We study pumping of magnons to the Dirac points of magnon's Brillouin zone of a ferromagnet on a honeycomb lattice. In particular, we consider second-order Suhl process, when due to interaction between magnons, a pair of magnons is created due to absorption of two electromagnetic wave quanta. We introduce a bosonic analog of the Cooper ladder for the magnon pair, which is shown to enhance the pairing of magnons at the Dirac points. As a result of pairing of the Dirac magnons, the system becomes unstable towards formation of a magnetic state with zero or reduced magnetization - the Dirac magnon paired state. In this case the resonant frequency of the pump equals to that of energy of the Dirac points. Our estimates suggest that the Dirac magnon paired state can be found in the CrBr$_{3}$ or CrCl$_{3}$ ferromagnet below in vicinity of the Curie temperature.
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.
We study the exchange between electron and magnon spins at the interface of an antiferromagnet and a heavy metal at finite temperatures. The underlying physical mechanism is based on spin torque associated with the creation/annihilation of thermal magnons with right-hand and left-hand polarization. The creation/annihilation process depends strongly on the relative orientation between the polarization of the electron and the magnon spins. For a sufficiently strong spin transfer torque (STT), the conversion process becomes nonlinear, generating a nonzero net spin pumping current in the AFM that …
We clarify the condition for the occurrence of magnon Bose-Einstein condensation (BEC) in spin pumping systems without using external pumping magnetic fields. The Goldstone model is generalized and the stability of the vacuum is closely investigated. By applying the generalized Goldstone model to spin pumping systems, the condition for the experimental realization of the stable magnon BEC in spin pumping systems is theoretically proposed.
We experimentally identify coherent spin pumping in the magnon-magnon hybrid modes of permalloy/yttrium iron garnet (Py/YIG) bilayers. Using broadband ferromagnetic resonance, an "avoided crossing" is observed between the uniform mode of Py and the spin wave mode of YIG due to the fieldlike interfacial exchange coupling. We also identify additional linewidth suppression and enhancement for the in-phase and out-of-phase hybrid modes, respectively, \textcolor{black}{which can be interpreted as concerted dampinglike torque from spin pumping}. Our analysis predicts inverse proportionality of both …
The combination of parametric pumping and spin-transfer torque is a powerful approach that enables high-level control over magnetic excitations in thin-film ferromagnets. The excitation parameters, such as pumping power and external field strength, affect the instabilities of individual magnon modes. We theoretically explore how the simultaneous effects of parametric pumping and spin transfer torque influence these magnetic instabilities in a thin-film ferromagnet. Within the Landau-Lifshitz-Gilbert framework, we perform micromagnetic simulations of magnon excitations in yttrium iron garnet by…
We demonstrate how a magnon chemical potential is generated in parametric parallel pumping. We study how a time-periodic magnetic field of this pumping affects magnon properties of a ferrimagnet in a nonequilibrium steady state. We show that the magnon distribution function of our nonequilibrium steady state becomes the Bose distribution function with $μ=ω_{\textrm{p}}/2$, where $μ$ is the magnon chemical potential and $ω_{\textrm{p}}$ is the pumping frequency. This result is distinct from the absence of the magnon chemical potential in the standard theory and can qualitatively explain its gen…
On the basis of the Schwinger-Keldysh formalism, we have closely investigated the temperature dependence of quantum spin pumping by electron spin resonance. We have clarified that three-magnon splittings excite non-zero modes of magnons and characterize the temperature dependence of quantum spin pumping. Our theoretical result qualitatively agrees with the experiment by Czeschka et al. that the mixing conductance is little influenced by temperature [F. D. Czeschka et al., Phys. Rev. Lett., 107, 046601 (2011)].
We experimentally show that exchange magnons can be detected using a combination of spin pumping and inverse spin-Hall effect (iSHE) proving its wavelength integrating capability down to the sub-micrometer scale. The magnons were injected in a ferrimagnetic yttrium iron garnet film by parametric pumping and the iSHE-induced voltage was detected in an attached Pt layer. The role of the density, wavelength, and spatial localization of the magnons for the spin pumping efficiency is revealed. This study opens the field of the magnon-based information processing to magnons with nano-scale wavelengt…
We propose to excite a large number of coherent magnons with high momentum in optical cavities. This is achieved by two counterpropagating optical modes that are detuned by the frequency of a selected magnon, similar to stimulated Raman scattering. In sub-mm size yttrium iron garnet spheres, a mW laser input power generates 10^6-10^8 coherent magnons. The large magnon population enhances Brillouin light scattering, a probe suitable to access their quantum properties.
We formulate a microscopic linear response theory of nonequilibrium magnonic torques and magnon pumping applicable to multiple-magnonic-band uniform ferromagnets with Dzyaloshinskii-Moriya interactions. From the linear response theory, we identify the extrinsic and intrinsic contributions where the latter is expressed via the Berry curvature of magnonic bands. We observe that in the presence of a time-dependent magnetization Dzyaloshinskii-Moriya interactions can act as fictitious electric fields acting on magnons. We study various current responses to this fictitious field and analyze the rol…
The richness in both the dispersion and energy of antiferromagnetic magnons has spurred the magnetism community to consider antiferromagnets for future spintronic/magnonic applications. However, the excitation and control of antiferromagnetic magnons remains challenging, especially when compared to ferromagnetic counterparts. A middle ground is found with synthetic antiferromagnet metamaterials, where acoustic and optical magnons exist at GHz frequencies. In these materials, the magnon energy spectrum can be tuned by static symmetry-breaking external fields or dipolar interactions hybridizing …
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…
We theoretically propose quantum spin pumping mediated by magnons, under a time-dependent transverse magnetic field, at the interface between a ferromagnetic insulator and a non-magnetic metal. The generation of a spin current under a thermal equilibrium condition is discussed by calculating the spin transfer torque, which breaks the spin conservation law for conduction electrons and operates the coherent magnon state. Localized spins lose spin angular momentum by emitting magnons and conduction electrons flip from down to up by absorbing the momentum. The spin transfer torque has a resonance …
We establish a general formulation for spin current pumped by magnons at the interface between a normal metal and a magnetic insulator, valid for any non-collinear magnetic configuration in the linear spin wave regime. This current is generated by driving the system in a non-equilibrium state, covering setups such as thermal spin injection (spin Seebeck effect) or spin voltage by irradiation of the insulator (spin pumping). We illustrate the formula in the special case of a honeycomb topological ferromagnet, for simplicity, and cover both the spin Seebeck and spin-pumping setups. We show how t…
Chiral spin pumping is the generation of a unidirectional spin current in half of ferromagnetic films or conductors by dynamic dipolar stray fields from close-by nanomagnets. We formulate a general theory of long-range chiral interactions between magnets mediated by unidirectional traveling waves, e.g., spin waves in a magnetic film or microwaves in a waveguide. The traveling waves emitted by an excited magnet can be perfectly trapped by a second, initially passive, magnet by a dynamical interference effect. When both magnets are excited by a uniform microwave, the chiral interaction between t…
We microscopically analyze thermal spin pumping mediated by magnons, at the interface between a ferromagnetic insulator and a non-magnetic metal, in the semiclassical regime. The generation of a spin current is discussed by calculating the thermal spin transfer torque, which breaks the spin conservation law for conduction electrons and operates the coherent magnon state. Inhomogeneous thermal fluctuations between conduction electrons and magnons induce a net spin current, which is pumped into the adjacent non-magnetic metal. The pumped spin current is proportional to the temperature difference…
Ultrafast optical excitation of magnons in 2D antiferromagnetic semiconductors via spin torque mediated by unbound electron-hole pairs and excitons: Signatures in magnonic charge pumping
Motivated by recent experiments on spin pumping from a ferromagnet into organic materials in which the charge transport is due to hopping, we study theoretically the generation and propagation of spin current in a hopping insulator. Unlike metals, the spin polarization at the boundary with ferromagnet is created as a result of magnon absorption within pairs of localized states and it spreads following the current-currying resistor network (although the charge current is absent). We consider a classic resonant mechanism of the ac absorption in insulators and adapt it to the absorption of magnon…
The spectral distribution of parametrically excited dipole-exchange magnons in an in-plane magnetized epitaxial film of yttrium-iron garnet was studied by means of frequency- and wavevector-resolved Brillouin light scattering spectroscopy. The experiment was performed in a parallel pumping geometry where an exciting microwave magnetic field was parallel to the magnetizing field. It was found that for both dipolar and exchange spectral areas parallel pumping excites the lowest volume magnon modes propagating in the film plane perpendicularly to the magnetization direction. In order to interpret…
We theoretically study spin pumping from a layered van der Waals antiferromagnet in its canted ground state into an adjacent normal metal. We find that the resulting dc spin pumping current bears contributions along all spin directions. Our analysis allows for detecting intra- and cross-sublattice spin-mixing conductances via measuring the two in-plane spin current components. We further show that sublattice symmetry-breaking Gilbert damping can be realized via interface engineering and induces a dissipative coupling between the optical and acoustic magnon modes. This realizes magnon level att…
We theoretically investigate spin transfer between a system of quasiequilibrated Bose-Einstein condensed magnons in an insulator in direct contact with a conductor. While charge transfer is prohibited across the interface, spin transport arises from the exchange coupling between insulator and conductor spins. In normal insulator phase, spin transport is governed solely by the presence of thermal and spin-diffusive gradients; the presence of Bose-Einstein condensation (BEC), meanwhile, gives rise to a temperature-independent condensate spin current. Depending on the thermodynamic bias of the sy…
Magnonics and magnon spintronics aim at the utilization of spin waves and magnons, their quanta, for the construction of wave-based logic networks via the generation of pure all-magnon spin currents and their interfacing with electrical charge transport. The promise of efficient parallel data processing and low power consumption renders this field one of the most promising research areas in spintronics. In this context, the process of parallel parametric amplification, i.e., the conversion of microwave photons into magnons at one half of the microwave frequency, has proven to be a versatile to…
We formulate a phenomenological description of thin ferromagnetic layers with inversion asymmetry where the single-domain magnetic dynamics experiences magnon current-induced torques and leads to magnon-motive forces. We first construct a phenomenological theory based on irreversible thermodynamics, taking into account the symmetries of the system. Furthermore, we confirm that these effects originate from Dzyaloshinskii-Moriya interactions from the analysis based on the stochastic Landau-Lifshitz-Gilbert equation. Our phenomenological results generalize to a general form of Dzyaloshinskii-Mori…
Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of rapid magnetic order recovery in materials with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify both localisation and coalescence regimes, whereby localised magnetic textures nucleate and subsequently evolve in accordance with a power law fo…
We report on the experimental observation of excitation and detection of parametric spin waves and spin currents in the bulk acoustic wave resonator. The hybrid resonator consists of ZnO piezoelectric film, yttrium iron garnet (YIG) films on gallium gadolinium garnet substrate, and a heavy metal Pt layer. Shear bulk acoustic waves are electrically excited in the ZnO layer due to piezoeffect at the resonant frequencies of the resonator. The magnetoelastic interaction in the YIG film emerges magnons (spin waves) excitation by acoustic waves either on resonator's eigenfrequencies or the half-valu…
We explore the formation and collective modes of Bose-Einstein condensate of Dirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an employed approach is general and could be used to describe Bose-Einstein condensates with linear quasiparticle spectrum in various systems. By using a phenomenological multicomponent model of pumped boson population together with bosons residing at Dirac nodes, the formation and time evolution of condensates of Dirac bosons is investigated. The condensate coherence and its multicomponent nature are manifested in the Rabi oscillations whose …
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…
Using newly developed quantum-classical hybrid framework, we investigate interaction between spin-polarized conduction electrons and a single spin wave (SW) coherently excited within a metallic ferromagnetic nanowire. When the nanowire hosting SW is attached to two normal metal (NM) leads, with no dc bias voltage applied between them, the SW pumps chiral electronic charge and spin currents into the leads---their direction is tied to the direction of SW propagation and they scale linearly with the frequency of the precession. This is in contrast to: standard pumping by the uniform precession mo…
We would like to point out the blind spots of the approach combining the spin pumping theory proposed by Tserkovnyak et al. with the Landau-Lifshitz-Gilbert equation; this method has been widely used for interpreting vast experimental results. The essence of the spin pumping effect is the quantum fluctuation. Thus, localized spin degrees of freedom should be quantized, i.e. be treated as magnons not as classical variables. Consequently, the precessing ferromagnet can be regarded as a magnon battery. This point of view will be useful for further progress of spintronics.
We study transport in ferromagnetic-superconductor/normal-metal systems. It is shown that charge and spin currents are pumped from ferromagnetic superconductors into adjacent normal metals by adiabatic changes in the order parameters induced by external electromagnetic fields. Spin and charge pumping identify the symmetry of the superconducting order parameter, e.g., singlet pairing or triplet pairing with opposite or equal spin pairing. Consequences for ferromagnetic-resonance experiments are discussed.
We theoretically investigate the fluctuation of a pure spin current induced by the spin Seebeck effect and spin pumping in a normal metal (NM)/ferromagnet (FM) bilayer system. Starting with a simple FI--NM interface model with both spin-conserving and spin-non-conserving processes, we derive general expressions of the spin current and the spin-current noise at the interface within second-order perturbation of the FI--NM coupling strength, and estimate them for an yttrium iron garnet (YIG) --platinum interface. We show that the spin-current noise can be used to determine the effective spin carr…
We study the effective interactions between Dirac fermions on the surface of a three-dimensional topological insulator due to the proximity coupling to the magnetic fluctuations in a ferromagnetic or antiferromagnetic insulator. Our results show that the magnetic fluctuations can mediate attractive interactions between Dirac fermions of both Amperean and BCS type. In the ferromagnetic case, we find pairing between fermions with parallel momenta, so-called Amperean pairing, whenever the effective Lagrangian for the magnetic fluctuations does not contain a quadratic term. The pairing interaction…
Nonlinear relaxation between spin waves (magnons) and the crystal lattice (phonons) in an insulating ferromagnet is investigated theoretically. Magnons and phonons are described by the equilibrium Bose-Einstein distributions with different temperatures. The nonlinear heat current from magnons to phonons is calculated microscopically in terms of the Cherenkov radiation of phonons by magnons. The results are discussed in comparison with the well-known theoretical results on the nonlinear electron-phonon relaxation in metals [Kaganov, Lifshitz, Tanatarov, J. Exp. Theor. Phys. 31, 232 (1956)]. The…
We study proximity effect in diffusive ferromagnet/normal-metal/superconductor junction with precessing magnetization of the ferromagnet. We find that the odd-frequency pairing induced in the normal metal is modified by spin pumping from the ferromagnet and hence can be tuned by changing the precessional frequency. At the frequency corresponding to twice the superconducting gap, the odd-frequency pairing is strongly enhanced. We find a crossover from the even- to the odd-frequency superconductivity in the normal metal by tuning the precessional frequency. This gives a clearcut signature of the…
We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with …
We investigate charge pumping in ferromagnet/triplet superconductor junctions where the magnetization of the ferromagnet is inhomogeneous and dynamical. It is shown that charge current is pumped due to the coupling of the localized spin with triplet vector spin chirality, vector spin chirality formed by the triplet vector of Cooper pairing. Physical mechanism of the charge pumping is also discussed.
We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization towards the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilt…
When subjected to parallel electric field $\mathbf E$ and magnetic field $\mathbf B$, Weyl semimetals exhibit the exotic transport property known as the chiral anomaly due to the pumping of electrons between Weyl cones of opposite chiralities. When one or both electromagnetic (EM) fields are replaced by strain-induced chiral pseudo-electromagnetic (pseudo-EM) fields, other types of quantum anomalies occur. In the present paper, we will show that such quantum anomalies can be reproduced in a completely different system -- a Weyl ferromagnet whose magnonic structure remarkably encodes Weyl physi…
Magnon-polaritons are hybrid light-matter quasiparticles originating from the strong coupling between magnons and photons. They have emerged as a potential candidate for implementing quantum transducers and memories. Owing to the dampings of both photons and magnons, the polaritons have limited lifetimes. However, stationary magnon-polariton states can be reached by a dynamical balance between pumping and losses, so the intrinsical nonequilibrium system may be described by a non-Hermitian Hamiltonian. Here we design a tunable cavity quantum electrodynamics system with a small ferromagnetic sph…
Thermal-bias-induced spin angular momentum transfer between a paramagnetic metal and ferromagnetic insulator is studied theoretically based on the stochastic Landau-Lifshitz-Gilbert (LLG) phenomenology. Magnons in the ferromagnet establish a nonequilibrium steady state by equilibrating with phonons via bulk Gilbert damping and electrons in the paramagnet via spin pumping, according to the fluctuation-dissipation theorem. Subthermal magnons and the associated spin currents are treated classically, while the appropriate quantum crossover is imposed on high-frequency magnetic fluctuations. We ide…
