The orbital diamagnetic susceptibility is calculated in monolayer and bilayer graphenes with band gap as well as in three-dimensional Dirac systems. It is demonstrated that the pseudo-spin degree of freedom such as valleys produces paramagnetic susceptibility in an equal manner as the real spin dominating over the Landau diamagnetism. The pseudo-spin paramagnetism explains the origin of a singular diamagnetism which is present only in the band-gap region and disappears rapidly inside the conduction and valence bands.
We have studied magnetization of graphene nanocrystals obtained by sonic exfoliation of graphite. No ferromagnetism is detected at any temperature down to 2 K. Neither do we find strong paramagnetism expected due to the massive amount of edge defects. Rather, graphene is strongly diamagnetic, similar to graphite. Our nanocrystals exhibit only a weak paramagnetic contribution noticeable below 50K. The measurements yield a single species of defects responsible for the paramagnetism, with approximately one magnetic moment per typical graphene crystallite.
The effects of magnetic flux in statistical magnetisms, including Pauli paramagnetism, Landau diamagnetism, and De Hass-van Alphen oscillation, are discussed. It is shown that the diamagnetism could be much increased by the fractional magnetic flux, and the amplitude of the magnetic oscillation of De Hass-van Alphen can be amplified by the quantum effect of the flux.
The surface of nominally diamagnetic colloidal CdSe nanoplatelets can demonstrate paramagnetism owing to the uncompensated spins of dangling bonds (DBSs). We reveal that by optical spectroscopy in high magnetic fields up to 15 Tesla using the exciton spin as probe of the surface magnetism. The strongly nonlinear magnetic field dependence of the circular polarization of the exciton emission is determined by the DBS and exciton spin polarization as well as by the spin-dependent recombination of dark excitons. The sign of the exciton-DBS exchange interaction can be adjusted by the nanoplatelet gr…
Orbital diamagnetism requires closed orbits according to the Liftshiftz-Kosevich theory. Therefore, one might expect that open Fermi surfaces do not have a diamagnetic response. Contrary to this expectation, we show that open orbits in finite systems do contribute a magnetic response which oscillates between diamagnetism and paramagnetism. The oscillations are similar to the Aharonov-Bohm effect, because the oscillation phase is set by the number of flux quanta through the area defined by the width of the sample and the distance between adjacent atomic layers. The magnetic response originates …
We study orbital magnetism in a three-dimensional (3D) quantum dot with a parabolic confining potential. We calculate the free energy of the system as a function of the magnetic field and the temperature. By this, we show that the temperature-field plane can be classified into three regions in terms of the characteristic behavior of the magnetization: the Landau diamagnetism, de Haas-van Alphen oscillation and mesoscopic fluctuation of magnetization. We also calculate numerically the magnetization of the system and then the current density distribution. As for the oscillation of the magnetizat…
We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called {\it modern theory of orbital magnetization} and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band -- either gapless or gapped -- systems. We po…
Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than to the energy level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy level structure. The susceptibility at charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structure…
For applications exploiting the valley pseudospin degree of freedom in transition metal dichalcogenide monolayers, efficient preparation of electrons or holes in a single valley is essential. Here, we show that a magnetic field of 7 Tesla leads to a near-complete valley polarization of electrons in MoSe2 monolayer with a density 1.6x10^{12} cm^{-2}; in the absence of exchange interactions favoring single-valley occupancy, a similar degree of valley polarization would have required a pseudospin g-factor exceeding 40. To investigate the magnetic response, we use polarization resolved photolumine…
The pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism with local magnetic moments ~ 1.5 per vacancy1-6. Theoretically, both the electrons and electrons of graphene contribute to the magnetic moment of the defects, and the pi magnetism is characterizing of two spin-split DOS (density-of-states) peaks close to the Dirac point1,6. Since its prediction, many experiments attempt to study this pi magnetism in graphene, whereas, only a notable resonance peak has been observed around the atomic defects6-9, leaving the pi magnetism …
The magnetism by the edge states in graphene is investigated theoretically. An instability of the pseudo-spin order of the edge states induces ferrimagnetic order in the presence of the Coulomb interaction. Although the next nearest-neighbor hopping can stabilize the pseudo-spin order, a strong Coulomb interaction makes the pseudo-spin unpolarized and real spin polarized. The magnetism of the edge states makes two peaks of the density of states in the conduction and valence energy bands near the Fermi point. Using a continuous model of the Weyl equation, we show that the edge-induced gauge fie…
Based on a multi-scale calculations, combining ab-initio methods with spin dynamics simulations, we perform a detailed study of the magnetic behavior of Ni2MnAl/Fe bilayers. Our simulations show that such a bilayer exhibits a small exchange bias effect when the Ni2MnAl Heusler alloy is in a disordered B2 phase. Additionally, we present an effective way to control the magnetic structure of the Ni2MnAl antiferromagnet, in the pseudo-ordered B2-I as well as the disordered B2 phases, via a spin-flop coupling to the Fe layer.
We investigate long-range chiral magnetic interactions among adatoms mediated by surface states spin-splitted by spin-orbit coupling. Using the Rashba model, the tensor of exchange interactions is extracted wherein a pseudo-dipolar interaction is found besides the usual isotropic exchange interaction and the Dzyaloshinskii-Moriya interaction. We find that, despite the latter interaction, collinear magnetic states can still be stabilized by the pseudo-dipolar interaction. The inter-adatom distance controls the strength of these terms, which we exploit to design chiral magnetism in Fe nanostruct…
We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp$^3$ covalent functionalizations. We describe graphene with the single orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. In order to circumvent artefacts related to periodic unit cells, we use either huge simulation cells of up to $8\times10^5$ sites, or an embedding scheme that allows the modelling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the a…
We study the orbital magnetism of graphene ribbon in the effective-mass approximation, to figure out the finite-size effect on the singular susceptibility known in the bulk limit. We find that the susceptibility at T = 0 oscillates between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the subband structure formed by quantum confinement. In increasing T, the oscillation rapidly disappears once the thermal broadening energy exceeds the subband spacing, and the susceptibility approaches the bulk limit i.e., a thermally broadened diamagnetic peak centered at zero…
We investigate electric and magnetic properties of graphene with rotationally symmetric strain. The strain generates large pseudo magnetic field with alternating sign in space, which forms a strongly confined quantum dot connected to six chiral channels. The orbital magnetism, degeneracy, and channel opening can be understood from the interplay between real and pseudo magnetic field which have different parities under time reversal and mirror reflection. While the orbital magnetic response of the confined state is diamagnetic, it can be paramagnetic if there is an accidental degeneracy with op…
We investigate theoretically spin and orbital pseudospin magnetic properties of a molecular orbital in parabolic and elliptic double quantum dots (DQDs). In our many body calculation we include intra- and inter-dot electron-electron interactions, in addition to the intradot exchange interaction of `p' orbitals. We find for parabolic DQDs that, except for the half or completely filled molecular orbital, spins in different dots are ferromagnetically coupled while orbital pseudospins are antiferromagnetically coupled. For elliptic DQDs spins and pseudospins are either ferromagnetically or antifer…
We consider the orbital magnetic properties of non-interacting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both, frombulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility $χ$ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e. temperature, Landau level spacing and chemical potential. We show that for finite tempera…
By expanding the wave function in plane waves, we use the pseudopotential method of density functional theory within the generalized gradient approximation to calculate the effective magnetic coupling energies of the S=5/2 spins in the Fe2 dimer, approximated as Fe$_2$O$_2$H$_2$. Setting the Fe-O bond length at the value corresponding to the minimum total energy, we find the difference in antiferromagnetic and ferromagnetic exchange energies as a function of the Fe-O-Fe bond angle $θ$. The effective interaction is antiferromagnetic for 63$^{\circ}<θ<105^{\circ}$, and is ferromagnetic otherwise…
We present analytical expressions for the current-current correlation function in graphene for arbitrary frequency, wave vector, doping, and band gap induced by a mass term. In the static limit we analyze the Landau (orbital) and Pauli magnetization, as well as the Lindhard correction which describes Friedel and RKKY oscillations. In the nonrelativistic limit we compare our results with the situation of the usual two-dimensional electron gas (2DEG). We find that the orbital magnetic susceptibility (OMS) in gapped graphene is smeared out on an energy scale given by the inverse mass. The nonrela…
The interplay between strong correlations and non-trivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of t…
Electric-field control of magnetism via inverse magnetostrictive effect is an efficient path towards improving energy-efficient storage and sensing devices based on giant magnetoresistance effect. In this letter, we report on lateral electric-field driven strain-mediated modulation of magnetic properties in Co$/$Cu$/$Py pseudo spin valve grown on ferroelectric PMN-PT substrate. We show a decrease of the giant magnetoresistance ratio of the pseudo spin valve with increasing electric field, which is attributed to the deviation of the Co layer magnetization from the initial direction due to strai…
