BiFeO3

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

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Asymmetric Modulation on Exchange Field in a Graphene/BiFeO3 Heterostructure by External Magnetic Field Hua-Ding Song,† Yan-Fei Wu,‡ Xin Yang,§ Zhaohui Ren,§ Xiaoxing Ke,∥ Mert Kurttepeli,⊥ Gustaaf Van Tendeloo,⊥ Dameng Liu,# Han-Chun Wu,∇ Baoming Yan,† Xiaosong Wu,†,○ Chun-Gang Duan,◆ Gaorong Han,§ Zhi-Min Liao,*,†,○ and Dapeng Yu†,‡ †

State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China Institute for Quantum Science and Engineering and Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China § State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China ∥ Institute of Microstructures and Properties of Advanced Materials, Beijing University of Technology, Beijing 100124, China ⊥ EMAT (Electron Microscopy for Material Science), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium # State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China ∇ School of Physics, Beijing Institute of Technology, Beijing 100081, China ○ Collaborative Innovation Center of Quantum Matter, Beijing 100871, China ◆ Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241, China ‡

S Supporting Information *

ABSTRACT: Graphene, having all atoms on its surface, is favorable to extend the functions by introducing the spin− orbit coupling and magnetism through proximity effect. Here, we report the tunable interfacial exchange field produced by proximity coupling in graphene/BiFeO3 heterostructures. The exchange field has a notable dependence with external magnetic field, and it is much larger under negative magnetic field than that under positive magnetic field. For negative external magnetic field, interfacial exchange coupling gives rise to evident spin splitting for N ≠ 0 Landau levels and a quantum Hall metal state for N = 0 Landau level. Our findings suggest graphene/BiFeO3 heterostructures are promising for spintronics. KEYWORDS: Graphene, BiFeO3, proximity effect, transport, spintronics state was observed. As applying positive external magnetic field, the Bex is small and the splitting of N ≠ 0 LLs was not observed. The results suggest that the external magnetic field is capable of adjusting the proximity effect by modulating the magnetization of the magnetic insulator. Device Characterizations. The BFO nanoplate was stacked on monolayer graphene by a dry transfer method using a micromanipulator, and the details of the fabrication process are illustrated in Figure S1. The cross-section of a graphene/BFO heterostructure is studied by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). As shown in Figure 1a, the BFO nanoplate and SiO2/Si substrate are clearly illustrated. The highresolution HAADF-STEM image of the cross-section illustrates

G

raphene is one of the most promising Dirac electronic systems. Its high mobility and long spin diffusion length provide a potential avenue for the next-generation spintronics.1−14 Through strong electronic hybridization with a proximal material, the band structure of graphene is expected to be modulated.15−22 A substantial exchange field Bex ∼ 14 T is reported in graphene coupled to a EuS magnetic insulator,15 and an anomalous Hall effect was observed in graphene−YIG heterostructures.16 Moreover, the enhancement of the Bex was predicted in graphene/BiFeO3 heterostructures due to the strong exchange interaction (∼1 eV) of Fe 3d states.17−19 A recent work reported the experimental signature of Bex in the graphene-coupled BiFeO3 (BFO) nanoplate.20 Here we report the asymmetric modulation on Bex in a graphene/BFO heterostructure by external magnetic field. A notable spin splitting of N ≠ 0 Landau levels was observed under negative magnetic field as low as −6 T, giving direct evidence for the large Bex. The large Bex results in that the spin splitting is larger than the valley splitting at N = 0 LL, and a quantum Hall metal © XXXX American Chemical Society

Received: December 31, 2017 Revised: March 6, 2018 Published: March 13, 2018 A

DOI: 10.1021/acs.nanolett.7b05480 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters

Figure 1. (a) HAADF-STEM image of a graphene/BFO heterostructure. The presence of the BFO nanoplate can be seen clearly. (b) Highresolution HAADF-STEM image of the BFO nanoplate cross-section. The BFO is projected at the zone axis of [2,4,-6,1]. The top surface of the BFO nanoplate is revealed as (012) plane. (c−f) EDS elemental mappings of the BFO/graphene heterostructure. It is confirmed that the Bi, O, and Fe elements are evenly distributed in the nanoplate. The O signal detected from the substrate is induced by the SiO2 layer. The signal of C elements is enhanced in the interface between BFO nanoplate and substrate, indicating the presence of graphene layer. The C element signal in the background is induced during TEM sample preparation.

Figure 2. (a) A schematic diagram for a typical graphene/BFO hybrid transistor. The red arrow indicates the direction of the positive magnetic field. (b) The longitudinal resistivity ρxx as a function of gate voltage of a graphene/BFO device. Inset: optical image of a graphene/BFO device and the white dashed lines indicate the Hall bar shape.

patterned into Hall bar shape after deposition of Pd/Au electrodes (5/80 nm). The mobility of the hybrid device investigated here is 104 cm2/(V s), calculated from the transverse curve (Figure 2b). The inset picture in Figure 2b shows the optical image of a typical graphene/BFO device. Asymmetric Magnetic Field response. The graphene/ BFO hybrid devices exhibit asymmetric transport behavior under reversed external perpendicular magnetic field (B), as shown in Figure 3. For the negative magnetic field, it is interesting to note that the N ≠ 0 LLs are split, while there is a resistance peak at the N = 0 LL (near the Dirac point) that only shows a little splitting under −14 T. The splitting of nonzero LLs is attributed to the spin splitting, because the lifting of valley degeneracy in nonzero LLs is much more difficult than that in N = 0 LL. Because the N ≠ 0 LL eigenstates for a single valley have equal distribution on A/B sublattice,24 breaking

the high quality single-crystal structure of the BFO nanoplate (Figure 1b). The BFO is projected along the [2,4,−6,1] zone axis as indexed from Figure 1b. The plane parallel to the exposed surface of BFO nanoplates is determined to be (012) plane in the BFO hexagonal representation, corresponding to (100)c lattice plane of pseudocubic representation.23 The energy dispersive X-ray spectroscopy (EDS) mappings at the heterostructure interface exhibit the uniform distribution of Bi, O, and Fe elements in the BFO nanoplate (Figures 1c−e). The signal of C element in the interface between BFO nanoplate and substrate indicates the presence of graphene layer (Figure 1f). During preparation of cross-section samples, protective layers of amorphous Pt-carbon composite were deposited, which cause the background signal of C element in Figure 1f. The schematic diagram of a typical graphene/BFO hybrid device is displayed in Figure 2a. The graphene layer was B

DOI: 10.1021/acs.nanolett.7b05480 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 3. Asymmetric magneto-transport behaviors under B = ±4−14 T. For B < 0, the nonzero Landau levels are split.

Figure 4. (a) The ρxx as a function of magnetic field at Vg = 13 V. (b) A diagram for the mechanism of the asymmetric dependence on B⊥ direction. The red arrows indicate the residual magnetization direction of the BFO nanoplates, which is induced by the canting of the antiferromagnetic sub lattices. Considering the residual magnetic moments of Fe atoms at graphene/BFO interface, the positive and negative magnetic fields have asymmetric influence on the perpendicular spin component of the Fe atoms. Red atoms, oxygen; yellow atoms, iron; purple atoms, bismuth.

inversion symmetry cannot lift the valley degeneracy in nonzero LLs. However, the N = 0 LL eigenstates for one valley have the precise distribution of residing on only one sublattice (A or B),

thus the breaking of inversion symmetry can directly lift the valley degeneracy. The Peierls instability induced by perpendicular magnetic field gives rise to sublattice distortion C

DOI: 10.1021/acs.nanolett.7b05480 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters

Figure 5. (a) Diagram for graphene Landau levels before and after the lifting of degeneracy. According to the 4-fold degeneracy, full population of N = 1, 2 LLs corresponds to the filling factor of v = 6, 10, respectively. Thus, the centers of N = 1, 2 LLs locate at νc = 4, 8 (the upper panel). The LL splitting gives that the centers of the N = 1, 2 LLs are at νc = 3, 5, 7, 9 (the bottom panel). (b) The longitudinal resistivity ρxx as a function of the filling factor ν. The curves for B = −6 ∼ −14 T are vertically shifted for clear illustration.

Figure 6. (a) Diagram for a splitting Landau level. Individual LLs are divided into localized and extended states separated by the mobility edge. EZ is the spin splitting energy. (b) A schematic diagram for the coexistence of bulk transport channels (provided by extended states of LLs) and quantum Hall edge states. The distribution of extended state wave functions is usually along equipotential contours (green curves), and hopping between the contours can be achieved at adjacent segments (black dashed circles), leading to dissipative bulk transport. (c) The fitting results for splitting N = 1 LLs under B = −12 T. (d) The ρxy as a function of Vg under B = −4, −6, −8, −10, −12, and −14 T, respectively.

Dirac point VD = 7 V), as shown in Figure 4a. The large ρxx peak splitting (N = 1 LL) was observed in the negative magnetic field side. For pristine graphene with a mobility of ∼104 cm2/(V s), such a significant splitting behavior can only occur under an extremely large external field.4,12 We propose a phenomenological model to interpret the asymmetric dependence on the B⊥ direction. For the BFO nanoplates, a clear magnetic hysteresis behavior with a coercive field of 150 Oe was observed at 5 K, as shown in Figure S2. Although the magnetic moments of BFO are coupled ferromagnetically within the pseudocubic (111) planes and antiferromagnetically between adjacent planes, the strong spin−

in graphene. Such distortion breaks the mirror symmetry regard to the graphene plane, which eventually results in the breaking of inversion symmetry of A/B sublattice.24 Previous experiments have confirmed that high magnetic field can lift the valley degeneracy in N = 0 LL, but the valley degeneracy can be preserved in N ≠ 0 LLs even under perpendicular field of B = 45 T.12 For the positive magnetic field, the splitting of N ≠ 0 LLs disappears, indicating the magnetic proximity effect is much weaker compared to the B < 0 situations. The resistivity peak splitting and asymmetric dependence on the B direction was also observed as sweeping the magnetic field at Vg = 13 V (the D

DOI: 10.1021/acs.nanolett.7b05480 Nano Lett. XXXX, XXX, XXX−XXX

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exponent.29,30 Therefore, the relation between ρxx and the filling factor ν can be established as ln(ρxx) ∝|ν − νc|γ/2. In Figure 6c, the measured ln(ρxx) curves of the split LLs show a good fit by this formula with critical exponent γ = 2.6 (more fitting results are displayed in Figure S5−8), which provide substantial evidence for the existence of extended states at each split individual LLs. However, the transverse resistivity ρxy still exhibits typical quantum Hall plateaus (Figure 6d). The spin polarized carriers in the splitting LLs may suffer significant scattering from the BFO surface with magnetic impurities, resulting in the broadening of the spin splitting LLs and the absence of new ρxy quantum plateaus. Transport in the N = 0 LL. As spin and valley splitting coexist in N = 0 LL, the electronic structure of graphene ground state is determined by the competition between spin splitting energy EZ and valley splitting energy u.24,33,34 A detailed illustration is displayed in Figure 7. For the valley

orbit coupling results in a canting of the antiferromagnetic sublattice and a macroscopic magnetization, and thus exhibiting weak ferromagnetism.25,26 In this work, the surface of BFO attached to graphene is the (100) pseudocubic plane, as shown in Figure 1b. The interfacial exchange splitting originates from the overlapping between the wave functions of localized moments and itinerant electrons at graphene/BFO interface.17,18,27 The exchange splitting energy can be described as Eex = cJex⟨SZ⟩,27 where c is the fractional density of Fe3+ ions to that of itinerant electrons in graphene at the interface, Jex is the spatial average of the exchange integral, and ⟨SZ⟩ is the spatial average of spins contributed by interfacial Fe layer. c and Jex should be symmetric under ±B⊥. Considering the breaking of mirror symmetry at the heterostructure interface and the net magnetic moments at the BFO surface, the positive and negative B⊥ can exert asymmetric modulations on ⟨SZ⟩. It is reported that the strong coupling at graphene/BFO interface can also change the intensity of ⟨SZ⟩ as a feedback with asymmetric behavior under ±B⊥.28 Therefore, there is an asymmetric Eex under ±B⊥. For clear illustration, the net magnetic moments at the BFO surface are schematically shown in Figure 4b. The red arrows indicate the residual magnetization direction of the BFO nanoplates, which is induced by the canting of the antiferromagnetic sublattices. The positive and negative magnetic fields have asymmetric influence on the net magnetic moments of Fe atoms. Therefore, the magnetic proximity effect at graphene/BFO interface can also have an asymmetric performance under ±B⊥. Transport in the N ≠ 0 LLs. For better tracking of the LL positions, we replaced the horizontal axis by the filling factor ν = nh/eB, where n is the carrier density. For monolayer graphene, the full population of the Nth LL in electron branch satisfies the relation of v = 4N + 2, considering the 4-fold degeneracy, as shown in Figure 5a, top panel. Thus, the centers of the LLs where the Nth LL is half populated can be labeled as vc = 4N when the LLs are significantly broadened. For example, the centers of N = 1, 2 LLs can be labeled as vc = 4, 8. For the situation of LL splitting, the half populated LL positions should locate at νc = 3, 5, 7, 9..., as displayed in Figure 5a bottom panel. As shown in Figure 5b, under B⊥ < 0, the ρxx peaks are welldistributed around νc = −7, −5, −3, 3, 5, 7, suggesting the degeneracy lifting of the LLs. The ρxx−Vg transfer curves under B = 0 ∼ −14 T are displayed in Figure S3. The position of the LL in Vg shows a linear dependence with B⊥, indicating that the Bex does not affect the Landau level degeneracy and would not provide any orbital effect. The minimum resistance inside N = 1 LL decreases with B⊥ from −4 to −14 T (Figure S4), indicating that the spin splitting EZ = gμB (Bex + B⊥) of LLs is enhanced with increasing the external field. The Landau level states are divided into localized and extended states separated by the mobility edge (Figure 6a). The extended states can provide bulk transport channels coexisting with the quantum Hall edge states,2−6,29,30 leading to ρxx peaks (Figure 6b). The resistivity in the extended states is described by ρxx = ρ0 e−

εc / εT

splitting dominant mechanism with EZ < u, the system is a quantum Hall insulator with gap opening in bulk and edge. For the spin-splitting dominant mechanism with EZ < 2u, the system is a quantum Hall metal, and gapless counter-circulating spin filtered edge states exist near the Dirac point. There is an intermediate phase as the spin splitting is comparable to the valley splitting, where the bulk LL gap near the Dirac point is very small. For pristine graphene, the valley splitting energy u ∼ 4.2[K] × B⊥[T] is always larger than the spin splitting energy EZ ∼ 1.4[K] × Btot[T] as only applying perpendicular magnetic field.3,24 In this situation, a quantum Hall insulator state appears at the Dirac point and the longitudinal conductance is closed to zero.33 In our graphene/BFO system, the large Bex under negative external magnetic field may result in the EZ > 2u, and a quantum Hall metal state is produced. The counter-circulating edge states provide transport phenomena similar to quantum spin Hall effect,34,35 where the system shows the quantized longitudinal conductance related to the measurement configuration and the Hall conductance σxy = 0. As shown in Figure 8a, the longitudinal conductance G near the Dirac point is

, where εT = kBT is the thermal activation

e2 4π ϵϵ0ξ 31,32

energy, and εc ∝

Figure 7. (a) The quantum Hall insulator phase (u > EZ). Large valley splitting induced by perpendicular magnetic field (u ∼ 4.2[K] × B⊥[T]) gives rise to the splitting of N = 0 LL, opening an obvious bulk energy gap. The spin splitting is weaker compared to the valley splitting. (b) An intermediate phase as the spin splitting is comparable to the valley splitting. The LL gap near the Dirac point is very small. For the system with large potential fluctuations of the Fermi level and a large amount of residual carriers at Dirac point, the highly conductive bulk states can dominate the transport at the Dirac point. (c) The quantum Hall metal phase with very large spin splitting (EZ > 2u). The crossing of spin splitting bands causes the existence of countercirculating spin-polarized edge states. Red, spin up states; green, spin down states.

is the hopping barrier calibrated by the

Coulomb gap. The localization length (ξ) indicates the spatial extension of the wave functions, which has been confirmed to follow a power-law behavior as a function of the filling factor ν: ξ(ν) = ξ0|ν − νc|−γ, where γ is the critical

stabilized around E

e2 h

as magnetic field B⊥ increased from −4 to DOI: 10.1021/acs.nanolett.7b05480 Nano Lett. XXXX, XXX, XXX−XXX

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at the Dirac point under B⊥ = −14 T may originate from the highly conductive bulk states. For the positive magnetic field, the Bex is small. Under low magnetic field, the valley splitting may be comparable with the spin splitting, and the N = 0 LL is at the intermediate phase. The highly conductive bulk states may also be responsible for the observed resistance dip at the Dirac point (Figure 3). Under positive magnetic field, the quantum Hall results (Figure S9) do not show any new plateau at the N = 0 LL, indicating the ρxx dip at the Dirac point is not from edge transport but from the bulk transport. As further increasing the magnetic field to 14 T, a resistance peak at the Dirac point is observed (Figure 3), which is due to the enhanced valley splitting. Origin of the Large Exchange Field. Previous theoretical reports provide substantial support for the large Bex in graphene/BFO interface. The first-principle calculations by Qiao et al. predicted a proximity-induced spin splitting up to ∼142 meV (corresponding to Bex ∼ 1183 T) in graphene coupled to BFO nanoplates.17,18 The graphene π-orbitals have a strong hybridization with the Fe 3d orbitals, because the Fe 3d orbitals provide a strong exchange energy (∼1 eV),25 leading to a large magnetic proximity effect in graphene/BFO heterostructures. The external field also plays an important role in the magnetic proximity effect. The magnetic moments of Fe atoms can be well aligned by the external magnetic field with the saturation of magnetization at