Session F41: Magnetism in 2D Systems

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Over the past few years, a growing family of van der Waals (vdW) materials have been discovered to host intrinsic magnetic ordering. These materials exhibit a wide array of magnetic orders in the atomically-thin limit, including both intra- and inter-layer ferro- and antiferromagnetism. Interfacing graphene with these 2D magnets offers intriguing possibilities for realizing new phenomena stemming from the magnetic proximity effect (MPE) owing to the high quality of the layered junction. Here, we investigate the MPE in heterostructures comprising graphene on XPS₃ (X=Ni/Fe/Mn) substrates. Our magnetotransport characterization reveals signatures of charge transfer effects in a variety of these heterostructures. We will additionally discuss ongoing efforts to fabricate pristine interfaces between graphene and the environmentally-sensitive 2D magnets.   

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The long spin-diffusion length, spin-lifetime and excellent optical absorption coefficient of graphene provide an attractive platform for building opto-electronic devices and spin-based logic in a nanometer regime. We analyze how the size and shape of graphene nanoflakes can be used to alter their magnetic structures and optical properties, using time-dependent density functional theory. As the edges of zigzag graphene nanoribbons are known to align anti-ferromagnetically and armchair ones are non-magnetic, a combination of both in a single nanoflake geometry can be used to optimize the ground-state magnetic structure to tailor the exchange coupling to ferro- or anti-ferromagnetic edge magnetism. This allows for optimizing the switching conditions between the two magnetic states, for example, tuning the energy-efficiency by countering the stability of the external field's magnitude. Additionally, we show that the magnetic ordering alters the optical response of the flake. Finally, we investigate how the high harmonic generation of a graphene nanoflake depends on its magnetic configuration and the polarization of the laser field.   

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Van der Waals heterostructures have emerged as a new playground for exploring electron-optics - the solid-state analogues of optical devices, such as lenses, beam splitters and interferometers. A fundamental building block for constructing these electron-optic devices is an electron source that can provide a narrow and collimated beam. In this work, we observe that the naturally occuring P-N junction formed at a metal-graphene interface leads to a strongly collimated beam of electrons, which can be turned on/off by simply changing the doping of the graphene. We non-invasively study this collimation by imaging magnetic focusing in real-space using a scanning single-electron transistor as an electrostatic potential probe.We observe a drastic transition of the potential landscape when the graphene doping changes sign, from featureless for electron-doped (no P-N junction) to oscillating for hole-doped. Additionally, we show that there is a universal relation between the measured contact resistance of the metal-graphene interface to the degree of collimation, which should be considered in future ballistic experiments.   

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CrTe₂ is a novel magnetic layered transition metal dichalcogenide that has been recently synthesized in a metastable 1T bulk phase with a high-curie temperature of 310 K. While its 1T phase has been investigated both experimentally and theoretically, detailed theoretical studies on the other possible phases and phase transition are imperative. In this work, we studied the structural, electronic, and magnetic properties of 1T, 1H, and 2H phases of CrTe₂ using density functional theory (DFT). The 1T phase of CrTe2 was found to be the ground state in both bulk and monolayer structures at low temperatures. The energy barriers of the phase transition between the 1T, 1H, and 2H phases were calculated by the Nudge Elastic Band (NEB) method. By applying the linear response method, we obtained the self-consistent U parameters in 1T, 1H, and 2H phases of CrTe₂. The 2H and 1H phases were predicted to be metallic and ferromagnetic with DFT+U correction, which is in contradiction to previous theoretical studies.   

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We report magneto-transport measurements in Hall bar and corbino geometry in the bilayer WSe₂ van der Waals heterostructure two-dimensional electron system, showing distinct behavior for electrons with spin-up and spin-down orientations. In WSe₂, several lowest LLs are spin-polarized (spin-up) due to the large g factor. When the spin-down levels are being filled, the conductivity is much lower than in spin-up levels, and at high fields it becomes completely localized, with the longitudinal conductance approaching zero and a wide Hall plateau lasting over a large filling factor range. Also, the conductance shows opposite temperature dependence - conductance of spin-down levels decreases with decreasing T (while the spin-up levels show the normal behavior, i.e., increasing with decreasing T). At the Landau level crossing position, we observe the manifestation of quantum Hall ferromagnetic state which gives rise to a resistance spike inside the gap.   

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Twisted bilayer graphene (TBG) has recently drawn great attention because of the wide variety of novel electronic and optical properties. Behind the new phenomena, for low twist angle, we can find the emergence of flat-bands produced by the localization of the electronic wave-function on the AA-stacked regions. In this regime, a paramagnetic response to an in-plane magnetic field is expected. Here, to induce the above-mentioned response electrically we created a TBG barrier putting a graphene flake on top of biased graphene nanoribbon. Our results [1] show that for low twist angles the applied electric field induces the formation of a well-defined Moiré superlattice of in-plane magnetic moments whose magnitude and orientation can be tuned the source-drain voltage. Our results are robust against lattice relaxation, lattice orientation and edge vacancies.

[1] D. A. Bahamon, G. Gómez-Santos, and T. Stauber, Nanoscale 12, 15383 (2020).   

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Here we investigate interlayer scattering in twisted double bilayer graphene with an intermediate twist (1.94°) angle. We focus on the decoupled regime where the wavefunctions are bilayer polarized and the device behaves as a weakly coupled double quantum well [1]. Two regimes show enhanced interlayer scattering that we observe through magneto interlayer (intersubband) oscillations [2]. In the regime around the Lifshitz transition, density and temperature dependent resistivity measurements qualitatively indicate increasing trend of interlayer electron-phonon scattering towards the Lifshitz transition that is in accordance with a simple el-ph model. Additionally, interlayer scattering is observed at the onset of the second subband. Observed negative compressibility and the flatness of the bands suggest electron-electron or impurity scattering as the dominant scattering mechanism. Since the nature of the superconducting state in twisted graphene heterostructures remains unknown, our observations can potentially improve the understanding of the coupling mechanism of electrons in twisted graphene.

[1] F. K. de Vries el al., arXiv:2002.05267 1 (2020)
[2] I. A. Dmitriev el al., Rev. Mod. Phys., 84(4):1709, 2012   

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We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe₂. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moiré valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moiré bands. We show that a layer potential difference, arising, for example, from an applied electric field, can drastically change the non-interacting moiré bands, tune the spin-orbit coupling in the Hubbard model, control the charge excitation gap of the Mott insulator at half filling, and generate an effective DzyaloshinskiiMoriya interaction in the effective Heisenberg model for the Mott insulator. Our theoretical results agree with transport experiments on the same system in several key aspects, and establish twisted bilayer WSe2 as a highly tunable system for studying and simulating strongly correlated phenomena in the Hubbard model.

Reference: PhysRevResearch.2.033087   

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We report on a magneto-infrared spectroscopy study of the new generation epigraphene grown on a nonpolar facet of SiC. We observe interband Landau level (LL) transitions that can be well described by a massless Dirac fermion model with a Fermi velocity of 1 x 10⁶ m/s. The transitions remain visible as the magnetic field is down to 0.25 T, indicating that the carrier density is no greater than 3.6 x 10¹⁰ cm^-2 as expected for charge-neutral nonpolar epigraphene. When the samples are grown thicker, LL transition splittings are spotted at high magnetic fields. Failing to explain the splittings with electron-hole asymmetry, we suggest that it could arise from the (twist) bilayer epigraphene components, which we will discuss with a numerical twist-bilayer model.   

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The valley degree of freedom in two-dimensional (2D) materials is promising for applications in quantum technologies such as information storage, processing, and reading. In general, however, the valley degree of freedom in 2D materials is difficult to control because valleys are often degenerate or possess different energies that are indistinguishable experimentally. Therefore, an important step toward the realization of valley-based quantum information technology is the capability and control of valley splitting. In this regard, Bernal stacked trilayer graphene (ABA-TLG) is promising because it has two valleys that can be configured to host giant opposite non-zero orbital magnetic moments. In this talk, I will show our recent scanning tunneling spectroscopy (STS) study of ABA-TLG with magnetic field and back gate modulation. By applying an out-of-plane magnetic field we couple to the orbital magnetic moments in ABA-TLG and realize giant valley splitting. Subsequently, by modulating the back gate voltage in our devices we can tune the valley splitting by a factor of 2 at a constant magnetic field.   

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We consider a triangular lattice of short carbon nanorings (cyclacenes). In the single molecule limit, each unit has 2 topologically protected zero modes. As a result, we could expect the low energy bands of the cyclacene crystal to be formed by such zero modes. When Coulomb repulsion is added into this picture, the low energy physics of this system should be similar to a Hubbard model of two weakly coupled triangular lattices. In the strong coupling limit, every ring should host 2 localized electrons, correlated antiferromagnetically with each other, and with the first neighbour ciclacene's, producing antiferromagnetically coupled frustrated S=1/2 triangular lattices. We carry out DFT calculations that confirm the main features of this scenario and show a non-collinear 120 antiferromagnetic phase ground state. Our results show a bottom-up route to engineer correlated electronic phases with narrow bands in carbon-based crystals, complementary to the top-bottom twisted bilayer approach.   

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We study direct magnetoexcitons in transition-metal dichalcogenides (TMDC) monolayers and indirect magnetoexcitons in double-layer TMDC heterostructures encapsulated by h-BN. The formations of direct and indirect magnetoexcitons occur in the presence of perpendicular to the layers magnetic field. We calculate the binding energies of 1s, 2s, 3s, and 4s Rydberg states of magnetoexcitons by numerical solution of the Schrödinger equation using both Rytova-Keldysh and Coulomb potentials, and electron and hole masses obtained in the framework of density functional theory. We report the energy contribution from the magnetic field to the binding energies and diamagnetic coefficients for Rydberg states. It is demonstrated that the binding energies of direct and indirect magnetoexcitons can be tuned by applying the external magnetic field. Our calculations show that the choice of the interaction potentials has a significant effect on the binding energies of magnetoexcitons and the diamagnetic coefficients.   

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The electronic properties of Graphene have been intensively investigated over the last decade, and signatures of the remarkable features of its Dirac spectrum have been displayed using transport and spectroscopy experiments. In contrast, the orbital magnetism of graphene, which is probably the most fundamental signature of graphene’s characteristic Berry phase, has not yet been measured at the level of a single flake. In particular, the striking prediction of a divergent diamagnetic response at zero doping calls for an experimental test.
Using a highly sensitive Giant Magnetoresistance sensor (GMR) we have measured the gate voltage-dependent magnetisation of a single graphene flake encapsulated between boron nitride (BN) crystals. The signal exhibits a diamagnetic peak at the Dirac point whose magnetic field and temperature dependences agree with theoretical predictions starting from the work of McClure in 1956 [1]. Our measurements open a new field of investigation of orbital currents in graphene and 2D topological materials, providing a new means of monitoring Berry phase singularities and exploring correlated states generated by combined effects of Coulomb interactions strain or Moiré potentials.

[1] McClure, J. W., Physical Review, 104(3), 666, 1956.   

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Superlattice-induced modulation of two-dimensional materials can give rise to a host of surprising yet counter-intuitive effects and impact electron transport in a variety of non-trivial ways. Twisted bilayer graphene (TBG) provides an exceptional platform in which to study these superlattice-enabled transport effects, as exemplified by numerous experiments revealing many intriguing interaction-driven phenomena in this system [1]. Integral to understanding transport properties of TBG systems is a knowledge of the electron scattering mechanisms that govern momentum relaxation in the superlattice. We show that at small twist angles, unlike in monolayer graphene, intervalley electron scattering plays a critical role in momentum relaxation. This scattering process reveals itself in high-temperature magnetooscillations [2], which allow us to estimate the intervalley scattering rate and determine the quasiparticle lifetime in small-angle TBG.

[1] E. Andrei and A. MacDonald, arXiv.2008.08129 (2020).
[2] I. A. Dmitriev et al., Rev. Mod. Phys. 84, 1709 (2012).   

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Magic-angle twisted bilayer graphene (TBG) has drawn great attention for its correlated electronic phases appearing at different doping concentrations. To understand such phases, low-energy band dispersions need to be calculated accurately as a function of doping. However, the large number of atoms in the moiré supercell has limited theoretical calculations of doping effects on electronic and magnetic properties. Here, we present an efficient method to calculate electronic and magnetic properties of electron- and hole-doped TBGs based on results of density functional theory calculations of undoped TBG. With this method, we investigate doping and temperature dependences of electronic and magnetic properties of doped TBGs. We discuss effects of doping on electrostatic screening, low-energy band dispersions, and magnetization of TBG.