Temperature-dependent and magnetism-controlled Fermi surface changes in magnetic Weyl semimetals

Letter
Open Access

Temperature-dependent and magnetism-controlled Fermi surface changes in magnetic Weyl semimetals

Nan Zhang, Xianyong Ding, Fangyang Zhan, Houpu Li, Hongyu Li, Kaixin Tang, Yingcai Qian, Senyang Pan, Xiaoliang Xiao, Jinglei Zhang, Rui Wang, Ziji Xiang, and Xianhui Chen

Phys. Rev. Research 5, L022013 – Published 18 April 2023

Abstract

The coupling between band structure and magnetism can lead to intricate Fermi surface modifications. Here we report on the comprehensive study of the Shubnikov–de Haas (SdH) effect in two rare-earth-based magnetic Weyl semimetals, NdAlSi and ${CeAlSi}_{0.8} {Ge}_{0.2}$ . The results show that the temperature evolution of topologically nontrivial Fermi surfaces strongly depends on magnetic configurations. In NdAlSi, the SdH frequencies vary with temperature in both the paramagnetic state and the magnetically ordered state with a chiral spin texture, but become temperature independent in the high-field fully polarized state. In ${CeAlSi}_{0.8} {Ge}_{0.2}$ , SdH frequencies are temperature dependent only in the ferromagnetic state with magnetic fields applied along the axis. First-principles calculations suggest that the notable temperature and magnetic-configuration dependence of Fermi surface morphology can be attributed to strong exchange coupling between the conduction electrons and local magnetic moments.

Received 23 September 2022
Revised 5 March 2023
Accepted 29 March 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.L022013

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)

Fermi surface First-principles calculations High magnetic fields Landau levels Magnetotransport Topological materials Transport phenomena

Ferromagnets Weyl semimetal

Quantum oscillation techniques Resistivity measurements Shubnikov-de Haas effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nan Zhang ^1,*, Xianyong Ding ^2,*, Fangyang Zhan ², Houpu Li¹, Hongyu Li¹, Kaixin Tang¹, Yingcai Qian^1,3, Senyang Pan ^1,3, Xiaoliang Xiao ², Jinglei Zhang³, Rui Wang ^2,†, Ziji Xiang ^1,‡, and Xianhui Chen ^1,4,§

¹CAS Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²Institute for Structure and Function, Department of Physics and Center for Quantum Materials and Devices, Chongqing University, Chongqing 400044, China
³High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, Anhui 230031, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*These authors contributed equally to this work.
^†rcwang@cqu.edu.cn
^‡zijixiang@ustc.edu.cn
^§chenxh@ustc.edu.cn

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Issue

Vol. 5, Iss. 2 — April - June 2023

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Images

Figure 1
(a) The oscillatory resistivity $Δ ρ_{x x}$ in NdAlSi as a function of inverse field (see Fig. S2 in [16] for raw data). Data were measured with $H ∥ c$ . The thin solid curve marks out the metamagnetic transition field $H_{m}$ . Gray thick curve denotes the crossover between the PM and FIP states. (b)–(d) FFT spectra of the SdH oscillations in NdAlSi in the (b) FIP, (c) PM, and (d) canted u-d-d states. Arrows guide the eye. (e) Main FFT frequencies plotted against $T$ . Error bars are defined as the half FFT peak width at $90 %$ of the peak height. Dashed and solid lines denote the frequency changes based on the analysis of Lifshitz-Kosevich (LK) fits and shifts of SdH peak positions ( $Δ B / B$ ), respectively (more discussions are presented in [16]). (f) $H − T$ phase diagram for NdAlSi obtained from magnetization and MR measurements (Figs. S1 and S2 in [16]). Spin configurations for the u-d-d and FIP states are illustrated. The PM and FIP states are separated here by a threshold field $H_{p}$ for spin polarization (dashed line in (a); see also Fig. S2 in [16]). The dark shaded area bounded by $T_{m}$ and $H_{L}$ (a low-field jump in MR; see Fig. S2 in [16]) may represent an SDW order [15].
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Figure 2
(a) FFT spectra of SdH oscillations in NdAlSi measured with varying tilt angle $θ$ (from $c$ axis toward $a$ axis) at $T$ = 1.7 K. FFTs are performed above $H_{m}$ , i.e., in the FIP state. (b) SdH frequencies as functions of $θ$ for the canted u-d-d (circles), PM (triangles), and FIP (squares) states. The solid line is fit to an ellipsoidal FS model (see text). (c) Best fits of the Lifshitz-Kosevich (LK) model (solid lines) to the oscillatory MR in the FIP state (circles) measured at $θ$ = $0^{\circ}$ (black), $10^{\circ}$ (blue), $35^{\circ}$ (purple), and $T$ = 2 K. Inset: $T$ -dependent SdH oscillation amplitudes measured at $θ ≃ 30^{\circ}$ and the LK fit (solid line). (d) DFT-calculated Fermi surfaces (FSs) in the FIP state of NdAlSi. Dark purple and green colors represent hole and electron FS pockets, respectively. An expanded view of the hole pocket ( $λ$ ) along the $Z − Σ^{'}$ direction is provided. The extremal orbits are highlighted accordingly.
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Figure 3
(a) $Δ ρ_{x x}$ measured in ${CeAlSi}_{0.8} {Ge}_{0.2}$ with $H ∥ c$ at different temperatures. Below $T_{c}$ = 6.5 K (horizontal line), SdH extrema start to shift with varying $T$ (dotted arrow). (b),(c) $T$ dependence of SdH frequencies (see Fig. S3 in [16] for FFT spectra) for (b) $H ∥ c$ and (c) $H ∥ a$ . In (b), the solid and hollow circles are data obtained in two samples $# 1$ and $# 2$ in the field intervals of $8 \leq B \leq 14$ T and $8 \leq B \leq 33$ T, respectively. Data presented in (c) were measured in sample $# 1$ , with FFT performed between 8 and 14 T. (d) The DFT calculated hole (yellow) and electron (blue) FS pockets for the polarized state with Ce $4 f$ moments aligning along $c$ in an out-of-plane $H$ (arrow). The expanded view shows the outer (spin-majority) and inner (spin-minority) FS sheets for the pocket $λ$ . Circles highlight the possible extremal orbits.
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Figure 4
(a)–(d) The evolution of spin-resolved band structures of NdAlSi obtained from first-principles calculations; the $z$ -axis component of the ${Nd}^{3 +}$ ion magnetic moment is constrained to $〈 M_{z} 〉$ values of (a) 0, (b) $1.0 μ_{B}$ , (c) $2.0 μ_{B}$ , and (d) $3.0 μ_{B}$ . Note that (a) corresponds to the PM phase under zero field and (d) corresponds to the case of free magnetism (i.e., a FM state from self-consistent calculations). Red and blue colors indicate the $z$ component of spin-up and spin-down states, respectively. (e) The spin-dependent extremal (minimum or maximum) cross-sectional areas on FS pocket $λ$ , as a function of the polarized local moment, $〈 M_{z} 〉$ , of the ${Nd}^{3 +}$ ions in NdAlSi. (f) and (g) show the spin-resolved band structures of CeAlSi in the FM (Ce $4 f$ moments align along the $c$ axis) and PM phases, respectively. All calculations include the SOC.
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