Stronger quantum fluctuation with larger spins: Emergent magnetism in the pressurized high-temperature superconductor FeSe

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Stronger quantum fluctuation with larger spins: Emergent magnetism in the pressurized high-temperature superconductor FeSe

Yuting Tan (譚宇婷), Tianyu Zhang, Tao Zou, A. M. dos Santos, Jin Hu, Dao-Xin Yao (姚道新), Z. Q. Mao, Xianglin Ke, and Wei Ku (顧威)

Phys. Rev. Research 4, 033115 – Published 10 August 2022

Abstract

A counterintuitive enhancement of quantum fluctuation with larger spins, together with a few physical phenomena, is discovered in studying the recently observed emergent magnetism in high-temperature superconductor FeSe under pressure. Starting with an experimental crystalline structure from our high-pressure x-ray refinement, we theoretically analyze the stability of the magnetically ordered state with a realistic spin-fermion model. We find, surprisingly, that in comparison with magnetically ordered Fe pnictides, the larger spins in FeSe suffer even stronger long-range quantum fluctuations that diminish their ordering at ambient pressure. This fail-to-order quantum spin-liquid state then develops into an ordered state above 1 GPa due to weakened fluctuation accompanying the reduction of anion height and carrier density. The ordering further benefits from the ferro-orbital order and shows the observed enhancement around 1 GPa. We further clarify the controversial nature of magnetism and its interplay with nematicity in FeSe in the same unified picture for all Fe-based superconductors. In addition, the versatile itinerant carriers produce interesting correlated metal behavior in a large region of phase space. Our paper establishes a generic exotic paradigm of stronger quantum fluctuation with larger spins that complements the standard knowledge of insulating magnetism.

Received 5 March 2017
Revised 19 April 2022
Accepted 23 June 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.033115

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Antiferromagnetism Magnetic order Magnetic phase transitions Magnons Methods in magnetism Nematic order Nematic phase transition Orbital order Phase diagrams Phase transitions Pressure effects Quantum phase transitions RKKY interaction Spin waves Structural order parameter

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuting Tan (譚宇婷)^1,2, Tianyu Zhang³, Tao Zou⁴, A. M. dos Santos⁵, Jin Hu ⁶, Dao-Xin Yao (姚道新)², Z. Q. Mao⁷, Xianglin Ke⁴, and Wei Ku (顧威)^3,8,9,*

¹Department of Physics & National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
²State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
³Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁴Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-2320, USA
⁵Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁶Department of Physics and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
⁷Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
⁸Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai 200240, China
⁹Shanghai Branch, Hefei National Laboratory, Shanghai 201315, China

^*weiku@sjtu.edu.cn

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Vol. 4, Iss. 3 — August - October 2022

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Images

Figure 1
(a) Experimental phase diagram of FeSe against pressure [21], showing magnetic order above 1 GPa; (b) Experimental lattice structure from our x-ray refinement at various pressures (the error bar is smaller than the size of the symbol). Notice a clear enhancement of magnetic order and a change of trend in the anion height (defined in the insect) inside the structural (ferro-orbital) ordered phase below 1.5 GPa.
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Figure 2
Calculated spin-wave dispersion of the magnetically ordered state along the high-symmetry paths: (a) pressure dependence showing stable ordered state above 1GPa, (c) local moment dependence at $P = 0.14 GPa$ showing unstable ordered state beyond $S = 1.5$ , and (d) orbital order dependence at $P = 0.93 GPa$ showing increased stability ordering by ferro-orbital order. Here $S = 1.7$ and $ε = 0 eV$ are used, unless specified explicitly. (b) Momentum distribution of theoretical (upper panels) and experimental [8] (lower panels) spectra of low-energy magnetic excitation at $10 \pm 1 meV$ for low-pressure fluctuating state (left panels) and high-pressure ordered state (right panels) in $\pm π / 2$ momentum range around ( $π$ ,0). (e) Underlying ordered-state electron, $e$ , and hole, $h$ , Fermi surfaces entering our calculations, showing a reduction of carrier density (area of the pockets) at higher pressure (especially above 1.5 GPa).
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Figure 3
Illustration of distinct channels of spin (upper panels) and orbital fluctuations (lower panels) of a spin- and orbital-ordered state through virtual processes (middle panels). Their different channels naturally lead to separate domes in the phase diagram (right most panels).
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Figure 4
Tendency to stretch the fluctuation region and emergence of correlated metal in Fe pnictides (a) against doping $δ$ and FeSe (b) against pressure $P$ . The versatile itinerant carriers tend to fluctuate the magnetic ordered state, moving its phase boundary from the spin-only system (dashed line) to that of the fermion-dressed system (solid line). They also fluctuate the normal Fermi liquid state (long dashed line), creating a rather large region of a correlated metal with strong short-range correlation but without long-range order.
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Figure 5
Momentum distribution of theoretical (a) and experimental [50] (b) spectra of low-energy magnetic excitation of Ba122 at $10 \pm 1 meV$ and $5 \sim 10 meV$ , respectively.
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Figure 6
Illustration of the ferro-orbital order and antiferromagnetic order in Fe-based superconducting materials.
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