We study the spin-wave excitations near the zigzag edge of graphene. It is rather interesting that we obtain a single branch of relativistic ferromagnetic magnon due to the presence of the open boundary. Note that magnons in antiferomagnets appear in pairs, while the single brach magnon in ferromagnets does not have relativistic dispersion. Thus, the magnon near the zigzag edge of graphene is a hybrid of both, signaling its intrinsic property as a boundary excitation that must be embedded in a higher dimensional bulk system.
We investigated the topological property of magnon bands in the collinear magnetic orders of zigzag and stripy phases for the antiferromagnetic honeycomb lattice and identified Berry curvature and symmetry constraints on the magnon band structure. Different symmetries of both zigzag and stripy phases lead to different topological properties, in particular, the magnon bands of the stripy phase being disentangled with a finite Dzyaloshinskii-Moriya (DM) term with non-zero spin Chern number. This is corroborated by calculating the spin Nernst effect. Our study establishes the existence of the non…
Magnon drag effect induced by an applied electric field in ferromagnetic metals is theoretically studied by a microscopic calculation of the force on magnons arising from magnon emission/absorption and scattering due to driven electrons. It is shown that magnon scattering contribution dominates over the emission/absorption one in a wide temperature regime in good metals with long elastic lifetime $\taue$, as the latter has a relative suppression factor of $(\Deltasd\taue)^{-2}$ due to the electron spin flip by the magnon, where $\Deltasd$ is the $sd$ exchange interaction energy. Spin-transfer …
Bilayer Heisenberg ferromagnetic insulators hold degenerate terahertz Dirac magnon modes associated with two opposite valleys of the hexagonal Brillouin zone. We show that this energy degeneracy can be removed by breaking of the inversion symmetry (I), leading to a topological magnon valley current. We show furthermore that this current leads to valley Seebeck effect for magnons and is thereby detectable. We perform calculations in the specific example of bilayer CrBr3, where I can be broken by electrostatic doping.
Magnon-mediated spin transport across nonmagnetic metal (NM) and ferromagnetic insulator (FI) interface depends critically on electron-magnon coupling. We propose a novel route to enhance electron-magnon coupling dynamically from transport viewpoint. Using non-equilibrium Green's function a theoretical formalism for magnon-mediated spin current is developed. In the language of transport, the effective electron-magnon coupling at NM/FI interface is determined by self-energy of FI lead, which is proportional to density of states (DOS) at NM/FI interface due to nonlinear process of electron-magno…
Despite the intense amount of attention and huge potential of two-dimensional (2D) magnets for applications in novel magnetic, magneto-optical, magneto-thermal and magneto-electronic devices, there has yet to be a robust strategy developed to systematically understand magnon-magnon (MMI) interactions at finite temperature. In this paper, we present a first-principles theoretical method to introduce the finite temperature magnon-magnon interaction into Heisenberg Hamiltonian through a nonlinear correction energy. The Wick theorem is used to decouple the four-magnon operators to two-magnon order…
We have performed a time-resolved and phase-sensitive investigation of three-magnon scattering of ferromagnetic resonance (FMR) over several orders of magnitude in excitation power. We observe a regime that hosts transient oscillations of the FMR magnon population, despite higher-order magnon interactions at large powers. Also at high powers, the scattering generates $180^\circ$ phase shifts of the FMR magnons. These phase shifts correspond to reversals in the three-magnon scattering direction, between splitting and confluence. These scattering reversals are most directly observed after removi…
An asymptotically exact theory of spectrum and transverse distribution of magnetization in long-wave magnons is presented. It is based on exact analytical solution of linearized Landau-Lifshitz equation in a film. The quantization of the transverse wave parameters and wave vectors is studied.
We present a model of the thermopower in a mesoscopic tunnel junction between two ferromagnetic metals based upon magnon-assisted tunneling processes. In our model, the thermopower is generated in the course of thermal equilibration between two baths of magnons, mediated by electrons. We predict a particularly large thermopower effect in the case of a junction between two half-metallic ferromagnets with antiparallel polarizations, $S_{AP} \sim - (k_B/e)$, in contrast to $S_{P} \approx 0$ for a parallel configuration.
Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb drag in bilayer two dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on m…
A temperature gradient applied to a ferromagnetic metal induces not only independent flows of electrons and magnons but also drag currents because of their mutual interaction. In this paper, we present a microscopic study of the electron flow induced by the drag due to magnons. The analysis is based on the $s$-$d$ model, which describes conduction electrons and magnons coupled via the $s$-$d$ exchange interaction. Magnetic impurities are introduced in the electron subsystem as a source of spin relaxation. The obtained magnon-drag electron current is proportional to the entropy of magnons and t…
The experimental observation of topological magnon bands and thermal Hall effect in a kagomé lattice ferromagnet Cu(1-3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii-Moriya (DM) spin-orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnets is an ideal candidate for this purpose because it is a variant of the kagomé lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kag…
We present a theoretical description of the thermopower due to magnon-assisted tunneling in a mesoscopic tunnel junction between two ferromagnetic metals. The thermopower is generated in the course of thermal equilibration between two baths of magnons, mediated by electrons. For a junction between two ferromagnets with antiparallel polarizations, the ability of magnon-assisted tunneling to create thermopower $S_{AP}$ depends on the difference between the size $Π_{\uparrow, \downarrow}$ of the majority and minority band Fermi surfaces and it is proportional to a temperature dependent factor $(k…
We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity ${κ^{xy}}$ at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes…
We investigated the dependence of N$\acute{\textrm{e}}$el temperature as a critical temperature on the electric field and hole-electron doping in the antiferromagnetically ordered zigzag graphene nanoribbon. The temperature was calculated by averaging the magnon energy in the Brillouin zone within the mean-field approximation. We employed the generalized Bloch theorem instead of the supercell approach to reduce the computational cost significantly to obtain the magnon spectrum. We showed that the N$\acute{\textrm{e}}$el temperature reduces when increasing both the electric field and the hole-e…
The simple Hubbard Hamiltonian with the mean field approximation is used to know about the energy bands and spin susceptibilities of zigzag graphene nanoribbons. Depending on the electron doping, antiferromagnetic or ferromagnetic configurations are possible; in the former, an energy gap exits which is proportional to the Hubbard parameter, while in the latter the up and down spin bands intersect the Fermi level. Due to the two dimensional nature of the system, a susceptibility square matrix is necessary to explain the self-correlations and correlations between spins in the ribbon unit cell. T…
We propose a general theory of microwave absorption spectroscopy for symmetry-breaking synthetic antiferromagnets (SAFs). Generally, inhomogeneity or different thickness of the two ferromagnetic sublayers of a SAF results in the intrinsic symmetry breaking, while out-of-plane components of dc magnetic fields lead to the extrinsic one. The broken symmetry of SAFs excludes the original symmetry-protected crossing between pure in-phase and out-of-phase resonance modes with opposite parity. Alternatively, new frequency branches become hybridization of original bare modes in terms of symmetry-break…
The paper addresses inelastic spin-flip tunneling accompanied by surface spin excitations (magnons) in ferromagnetic junctions. The inelastic tunneling current is proportional to the magnon density of states which is energy-independent for the surface waves and, for this reason, cannot account for the bias-voltage dependence of the observed inelastic tunneling spectra. This paper shows that the bias-voltage dependence of the tunneling spectra can arise from the tunneling matrix elements of the electron-magnon interaction. These matrix elements are derived from the Coulomb exchange interaction …
We develop a non-equilibrium Green's function formalism to study magnonic spin transport through a strongly anisotropic ferromagnetic insulator contacted by metallic leads. We model the ferromagnetic insulator as a finite-sized one-dimensional spin chain, with metallic contacts at the first and last sites that inject and detect spin in the form of magnons. In the presence of anisotropy, these ferromagnetic magnons become elliptically polarized, and spin conservation is broken. We show that this gives rise to a novel parasitic spin conductance, which becomes dominant at high anisotropy. Moreove…
One dimensional Cherenkov processes in ferromagnetic isolators are studied with perturbation theory under the constraint condition of conservation of energy and momentum. It is shown that the magnon-phonon interaction channels are limited and wave number dependent, which result in respectively $1/k^{2}$ and $1/k^{4}$ dependence of the lifetime and the relaxation time of long wavelength magnons. The reciprocal of relaxation time between magnons and phonons, $1/τ_{mp}$, is found to be a linearly increasing function of the temperature as $T>$ 70 K. Based on the Sanders-Walton model, we further sh…
Zigzag graphene nanoribbons can have magnetic ground states with ferromagnetic, antiferromagnetic, or canted configurations, depending on carrier density. We show that an electric field directed across the ribbon alters the magnetic state, favoring antiferromagnetic configurations. This property can be used to prepare ribbons with a prescribed spin-orientation on a given edge.
The NV center in diamond has proven to be a powerful tool for locally characterizing the magnetic response of microwave excited ferromagnets. To date, this has been limited by the requirement that the FMR excitation frequency be less than the NV spin resonance frequency. Here we report NV relaxometry based on a two-magnon Raman-like process, enabling detection of FMR at frequencies higher than the NV frequency. For high microwave drive powers, we observe an unexpected field-shift of the NV response relative to a simultaneous microwave absorption signal from a low damping ferrite film. We show …
The magnon pumping effect in ferromagnetic insulators under an external time-dependent transverse magnetic field is theoretically studied. Generation of a magnon current is discussed by calculating the magnon source term in the spin continuity equation. This term represents the non-conservation of magnons arising from an applied transverse magnetic field. The magnon source term has a resonance structure as a function of the angular frequency of the transverse field, and this fact is useful to enhance the pumping effect.
Magnetic excitation in a spin dimer system on a bilayer honeycomb lattice is investigated in the presence of a zigzag edge, where disordered and ordered phases can be controlled by a quantum phase transition. In analogy with the case of graphene with a zigzag edge, a flat edge magnon mode appears in the disordered phase. In an ordered phase, a finite magnetic moment generates a mean-field potential to the magnon. Since the potential is nonuniform on the edge and bulk sites, it affects the excitation, and the dispersion of the edge mode deviates from the flat shape. We investigate how the edge …
Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry de…
Spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. Using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering because of the imbalance between magnon emission and absorption caused by either non-equilibrium distribution of magnons or non-equilibrium between magnons and electrons. A temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current w…
In a semiconductor hererostructure, the Coulomb interaction is responsible for the electric current drag between two 2D electron gases across an electron impenetrable insulator. For two metallic layers separated by a ferromagnetic insulator (FI) layer, the electric current drag can be mediated by a nonequilibrium magnon current of the FI. We determine the drag current by using the semiclassical Boltzmann approach with proper boundary conditions of electrons and magnons at the metal-FI interface.
We investigate the spin-pumping-induced electric current on the surface of a three-dimensional topological insulator hybridized with a ferromagnet, namely, ferromagnetic topological insulator. In order to do this, we establish the microscopic formalism and construct the perturbation theory using a Keldysh Green's function approach. We analyze how this electric current is generated by an exchange interaction and an external ac magnetic field, which is the driving force of ferromagnetic resonance as well as the spin pumping. The mechanism is as follows. First, the ferromagnetic resonance is driv…
A theoretical study of the magnon-drag Peltier and Seebeck effects in ferromagnetic metals is presented. A magnon heat current is described perturbatively from the microscopic viewpoint with respect to electron--magnon interactions and the electric field. Then, the magnon-drag Peltier coefficient $Π_\MAG$ is obtained as the ratio between the magnon heat current and the electric charge current. We show that $Π_\MAG=C_\MAG T^{5/2}$ at a low temperature $T$; that the coefficient $C_\MAG$ is proportional to the spin polarization $P$ of the electric conductivity; and that $P>0$ for $C_\MAG<0$, but …
The recent experiment [Y. Wang et al., Science 366, 1125 (2019)] on magnon-mediated spin-transfer torque (MSTT) was interpreted in terms of a picture where magnons are excited within an antiferromagnetic insulator (AFI), by applying nonequilibrium electronic spin density at one of its surfaces, so that their propagation across AFI deprived of conduction electrons eventually leads to reversal of magnetization of a ferromagnetic metal (FM) attached to the opposite surface of AFI. We employ a recently developed time-dependent nonequilibrium Green functions combined with the Landau-Lifshitz-Gilber…
Chiral coupling at the single-quantum level promises to be a remarkable potential for quantum information processing. Here we propose to achieve a chiral interaction between a magnon mode in a ferromagnetic sphere and a superconducting qubit mediated by a one-dimensional coupled-cavity array. When the qubit is coupled to two lattice sites of the array and each one is encoded with a tunable phase, we can acquire a directional qubit-magnon interaction via the quantum interference effect. This work opens up a new route to construct chiral devices, which are expected to become a building block in …
We demonstrate the dispersive measurement of ferromagnetic resonance in a yttrium iron garnet sphere embedded within a microwave cavity. The reduction in the longitudinal magnetization at resonance is measured as a frequency shift in the cavity mode coupled to the sphere. This measurement is a result of the intrinsic non-linearity in magnetization dynamics, indicating a promising route towards experiments in magnon cavity quantum electro-dynamics.
The purpose of this article is to develop a systematic approach to the solution of the Landau-Lifshitz equation in terms of the magnon wave function ψ (r) and apply it to physical phenomena in a thin ferromagnetic film. This article has also a purpose to represent the modern state of art for the properties of ferromagnetic films and the pumping-induced Bose-Einstein condensation of magnons in them at room temperature. Thus, it can be considered as a review on basic principles and the recent advances in the field.
Excitation of coherent high-frequency magnons (quanta of spin waves) is critical to the development of high-speed magnonic devices. Here we computationally demonstrate the excitation of coherent sub-terahertz (THz) magnons in ferromagnetic (FM) and antiferromagnetic (AFM) thin films by a photoinduced picosecond acoustic pulse. Analytical calculations are also performed to reveal the magnon excitation mechanism. Through spin pumping and spin-charge conversion, these magnons can inject sub-THz charge current into an adjacent heavy-metal film which in turn emits electromagnetic (EM) waves. Using …
We consider electron drag in a system of two ferromagnetic layers separated by an insulating interface. The source of it is expected to be magnon-electron interactions. Namely, we assume that the external voltage is applied to the "active" layer stimulating electric current through this layer. In its turn, the scattering of the current-carrying electrons by magnons leads to a magnon drag current within this layer. The 3-magnons interactions between magnons in the two layers (being of non-local nature) lead to magnon drag within the "passive" layer which, correspondingly, produce electron drag …
We investigate a heat- to charge-current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nano engine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency.
We present a microscopic theory of magnon transport in ferromagnetic insulators (FIs). Using magnon injection through microwave pumping, we propose a way to generate magnon dc currents and show how to enhance their amplitudes in hybrid ferromagnetic insulating junctions. To this end focusing on a single FI, we first revisit microwave pumping at finite (room) temperature from the microscopic viewpoint of magnon injection. Next, we apply it to two kinds of hybrid ferromagnetic insulating junctions. The first is the junction between a quasi-equilibrium magnon condensate and magnons being pumped b…
Achieving control over magnon spin currents in insulating magnets - where dissipation due to Joule heating is highly suppressed - is an active area of research that could lead to energy-efficient spintronics applications. However, magnon spin currents supported by conventional systems with uniform magnetic order have proven hard to control. An alternative approach that relies on topologically protected magnonic edge states of spatially periodic magnetic textures has recently emerged. A prime example of such textures is the ferromagnetic skyrmion crystal which hosts chiral edge states providing…
Hybrid magnonics involving coupling between magnons and different quantum particles have been extensively studied during past few years for varied interests including quantum electrodynamics. In such systems, magnons in magnetic materials with high spin density are utilized where the coupling strength is collectively enhanced by the square root of the number of spins to overcome the weaker coupling between individual spins and the microwave field. However, achievement of strong magnon-magnon coupling in a confined nanomagnets would be essential for on-chip integration of such hybrid systems. H…
Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL), including exchange and Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topologi…
We investigated the reduction of the spin stiffness and the appearance of the spiral spin density waves when the electric field is applied on the zigzag graphene nanoribbons for the ferromagnetic and antiferromagnetic edge states. For that purpose, we exploited the generalized Bloch theorem combined with a constraint method to keep the direction of the magnetic moment of the carbon atom at the edges. We found that the ground state of ferromagnetic configuration is unstable and leads to the spiral ground state while the ground state of the antiferromagnetic configuration is robust. We also show…
Brillouin light scattering in ferromagnetic materials usually involves one magnon and two photons and their total angular momentum is conserved. Here, we experimentally demonstrate the presence of a helicity-changing two-magnon Brillouin light scattering in a ferromagetic crystal, which can be viewed as a four-wave mixing process involving two magnons and two photons. Moreover, we observe an unconventional helicity-changing one-magnon Brillouin light scattering, which apparently infringes the conservation law of the angular momentum. We show that the crystal angular momentum intervenes to comp…
We study the temperature dependent magnetic susceptibility of a strained graphene quantum dot by using the determinant quantum Monte Carlo method. Within the Hubbard model on a honeycomb lattice, our unbiased numerical results show that a relative small interaction $U$ may lead to a edge ferromagnetic like behavior in the strained graphene quantum dot, and a possible room temperature transition is suggested. Around half filling, the ferromagnetic fluctuations at the zigzag edge is strengthened both markedly by the on-site Coulomb interaction and the strain, especially in low temperature region…
We demonstrate large normal-mode splitting between a magnetostatic mode (the Kittel mode) in a ferromagnetic sphere of yttrium iron garnet and a microwave cavity mode. Strong coupling is achieved in the quantum regime where the average number of thermally or externally excited magnons and photons is less than one. We also confirm that the coupling strength is proportional to the square root of the number of spins. A nonmonotonic temperature dependence of the Kittel-mode linewidth is observed below 1 K and is attributed to the dissipation due to the coupling with a bath of two-level systems.
Energy harvesting is a modern concept which makes dissipated heat useful by transferring thermal energy to other excitations. Most of the existing principles for energy harvesting are realized in systems which are heated continuously, for example generating DC voltage in thermoelectric devices. Here we present the concept of high-frequency energy harvesting where the dissipated heat in a sample excites resonant magnons in a 5-nm thick ferromagnetic metal layer. The sample is excited by femtosecond laser pulses with a repetition rate of 10 GHz which results in temperature modulation at the same…
At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.
Valleytronics is a pioneering technological field relying on the valley degree of freedom to achieve novel electronic functionalities. Topological valley-polarized electrons confined to domain walls in bilayer graphene were extensively studied in view of their potentials in valleytronics. Here, we study the magnonic version of domain wall excitations in 2D honeycomb ferromagnetic bilayers (FBL) with collinear order. In particular, we explore the implications of Dzyaloshinskii-Moriya interaction (DMI) and electrostatic doping (ED) on the existence and characteristics of 1D magnons confined to l…
The electronic structure and conductance of substitutionally edge-doped zigzag silicene nanoribbons (ZSiNRs) are investigated using the nonequilibrium Green's function method combined with the density functional theory. Two-probe systems of ZSiNRs in both ferromagnetic and antiferromagnetic states are considered. Doping effects of elements from groups III and V, in a parallel or antiparallel magnetic configuration of the two electrodes, are discussed. Switching on and off the external magnetic field, we may convert the metallic ferromagnetic ZSiNRs into insulating antiferromagnetic ZSiNRs. In …
