Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions

Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Irbased pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak electron-electron interaction, we predict that Ir electrons are in a metallic phase at weak spinorbit interaction, and in a topological band insulator phase at strong spin-orbit interaction. Very generally, we show that with increasing strength of the electron-electron interaction, the effective spin-orbit coupling is enhanced, increasing the domain of the topological band insulator. Furthermore, in our model, we argue that with increasing interactions, the topological band insulator is transformed into a "topological Mott insulator" phase, which is characterized by gapless surface spin-only excitations. The full phase diagram also includes a narrow region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron-electron interaction. Introduction: The spin-orbit interaction (SOI), though apparently a "weak" relativistic correction to the Schrödinger equation (outside of high energy physics), is coming increasingly to the fore in modern condensed matter physics. The discovery of Topological Band Insulators (TBIs) in theory [1, 2,3,4] and experiment [5,6] has revealed a surprising omission in the "textbook" Bloch theory of the electronic structure of weakly correlated solids. In these remarkable materials, strong spin-orbit interactions allow a non-trivial topology of the electron bands, resulting in protected "helical" edge and surface states in two and three dimensional systems. Many other interesting phenomena, including quantum number fractionalization and magneto-electric effects have been predicted to occur in these systems, and are the subjects of a growing experimental effort. In parallel, strong SOIs have been identified in a growing variety of Mott insulators, in which the insulating behavior is driven by electron correlation rather than band structure. For instance, SOIs are likely responsible for the large Wilson ratios observed in many frustrated magnets at low temperature [7,8], and may be the driving force for the formation of a "spin-orbital liquid" in some Fe-spinels [9]. They have been experimentally shown to control the orbital state in the Ir oxide Sr 2 IrO 4 using resonant x-ray scattering [10]. A natural question is how these two classes of phenomena are connected -how does a material progress from weak to strong correlation with strong SOIs? This is the subject of the Mott transition with strong SOIs.In the search for strong SOIs, one is driven t...

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“…Spin ordering in this model was considered in Ref. [20]. Our DM term corresponds to the "indirect" case of Ref.…”

Section: Figmentioning

confidence: 99%

“…Our DM term corresponds to the "indirect" case of Ref. [20], and |D 01 |/J ≈ 0.63, i.e. very large DM interactions.…”

Section: Figmentioning

confidence: 99%

Mott physics and band topology in materials with strong spin–orbit interaction

Pesin

Balents²

2010

Nature Phys

1,044

1,266

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“…At H = H s we have cos ϕ ≃ D 1/3 , which yields ∆ ππ ∝ D 2/3 from Eq. (21). For an interesting discussion of that fractional power see Ref.…”

Section: In-plane Fieldmentioning

confidence: 99%

“…This is important for the systems close to the spin-liquid state, such as triangular lattice AF Cs 2 CuCl 4 where the DM term is significant, 17,18,19 and also for the frustrated spin systems where quantum effects may help to select the ground state. 20,21 In this work we study the excitation spectrum and various T = 0 static properties of the square lattice, spin-S Heisenberg model with the DM interaction. This is the simplest case of a higher-dimensional system in which generic trends of the mutual effect of the DM interaction, external field, and quantum fluctuations on the properties of an ordered AF can be studied.…”

Section: Introductionmentioning

confidence: 99%

Effects of an external magnetic field on the gaps and quantum corrections in an ordered Heisenberg antiferromagnet with Dzyaloshinskii-Moriya anisotropy

Chernyshev

2005

Phys. Rev. B

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We study the effects of external magnetic field on the properties of an ordered Heisenberg antiferromagnet with the Dzyaloshinskii-Moriya (DM) interaction. Using the spin-wave theory quantum correction to the energy, on-site magnetization, and uniform magnetization are calculated as a function of the field H and the DM anisotropy constant D. It is shown that the spin-wave excitations exhibit an unusual field-evolution of the gaps. This leads to various non-analytic dependencies of the quantum corrections on H and D. It is also demonstrated that, quite generally, the DM interaction suppresses quantum fluctuations, thus driving the system to a more classical ground state. Most of the discussion is devoted to the spin-S, two-dimensional square lattice antiferromagnet, whose S = 1 2 case is closely realized in K2V3O8 where at H = 0 the DM anisotropy is hidden by the easy-axis anisotropy but is revealed in a finite field. The theoretical results for the field-dependence of the spin-excitation gaps in this material are presented and the implications for other systems are discussed.

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“…Of exchange origin, all these couplings can be positive or negative. Unit vectorsd ij are chosen such that positive and negative J DM correspond to direct and indirect DM interactions, respectively [50].ẑ i is the local cubic [111] direction at site i and Λ (αβ) ij ≡ (δ αβ /r 3 ij − 3r ij;α r ij;β /r 5 ij ). H dip is the long-range magnetostatic dipoledipole interaction with strength J dip = µ0µ 2 4πr 3 nn , where r nn is the nearest-neighbor distance.…”

Section: A) B)mentioning

confidence: 99%

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

et al. 2015

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We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k = { 1 2 1 2 1 2 }. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second-and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature. Highly frustrated magnetism is one of the paradigms of modern condensed matter physics [1]. In frustrated magnets, the combination of lattice geometry and competing interactions often leads to degenerate classical states. The degeneracies are generally accidental as they are not protected by the symmetries of the spin Hamiltonian. Yet, the degenerate states may be related by transformations that form an emergent symmetry group. Near a continuous phase transition, these approximate symmetries provide "organizing principles" in determining the critical properties by distinguishing relevant perturbations from irrelevant ones. In the most interesting case, the leading degeneracy-lifting perturbations, which may be relevant or irrelevant in the renormalization group sense, are thermal or quantum fluctuations -a phenomenon called order-by-disorder (ObD) [2][3][4][5]. The competition among diverse degeneracy-lifting effects can result in a modulated long-range ordered state at nonzero wave vector k, which may or may not be commensurate with the lattice [6][7][8][9][10][11][12]. In some cases, a number of superposed symmetryrelated k modes within the first Brillouin zone form a socalled multiple-k order [6,7,13,14]. A particular interesting form of such modulated magnetism is a partially ordered state (POS) with periodically arranged "paramagnetic" sites [15][16][17][18]. These fluctuating magnetic moments decimate a fraction of the energy-costly frustrated bonds while retaining an extensive entropy, hence lowering the free energy.In this Letter, we study the convergence of the aforementioned phenomena (emergent symmet...

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Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions

Cited by 145 publications

References 34 publications

Mott physics and band topology in materials with strong spin–orbit interaction

Mott physics and band topology in materials with strong spin–orbit interaction

Effects of an external magnetic field on the gaps and quantum corrections in an ordered Heisenberg antiferromagnet with Dzyaloshinskii-Moriya anisotropy

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

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