Analysis of the optical conductivity forA2IrO3(A=Na, Li)from first principles

Abstract

We present results for the optical conductivity of Na2IrO3 within density functional theory by including spin-orbit (SO) and correlation effects (U) as implemented in GGA+SO+U. We identify the various interband transitions and show that the underlying quasi-molecular-orbital nature of the electronic structure in Na2IrO3 translates into distinct features in the optical conductivity. Most importantly, the parity of the quasi-molecular orbitals appears to be the main factor in determining strong and weak optical transitions. We also present optical conductivity calculations for Li2IrO3 and discuss the similarities and differences with Na2IrO3.The family of honeycomb iridates A 2 IrO 3 (A = Na, Li) has recently been a subject of intensive discussion due to its complex electronic and magnetic behavior arising from an interplay of spin-orbit effects, correlations and lattice geometry. These materials are insulators and order antiferromagnetically at low temperatures 1 . While Na 2 IrO 3 shows a zigzag-like magnetic pattern 2 , a spiral order with a small nonzero wave vector inside the first Brillouin zone has been reported for Li 2 IrO 3 3,4 . Photoemission and optical conductivity measurements 5 for Na 2 IrO 3 confirm this insulating behavior with a gap of 340 meV. Attempts to understand the different behavior of the end members through the series (Na 1−x Li x ) 2 IrO 3 have been pursued 6,7 with partly contradicting results, while Manni et al.6 find that only for x ≤ 0.25 does the system form uniform solid solutions and otherwise the system shows a miscibility gap and phase separates, Cao et al.7 report a homogeneous phase at x ∼ 0.7 with a disappearance of long range magnetic order.From a theoretical point of view, these materials have been suggested to be a realization of the HeisenbergKitaev model with bond-dependent anisotropic interactions between j eff = 1/2 spin-orbit-coupled Ir moments [8][9][10][11][12][13] . Such a model is obtained under the assumption of large spin-orbit coupling, so that Ir 5d t 2g orbitals can be written in terms of j eff = 1/2 and lower lying j eff = 3/2 relativistic orbitals.Alternatively, a description of the electronic structure of these systems in terms of quasi-molecular orbitals was also recently proposed 14,15 . Following the observation that the contributing energy scales in these systems are of the same order of magnitude, namely the bandwidth for 5d orbitals is 1.5-2 eV, the onsite Coulomb repulsion U is about 1-2 eV, the Hund's coupling constant is about 0.5 eV and the spin-orbit coupling is λ ∼ 0.4-0.5 eV it was shown 14,15 that the underlying electronic behavior can be described in terms of molecular orbitals formed by the Ir t 2g states on an hexagon with each of the three t 2g Ir orbitals on a site contributing to three neighboring molecular orbitals. In Ref. 15 it was further demonstrated that both descriptions, i.e. a localized description in terms of j eff and an itinerant description in terms of molecular orbitals are equally compatible.Presently, only optical condu...

Multibandd−pmodel and self-doping in the electronic structure ofBa2IrO4

“…A rather low value of U d ∈ [1.0, 2.0] eV was first suggested by Mazin et al [34], but we argue that a more probable value is U d = 3.0 eV. This value (and J d = 0.6 eV) were used in local density approximation (LDA+U ) computations for Na 2 IrO 3 [35,36] and also for Ba 2 IrO 4 [13]. A similar value of U d = 2.72 eV was obtained by constrained random phase approximation in Na 2 IrO 3 [37].…”

“…The same value was used in Refs. [8,34] while slightly smaller (J d = 0.4 eV [13]), very small (J d = 0.14 eV [3]), or larger (J d = 0.6 eV [35,36]) values were also considered. For the sake of fixing precisely Hund's coupling tensor elements J d,µν we use Table I from Ref.…”

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

“…This weak coupling approach naturally explains the zigzag AFM order with a concomitantly induced band gap [36][37][38][39]. However, it is difficult to fully describe the observed excitations in the OC and RIXS for Na 2 IrO 3 [40][41][42]. Because the hopping integral, Coulomb repulsion, and SOC are of similar energy scale, either of these two opposite pictures cannot be ruled out.…”

Tracking local magnetic dynamics via high-energy charge excitations in a relativistic Mott insulator

“…Quantitatively, this can be demonstrated by a differential fitting procedure, that builds on a multi Lorentzian model of the equilibrium dielectric function [27]. Both the position and the amplitude of the five oscillators used to reproduce the dielectric function perfectly map the transitions expected in the QMOs picture [24] (for a detailed discussion see Ref. 27).…”