Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of ${\mathrm{CrGeTe}}_{3}$

Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of ${CrGeTe}_{3}$

Matthew D. Watson, Igor Marković, Federico Mazzola, Akhil Rajan, Edgar A. Morales, David M. Burn, Thorsten Hesjedal, Gerrit van der Laan, Saumya Mukherjee, Timur K. Kim, Chiara Bigi, Ivana Vobornik, Monica Ciomaga Hatnean, Geetha Balakrishnan, and Philip D. C. King

Phys. Rev. B 101, 205125 – Published 18 May 2020

Abstract

We investigate the temperature-dependent electronic structure of the van der Waals ferromagnet, ${CrGeTe}_{3}$ . Using angle-resolved photoemission spectroscopy, we identify atomic- and orbital-specific band shifts upon cooling through $T_{C}$ . From these, together with x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements, we identify the states created by a covalent bond between the Te $5 p$ and the Cr $e_{g}$ orbitals as the primary driver of the ferromagnetic ordering in this system, while it is the Cr $t_{2 g}$ states that carry the majority of the spin moment. The $t_{2 g}$ states furthermore exhibit a marked bandwidth increase and a remarkable lifetime enhancement upon entering the ordered phase, pointing to a delicate interplay between localized and itinerant states in this family of layered ferromagnets.

Received 23 December 2019
Accepted 16 April 2020
Corrected 3 December 2021

DOI:https://doi.org/10.1103/PhysRevB.101.205125

Physics Subject Headings (PhySH)

Exchange interaction Magnetism

Ferromagnets Van der Waals systems

Angle-resolved photoemission spectroscopy X-ray magnetic circular dichroism

Condensed Matter, Materials & Applied Physics

Corrections

3 December 2021

Correction: The omission of a support statement in the Acknowledgment section has been fixed.

Authors & Affiliations

Matthew D. Watson ^1,*, Igor Marković ^1,2, Federico Mazzola¹, Akhil Rajan ¹, Edgar A. Morales^1,2, David M. Burn ³, Thorsten Hesjedal ⁴, Gerrit van der Laan ³, Saumya Mukherjee ⁵, Timur K. Kim⁵, Chiara Bigi ^6,7, Ivana Vobornik⁶, Monica Ciomaga Hatnean ⁸, Geetha Balakrishnan ⁸, and Philip D. C. King ^1,†

¹SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, United Kingdom
²Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany
³Magnetic Spectroscopy Group, Diamond Light Source, Didcot OX11 0DE, United Kingdom
⁴Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
⁵Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
⁶Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, Area Science Park, S.S.14, Km 163.5, 34149 Trieste, Italy
⁷Department of Physics, University of Milano, 20133 Milano, Italy
⁸Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

^*matthew.watson@diamond.ac.uk
^†philip.king@st-andrews.ac.uk

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Vol. 101, Iss. 20 — 15 May 2020

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Figure 1
Paramagnetic electronic structure of ${CrGeTe}_{3}$ . (a) Crystal structure of ${CrGeTe}_{3}$ , with trilayer stacking in the unit cell, and (b) corresponding 3D Brillouin zone. High-symmetry points are shown, as well as their projection into the hexagonal surface Brillouin zone (barred notation). (c) ARPES intensity map ( $h ν = 80 eV$ ) at an energy 0.1 eV below the top of the valence band, showing slightly trigonally warped contours derived from $p_{x / y}$ states located at each $\bar{Γ}$ point. (d) ARPES dispersion measured ( $h ν = 80 eV$ ) along high-symmetry directions of the surface Brillouin zone, over an extended binding energy range. A pronounced state with only weak dispersion is evident in addition to the strongly dispersive states. The energy scale is referenced to the valence band maximum, $E_{vb}$ ; the chemical potential lies within the band gap, and for the sample shown here is located 0.165 eV above the valence band top (dashed red line). (e),(f) Detailed valence band dispersions at high-symmetry points of the 3D Brillouin zone [(e) $Γ$ , $h ν = 22$ eV; (f) T, $h ν = 61 eV$ ]. The $p_{z}$ band disperses significantly along $k_{z}$ such that it is at higher binding energies than the range shown in (f) for the T point. All data are measured in the paramagnetic phase at $T = 100 K$ .
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Figure 2
Resonant ARPES measurements. (a),(b) ARPES measurements in the paramagnetic state ( $T = 80 K$ ) (a) off ( $h ν = 44 eV$ ) and (b) on ( $h ν = 50 eV$ ) resonance with the Cr $3 p$ to $3 d$ transition. The color map is fixed to the same intensity range in both plots, highlighting the extra intensity from the Cr $3 d$ weight on resonance. (c) Photon energy-dependent energy distribution curves (EDCs) measured at $\bar{Γ}$ as a function of photon energy across the resonance. (d) The photon energy-dependent spectral weight of peaks located 1.19 eV and 2.05 eV below the valence band top [arrows in (c)], identify the near pure Cr ( $t_{2 g}$ ) and partial Cr ( $e_{g}$ ) character of the corresponding states, indicating that the latter are hybridized with Te $5 p$ states.
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Figure 3
Evidence for partial occupation of the $e_{g}$ orbitals from XAS and XMCD. (a) Dichroic absorption spectra for the Cr $L_{2, 3}$ edges measured in an applied field of 2 T, which saturates the magnetization (see methods). (b) Simulation of XAS and XMCD from multiplet calculations, reproducing the essential features of the experimental spectra. (c) Edge-sharing ${CrTe}_{6}$ octahedra. (d) For perfect octahedra and exact bond angles, $σ$ hopping is forbidden from the $5 p$ to the $t_{2 g}$ states by symmetry. (e) In contrast, at least one of the $e_{g}$ orbitals is available for $σ$ hopping. (f) Schematic representation of the nominal ionic configuration of two adjacent Cr atoms and one of the two intermediary Te atoms. The orbitals are defined as in (d),(e) with $n o n$ representing an additional nonbonding $5 p$ state. (g) Corresponding orbital configuration for a state that additionally hosts a significant $5 p σ - e_{g}$ covalent bonding. The unpaired spins on the Te site interact according to $J_{H}^{Te}$ , which gives an energy gain for on-site alignment of spins; this process thus mediates a net ferromagnetic superexchange between the Cr sites.
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Figure 4
Temperature-dependent band shifts. (a),(b) ARPES measurements through the $Γ$ point ( $h ν = 48 eV$ , also on resonance) (a) above and (b) below $T_{C}$ . (c) Temperature-dependent EDCs at $Γ$ and (d) corresponding band positions extracted from fitting these EDCs. (e),(f) Equivalent (e) EDCs and (f) band positions at $k = 0.4 Å^{- 1}$ [see arrow in (a)].
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Figure 5
Lifetime enhancements below $T_{C}$ . (a)–(c) Temperature-dependent ARPES measurements at the T point ( $h ν = 61 eV$ ) at temperatures of (a) 102 K, (b) 66 K, and (c) 25 K. (d) Corresponding EDCs at the T point. (e) The extracted full width at half maximum of the uppermost $t_{2 g}$ state, determined from fits to these EDCs, shows a remarkable sharpening upon cooling thought the ferromagnetic ordering transition. This indicates a pronounced increase in lifetime of this state, in contrast to the almost temperature-independent lifetime of the uppermost valence band states. For fit details, see Fig. SM3 in SM [14].
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Physical Review B

covering condensed matter and materials physics

Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of ${CrGeTe}_{3}$

Matthew D. Watson, Igor Marković, Federico Mazzola, Akhil Rajan, Edgar A. Morales, David M. Burn, Thorsten Hesjedal, Gerrit van der Laan, Saumya Mukherjee, Timur K. Kim, Chiara Bigi, Ivana Vobornik, Monica Ciomaga Hatnean, Geetha Balakrishnan, and Philip D. C. King

Phys. Rev. B 101, 205125 – Published 18 May 2020

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Physical Review B

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Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of CrGeTe3

Matthew D. Watson, Igor Marković, Federico Mazzola, Akhil Rajan, Edgar A. Morales, David M. Burn, Thorsten Hesjedal, Gerrit van der Laan, Saumya Mukherjee, Timur K. Kim, Chiara Bigi, Ivana Vobornik, Monica Ciomaga Hatnean, Geetha Balakrishnan, and Philip D. C. King

Phys. Rev. B 101, 205125 – Published 18 May 2020

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Direct observation of the energy gain underpinning ferromagnetic superexchange in the electronic structure of ${CrGeTe}_{3}$