Indirect Exchange and Ruderman–Kittel–Kasuya–Yosida (RKKY) Interactions in Magnetically-Doped Graphene

Zero bias conductance peak related to spin triplet states in noncollinear magnetized graphene superconducting junctions

We investigated the zero-bias conductance peak in a graphene-based ferromagnet/ferromagnet/barrier/d-wave superconductor (F/F/B/d-wave SC) heterojunction. Our research indicates that the spin-triplet pairing states induced by non-collinear magnetizations do not lead to the splitting of the zero-bias conductance peak (ZBCP), and the anomalous Andreev reflection makes a significant contribution to the ZBCP. In the case of half-metal, the triplet bound states appear at zero incident energy due to Klein tunneling, which is coincide with the singlet bound states, resulting in the ZBCP arises solely due to spin-triplet pairing states. The ZBCP can be modulated by the exchange field strength, Fermi level and magnetizations angle. These findings offer deeper understanding of the influence of non-collinear magnetizations on anomalous Andreev reflection in graphene-based F/F/B/d-wave SC heterojunctions and hold promise for the development of graphene-based superconducting spintronic devices.

Theory for magnetic impurity modes in two-dimensional van der Waals ferromagnetic films

A spin-wave analysis is developed to calculate the energies of the localized excitations occurring in two-dimensional ferromagnetic van der Waals monolayers when a substitutional magnetic impurity is introduced. The magnetic ions lie on a bipartite honeycomb lattice (similar to that for graphene) and the theory includes the effects of both Ising anisotropy and single-ion anisotropy to stabilize the magnetic ordering perpendicular to the atomic plane at low temperatures. A Dyson-equation formalism, together with the spin-dependent Green's functions derived for van der Waals monolayers, is employed to evaluate the existence conditions and energies for the impurity modes, which lie above the band of spin-wave states of the pure host material. For realistic parameter values it is found that typically two impurity modes may exist, depending on the spin quantum number for the magnetic impurity atom. Numerical applications are made to CrI3and Cr2Ge2Te6as the host materials.

Quantum Confinement in Epitaxial Armchair Graphene Nanoribbons on SiC Sidewalls

The integration of graphene into devices necessitates large-scale growth and precise nanostructuring. Epitaxial growth of graphene on SiC surfaces offers a solution by enabling both simultaneous and targeted realization of quantum structures. We investigated the impact of local variations in the width and edge termination of armchair graphene nanoribbons (AGNRs) on quantum confinement effects using scanning tunneling microscopy and spectroscopy (STM, STS), along with density-functional tight-binding (DFTB) calculations. AGNRs were grown as an ensemble on refaceted sidewalls of SiC mesas with adjacent AGNRs separated by SiC(0001) terraces hosting a buffer layer seamlessly connected to the AGNRs. Energy band gaps measured by STS at the centers of ribbons of different widths align with theoretical expectations, indicating that hybridization of π-electrons with the SiC substrate mimics sharp electronic edges. However, regardless of the ribbon width, band gaps near the edges of AGNRs are significantly reduced. DFTB calculations successfully replicate this effect by considering the role of edge passivation, while strain or electric fields do not account for the observed effect. Unlike idealized nanoribbons with uniform hydrogen passivation, AGNRs on SiC sidewalls generate additional energy bands with non-pz character and nonuniform distribution across the nanoribbon. In AGNRs terminated with Si, these additional states occur at the conduction band edge and rapidly decay into the bulk of the ribbon. This agrees with our experimental findings, demonstrating that edge passivation is crucial in determining the local electronic properties of epitaxial nanoribbons.

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green's function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.

Distribution of RKKY coupling value in 1D crystal with disorder. Specific heat in XY model

The presence of disorder in one-dimensional crystals leads to the localization of all charge carriers and the calculation of the indirect exchange interaction (Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction) cannot be performed perturbatively on disorder. In two and three-dimensional systems it makes sense to calculate the magnitude of RKKY interaction perturbatively treating nearly free carriers scattering on the random potential, and this approach results in a rather high magnitude of the exchange interaction due to interference effects similar to weak localization. We show that in one-dimensional systems the indirect exchange interaction should be described as a random value with heavy-tail distribution function, which is calculated in this work, on scales of carriers localization length. We also demonstrate that heavy tails and the absence of a characteristic value of RKKY interaction magnitude leads to a significant change in observables for these systems. We calculate a specific heat for the one-dimensional XY model taking into account the effect of disorder and assuming that typical distance between impurities exceeds the localization length. In contrast to an ideal system, where specific heat temperature dependence has a peak at a certain temperature proportional to exchange constant describing characteristic energy scale, disorder eliminates the peak as soon as there is no characteristic excitation energy in this case anymore.

Magnetic hysteresis and strong ferromagnetic coupling of sulfur-bridged Dy ions in clusterfullerene Dy2S@C82

Two isomers of metallofullerene Dy₂S@C₈₂ with sulfur-bridged Dy ions exhibit broad magnetic hysteresis with sharp steps at sub-Kelvin temperature. Analysis of the level crossing events for different orientations of a magnetic field showed that even in powder samples, the hysteresis steps caused by quantum tunneling of magnetization can provide precise information on the strength of intramolecular Dy⋯Dy inter-actions. A comparison of different methods to determine the energy difference between ferromagnetic and antiferromagnetic states showed that sub-Kelvin hysteresis gives the most robust and reliable values. The ground state in Dy₂S@C₈₂ has ferromagnetic coupling of Dy magnetic moments, whereas the state with antiferromagnetic coupling in C _s and C _3v cage isomers is 10.7 and 5.1 cm^-1 higher, respectively. The value for the C _s isomer is among the highest found in metallofullerenes and is considerably larger than that reported in non-fullerene dinuclear molecular magnets. Magnetization relaxation times measured in zero magnetic field at sub-Kelvin temperatures tend to level off near 900 and 3200 s in C _s and C _3v isomers. These times correspond to the quantum tunneling relaxation mechanism, in which the whole magnetic moment of the Dy₂S@C₈₂ molecule flips at once as a single entity.

Tailoring Electronic and Magnetic Properties of Graphene by Phosphorus Doping

The electronic and magnetic properties of graphene can be modulated by doping it with other elements, especially those with a different number of valence electrons. In this article, we first provide a three-dimensional reconstruction of the atomic structure of a phosphorus substitution in graphene using aberration-corrected scanning transmission electron microscopy. Turning then to theoretical calculations based on the density functional theory (DFT), we show that doping phosphorus in various bonding configurations can induce magnetism in graphene. Our simulations reveal that the electronic and magnetic properties of P-doped (Gr-P) and/or phosphono-functionalized graphene (Gr-PO₃H₂) can be controlled by both the phosphorus concentration and configurations, ultimately leading to ferromagnetic (FM) and/or antiferromagnetic (AFM) features with the transition temperature up to room temperature. We also calculate core-level binding energies of variously bonded P to facilitate X-ray photoelectron spectroscopy-based identification of its chemical form present in P-doped graphene-based structures. These results may enable the design of graphene-based organic magnets with tailored properties for future magnetic or spintronic applications.

Magnetic properties of N-doped graphene with high Curie temperature

N-doped graphene with Curie temperature higher than room temperature is a good candidate for nanomagnetic applications. Here we report a kind of N-doped graphene that exhibits ferromagnetic property with high Curie temperature (>600 K). Four graphene samples were prepared through self-propagating high-temperature synthesis (SHS), and the doped nitrogen contents of in the samples were 0 at.%, 2.53 at.%, 9.21 at.% and 11.17 at.%. It has been found that the saturation magnetization and coercive field increase with the increasing of nitrogen contents in the samples. For the sample with the highest nitrogen content, the saturation magnetizations reach 0.282 emu/g at 10 K and 0.148 emu/g at 300 K; the coercive forces reach 544.2 Oe at 10 K and 168.8 Oe at 300 K. The drop of magnetic susceptibility at ~625 K for N-doped graphene is mainly caused by the decomposition of pyrrolic N and pydinic N. Our results suggest that SHS method is an effective and high-throughput method to produce N-doped graphene with high nitrogen concentration and that N-doped graphene produced by SHS method is promising to be a good candidate for nanomagnetic applications.

The characterization of Co-nanoparticles supported on graphene

Cobalt nanoclusters on graphene spontaneously form CoO at very low thickness, which is converted to Co[OH]₂ when layers are formed.

Realization of ferromagnetic graphene oxide with high magnetization by doping graphene oxide with nitrogen

The long spin diffusion length makes graphene very attractive for novel spintronic devices, and thus has triggered a quest for integrating the charge and spin degrees of freedom. However, ideal graphene is intrinsic non-magnetic, due to a delocalized π bonding network. Therefore, synthesis of ferromagnetic graphene or its derivatives with high magnetization is urgent due to both fundamental and technological importance. Here we report that N-doping can be an effective route to obtain a very high magnetization of ca. 1.66 emu/g, and can make graphene oxide (GO) to be ferromagnetism with a Curie-temperature of 100.2 K. Clearly, our findings can offer the easy realization of ferromagnetic GO with high magnetization, therefore, push the way for potential applications in spintronic devices.

Variable range of the RKKY interaction in edged graphene

The indirect exchange interaction is one of the key factors in determining the overall alignment of magnetic impurities embedded in metallic host materials. In this work we examine the range of this interaction in magnetically doped graphene systems in the presence of armchair edges using a combination of analytical and numerical Green function approaches. We consider both a semi-infinite sheet of graphene with a single armchair edge, and also quasi-one-dimensional armchair-edged graphene nanoribbons (GNRs). While we find signals of the bulk decay rate in semi-infinite graphene and signals of the expected one-dimensional decay rate in GNRs, we also find an unusually rapid decay for certain instances in both, which manifests itself whenever the impurities are located at sites which are a multiple of three atoms from the edge. This decay behavior emerges from both the analytic and numerical calculations, and the result for semi-infinite graphene can be interpreted as an intermediate case between ribbon and bulk systems.

Indirect RKKY interaction between localized magnetic moments in armchair graphene nanoribbons

A form of indirect Ruderman-Kittel-Kasuya-Yosida (RKKY)-like coupling between magnetic on-site impurities in armchair graphene nanoribbons is studied theoretically. The calculations are based on a tight-binding model for a finite nanoribbon system with periodic boundary conditions. A pronounced Friedel-oscillation-like dependence of the coupling magnitude on the impurity position within the nanoribbon resulting from quantum size effects is found and investigated. In particular, the distance dependence of coupling is analysed. For semiconducting nanoribbons, this dependence is exponential-like, resembling the Bloembergen-Rowland interaction. For metallic nanoribbons, interesting behaviour is found for finite length systems, in which zero-energy states make an important contribution to the interaction. In such situations, the coupling decay with distance can then be substantially slower.