Spectral Evidence for Emergent Order in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Na}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$

Spectral Evidence for Emergent Order in ${Ba}_{1 - x} {Na}_{x} {Fe}_{2} {As}_{2}$

M. Yi, A. Frano, D. H. Lu, Y. He, Meng Wang, B. A. Frandsen, A. F. Kemper, R. Yu, Q. Si, L. Wang, M. He, F. Hardy, P. Schweiss, P. Adelmann, T. Wolf, M. Hashimoto, S.-K. Mo, Z. Hussain, M. Le Tacon, A. E. Böhmer, D.-H. Lee, Z.-X. Shen, C. Meingast, and R. J. Birgeneau

Phys. Rev. Lett. 121, 127001 – Published 18 September 2018

Abstract

We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, ${Ba}_{1 - x} {Na}_{x} {Fe}_{2} {As}_{2}$ . This system harbors the recently discovered double- $Q$ magnetic order appearing in a reentrant $C_{4}$ phase deep within the underdoped regime of the phase diagram that is otherwise dominated by the coupled nematic phase and collinear antiferromagnetic order. From a detailed temperature-dependence study, we identify the electronic response to the nematic phase in an orbital-dependent band shift that strictly follows the rotational symmetry of the lattice and disappears when the system restores $C_{4}$ symmetry in the low temperature phase. In addition, we report the observation of a distinct electronic reconstruction that cannot be explained by the known electronic orders in the system.

Received 13 January 2018
Revised 5 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.127001

Physics Subject Headings (PhySH)

Unconventional superconductors

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Yi^1,2,*, A. Frano^1,3,‡, D. H. Lu⁴, Y. He^5,6, Meng Wang⁷, B. A. Frandsen⁸, A. F. Kemper⁹, R. Yu¹⁰, Q. Si², L. Wang^11,12, M. He¹¹, F. Hardy¹¹, P. Schweiss¹¹, P. Adelmann¹¹, T. Wolf¹¹, M. Hashimoto⁴, S.-K. Mo³, Z. Hussain³, M. Le Tacon¹¹, A. E. Böhmer¹¹, D.-H. Lee^1,8, Z.-X. Shen^5,6, C. Meingast¹¹, and R. J. Birgeneau^1,8,13,†

¹Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
²Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
³Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
⁴Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁵Stanford Institute of Materials and Energy Sciences, Stanford University, Stanford, California 94305, USA
⁶Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
⁷School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
⁸Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁹Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
¹⁰Department of Physics, Renmin University of China, Beijing 100872, China
¹¹Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
¹²Kirchhoff-Institute for Physics, Universitt Heidelberg, D-69120 Heidelberg, Germany
¹³Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA

^*mingyi@berkeley.edu; mingyi@rice.edu
^†robertjb@berkeley.edu
^‡Present address: Department of Physics, University of California, San Diego, California 95203, USA.

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Vol. 121, Iss. 12 — 21 September 2018

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Figure 1
${Ba}_{1 - x} {Na}_{x} {Fe}_{2} {As}_{2}$ phase diagram and dilatometry measurements. (a) Phase diagram adapted from Ref. [9]. The inset shows the DQMO in the reentrant $C_{4}$ phase. (b) Temperature dependence of the thermal expansion coefficient $α$ plotted as $α / T$ , and relative thermal expansion $Δ L_{b} / L_{b}$ for the samples measured by ARPES. The inset shows $α / T$ measured along the twinned ([100]) direction of BN25.
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Figure 2
Temperature dependence of BN40 and BN18. Second derivative of the measured band dispersions along the $Γ - X$ direction of BN40, taken at 15 K. (b) Same measurement for the twinned orthorhombic phase of BN18 at 15 K. (c)–(d) Fine temperature dependence at the selected momenta on BN40. (e)–(f) Fine temperature dependence at the selected momenta on BN18. All measurements were taken with 25 eV photons under polarization odd with respect to the cut direction.
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Figure 3
Temperature dependence of BN25. Band dispersions are shown along $Γ - X$ for (a) $T > T_{S} = T_{N}$ , (b) $T_{S} = T_{N} > T > T_{DQ}$ , and (c) $T < T_{DQ}$ . Temperature-dependent EDCs are shown for $k_{1}$ (d) and $k_{2}$ (e) as marked by arrows in (a). All image plots are second energy derivatives. (f) Fitted band positions of the temperature dependence at $k_{1}$ using one peak for the $C_{4}$ phases ( $T < T_{DQ}$ and $T > T_{S}$ ) and two peaks for the $C_{2}$ phase ( $T_{DQ} < T < T_{S}$ ). (g) Band splitting (black) is compared to the lattice distortion measured by dilatometry (blue). Each second derivative EDC in (d)–(e) is fitted by a constant background and a single Gaussian peak where anomalous broadening suggests band splitting [18]. Fitted single-peak FWHM for $k_{1}$ (h) and $k_{2}$ (i) shown as a function of temperature. The black line for $k_{2}$ is a fitted linear background extrapolating the behavior of a system without any ordering [18]. The low temperature EDCs in (e) are also fitted by two peaks, where the extracted splitting size is shown in magenta in (i) [18]. All measurements were taken with 25 eV photons under LH polarization.
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Figure 4
Simulated effects for different electronic orders. A tight-binding fit of undoped ${BaFe}_{2} {As}_{2}$ to DFT band structure is used, with an overall shift of 0.12 eV and renormalization of 4.3 to best match the measured dispersions in the normal state of BN25. (a) Calculated dispersions along $Γ - X$ in the normal state. (b) Schematic of the FS showing the relevant folding vectors. Simulated reconstructed bands in the box region in (a) are shown for (c) the CAF order with $q_{1} = (π / 2, π / 2, π)_{T}$ , (d) the double-Q order with both $q_{1} = (π / 2, π / 2, π)_{T}$ and $q_{2} = (π / 2, - π / 2, π)_{T}$ , and (e) the CO with $q_{3} = (π, 0, 0)_{T}$ , where the doubling of bands is observed around $X$ (white arrows). Blue arrows point to magnetic energy gaps.
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Physical Review Letters

Spectral Evidence for Emergent Order in Ba1−xNaxFe2As2

M. Yi, A. Frano, D. H. Lu, Y. He, Meng Wang, B. A. Frandsen, A. F. Kemper, R. Yu, Q. Si, L. Wang, M. He, F. Hardy, P. Schweiss, P. Adelmann, T. Wolf, M. Hashimoto, S.-K. Mo, Z. Hussain, M. Le Tacon, A. E. Böhmer, D.-H. Lee, Z.-X. Shen, C. Meingast, and R. J. Birgeneau

Phys. Rev. Lett. 121, 127001 – Published 18 September 2018

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Spectral Evidence for Emergent Order in ${Ba}_{1 - x} {Na}_{x} {Fe}_{2} {As}_{2}$