Coexistence of static and dynamic magnetism in the Kitaev spin liquid material ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$

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Coexistence of static and dynamic magnetism in the Kitaev spin liquid material ${Cu}_{2} {IrO}_{3}$

Eric M. Kenney, Carlo U. Segre, William Lafargue-Dit-Hauret, Oleg I. Lebedev, Mykola Abramchuk, Adam Berlie, Stephen P. Cottrell, Gediminas Simutis, Faranak Bahrami, Natalia E. Mordvinova, Gilberto Fabbris, Jessica. L. McChesney, Daniel Haskel, Xavier Rocquefelte, Michael J. Graf, and Fazel Tafti

Phys. Rev. B 100, 094418 – Published 12 September 2019

Abstract

Searching for a Kitaev spin liquid phase motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hindered by magnetic ordering. ${Cu}_{2} {IrO}_{3}$ is a new honeycomb iridate without thermodynamic signatures of a long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of ${Cu}_{2} {IrO}_{3}$ . We find a two-component depolarization with slow- and fast-relaxation rates corresponding to distinct regions with dynamic and static magnetism coexisting in the material. X-ray absorption spectroscopy and first-principles calculations identify a mixed copper valence as the origin of this behavior. Our results suggest that a minority of ${Cu}^{2 +}$ ions nucleate regions of static magnetism, whereas the majority of ${Cu}^{+} / {Ir}^{4 +}$ on the honeycomb lattice give rise to a Kitaev spin liquid.

Received 4 April 2019
Revised 28 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.094418

Physics Subject Headings (PhySH)

Quantum spin liquid

Kitaev model Muon spin relaxation & rotation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Eric M. Kenney¹, Carlo U. Segre², William Lafargue-Dit-Hauret³, Oleg I. Lebedev⁴, Mykola Abramchuk¹, Adam Berlie⁵, Stephen P. Cottrell⁵, Gediminas Simutis⁶, Faranak Bahrami¹, Natalia E. Mordvinova⁴, Gilberto Fabbris⁷, Jessica. L. McChesney⁷, Daniel Haskel⁷, Xavier Rocquefelte³, Michael J. Graf¹, and Fazel Tafti ^1,*

¹Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
²Department of Physics & CSRRI, Illinois Institute of Technology, Chicago, Illinois 60616, USA
³Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) UMR 6226, F-35000 Rennes, France
⁴Laboratoire CRISMAT, ENSICAEN-CNRS UMR6508, 14050 Caen, France
⁵ISIS Neutron and Muon Source, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
⁶Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
⁷Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

^*fazel.tafti@bc.edu

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Vol. 100, Iss. 9 — 1 September 2019

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Figure 1
(a) Representative zero field (ZF) spectra obtained at 300 K (green squares), 16 K (red diamonds), 4.5 K (blue triangles), and 0.05 K (gray circles). Continuous lines are fits to the data. (b) Temperature dependence of the slow-depolarization rate $λ_{slow}$ shows a plateau below 2 K at both ZF and LF of 1000 Oe with data extending over two decades of temperature from 20 to 0.05 K. (c) Temperature dependence of the fast-depolarization fraction $f$ shows a plateau below 2 K. (d) DC magnetic susceptibility shows a small peak at 2 K and a splitting between field-cooled (FC) and zero-field-cooled (ZFC) at 10 K. (e) $μ SR$ spectra at 75 mK in several longitudinal fields show a persistent slow depolarization and a vanishing fast-depolarization component.
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Figure 2
(a) A unit cell of ${Cu}_{2} {IrO}_{3}$ viewed down the $a$ axis with four distinct copper sites. Cu1 in octahedral coordination is within the honeycomb layers, whereas Cu2, Cu3, and Cu4 in dumbbell coordination are between the layers. (b) Normalized absorption coefficient plotted as a function of energy in ${Cu}_{2} {IrO}_{3}$ . The $μ (E)$ curves are identical at 85 and 300 K. (c) Comparing $μ (E)$ between ${Cu}_{2} {IrO}_{3}$ and three standard references. (d) Calculated absorption edge of Cu1 to Cu4 using the FEFF software. (e) Absorption spectrum of the Cu $K$ edge is calculated by summing over the partial contributions from Cu1 to Cu4 with equal weights. The calculated signal is shifted by 5.3 eV to match the experimental data with acceptable but not perfect agreement. (f) A fit is made to the experimental XANES data where the weight of each partial contribution is a free parameter. The resulting weights for Cu1 to Cu4 are reported. Cu3 and Cu4 have the same weight. The fit errors are $\pm 1 %$ for Cu1 and $\pm 4 %$ for Cu2, Cu3, and Cu4.
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Figure 3
(a) Cu $L_{2}$ - and $L_{3}$ -edge x-ray absorption data for ${Cu}_{2} {IrO}_{3}$ together with ${Cu}^{+}$ and ${Cu}^{2 +}$ reference spectra taken from the literature [35]. Data were normalized to Cromer-Liberman calculations of the single-atom x-ray absorption cross section [36]. The ${Cu}^{2 +}$ content was estimated from white line intensity ratios in sample and references, averaged over $L_{2}$ and $L_{3}$ edges. (b) Iridium $L_{3}$ (11.22 keV) and $L_{2}$ (12.83 keV) edges are measured using XANES. The green area under each peak represents the absorption cross section with a branching ratio of $R = I (L_{3}) / I (L_{2}) = 6$ .
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Figure 4
(a) STEM is used to reveal perfect honeycomb ordering and twinned stacking disorder in ${Cu}_{2} {IrO}_{3}$ . The top left image is an electron diffraction pattern along [100] where the streaking reveals stacking disorder along the $c$ axis. The middle panel shows a HAADF-STEM image along [100] with a zigzag stacking that is modeled in the left inset as a twinning between [100], [110], and $[\bar{1} 10]$ directions. Yellow, blue, and red circles represent Ir, Cu, and O atoms, respectively. The right top and bottom panels are magnified HAADF-STEM and ABF-STEM images, respectively. In each image, one unit cell along [100] and one unit cell along $[\bar{1} 10]$ are modeled. Perfect honeycomb ordering is observed within each layer. (b) Experimental EELS spectra are compared between the stannates, ${Cu}_{1.5} {Li}_{0.5} {SnO}_{3}$ and ${Cu}_{1.5} {Na}_{0.5} {SnO}_{3}$ , and the iridate ${Cu}_{2} {IrO}_{3}$ . Only one $L_{3}$ peak is observed in the stannates corresponding to ${Cu}^{+}$ (note the CuO reference). ${Cu}_{2} {IrO}_{3}$ shows two $L_{3}$ peaks corresponding to ${Cu}^{+}$ and ${Cu}^{2 +}$ . (c) Self-consistent DFT calculations reproduce EELS spectra in agreement with the experiments. The calculations reveal one peak in stannates corresponding to ${Cu}^{+}$ in dumbbell coordination but two peaks in ${Cu}_{2} {IrO}_{3}$ due to mixed valence of copper (see Supplemental Material for details of DFT calculations [30]).
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Physical Review B

covering condensed matter and materials physics

Coexistence of static and dynamic magnetism in the Kitaev spin liquid material ${Cu}_{2} {IrO}_{3}$

Eric M. Kenney, Carlo U. Segre, William Lafargue-Dit-Hauret, Oleg I. Lebedev, Mykola Abramchuk, Adam Berlie, Stephen P. Cottrell, Gediminas Simutis, Faranak Bahrami, Natalia E. Mordvinova, Gilberto Fabbris, Jessica. L. McChesney, Daniel Haskel, Xavier Rocquefelte, Michael J. Graf, and Fazel Tafti

Phys. Rev. B 100, 094418 – Published 12 September 2019

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Physical Review B

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Coexistence of static and dynamic magnetism in the Kitaev spin liquid material Cu2IrO3

Eric M. Kenney, Carlo U. Segre, William Lafargue-Dit-Hauret, Oleg I. Lebedev, Mykola Abramchuk, Adam Berlie, Stephen P. Cottrell, Gediminas Simutis, Faranak Bahrami, Natalia E. Mordvinova, Gilberto Fabbris, Jessica. L. McChesney, Daniel Haskel, Xavier Rocquefelte, Michael J. Graf, and Fazel Tafti

Phys. Rev. B 100, 094418 – Published 12 September 2019

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Coexistence of static and dynamic magnetism in the Kitaev spin liquid material ${Cu}_{2} {IrO}_{3}$