Spin-Orbit Coupling in the Mott Insulator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Ca</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>RuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Mizokawa, T.; Tjeng, L. H.; Sawatzky, G. A.; Ghiringhelli, G.; Tjernberg, Oscar; Brookes, N. B.; Fukazawa, Hideto; Nakatsuji, Satoru; Maeno, Y.

doi:10.1103/physrevlett.87.077202

Cited by 202 publications

(221 citation statements)

References 23 publications

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“…This striking manifestation of orbital magnetism in Ca 2 RuO 4 leads us to consider the limit of strong spin-orbit coupling described in terms of a singlet and a triplet separated in energy by λ (Fig. 1), which was estimated in earlier experiments [14][15][16] to be in the range ∼75-100 meV. In this limit, the ground state is non-magnetic with zero total angular momentum, and therefore a QCP separating it from a magnetically ordered phase is expected as a matter of principle.…”

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confidence: 84%

Higgs mode and its decay in a two-dimensional antiferromagnet

et al. 2017

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Condensed-matter analogues of the Higgs boson in particle physics allow insights into its behaviour in di erent symmetries and dimensionalities 1 . Evidence for the Higgs mode has been reported in a number of di erent settings, including ultracold atomic gases 2 , disordered superconductors 3 , and dimerized quantum magnets 4 . However, decay processes of the Higgs mode (which are eminently important in particle physics)have not yet been studied in condensed matter due to the lack of a suitable material system coupled to a direct experimental probe. A quantitative understanding of these processes is particularly important for low-dimensional systems, where the Higgs mode decays rapidly and has remained elusive to most experimental probes. Here, we discover and study the Higgs mode in a two-dimensional antiferromagnet using spin-polarized inelastic neutron scattering. Our spin-wave spectra of Ca 2 RuO 4 directly reveal a well-defined, dispersive Higgs mode, which quickly decays into transverse Goldstone modes at the antiferromagnetic ordering wavevector. Through a complete mapping of the transverse modes in the reciprocal space, we uniquely specify the minimal model Hamiltonian and describe the decay process. We thus establish a novel condensed-matter platform for research on the dynamics of the Higgs mode.For a system of interacting spins, amplitude fluctuations of the local magnetization-the Higgs mode-can exist as well-defined collective excitations near a quantum critical point (QCP). We consider here a magnetic instability driven by the intra-ionic spinorbit coupling, which tends towards a non-magnetic state through complete cancellation of orbital (L) and spin (S) moments when they are antiparallel and of equal magnitude 5,6 . This mechanism should be broadly relevant for d 4 compounds of such ions as Ir(V), Ru(IV), Os(IV) and Re(III) with sizable spin-orbit coupling but remains little explored. We investigate the magnetic insulator Ca 2 RuO 4 , a quasi-two-dimensional antiferromagnet 7 with nominally L = 1 and S = 1 (Fig. 1). Because the local symmetry around the Ru(IV) ion is very low 8,9 (having only inversion symmetry), it is widely believed that the orbital moment is completely quenched by the crystalline electric field 10-13 , which is dominated by the compressive distortion of the RuO 6 octahedra along the c-axis (Fig. 1). In the absence of an orbital moment, the nearest-neighbour magnetic exchange interaction is necessarily isotropic. Deviations from this behaviour are a sensitive indicator of an unquenched orbital moment. If this moment is sufficiently strong, it can drive Ca 2 RuO 4 close to a QCP with novel Higgs physics.Our comprehensive set of time-of-flight (TOF) inelastic neutron scattering (INS) data over the full Brillouin zone (Fig. 2a) indeed reveal qualitative deviations of the transverse spin-wave dispersion from those of a Heisenberg antiferromagnet. In particular, the global maximum of the dispersion is found at q = (0,0), in sharp contrast to a Heisenberg antiferromagnet, which has a...

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confidence: 84%

Higgs mode and its decay in a two-dimensional antiferromagnet

et al. 2017

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“…The technical implementation is the same as described in Refs. [25,26,46]. Namely, the local Coulomb interaction Hamiltonian H int is replaced by mean field terms derived in HF approximation.…”

Section: The Unrestricted Hartree-fock Approximationmentioning

confidence: 99%

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

Rościszewski

Oleś

2016

Phys. Rev. B

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We introduce and investigate the multiband d − p model describing a IrO4 layer (such as realized in Ba2IrO4) where all 34 orbitals per unit cell are partly occupied, i.e., t2g and eg orbitals at iridium and 2p orbitals at oxygen ions. The model takes into account anisotropic iridium-oxygen d − p and oxygen-oxygen p − p hopping processes, crystal-field splittings, spin-orbit coupling, and the on-site Coulomb interactions, both at iridium and at oxygen ions. We show that the predictions based on assumed idealized ionic configuration (with n0 = 5 + 4 × 6 = 29 electrons per IrO4 unit) do not explain well the independent ab initio data and the experimental data for Ba2IrO4. Instead we find that the total electron density in the d − p states is smaller, n = 29 − x < n0 (x > 0). When we fix x = 1, the predictions for the d − p model become more realistic and weakly insulating antiferromagnetic ground state with the moments lying within IrO2 planes along (110) direction is found, in agreement with experiment and ab initio data. We also show that: (i) holes delocalize over the oxygen orbitals and the electron density at iridium ions is enhanced, hence (ii) their eg orbitals are occupied by more than one electron and have to be included in the multiband d − p model describing iridates.

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“…Then, the kinetic part of the Hamiltonian H t + H so can be diagonalized and the new energy dispersions are obtained [38]. Note, we use λ = 80meV in accordance with earlier estimations [36,37]. Most importantly, the spin-orbit coupling does not break the time-reversal symmetry and therefore the Kramers degeneracy between the spin up and down is not removed.…”

Section: Spin-orbit Coupling Effects In the Normal And Superconductinmentioning

confidence: 99%

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

et al. 2004

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Key words unconventional triplet superconductivity, spin fluctuations, strong electronic correlations PACS 74.20.Mn, 74.70.Pq We review the normal and superconducting state properties of the unconventional triplet superconductor Sr2RuO4 with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru d-orbitals and a strong magnetic anisotropy occurs (χ +− < χ zz ) due to spin-orbit coupling. The latter results mainly from different values of the g-factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation-induced Cooper-pairing scenario in application to Sr2RuO4 we show how p-wave Cooper-pairing with line nodes between neighboring RuO2-planes may occur.We also discuss the open issues in Sr2RuO4 like the influence of magnetic and non-magnetic impurities on the superconducting and normal state of Sr2RuO4. It is clear that the physics of triplet superconductivity in Sr2RuO4 is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy-fermion systems exhibiting spin fluctuations.

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Spin-Orbit Coupling in the Mott InsulatorCa2RuO4

Cited by 202 publications

References 23 publications

Higgs mode and its decay in a two-dimensional antiferromagnet

Higgs mode and its decay in a two-dimensional antiferromagnet

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

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

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