Direct observation of hidden spin polarization in $2H\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$

Direct observation of hidden spin polarization in $2 H − MoT e_{2}$

J. Tu, X. B. Chen, X. Z. Ruan, Y. F. Zhao, H. F. Xu, Z. D. Chen, X. Q. Zhang, X. W. Zhang, J. Wu, L. He, Y. Zhang, R. Zhang, and Y. B. Xu

Phys. Rev. B 101, 035102 – Published 3 January 2020

Abstract

Centrosymmetric (CS) nonmagnetic materials with hidden spin polarization induced by non-CS site symmetries and spin-orbit coupling are promising candidates for spintronic applications, in light of the zero net spin polarization and modulatable spin effects hidden in the local structures. There is, however, an open issue regarding the possible spin splitting induced by broken inversion symmetry at the sample surface. Here, we performed combinatorial experimental and theoretical studies on the potentially hidden spin polarization in $2 H − MoT e_{2}$ and its mechanism. A large spin splitting of 236 meV and opposite spin polarizations up to 80% along out-of-plane direction ( $z$ axis) in $K$ and $K^{'}$ valleys were observed from both spin- and angle-resolved photoemission spectroscopy (spin-ARPES) and density functional theory (DFT). We further found from the DFT calculations that a medium dipole field mimicked the surface symmetry breaking in ARPES measurements induces negligible variation of spin polarization. Our study demonstrates the existence of the intrinsic hidden spin effects in $2 H − MoT e_{2}$ and opens a way of utilizing these effects in spintronic devices.

Received 17 August 2019
Revised 29 November 2019

DOI:https://doi.org/10.1103/PhysRevB.101.035102

Physics Subject Headings (PhySH)

Electronic structure Spin polarization

Transition metal dichalcogenides

Angle-resolved photoemission spectroscopy Density functional theory Spin-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Tu^1,*, X. B. Chen^2,*, X. Z. Ruan^1,†, Y. F. Zhao¹, H. F. Xu¹, Z. D. Chen¹, X. Q. Zhang¹, X. W. Zhang^2,‡, J. Wu³, L. He¹, Y. Zhang⁴, R. Zhang¹, and Y. B. Xu^1,3,§

¹Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, Collaborative Innovation Center of Advanced Microstructures, School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
²Shenzhen Key Laboratory of Flexible Memory Materials and Devices, College of Electronic Science and Technology, Shenzhen University, Nanhai Ave. 3688, Shenzhen, Guangdong 518060, China
³York-Nanjing Joint Center in Spintronics, Department of Electronic Engineering and Department of Physics, The University of York, York, YO10 5DD, United Kingdom
⁴Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom

^*These authors contributed equally to this work.
^†Correspondence and requests for materials should be addressed to: xzruan@nju.edu.cn
^‡Correspondence and requests for materials should be addressed to: xiuwenzhang@szu.edu.cn
^§Correspondence and requests for materials should be addressed to: ybxu@nju.edu.cn

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Vol. 101, Iss. 3 — 15 January 2020

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Figure 1
(a) Top and (b) side views of the lattice structure. The upper and lower layers in the unit cell denoted as α and β sectors are inversion partners. (c) Brillouin zone of $2 H − MoT e_{2}$ in reciprocal space. (d) Raman signal of $2 H − MoT e_{2}$ . $A_{1 g}$ and $E_{2 g}^{1}$ denote the phonon modes of $2 H − MoT e_{2}$ . (e) XRD pattern of $2 H − MoT e_{2}$ .
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Figure 2
(a) Electronic band structure of $2 H − MoT e_{2}$ along the high-symmetry points $M - K - Γ - M$ acquired from ARPES. [(b) and (c)] EDC at $K$ and $M$ . Spin splitting of 236 meV at $K$ valley is displayed in (b). [(d) and (e)] Spin polarizations vertical to the sample plane at $K (K^{'})$ and $M$ . In (d), black and red curves correspond to $K$ and $K^{'}$ , respectively.
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Figure 3
(a) Evaluated band structure of bulk $2 H − MoT e_{2}$ by DFT+SOC. The dotted lines with different colors denote the band projection onto different atomic orbitals, indicating that the first two valence bands (VB1 and VB2 with energy difference of 283 meV) at $K$ point mainly consist of Mo $d$ states. [(b) and (c)] Spin-orbital-projected band structure near $K$ point for the α and β sectors in $MoT e_{2}$ , respectively. The dotted lines with different colors denote the band projection onto different spin and orbit states, with ↑(↓) indicating the spin projection with the spin polarization axis along the $z$ direction and $d_{x^{2} - y^{2}}$ being the majority Mo $d$ state for the plotted bands, illustrating that the inversion partners (α and β sectors) possess opposite local spin polarizations.
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Figure 4
(a) Projected local spin polarization for VB1 in the $K$ valley of centrosymmetric $2 H − MoT e_{2}$ . Red (blue) arrows denote the spin polarizations on α (β) sector. (b) Projected local spin polarization of VB2. (c) Spin projection with the spin polarization axis along the $z$ direction $(S_{z})$ for VB1 and VB2, evaluated from the local spin polarization in bulk $2 H − MoT e_{2}$ considering the escape depth of photoelectrons. The escape probability of photoelectrons is represented by an exponential function $e^{- \frac{z}{Δ}}$ with $Δ = 6 Å$ and $z$ being the distance from the sample surface. The black and red squares indicate the spin polarizations $(S_{z})$ at $K$ and $K^{'}$ , respectively.
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Figure 5
(a) Spin polarization for the first valence band $(VB 1_{a})$ in the $K$ valley of $2 H − MoT e_{2}$ with a medium dipole field (50 kV/cm) applied along $z$ direction to break the inversion symmetry and to split the VB1 (VB2) state in pristine $MoT e_{2}$ into nearly degenerate $VB 1_{a}$ and $VB 1_{b}$ ( $VB 2_{a}$ and $VB 2_{b}$ ) states for considering broken inversion symmetry at the surface in experiments. (b) Spin polarization for $VB 2_{a}$ . [(c) and (d)] Spin polarizations for $VB 1_{b}$ and $VB 2_{b}$ , respectively. (e) Spin projection with the spin polarization axis along the $z$ direction $(S_{z})$ for $VB 1_{a, b}$ (sum of $S_{z}$ for $VB 1_{a}$ and $VB 1_{b}$ ) and $VB 2_{a, b}$ (sum of $S_{z}$ for $VB 2_{a}$ and $VB 2_{b}$ ), evaluated using the same method as in Fig. 4 for comparison. The black and red squares indicate the spin polarizations $(S_{z})$ at $K$ and $K^{'}$ , respectively.
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Physical Review B

covering condensed matter and materials physics

Direct observation of hidden spin polarization in $2 H − MoT e_{2}$

J. Tu, X. B. Chen, X. Z. Ruan, Y. F. Zhao, H. F. Xu, Z. D. Chen, X. Q. Zhang, X. W. Zhang, J. Wu, L. He, Y. Zhang, R. Zhang, and Y. B. Xu

Phys. Rev. B 101, 035102 – Published 3 January 2020

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Physical Review B

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Direct observation of hidden spin polarization in 2H−MoTe2

J. Tu, X. B. Chen, X. Z. Ruan, Y. F. Zhao, H. F. Xu, Z. D. Chen, X. Q. Zhang, X. W. Zhang, J. Wu, L. He, Y. Zhang, R. Zhang, and Y. B. Xu

Phys. Rev. B 101, 035102 – Published 3 January 2020

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Direct observation of hidden spin polarization in $2 H − MoT e_{2}$