Persistent exchange splitting in the chiral helimagnet ${\mathrm{Cr}}_{1/3}{\mathrm{NbS}}_{2}$

Persistent exchange splitting in the chiral helimagnet ${Cr}_{1 / 3} {NbS}_{2}$

Na Qin, Cheng Chen, Shiqiao Du, Xian Du, Xin Zhang, Zhongxu Yin, Jingsong Zhou, Runzhe Xu, Xu Gu, Qinqin Zhang, Wenxuan Zhao, Yidian Li, Sung-Kwan Mo, Zhongkai Liu, Shilei Zhang, Yanfeng Guo, Peizhe Tang, Yulin Chen, and Lexian Yang

Phys. Rev. B 106, 035129 – Published 18 July 2022

Abstract

Using high-resolution angle-resolved photoemission spectroscopy and ab initio calculation, we systematically investigate the electronic structure of the chiral helimagnet ${Cr}_{1 / 3} {NbS}_{2}$ and its temperature evolution. The comparison with ${NbS}_{2}$ suggests that the electronic structure of ${Cr}_{1 / 3} {NbS}_{2}$ is strongly modified by the intercalation of Cr atoms. Our ab initio calculation, consistent with experimental results, suggests strong hybridization between Nb- and Cr-derived states near the Fermi level. In the chiral helimagnetic state (below the Curie temperature, $T_{c}$ ), we observe exchange splitting of the energy bands crossing the Fermi level, which follows the temperature evolution of the magnetic moment, suggesting a strong interaction between the conduction electrons and Cr spin moments. Interestingly, the exchange splitting persists far above $T_{c}$ with weak temperature dependence, in drastic contrast to the itinerant ferromagnetism described by the Stoner model, indicating the existence of short-range magnetic order. Our results provide important insights into the interplay between the electronic structure and magnetism in ${Cr}_{1 / 3} {NbS}_{2}$ , which is helpful for understanding the microscopic mechanism of chiral helimagnetic ordering.

Received 23 February 2022
Revised 4 May 2022
Accepted 29 June 2022

DOI:https://doi.org/10.1103/PhysRevB.106.035129

Physics Subject Headings (PhySH)

Electronic structure

Chiral magnets

Ab initio calculations Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Na Qin^1,*, Cheng Chen^2,*, Shiqiao Du^1,*, Xian Du ¹, Xin Zhang ³, Zhongxu Yin¹, Jingsong Zhou¹, Runzhe Xu¹, Xu Gu¹, Qinqin Zhang¹, Wenxuan Zhao¹, Yidian Li¹, Sung-Kwan Mo ², Zhongkai Liu^3,4, Shilei Zhang^3,4, Yanfeng Guo^3,4, Peizhe Tang ^5,6, Yulin Chen^1,3,4,7,†, and Lexian Yang^1,8,‡

¹State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
²Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³School of Physical Science and Technology, ShanghaiTech University and CAS-Shanghai Science Research Center, Shanghai 201210, China
⁴ShanghaiTech Laboratory for Topological Physics, Shanghai 200031, China
⁵School of Materials Science and Engineering, Beihang University, Beijing 100191, China
⁶Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
⁷Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
⁸Frontier Science Center for Quantum Information, Beijing 100084, China

^*These authors contributed equally to this work.
^†yulin.chen@physics.ox.ac.uk
^‡lxyang@tsinghua.edu.cn

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Vol. 106, Iss. 3 — 15 July 2022

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Figure 1
(a) Crystal structure of ${Cr}_{1 / 3} {NbS}_{2}$ . Cr atoms are intercalated in 2H- ${NbS}_{2}$ , occupying the octahedral interstitial sites between two ${NbS}_{2}$ layers and forming a $(\sqrt 3 \times \sqrt 3) R (30^{\circ})$ superstructure. (b) Schematic illustration of the magnetic helix along the $c$ -axis showing 1/4 period. (c) Magnetic moment as a function of temperature measured by heating the sample under a magnetic field of 100 Oe parallel to the $a b$ plane. The sample was cooled down to 15 K under a magnetic field of 1 T and without magnetic field for the FC and ZFC measurements, respectively.
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Figure 2
(a), (b) Fermi surface of ${NbS}_{2}$ (a) and ${Cr}_{1 / 3} {NbS}_{2}$ (b) measured by integrating ARPES intensity over an energy window of 30 meV near the Fermi level ( $E_{F}$ ). (c)–(f) Band structure of ${NbS}_{2}$ (c, e) and ${Cr}_{1 / 3} {NbS}_{2}$ (d, f) along high-symmetry directions as indicated. Data of ${NbS}_{2}$ ( ${Cr}_{1 / 3} {NbS}_{2}$ ) were collected using 90-eV photons at 12 (20) K.
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Figure 3
(a)–(h) Band structure of ${Cr}_{1 / 3} {NbS}_{2}$ along $\bar{Γ} \bar{M}$ measured at selected photon energies. Data were measured at 20 K.
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Figure 4
(a)–(e) Ab initio calculation of the electronic structure of ${NbS}_{2}$ (a) and ${Cr}_{1 / 3} {NbS}_{2}$ (b–e). The calculation in (a) is folded into a $(\sqrt 3 \times \sqrt 3) R (30^{\circ})$ superstructured BZ for better comparison with the result in ${Cr}_{1 / 3} {NbS}_{2}$ . The calculations in (b) and (c) were performed for paramagnetic and FM states, respectively. The black (red) lines in (c) represent spin up (down) bands. (d) Comparison between the calculated electronic structure in the CHM (solid black) and FM (dotted red) states showing a negligible difference. (e) Orbital-projected calculation of the spin-split band structure of the FM state (left: spin up, right: spin down).
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Figure 5
(a)–(e) Band structure of ${Cr}_{1 / 3} {NbS}_{2}$ along $\bar{Γ} \bar{M}$ measured at selected temperatures. (f) Temperature evolution of the MDCs at $E_{F}$ . The colored markers are a guide to help one note the temperature evolution of the peak positions. (g) False-color plot of the temperature evolution of the MDCs at $E_{F}$ . The orange circles, blue triangles, and gray diamonds indicate MDC peak positions extracted by fitting the MDCs to multiple Lorentzians. (h) The exchange splitting between the $β_{1}$ and $β_{2}$ bands as a function of temperature (Supplementary Materials Fig. S1 [34]). The dashed line is a guide to help one note the evolution of the exchange splitting. The temperature evolution of the magnetic moment is also shown for comparison.
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Physical Review B

covering condensed matter and materials physics

Persistent exchange splitting in the chiral helimagnet ${Cr}_{1 / 3} {NbS}_{2}$

Na Qin, Cheng Chen, Shiqiao Du, Xian Du, Xin Zhang, Zhongxu Yin, Jingsong Zhou, Runzhe Xu, Xu Gu, Qinqin Zhang, Wenxuan Zhao, Yidian Li, Sung-Kwan Mo, Zhongkai Liu, Shilei Zhang, Yanfeng Guo, Peizhe Tang, Yulin Chen, and Lexian Yang

Phys. Rev. B 106, 035129 – Published 18 July 2022

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Physical Review B

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Persistent exchange splitting in the chiral helimagnet Cr1/3NbS2

Na Qin, Cheng Chen, Shiqiao Du, Xian Du, Xin Zhang, Zhongxu Yin, Jingsong Zhou, Runzhe Xu, Xu Gu, Qinqin Zhang, Wenxuan Zhao, Yidian Li, Sung-Kwan Mo, Zhongkai Liu, Shilei Zhang, Yanfeng Guo, Peizhe Tang, Yulin Chen, and Lexian Yang

Phys. Rev. B 106, 035129 – Published 18 July 2022

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Persistent exchange splitting in the chiral helimagnet ${Cr}_{1 / 3} {NbS}_{2}$