Non-Fermi-liquid behavior and saddlelike flat band in the layered ferromagnet ${\mathrm{AlFe}}_{2}{\mathrm{B}}_{2}$

Non-Fermi-liquid behavior and saddlelike flat band in the layered ferromagnet ${AlFe}_{2} B_{2}$

Zhonghao Liu, Shuai Yang, Hao Su, Liqin Zhou, Xiangle Lu, Zhengtai Liu, Jiacheng Gao, Yaobo Huang, Dawei Shen, Yanfeng Guo, Hongming Weng, and Shancai Wang

Phys. Rev. B 101, 245129 – Published 8 June 2020

Abstract

${AlFe}_{2} B_{2}$ , a layered ferromagnet with a Curie temperature near room temperature ( $T_{c} \sim 270$ K), has attracted growing attention recently in condensed-matter physics and materials science. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, we provide evidence of a linear band and a saddlelike flat band in the vicinity of the Fermi energy ( $E_{F}$ ) in ${AlFe}_{2} B_{2}$ , consisting of slabs of ${Fe}_{2} B_{2}$ atoms separated by layers of Al. The anomalous scattering rate of the linear band varies linearly with the kinetic energy up to 120 meV, showing non-Fermi-liquid behavior consistent with T-linear dependence of resistivity. The flat band with $d_{x y}$ orbital character and with strong $k_{y}$ dispersion may be associated with spin orientation along the $a$ axis in layered ${AlFe}_{2} B_{2}$ . Electronic and magnetic correlation can be modulated by tuning the flat band near $E_{F}$ in layered ternary borides. Our findings have important implications to exploit emergent physics and quantum phases in $3 d$ transition metals.

Received 21 March 2020
Revised 21 May 2020
Accepted 22 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.245129

Physics Subject Headings (PhySH)

Electronic structure

2-dimensional systems Ferromagnets

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhonghao Liu^1,2,*, Shuai Yang^1,2, Hao Su³, Liqin Zhou^4,5, Xiangle Lu^1,2, Zhengtai Liu¹, Jiacheng Gao^4,5, Yaobo Huang⁶, Dawei Shen ^1,2, Yanfeng Guo ^3,†, Hongming Weng^4,5,‡, and Shancai Wang^7,§

¹State Key Laboratory of Functional Materials for Informatics and Center for Excellence in Superconducting Electronics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
²College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
³School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
⁴Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
⁶Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201204, China
⁷Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials & Micro-Nano Devices, Renmin University of China, Beijing 100872, China

^*lzh17@mail.sim.ac.cn
^†guoyf@shanghaitech.edu.cn
^‡hmweng@iphy.ac.cn
^§scw@ruc.edu.cn

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Vol. 101, Iss. 24 — 15 June 2020

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Figure 1
(a) Crystal structure of ${AlFe}_{2} B_{2}$ with space group $C m m m$ (No. 65). The spin orientation of Fe along $a$ below $T_{c}$ . (b) Temperature-dependent resistivity at zero field for the $a c$ plane shows a drop at $T_{c} \sim 270$ K. Inset: Picture of a single crystal against the 1- $m m$ scale. (c) Crossover from underlying phonon ( $\propto T$ ) and FM ( $\propto T^{5 / 3}$ ) scattering to Planckian dissipation limit ( $\propto k_{B} T$ ). The black solid lines are fits to the data using $ρ = ρ_{0} + a T$ at low temperatures below $\sim 40$ K and $ρ = ρ_{0}^{'} + b T + c T^{5 / 3}$ at high temperatures from $\sim 40$ to 180 K. (d) Temperature-dependent magnetization with a 0.01 T applied field along the [100] direction, measured while warming and cooling. (e) 3D BZ with marked high-symmetry points. $\bar{Γ} - \bar{Z} - \bar{A} - \bar{X}$ plane is a projected 2D BZ on (010) plane.
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Figure 2
(a) Projected DOS at the five Fe $3 d$ orbitals around $E_{F}$ . The different colors indicate the different orbitals. (b) Calculated bands with SOC and with orbital characters along high-symmetry directions. Orbital characters are indicated by colors the same as in (a). The flat band (FB) and the linear band (LB) near $E_{F}$ are indicated by the color arrows. (c) Integrated intensity plots ( $E_{F} \pm 10$ meV) on the $k_{y} \sim 0$ ( $Γ - Z - A - X$ ) plane taken with 114-eV photons. The red dashed lines indicate the 2D BZ and high-symmetry lines. The black arrow indicates the shadow FS formed by the flat band. (d) Schematic FSs are formed by the $α$ , $β$ , $γ$ , $κ$ , $δ$ , and $ω$ bands, corresponding to (c).
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Figure 3
(a) Integrated intensity plots ( $\pm 10$ meV) on the $k_{z} – k_{y}$ plane taken at $E_{F}$ and $E_{F} - 0.5$ eV, respectively. Photon energies used for the $k_{y}$ dispersion measurement were from 46 to 124 eV. (b) Intensity plot and corresponding second derivative plot along the $Γ - Z$ direction taken with 114-eV photons ( $k_{y} \sim 0$ ). The second derivative is made by the Laplacian model [36]. The red solid lines are calculated bands renormalized by a factor of $\sim 1.4$ . The measured bands are indicated by Greek letters, i.e., $α$ , $δ$ , and $κ$ . The calculated bands are indicated by corresponding alphabets, i.e., a, d, and k. (c) EDCs of (b), shows linear band (LB) and flat band (FB) top at the $Z$ point. The black sticks are guides to the bands. (d) Occupied parts of the symmetrized EDCs remove the effect of the Fermi-Dirac function around the $Z$ point and show the $κ$ band top. The blue dashed line at 50 meV below $E_{F}$ is a guide to the peaks. (e) MDCs of (b). The linear bands are fitted by using the Lorentz function, as indicated by black solid curves. (f) Energy-dependent scattering rate obtained from the HWHM of the fitted MDCs in (e). The size of squares represents a maximum fitting error of $\sim 0.01$ $1 / Å$ . Black squares are for the left branch, red ones are for the right branch, and green crosses are for the average value of both branches. The data are linearly fitted as indicated by the lines with different colors.
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Figure 4
(a), (b) Intensity plots and corresponding second derivative plots taken with 114-eV photons ( $k_{y} \sim 0$ ) along the $Z - A$ (perpendicular to $Γ - Z$ ) and $Γ - X$ directions, respectively. The second derivative is made by the Laplacian model [36]. The red solid lines are calculated bands renormalized by a factor of $\sim 1.4$ . The measured bands are indicated by $κ$ , $δ$ , $ω$ , $α$ , $β$ , and $γ$ . The corresponding calculated bands are indicated by k, d, w, a, b, and r. (c) EDCs of (a). The black sticks are guides to the bands. (d) Occupied parts of the symmetrized EDCs remove the effect of the Fermi-Dirac function around the $Z$ point and show the $κ$ band bottom. The blue dashed line at 50 meV below $E_{F}$ is a guide to the peaks.
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Figure 5
(a), (b) Intensity plots and corresponding second derivative plots taken with 90-eV photons ( $k_{y} \sim π$ ) along the $Y - T$ and $Y - X 1$ directions, respectively. The second derivative is made by the Laplacian model [36]. The red solid lines are calculated bands renormalized by a factor of $\sim 1.4$ . The corresponding calculated bands are indicated by a, d, and k.
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Physical Review B

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Non-Fermi-liquid behavior and saddlelike flat band in the layered ferromagnet ${AlFe}_{2} B_{2}$

Zhonghao Liu, Shuai Yang, Hao Su, Liqin Zhou, Xiangle Lu, Zhengtai Liu, Jiacheng Gao, Yaobo Huang, Dawei Shen, Yanfeng Guo, Hongming Weng, and Shancai Wang

Phys. Rev. B 101, 245129 – Published 8 June 2020

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Non-Fermi-liquid behavior and saddlelike flat band in the layered ferromagnet AlFe2B2

Zhonghao Liu, Shuai Yang, Hao Su, Liqin Zhou, Xiangle Lu, Zhengtai Liu, Jiacheng Gao, Yaobo Huang, Dawei Shen, Yanfeng Guo, Hongming Weng, and Shancai Wang

Phys. Rev. B 101, 245129 – Published 8 June 2020

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Non-Fermi-liquid behavior and saddlelike flat band in the layered ferromagnet ${AlFe}_{2} B_{2}$