Transition between canted antiferromagnetic and spin-polarized ferromagnetic quantum Hall states in graphene on a ferrimagnetic insulator

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Transition between canted antiferromagnetic and spin-polarized ferromagnetic quantum Hall states in graphene on a ferrimagnetic insulator

Yang Li, Mario Amado, Timo Hyart, Grzegorz P. Mazur, Vetle Risinggård, Thomas Wagner, Lauren McKenzie-Sell, Graham Kimbell, Joerg Wunderlich, Jacob Linder, and Jason W. A. Robinson

Phys. Rev. B 101, 241405(R) – Published 1 June 2020

Abstract

In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator $Y_{3} F e_{5} O_{12}$ . From nonlocal transport measurements, we demonstrate an induced magnetic exchange field in graphene, which lowers the magnetic field required to modulate the magnetic state in graphene. These results show that a magnetic proximity effect in graphene is an important ingredient for the development of two-dimensional materials in which it is desirable for ordered states of matter to be tunable with relatively small applied magnetic fields (>6 T).

Received 14 June 2019
Revised 8 October 2019
Accepted 22 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.241405

Physics Subject Headings (PhySH)

Edge states Exchange interaction Landau levels Spin state transition

Ferrimagnets Magnetic insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yang Li^1,2,*, Mario Amado^1,*, Timo Hyart³, Grzegorz P. Mazur³, Vetle Risinggård^4,5, Thomas Wagner^1,6, Lauren McKenzie-Sell^1,7, Graham Kimbell¹, Joerg Wunderlich^6,8,9, Jacob Linder^4,5, and Jason W. A. Robinson^1,†

¹Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
²Cambridge Graphene Centre, University of Cambridge, 9 JJ Thomson Avenue, Cambridge CB3 0FA, United Kingdom
³International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
⁴Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
⁵Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
⁶Hitachi Cambridge Laboratory, Cambridge CB3 0HE, United Kingdom
⁷Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
⁸Institute of Experimental and Applied Physics, University of Regensburg, Universitätsstrasse 31, 93051 Regensburg, Germany
⁹Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, 162 00, Praha 6, Czech Republic

^*These authors contributed equally to this work.
^†Corresponding author: jjr33@cam.ac.uk

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Vol. 101, Iss. 24 — 15 June 2020

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Images

Figure 1
Energy spectra for the (a) AF, (b) F, and (c) CAF states in graphene, which arise depending on the total magnetic field ( $M_{T}$ ) applied to graphene and the angle (θ) between $M_{T}$ and the sublattice spins. Color scale bar shows −1 (spin direction antiparallel to $M_{T}$ ) to 1 (spin direction parallel to $M_{T}$ ). Top insets in (a)–(c): Schematic diagrams illustrating the sublattice spins in graphene (left) which make an angle θ with respect to $M_{T}$ (right). Bottom insets in (a)–(c): $R_{nl}$ vs $V_{TG}$ for AF, F, and CAF states near $V_{D}$ . (a) The AF state forms when $M_{T}$ is zero (sublattice spins are antiparallel). (b) The F state forms when $M_{T}$ is larger than a critical value (determined by the Coulomb interaction) and the sublattice spins are parallel to $M_{T}$ . (c) The CAF state is a mixture of AF and F states and forms when $M_{T}$ is nonzero, but smaller than a critical value (sublattice spins are noncollinear to $M_{T}$ ). (d) Schematic diagram of a graphene Hall bar on YIG in which the YIG magnetization ( $M_{sub}$ ) induces a nonzero $M_{ex}$ in graphene that adds to the Zeeman field ( $\frac{g}{2} B$ ).
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Figure 2
(a) X-ray reflectivity of YIG (84-nm-thick with a roughness of 0.14 nm) on GGG. Upper inset: Raman spectra at 293 K for different structures (labeled) in which the background Raman spectra from hBN and YIG/GGG are subtracted. The G-peak ( $\approx 1580 c m^{- 1}$ ) and 2D-peak ( $\approx 2700 c m^{- 1}$ ) positions of graphene on different substrates vary due to different doping levels [20]. Lower inset: X-ray diffraction trace showing single-phase (1 1 0) YIG. (b), (c) $R_{nl}$ vs $V_{TG} - V_{D}$ at 9 K for an hBN/graphene Hall bar on YIG (device I) and a control Hall bar (labeled) with insets (right) showing $R_{x x}$ / $R_{x x, D}$ and $R_{nl}$ / $R_{nl, D}$ vs $V_{TG} - V_{D}$ for the same Hall bar in zero magnetic field. Left inset of (b): False color optical image of an hBN/graphene Hall bar on YIG.
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Figure 3
(a) Gate-voltage dependence of $R_{x x}$ / $R_{x x, D}$ and $R_{nl}$ / $R_{nl, D}$ with $B_{⊥} = 2.5 T$ . (b) $R_{nl, D}$ with $B_{⊥}$ for device I compared to the hBN/graphene/ $Al O_{x}$ /YIG control Hall bar. (c) $R_{nl, D}$ vs $B_{⊥}$ for reverse electrical connections showing that the Onsager relation is obeyed in device I. (d) Landau level fan diagram where the dashed lines are calculated fitting results. Filling factors are shown beside the dashed lines. All data are recorded at 9 K.
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Figure 4
(a)–(d) Gate-voltage dependence of the longitudinal conductance ( $σ_{x x}$ ) for increasing $B_{⊥}$ (labeled) and (e)–(h) the corresponding Hall conductance ( $σ_{x y}$ ) over the same magnetic field range. Inset of (d) shows the longitudinal resistivity ( $ρ_{x x, D}$ ) at $V_{D}$ vs $B_{⊥}$ for device I and the hBN/graphene/ $Al O_{x}$ /YIG control Hall bar. All data are recorded at 2.7 K.
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Figure 5
(a)–(f) Gate-voltage dependence of $R_{nl}$ for different values of $B_{⊥}$ (labeled) for (a)–(c) device I and (d)–(f) device II. (g) $R_{nl, D}$ vs α with B from 2 to 12 T for device II. Dashed lines are a guide to the eye. A ±5° operational error due to manual rotation of the sample holder leads to the small asymmetry in $R_{nl, D}$ at $α = 60^{\circ}$ and 120°. (h) Magnetic phase diagram ( $M_{T}$ vs $B_{⊥}$ ) for graphene in which the solid (red) line $M_{T} \approx 9.9 B_{⊥} + 4.9$ is calculated from Ref. [9] using the extracted data in red as explained in the main text and SM [21]. The blue data represent the estimated phases for devices I and II with $B_{⊥}$ only. For small $B_{⊥}$ , the quantum Hall state is not well developed. By increasing $B_{⊥}$ , there exists a transition between the F and CAF state. For reasonably small $B_{⊥}$ and large $M_{T}$ , the F state is realized, whereas by increasing the ratio of $B_{⊥}$ / $M_{T}$ , the CAF state becomes energetically favored. All data are recorded at 2.7 K except the data from Ref. [9], which are at 300 mK.
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