Momentum-resolved lattice dynamics of parent and electron-doped ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$

Momentum-resolved lattice dynamics of parent and electron-doped ${Sr}_{2} {IrO}_{4}$

C. D. Dashwood, H. Miao, J. G. Vale, D. Ishikawa, D. A. Prishchenko, V. V. Mazurenko, V. G. Mazurenko, R. S. Perry, G. Cao, A. de la Torre, F. Baumberger, A. Q. R. Baron, D. F. McMorrow, and M. P. M. Dean

Phys. Rev. B 100, 085131 – Published 19 August 2019

Abstract

The mixing of orbital and spin character in the wave functions of the $5 d$ iridates has led to predictions of strong couplings among their lattice, electronic, and magnetic degrees of freedom. As well as realizing a novel spin-orbit assisted Mott-insulating ground state, the perovskite iridate ${Sr}_{2} {IrO}_{4}$ has strong similarities with the cuprate ${La}_{2} {CuO}_{4}$ , which on doping hosts a charge-density wave that appears intimately connected to high-temperature superconductivity. These phenomena can be sensitively probed through momentum-resolved measurements of the lattice dynamics, made possible by $meV$ -resolution inelastic x-ray scattering. Here we report the first such measurements for both parent and electron-doped ${Sr}_{2} {IrO}_{4}$ . We find that the low-energy phonon dispersions and intensities in both compounds are well described by the same nonmagnetic density functional theory calculation. In the parent compound, no changes of the phonons on magnetic ordering are discernible within the experimental resolution, and in the doped compound no anomalies are apparent due to charge-density waves. These measurements extend our knowledge of the lattice properties of ( ${Sr}_{1 - x} {La}_{x})_{2} {IrO}_{4}$ and constrain the couplings of the phonons to magnetic and charge order.

Received 24 April 2019

DOI:https://doi.org/10.1103/PhysRevB.100.085131

Physics Subject Headings (PhySH)

Charge density waves Magnetism Phonons Spin-orbit coupling

Iridates Strongly correlated systems

DFT+U Density functional calculations Density functional theory X-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. D. Dashwood^1,*, H. Miao², J. G. Vale¹, D. Ishikawa³, D. A. Prishchenko⁴, V. V. Mazurenko⁴, V. G. Mazurenko⁴, R. S. Perry¹, G. Cao⁵, A. de la Torre^6,7, F. Baumberger⁷, A. Q. R. Baron³, D. F. McMorrow¹, and M. P. M. Dean^2,†

¹London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973, USA
³Materials Dynamics Laboratory, RIKEN SPring-8 Center, RIKEN, Sayo Hyogo 697-5148, Japan
⁴Department of Theoretical Physics and Applied Mathematics, Ural Federal University, 19 Mira Street, Ekaterinburg 620002, Russia
⁵Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
⁶Institute for Quantum Information and Matter and Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
⁷Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland

^*cameron.dashwood.17@ucl.ac.uk
^†mdean@bnl.gov

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Vol. 100, Iss. 8 — 15 August 2019

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Figure 1
(a) Phonon band structure (black lines) and projected phonon DOS for Ir (red), Sr (green), and O (blue), calculated in the LDA on a $2 \times 2 \times 1$ supercell. The high-symmetry points of the $I 4_{1} / a c d$ space group are defined as $Γ = (0, 0, 0)$ , $M = (0.5, 0, 0)$ , $X = (0.5, 0.5, 0)$ , and $P = (0.5, 0.5, 0.5)$ . (b) Brillouin zone map (structural and magnetic zones are equivalent in the $I 4_{1} / a c d$ notation) showing the measured $Q$ points for the parent compound relative to $(4, 5, 0)$ as empty circles and for the doped compound relative to $(0, 0, 26)$ as filled circles. The points have been projected onto the $h − k$ plane, with $l$ values indicated by color. The red crosses show the equivalent in-plane wave vector of the cuprate CDW [29] and orange crosses those of the purported SDW in doped ${Sr}_{2} {IrO}_{4}$ [24] (shown magnified in the inset). The black lines indicate the reciprocal space directions for which data are shown in this manuscript, with spectra at the other $Q$ points contained in the Supplemental Material [37].
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Figure 2
Representative IXS spectra at momenta along $[\bar{1}, 1, 0]$ out from the magnetic Bragg peak position at $(4, 5, 0)$ in the parent compound at $100 K$ (black points) compared to $S (Q, ω)$ calculated with DFT in the LDA on $2 \times 2 \times 1$ supercell (red solid lines) and $LDA + SOC + U$ on a $1 \times 1 \times 1$ supercell at the zone center (blue dashed line). While the LDA calculation matches the measured intensities well across the Brillouin zone, it underestimates the mode energies toward the zone center. The spectra are offset vertically for clarity.
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Figure 3
Bose-factor-corrected IXS spectra in the parent compound (points) and $χ^{″} (Q, ω)$ calculated with DFT in the LDA on $2 \times 2 \times 1$ supercell (solid lines) at $100 K$ (orange) and $260 K$ (purple) for momentum transfers of (a) $(4, 5, 0)$ and (b) $(3.60, 5.37, - 0.04)$ . There is no apparent softening or changes in linewidth for any of the modes, while the intensity changes are fully accounted for by the Debye-Waller factor.
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Figure 4
Phonon dispersions at $250 K$ (white circles) and $9 K$ (red circles) extracted from fits to the IXS spectra of the doped compound. These are overlaid on a colormap of the dynamic structure factor calculated with DFT in the LDA on $2 \times 2 \times 1$ supercell. Vertical error bars represent the statistical errors from fitting. The dispersions are identical within error at the two temperatures, with no apparent softening, and agree well with the calculation.
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Figure 5
Phonon band structures (black lines) and projected phonon DOS for Ir (red), Sr (green), and O (blue), calculated (a) in the LDA on a $2 \times 2 \times 1$ supercell, (b) in the LDA on a $1 \times 1 \times 1$ supercell, and (c) with $LDA + SOC + U$ on a $1 \times 1 \times 1$ supercell. The addition of $SOC + U$ results in small changes in the phonon dispersions, most prominently in the O modes above $30 meV$ , while the increasing the cell size leads to far more significant changes.
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Figure 6
Comparison of IXS spectra (black points) to $S (Q, ω)$ calculated with LDA on a $2 \times 2 \times 1$ supercell (red), LDA on a $1 \times 1 \times 1$ supercell (green), and $LDA + SOC + U$ on a $1 \times 1 \times 1$ supercell (blue) at momentum transfers of (a) $(4, 5, 0)$ and (b) $(3.60, 5.37, - 0.04)$ . At the zone center the calculations differ by only a small shift in the mode energies, while further out in the Brillouin zone the $1 \times 1 \times 1$ supercell calculations predict intense modes that are not present in the experimental data.
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Physical Review B

covering condensed matter and materials physics

Momentum-resolved lattice dynamics of parent and electron-doped ${Sr}_{2} {IrO}_{4}$

C. D. Dashwood, H. Miao, J. G. Vale, D. Ishikawa, D. A. Prishchenko, V. V. Mazurenko, V. G. Mazurenko, R. S. Perry, G. Cao, A. de la Torre, F. Baumberger, A. Q. R. Baron, D. F. McMorrow, and M. P. M. Dean

Phys. Rev. B 100, 085131 – Published 19 August 2019

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Momentum-resolved lattice dynamics of parent and electron-doped Sr2IrO4

C. D. Dashwood, H. Miao, J. G. Vale, D. Ishikawa, D. A. Prishchenko, V. V. Mazurenko, V. G. Mazurenko, R. S. Perry, G. Cao, A. de la Torre, F. Baumberger, A. Q. R. Baron, D. F. McMorrow, and M. P. M. Dean

Phys. Rev. B 100, 085131 – Published 19 August 2019

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Momentum-resolved lattice dynamics of parent and electron-doped ${Sr}_{2} {IrO}_{4}$