Spin dynamics of counterrotating Kitaev spirals via duality

Rapid Communication

Spin dynamics of counterrotating Kitaev spirals via duality

Itamar Kimchi and Radu Coldea

Phys. Rev. B 94, 201110(R) – Published 16 November 2016

Abstract

Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family ${Li}_{2} {IrO}_{3}$ shows an incommensurate order where spirals on neighboring sublattices are counterrotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: The Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we propose an approach via a (Klein) duality transformation into a conventional spiral of a frustrated Heisenberg model, allowing a direct derivation of the dynamical structure factor. We analyze both Kitaev and Dzyaloshinskii-Moriya based models, both of which can stabilize counterrotating spirals, but with different spin dynamics, and we propose experimental tests to identify the origin of counterrotation.

Received 16 June 2016
Revised 26 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.201110

Physics Subject Headings (PhySH)

Exchange interaction Frustrated magnetism Magnetic texture

Kitaev-Heisenberg model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Itamar Kimchi¹ and Radu Coldea²

¹Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Clarendon Laboratory, University of Oxford Physics Department, Parks Road, Oxford OX1 3PU, United Kingdom

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 94, Iss. 20 — 15 November 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Counterrotating spiral order of $α, β, γ − {Li}_{2} {IrO}_{3}$ as the Klein dual of a conventional (co-rotating) spiral. (a): The counterrotating spiral on a zigzag chain is the unifying common feature of the magnetic structures of all three $α, β, γ − {Li}_{2} {IrO}_{3}$ honeycomb iridates. The bottom sublattice rotates clockwise, while the top rotates counterclockwise. (b): The co-rotating spiral, of a conventional Heisenberg $J_{1} − J_{2}$ model, transforms by Klein duality into a counterrotating spiral with a Kitaev- $J_{1} − J_{2}$ model and $x y$ anisotropy. (c): Competing models to stabilize counterrotation: Kitaev exchange ( $x, y$ ) or second-neighbor Dzyaloshinskii-Moriya (DM) exchange (out/in for top/bottom bonds). The Klein transformation $μ \in {1, x, y, z}$ acts as identity 1 or by $π$ rotation around a spin's $x, y, z$ axis. This exact duality for the counterrotating spiral shows its stability and circumvents the magnetic umklapp of its Kitaev exchange for computing its dynamical structure factor.
Reuse & Permissions
Figure 2
Duality of classical spirals. The classical Heisenberg $J_{1} − J_{2}$ model with ferromagnetic $J_{1} < 0$ and frustrating second-neighbor $J_{2} > 0$ has a (co-rotating) spiral ground state with nonzero wavevector $q$ for $| J_{2} / J_{1} | > 0.25$ (gray curve). With easy-plane $x y$ anisotropy, the resulting $x y$ -plane spiral is independent of $J_{1}^{z}, J_{2}^{z}$ and depends only on $J_{2}^{x y} / J_{1}^{x y}$ . The Klein transformation produces a counterrotating spiral with $q \to π / a_{1} - q$ (blue curve) while flipping the signs of $J_{1}^{x y}, J_{2}^{x y}, J_{1}^{z}$ , preserving $J_{2}^{z}$ and creating a Kitaev exchange $K = - 2 J_{1}^{x y}$ . The resulting model has the counterrotating spiral shown in Fig. 1 as its classical ground state.
Reuse & Permissions
Figure 3
Dynamical structure factor signature of Kitaev exchange. The dynamical correlations of various spin polarizations [ $a, b, c$ axes defined in Fig. 1] are computed via spin wave theory for two possible models of the counterrotating spiral: decoupled sublattices with pure-second-neighbor DM exchanges of opposite signs (column b), and nearest-neighbor Kitaev exchange together with smaller easy-plane $J_{1} − J_{2}$ (column c). The plots shown were computed for the minimal models with $J_{1}^{z}, J_{2}^{z} \to 0$ . (Color is the dynamical spin structure factor, convolved with a $σ = 0.025$ energy Gaussian; thin blue lines are underlying spin wave dispersions.) Magnetic umklapp scattering, which usually breaks down spin waves of the Kitaev exchange, was avoided by tuning to the duality with the conventional co-rotating spiral of a $J_{1} − J_{2}$ XY model (panel a). The Klein duality between panels (a) and (c) shifts wave vectors by $\pm π / a_{1}$ for $S^{a}, S^{c}$ and by $2 π / a_{1}$ for $S^{b}$ , producing distinctive signatures for the Kitaev exchange; for example, the shifted $S^{b b}$ is evident in the spherical average, via the strong signal at high energy and low momentum.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics