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Liu C, Bourges P, Sidis Y, Xie T, He G, Bourdarot F, Danilkin S, Ghosh H, Ghosh S, Ma X, Li S, Li Y, Luo H. Preferred Spin Excitations in the Bilayer Iron-Based Superconductor CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with Spin-Vortex Crystal Order. PHYSICAL REVIEW LETTERS 2022; 128:137003. [PMID: 35426714 DOI: 10.1103/physrevlett.128.137003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 02/23/2022] [Indexed: 06/14/2023]
Abstract
Spin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK(Fe_{0.96}Ni_{0.04})_{4}As_{4} with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe_{4}As_{4} but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. These results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below T_{c} regardless of the details of magnetic pattern or lattice symmetry.
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Affiliation(s)
- Chang Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Philippe Bourges
- Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Yvan Sidis
- Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
| | - Tao Xie
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Guanghong He
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | | | - Sergey Danilkin
- Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organization, Lucas Heights NSW-2234, Australia
| | - Haranath Ghosh
- Human Resources Development Section, Raja Ramanna Centre for Advanced Technology, Indore 452013, India
- Homi Bhabha National Institute, BARC training school complex 2nd floor, Anushakti Nagar, Mumbai 400094, India
| | - Soumyadeep Ghosh
- Human Resources Development Section, Raja Ramanna Centre for Advanced Technology, Indore 452013, India
- Homi Bhabha National Institute, BARC training school complex 2nd floor, Anushakti Nagar, Mumbai 400094, India
| | - Xiaoyan Ma
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Shiliang Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Yuan Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Huiqian Luo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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2
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Iron pnictides and chalcogenides: a new paradigm for superconductivity. Nature 2022; 601:35-44. [PMID: 34987212 DOI: 10.1038/s41586-021-04073-2] [Citation(s) in RCA: 30] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 09/29/2021] [Indexed: 11/09/2022]
Abstract
Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.
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3
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Riedl K, Gati E, Zielke D, Hartmann S, Vyaselev OM, Kushch ND, Jeschke HO, Lang M, Valentí R, Kartsovnik MV, Winter SM. Spin Vortex Crystal Order in Organic Triangular Lattice Compound. PHYSICAL REVIEW LETTERS 2021; 127:147204. [PMID: 34652199 DOI: 10.1103/physrevlett.127.147204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 08/25/2021] [Indexed: 06/13/2023]
Abstract
Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.
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Affiliation(s)
- Kira Riedl
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - Elena Gati
- Physikalisches Institut, Goethe-Universität Frankfurt, Max von Laue Str 1, 60438 Frankfurt am Main, Germany
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - David Zielke
- Physikalisches Institut, Goethe-Universität Frankfurt, Max von Laue Str 1, 60438 Frankfurt am Main, Germany
| | - Steffi Hartmann
- Physikalisches Institut, Goethe-Universität Frankfurt, Max von Laue Str 1, 60438 Frankfurt am Main, Germany
| | - Oleg M Vyaselev
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia
| | - Nataliya D Kushch
- Institute of Problems of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia
| | - Harald O Jeschke
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Michael Lang
- Physikalisches Institut, Goethe-Universität Frankfurt, Max von Laue Str 1, 60438 Frankfurt am Main, Germany
| | - Roser Valentí
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - Mark V Kartsovnik
- Walther-Meissner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meissner-Strasse 8, Garching D-85748, Germany
| | - Stephen M Winter
- Department of Physics and Center for Functional Materials, Wake Forest University, Winston-Salem, North Carolina 27109, USA
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4
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Abstract
Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.
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5
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Xu B, Cappelluti E, Benfatto L, Mallett BPP, Marsik P, Sheveleva E, Lyzwa F, Wolf T, Yang R, Qiu XG, Dai YM, Wen HH, Lobo RPSM, Bernhard C. Scaling of the Fano Effect of the In-Plane Fe-As Phonon and the Superconducting Critical Temperature in Ba_{1-x}K_{x}Fe_{2}As_{2}. PHYSICAL REVIEW LETTERS 2019; 122:217002. [PMID: 31283343 DOI: 10.1103/physrevlett.122.217002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Indexed: 06/09/2023]
Abstract
By means of infrared spectroscopy, we determine the temperature-doping phase diagram of the Fano effect for the in-plane Fe-As stretching mode in Ba_{1-x}K_{x}Fe_{2}As_{2}. The Fano parameter 1/q^{2}, which is a measure of the phonon coupling to the electronic particle-hole continuum, shows a remarkable sensitivity to the magnetic and structural orderings at low temperatures. Most strikingly, at elevated temperatures in the paramagnetic tetragonal state we observe a linear correlation between 1/q^{2} and the superconducting critical temperature T_{c}. Based on theoretical calculations and symmetry considerations, we identify the relevant interband transitions that are coupled to the Fe-As mode. In particular, we show that a sizable xy orbital component at the Fermi level is fundamental for the Fano effect and, thus, possibly also for the superconducting pairing.
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Affiliation(s)
- B Xu
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| | - E Cappelluti
- Istituto di Struttura della Materia, CNR, 34149 Trieste, Italy
| | - L Benfatto
- ISC-CNR and Department of Physics, Sapienza University of Rome, P. le A. Moro 5, 00185 Rome, Italy
| | - B P P Mallett
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
- The Photon Factory, Department of Physics, University of Auckland, 38 Princes Street, Auckland 1010, New Zealand
| | - P Marsik
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| | - E Sheveleva
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| | - F Lyzwa
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| | - Th Wolf
- Institute of Solid State Physics, Karlsruhe Institute of Technology, Postfach 3640, Karlsruhe 76021, Germany
| | - R Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - X G Qiu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Y M Dai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - H H Wen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - R P S M Lobo
- LPEM, ESPCI Paris, PSL University, CNRS, F-75005 Paris, France
- Sorbonne Université, CNRS, LPEM, F-75005 Paris, France
| | - C Bernhard
- University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
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6
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Zheng X, Huang Z, Li H, Yang F, Lin H. Universal understanding of nematicity and magnetism in Fe-pnictides and FeSe. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:055601. [PMID: 30524101 DOI: 10.1088/1361-648x/aaf404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
By employing the mean field and variational Monte Carlo methods, we investigate the iron-based superconductors (FeSCs) based on a realistic five-orbital Hubbard model in which an off-site Coulomb interaction [Formula: see text] is explicitly included. Our results demonstrate that [Formula: see text] plays an important role in stabilizing the nematic state in both Fe-pnictides and FeSe. Below a critical [Formula: see text], the model is shown to lie in the striped antiferromagnetic ground state, and an increasing of [Formula: see text] leads to an energy degeneracy between different magnetic configurations. This finding provides a natural explanation for the magnetism in Fe-pnictides with relatively small [Formula: see text], and more importantly, unveils the microscopic mechanism behind the absence of magnetic order in FeSe with larger [Formula: see text]. Simultaneously, the common anisotropy of [Formula: see text] and [Formula: see text] orbital occupations in different magnetic configurations accounts for the similar orbital ordering observed in Fe-pnictides and FeSe. In addition, the unusual smallness of the Fermi surfaces in FeSe can be obtained when the renormalization effect of [Formula: see text] on the band structure is taken into account.
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Affiliation(s)
- Xiaojun Zheng
- College of Science, Guilin University of Technology, Guilin 541004, People's Republic of China
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7
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Yi M, Frano A, Lu DH, He Y, Wang M, Frandsen BA, Kemper AF, Yu R, Si Q, Wang L, He M, Hardy F, Schweiss P, Adelmann P, Wolf T, Hashimoto M, Mo SK, Hussain Z, Le Tacon M, Böhmer AE, Lee DH, Shen ZX, Meingast C, Birgeneau RJ. Spectral Evidence for Emergent Order in Ba_{1-x}Na_{x}Fe_{2}As_{2}. PHYSICAL REVIEW LETTERS 2018; 121:127001. [PMID: 30296157 DOI: 10.1103/physrevlett.121.127001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2018] [Revised: 07/05/2018] [Indexed: 06/08/2023]
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.
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Affiliation(s)
- M Yi
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - A Frano
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - D H Lu
- Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Y He
- Stanford Institute of Materials and Energy Sciences, Stanford University, Stanford, California 94305, USA
- Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
| | - Meng Wang
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - B A Frandsen
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - A F Kemper
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - R Yu
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Q Si
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - L Wang
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
- Kirchhoff-Institute for Physics, Universitt Heidelberg, D-69120 Heidelberg, Germany
| | - M He
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - F Hardy
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - P Schweiss
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - P Adelmann
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - T Wolf
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - M Hashimoto
- Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - S-K Mo
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - Z Hussain
- Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| | - M Le Tacon
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - A E Böhmer
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - D-H Lee
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Z-X Shen
- Stanford Institute of Materials and Energy Sciences, Stanford University, Stanford, California 94305, USA
- Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
| | - C Meingast
- Institute for Solid State Physics, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - R J Birgeneau
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
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8
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Christensen MH, Orth PP, Andersen BM, Fernandes RM. Emergent Magnetic Degeneracy in Iron Pnictides due to the Interplay between Spin-Orbit Coupling and Quantum Fluctuations. PHYSICAL REVIEW LETTERS 2018; 121:057001. [PMID: 30118255 DOI: 10.1103/physrevlett.121.057001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 06/08/2023]
Abstract
Recent experiments in iron pnictide superconductors reveal that, as the putative magnetic quantum critical point is approached, different types of magnetic order coexist over a narrow region of the phase diagram. Although these magnetic configurations share the same wave vectors, they break distinct symmetries of the lattice. Importantly, the highest superconducting transition temperature takes place close to this proliferation of near-degenerate magnetic states. In this Letter, we employ a renormalization group calculation to show that such a behavior naturally arises due to the effects of spin-orbit coupling on the quantum magnetic fluctuations. Formally, the enhanced magnetic degeneracy near the quantum critical point is manifested as a stable Gaussian fixed point with a large basin of attraction. Implications of our findings to the superconductivity of the iron pnictides are also discussed.
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Affiliation(s)
- Morten H Christensen
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Peter P Orth
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
- Ames Laboratory, U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - Brian M Andersen
- Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100, Denmark
| | - Rafael M Fernandes
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
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9
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Scherer DD, Andersen BM. Spin-Orbit Coupling and Magnetic Anisotropy in Iron-Based Superconductors. PHYSICAL REVIEW LETTERS 2018; 121:037205. [PMID: 30085777 DOI: 10.1103/physrevlett.121.037205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2017] [Indexed: 06/08/2023]
Abstract
We determine theoretically the effect of spin-orbit coupling on the magnetic excitation spectrum of itinerant multiorbital systems, with specific application to iron-based superconductors. Our microscopic model includes a realistic ten-band kinetic Hamiltonian, atomic spin-orbit coupling, and multiorbital Hubbard interactions. Our results highlight the remarkable variability of the resulting magnetic anisotropy despite constant spin-orbit coupling. At the same time, the magnetic anisotropy exhibits robust universal behavior upon changes in the band structure corresponding to different materials of iron-based superconductors. A natural explanation of the observed universality emerges when considering optimal nesting as a resonance phenomenon. Our theory is also of relevance to other itinerant systems with spin-orbit coupling and nesting tendencies in the band structure.
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Affiliation(s)
- Daniel D Scherer
- Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark
| | - Brian M Andersen
- Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark
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10
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Scanning tunnelling spectroscopy as a probe of multi-Q magnetic states of itinerant magnets. Nat Commun 2017; 8:14317. [PMID: 28176779 PMCID: PMC5309833 DOI: 10.1038/ncomms14317] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Accepted: 12/16/2016] [Indexed: 11/14/2022] Open
Abstract
The combination of electronic correlations and Fermi surfaces with multiple nesting vectors can lead to the appearance of complex multi-Q magnetic ground states, hosting unusual states such as chiral density waves and quantum Hall insulators. Distinguishing single-Q and multi-Q magnetic phases is however a notoriously difficult experimental problem. Here we propose theoretically that the local density of states (LDOS) near a magnetic impurity, whose orientation may be controlled by an external magnetic field, can be used to map out the detailed magnetic configuration of an itinerant system and distinguish unambiguously between single-Q and multi-Q phases. We demonstrate this concept by computing and contrasting the LDOS near a magnetic impurity embedded in three different magnetic ground states relevant to iron-based superconductors—one single-Q and two double-Q phases. Our results open a promising avenue to investigate the complex magnetic configurations in itinerant systems via standard scanning tunnelling spectroscopy, without requiring spin-resolved capability. It remains difficult to distinguish single-Q and multi-Q magnetic states experimentally. Here, Gastiasoro et al. show that the magnetic configuration of an itinerant system can be mapped out to the local density of states near a magnetic impurity, distinguishing unambiguously between single-Q and multi-Q phases.
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11
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Fernandes RM, Chubukov AV. Low-energy microscopic models for iron-based superconductors: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:014503. [PMID: 27876709 DOI: 10.1088/1361-6633/80/1/014503] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The development of sensible microscopic models is essential to elucidate the normal-state and superconducting properties of the iron-based superconductors. Because these materials are mostly metallic, a good starting point is an effective low-energy model that captures the electronic states near the Fermi level and their interactions. However, in contrast to cuprates, iron-based high-T c compounds are multi-orbital systems with Hubbard and Hund interactions, resulting in a rather involved 10-orbital lattice model. Here we review different minimal models that have been proposed to unveil the universal features of these systems. We first review minimal models defined solely in the orbital basis, which focus on a particular subspace of orbitals, or solely in the band basis, which rely only on the geometry of the Fermi surface. The former, while providing important qualitative insight into the role of the orbital degrees of freedom, do not distinguish between high-energy and low-energy sectors and, for this reason, generally do not go beyond mean-field. The latter allow one to go beyond mean-field and investigate the interplay between superconducting and magnetic orders as well as Ising-nematic order. However, they cannot capture orbital-dependent features like spontaneous orbital order. We then review recent proposals for a minimal model that operates in the band basis but fully incorporates the orbital composition and symmetries of the low-energy excitations. We discuss the results of the renormalization group study of such a model, particularly of the interplay between superconductivity, magnetism, and spontaneous orbital order, and compare theoretical predictions with experiments on iron pnictides and chalcogenides. We also discuss the impact of the glide-plane symmetry on the low-energy models, highlighting the key role played by the spin-orbit coupling.
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12
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Böhmer AE, Hardy F, Wang L, Wolf T, Schweiss P, Meingast C. Superconductivity-induced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2. Nat Commun 2015; 6:7911. [PMID: 26227915 PMCID: PMC4532874 DOI: 10.1038/ncomms8911] [Citation(s) in RCA: 122] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2015] [Accepted: 06/22/2015] [Indexed: 11/28/2022] Open
Abstract
Detailed knowledge of the phase diagram and the nature of the competing magnetic and superconducting phases is imperative for a deeper understanding of the physics of iron-based superconductivity. Magnetism in the iron-based superconductors is usually a stripe-type spin-density-wave, which breaks the tetragonal symmetry of the lattice, and is known to compete strongly with superconductivity. Recently, it was found that in some systems an additional spin-density-wave transition occurs, which restores this tetragonal symmetry, however, its interaction with superconductivity remains unclear. Here, using thermodynamic measurements on Ba1−xKxFe2As2 single crystals, we show that the spin-density-wave phase of tetragonal symmetry competes much stronger with superconductivity than the stripe-type spin-density-wave phase, which results in a novel re-entrance of the latter at or slightly below the superconducting transition. The interplay between magnetic and superconducting phases is important to understand the physics of iron-based superconductivity. Here, the authors use thermodynamic measurements on Ba1−xKxFe2As2 single crystals to provide details of its phase diagram and the re-entrance of a C2 spin-density-wave phase.
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Affiliation(s)
- A E Böhmer
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - F Hardy
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - L Wang
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - T Wolf
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - P Schweiss
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - C Meingast
- Institut für Festkörperphysik, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
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13
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Liu GK, Huang ZB, Wang YJ. Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:325601. [PMID: 25029986 DOI: 10.1088/0953-8984/26/32/325601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Using the constrained-path Monte Carlo method, a two-orbital model for the pnictide superconductors is studied at half filling and in both the electron- and hole-doped cases. At half filling, a stable (π, 0)/(0, π) magnetic order is explicitly observed and the system tends to be in an orthomagnetic order rather than the striped antiferromagnetic order on increasing the Coulomb repulsion U. In the electron-doped case, the (π, 0)/(0, π) magnetic order is enhanced upon doping and suppressed eventually and a s(±) pairing state dominates all the possible nearest-neighbour-bond pairings. Whereas in the hole-doped case, the magnetic order is straightforwardly suppressed and two nearly degenerate A(1g) and B(1g) intraband pairings become the dominant ones.
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Affiliation(s)
- Guang-Kun Liu
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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Gastiasoro MN, Andersen BM. Enhancement of magnetic stripe order in iron-pnictide superconductors from the interaction between conduction electrons and magnetic impurities. PHYSICAL REVIEW LETTERS 2014; 113:067002. [PMID: 25148344 DOI: 10.1103/physrevlett.113.067002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2014] [Indexed: 06/03/2023]
Abstract
Recent experimental studies have revealed several unexpected properties of Mn-doped BaFe(2)As(2). These include extension of the stripelike magnetic (π,0) phase to high temperatures above a critical Mn concentration only, the presence of diffusive and weakly temperature dependent magnetic (π,π) checkerboard scattering, and an apparent absent structural distortion from tetragonal to orthorhombic symmetry. Here, we study the effects of magnetic impurities both below and above the Néel transition temperature within a real-space five-band model appropriate to the iron pnictides. We show how these experimental findings can be explained by a cooperative behavior of the magnetic impurities and the conduction electrons mediating the Ruderman-Kittel-Kasuya-Yosida interactions between them.
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Affiliation(s)
- Maria N Gastiasoro
- Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - Brian M Andersen
- Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
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Brzezicki W, Dziarmaga J, Oleś AM. Noncollinear magnetic order stabilized by entangled spin-orbital fluctuations. PHYSICAL REVIEW LETTERS 2012; 109:237201. [PMID: 23368254 DOI: 10.1103/physrevlett.109.237201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2012] [Indexed: 06/01/2023]
Abstract
Quantum phase transitions in the two-dimensional Kugel-Khomskii model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization Ansatz. When 3z(2)-r(2) orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order that consists of four sublattices with mutually orthogonal nearest-neighbor and antiferromagnetic second-neighbor spins. We derive an effective frustrated spin model with second- and third-neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.
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Affiliation(s)
- Wojciech Brzezicki
- Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, PL-30059 Kraków, Poland
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Venderbos JWF, Daghofer M, van den Brink J, Kumar S. Switchable quantum anomalous Hall state in a strongly frustrated lattice magnet. PHYSICAL REVIEW LETTERS 2012; 109:166405. [PMID: 23215101 DOI: 10.1103/physrevlett.109.166405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2012] [Indexed: 06/01/2023]
Abstract
We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux phases. For weak itineracy the flux phase is coplanar and the electronic dispersion takes the shape of graphenelike Dirac fermions. Stronger itineracy drives the formation of a noncoplanar, chiral flux phase, in which the Dirac fermions acquire a topological mass that is proportional to a ferromagnetic spin polarization. Consequently the system self-organizes into a ferromagnetic quantum anomalous Hall state in which the direction of its dissipationless edge currents can be switched by an applied magnetic field.
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Quan YM, Zou LJ, Liu DY, Lin HQ. Influence of electronic correlations on orbital polarizations in the parent and doped iron pnictides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:085603. [PMID: 22310654 DOI: 10.1088/0953-8984/24/8/085603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Orbital polarization and electronic correlation are two essential aspects in understanding the normal-state and superconducting properties of multi-orbital FeAs-based superconductors. In this paper, we present a systematic study on the orbital polarization of iron pnictides from weak to strong Coulomb correlations within the Kotliar-Ruckenstein slave boson approach. The magnetic phase diagram of the two-orbital model for LaFeAsO clearly shows that a striped antiferromagnetic metallic phase with orbital polarization exists over a wide doping range, in addition to the Slater-type insulator, Mott insulator and paramagnetic phases. A reversal of the orbital polarization occurs in the intermediate correlation regime in the absence of the crystal field splitting; however, a small crystal field splitting considerably enhances the orbital polarization, and stabilizes the xz-type orbital order. We argue that the ferro-orbital polarization is characteristic of a density wave, and leads to a pseudogap-like behavior in the density of states.
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Affiliation(s)
- Ya-Min Quan
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, People's Republic of China
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Giovannetti G, Ortix C, Marsman M, Capone M, van den Brink J, Lorenzana J. Proximity of iron pnictide superconductors to a quantum tricritical point. Nat Commun 2011; 2:398. [PMID: 21772269 PMCID: PMC3160143 DOI: 10.1038/ncomms1407] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2011] [Accepted: 06/20/2011] [Indexed: 11/13/2022] Open
Abstract
In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO(1-x)F(x). We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.
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Affiliation(s)
- Gianluca Giovannetti
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, SISSA, Via Bonomea 265, 34136 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Condensed Matter Sector, Via Bonomea 265, Trieste 34136, SISSA, Via Bonomea 265, 34136 Trieste, Italy
| | - Carmine Ortix
- Institute for Theoretical Solid State Physics, IFW-Dresden, PF 270116, Dresden 01171, Germany
| | - Martijn Marsman
- Faculty of Physics and Center for Computational Materials Science, University Vienna, Sensengasse 8/12, Vienna A-1090, Austria
| | - Massimo Capone
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, SISSA, Via Bonomea 265, 34136 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Condensed Matter Sector, Via Bonomea 265, Trieste 34136, SISSA, Via Bonomea 265, 34136 Trieste, Italy
| | - Jeroen van den Brink
- Institute for Theoretical Solid State Physics, IFW-Dresden, PF 270116, Dresden 01171, Germany
| | - José Lorenzana
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
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Brydon PMR, Daghofer M, Timm C. Magnetic order in orbital models of the iron pnictides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:246001. [PMID: 21613725 DOI: 10.1088/0953-8984/23/24/246001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We examine the appearance of the experimentally observed stripe spin-density-wave magnetic order in five different orbital models of the iron pnictide parent compounds. A restricted mean-field ansatz is used to determine the magnetic phase diagram of each model. Using the random phase approximation, we then check this phase diagram by evaluating the static spin susceptibility in the paramagnetic state close to the mean-field phase boundaries. The momenta for which the susceptibility is peaked indicate in an unbiased way the actual ordering vector of the nearby mean-field state. The dominant orbitally resolved contributions to the spin susceptibility are also examined to determine the origin of the magnetic instability. We find that the observed stripe magnetic order is possible in four of the models, but it is extremely sensitive to the degree of nesting between the electron and hole Fermi pockets. In the more realistic five-orbital models, this order competes with a strong-coupling incommensurate state which appears to be controlled by details of the electronic structure below the Fermi energy. We conclude by discussing the implications of our work for the origin of the magnetic order in the pnictides.
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Affiliation(s)
- P M R Brydon
- Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany.
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