations become insulator with the gap of ∼ 1 eV between the lower and upper Hubbard bands at U eff = 2 eV. DOS for the resulting phases are almost identical to the one from single-layer calculation 10 and show no significant difference compared to each other, so we do not present the DOS plots here. Table III shows the optimization results.…”

Section: Stacking With Zigzag Magnetic Ordermentioning

confidence: 99%

“…One promising candidate is α-RuCl 3 , where edge-sharing RuCl 6 octahedra form two-dimensional RuCl 3 layers in which Ru honeycomb layers reside [3][4][5][6][7][8][9][10][11] . Compared to its 5d transition metal oxide counterparts α-A 2 IrO 3 (A=Li,Na) [12][13][14][15][16] , α-RuCl 3 has closer-to-ideal RuCl 6 octahedra 3 , so it was proposed as an excellent platform to explore the Kitaev physics and related magnetism despite weaker SOC 4,9,11,17,18 .…”

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confidence: 99%

Crystal structure and magnetism inα−RuCl3: Anab initiostudy

2016

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α-RuCl3 has been proposed recently as an excellent playground for exploring Kitaev physics on a twodimensional (2D) honeycomb lattice. However, structural clarification of the compound has not been completed, which is crucial in understanding the physics of this system. Here, using ab-initio electronic structure calculations, we study a full three dimensional (3D) structure of α-RuCl3 including the effects of spin-orbit coupling (SOC) and electronic correlations. Three major results are as follows; i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural Li2RuO3, and making the honeycomb closer to an ideal one. ii) The nearest-neighbor Kitaev exchange interaction between the j eff =1/2 pseudospin depends strongly on the Ru-Ru distance and the Cl position, originating from the nature of the edge-sharing geometry.iii) The optimized 3D structure without electronic correlations has P31m space group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either C2/m or Cmc21 within 0.1 meV per formula unit (f.u.) energy difference. The reported P 3112 structure is also close in energy. The interlayer spin exchange coupling is a few percent of in-plane spin exchange terms, confirming α-RuCl3 is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds new light in realizing Kitaev spin liquid phase in this system.

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“…In recent years, a remarkable theoretical and experimental progress has been achieved in understanding that fractionalization is one of the most promising hallmarks of a QSL. Indeed, it has been demonstrated that fractionalized excitations, which are Majorana fermions and Z 2 gauge fluxes for KSLs, can be probed by conventional spectroscopic techniques, such as inelastic neutron scattering (INS) [26,[31][32][33][34], Raman scattering with visible light [21,25,[35][36][37][38][39], and resonant inelastic X-ray scattering (RIXS) [40][41][42].…”

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confidence: 99%

“…The Kitaev spin liquid (KSL) on the honeycomb lattice [3] and its generalizations on tricoordinated threedimensional (3D) lattices [4][5][6][7][8] are quintessential examples of such QSL phases. Importantly, recent years have seen much progress in identifying a large number of candidate materials for realizing these KSL phases [9][10][11][12], such as the honeycomb iridates Na 2 IrO 3 [13][14][15][16][17][18] and α-Li 2 IrO 3 [19], the honeycomb ruthenium chloride α-RuCl 3 [20][21][22][23][24][25][26], and the 3D harmonichoneycomb iridates β-and γ-Li 2 IrO 3 [27][28][29][30].…”

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confidence: 99%

Probing Spinon Nodal Structures in Three-Dimensional Kitaev Spin Liquids

2017

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We propose that resonant inelastic X-ray scattering (RIXS) is an effective probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin liquids. While the non-spin-conserving RIXS responses are dominated by the gauge-flux excitations and reproduce the inelastic-neutron-scattering response, the spin-conserving (SC) RIXS response picks up the Majorana-fermion excitations and detects whether they are gapless at Weyl points, nodal lines, or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS response is suppressed around the Γ point. On a technical level, we calculate the exact SC RIXS responses of the Kitaev models on the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices, arguing that our main results also apply to generic 3D Kitaev spin liquids beyond these exactly solvable models.Quantum spin liquids (QSLs) are exotic and entirely quantum phases of matter [1,2] From a theoretical point of view, KSLs are particularly appealing because each of them has an exactly solvable limit governed by a Kitaev model [3]. In general, the Kitaev model is defined on a tricoordinated lattice with S = 1/2 spins σ x,y,z r at the sites r, which are coupled to their neighbors via bonddependent Ising interactions. The Hamiltonian readswhere J x,y,z are the coupling constants for the three types of bonds x, y, and z. Remarkably, this model is exactly solvable whenever there is precisely one bond of each type around each site of the tricoordinated lattice.These exactly solvable Kitaev models have been defined on a wide range of tricoordinated 3D lattices [4][5][6][7][8], including the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices (see Fig. 1). In the experimentally relevant isotropic regime (J x ≈ J y ≈ J z ), the ground state is a gapless Z 2 QSL, while the (fractionalized) excitations are gapless Majorana fermions and gapped Z 2 gauge fluxes. Importantly, the Majorana fermions (spinons) exhibit a rich variety of nodal structures due to the different (projective) ways symmetries can act on them [5][6][7]. Indeed, they are gapless along nodal lines for the hyperhoneycomb and the stripyhoneycomb models [4], on Fermi surfaces for the hyperoctagon model [5], and at Weyl points for the hyperhexagon model [7].From an experimental point of view, however, it is difficult to identify and characterize QSLs due to the lack of any local order parameters that could be used as "smoking-gun" signatures. In recent years, a remarkable theoretical and experimental progress has been achieved in understanding that fractionalization is one of the most promising hallmarks of a QSL. Indeed, it has been demonstrated that fractionalized excitations, which are Majorana fermions and Z 2 gauge fluxes for KSLs, can be probed by conventional spectroscopic techniques, such as inelastic neutron scattering (INS) [26,[31][32][33][34], Raman scattering with visible light [21,25,[35][36][37][38][39], and resonant inelastic X-ray scattering (RIXS) [40][41][42].In this Letter, we propo...

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Spin-orbit excitations and electronic structure of the putative Kitaev magnetα−RuCl3

Cited by 186 publications

References 58 publications

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t2g5 Systems with a Honeycomb Lattice Structure

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t2g5 Systems with a Honeycomb Lattice Structure

Crystal structure and magnetism inα−RuCl3: Anab initiostudy

Probing Spinon Nodal Structures in Three-Dimensional Kitaev Spin Liquids

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