The spin-wave transportation through a transverse magnetic domain wall (DW) in a magnetic nanowire is studied. It is found that the spin wave passes through a DW without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic spin-transfer torque can efficiently drive a DW to propagate in the opposite direction to that of the spin wave.

We formulate a scattering theory to study magnetic films in microwave cavities beyond the independent-spin and rotating-wave approximations of the Tavis-Cummings model. We demonstrate that strong coupling can be realized not only for the ferromagnetic resonance mode, but also for spin-wave resonances; the coupling strengths are mode dependent and decrease with increasing mode index. The strong-coupling regime can also be accessed electrically by spin pumping into a metal contact.

No abstract

We theoretically study field-induced domain wall motion in an electrically insulating ferromagnet with hard-and easy-axis anisotropies. Domain walls can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the usual Walker rigid-body propagation mode can become unstable for a magnetic field smaller than the Walker breakdown field. DOI: 10.1103/PhysRevLett.109.167209 PACS numbers: 75.60.Jk, 75.30.Ds, 75.60.Ch, 85.75.Àd Magnetic domain wall (DW) propagation in nanowires has attracted attention because of the academic interest of a unique nonlinear system [1][2][3][4] and potential applications in data storage and logic devices [4][5][6]. The field-driven DW dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) equation [1], which has analytical solutions in limiting cases [1,7], such as the soliton solution [8] in the absence of both dissipations and external magnetic fields. The interplay between spin waves (SWs) and DWs has also received attention, including DW propagation driven by externally generated SWs [9][10][11] and SW generation by a moving DW [12,13]. Our understanding of the fieldinduced DW motion is nevertheless far from complete. According to conventional wisdom, DWs move under a static magnetic field only in the presence of energy dissipation [1,14]. Numerical evidence against this view therefore came as a surprise [12,15].We report here a physical picture for the SW emissioninduced domain wall motion for a head-to-head DW in a magnetic nanowire with the easy axis along the wire (z direction) as shown in Fig. 1. Let K k and K ? be anisotropy coefficients of the easy and hard axis (along the x direction), respectively. An external field along the wire rotates the DW out of the yz plane. The DW structure thereby experiences an internal field in the x direction twisting the DW plane and generating a nonuniform internal field along the wire. This field causes periodic deformations of the DW structure, such as ''breathing'' [1] by which the entire DW precesses around the wire axis while its width shrinks and expands periodically. The local modulation of the magnetization texture generates SWs (wavy lines with arrows in Fig. 1) that radiate away from the DW center. The energy needed to generate the SWs has to come from the Zeeman energy [14] that is released by propagating the DW. The DW velocity of a dissipationless ferromagnet in the steady state may then be expected to be proportional to the SW emission rate.In this Letter, we numerically solve the LLG equation, initially without damping in order to confirm the above mentioned relation between spin wave emission and DW propagation. Depending on K ? and the magnetic field, breathing or more complicated periodic transformations of the DW emit spin waves. The DW propagation at low fields tends to lock into a particular soliton mode in which the energy dissipation rate due to the SW emission is balanced by the Zeeman energy gain. We predict robust spin wa...

We model the injection of elastic waves into a ferromagnetic film (F) by a nonmagnetic transducer (N). We compare the configurations in which the magnetization is normal and parallel to the wave propagation. The lack of axial symmetry in the former results in the emergence of evanescent interface states. We compute the energy-flux transmission across the N|F interface and sound-induced magnetization dynamics in the ferromagnet. We predict efficient acoustically induced pumping of spin current into a metal contact attached to F.

A global picture of magnetic domain wall (DW) propagation in a nanowire driven by a magnetic field is obtained: A static DW cannot exist in a homogeneous magnetic nanowire when an external magnetic field is applied. Thus, a DW must vary with time under a static magnetic field. A moving DW must dissipate energy due to the Gilbert damping. As a result, the wire has to release its Zeeman energy through the DW propagation along the field direction. The DW propagation speed is proportional to the energy dissipation rate that is determined by the DW structure. An oscillatory DW motion, either the precession around the wire axis or the breath of DW width, should lead to the speed oscillation.Magnetic domain-wall (DW) propagation in a nanowire due to a magnetic field [1,2,3,4,5] reveals many interesting behaviors of magnetization dynamics. For a tail-to-tail (TT) DW or a head-to-head (HH) DW (shown in Fig. 1) in a nanowire with its easy-axis along the wire axis, the DW will propagate in the wire under an external magnetic field parallel to the wire axis. The propagation speed v of the DW depends on the field strength [3,4]. There exists a so-called Walker's breakdown field H W [6]. v is proportional to the external field H for H < H W and H ≫ H W . The linear regimes are characterized by the DW mobility µ ≡ v/H. Experiments showed that v is sensitive to both DW structures and wire width [1,2,3]. DW velocity v decreases as the field increases between the two linear H-dependent regimes, leading to the so-called negative differential mobility phenomenon. For H ≫ H W , the DW velocity, whose time-average is linear in H, oscillates in fact with time [3,6].Schematic diagram of a HH DW of width ∆ in a magnetic nanowire of cross-section A. The wire consists of three phases, two domains and one DW. The magnetization in domains I and II is along +z-direction (θ = 0) and -zdirection (θ = π), respectively. III is the DW region whose magnetization structure could be very complicate. H is an external field along +z-direction.It has been known for more than fifty years that the magnetization dynamics is govern by the LandauLifshitz-Gilbert (LLG) [7] equation that is nonlinear and can only be solved analytically for some special problems [6,8]. The field induced domain-wall (DW) propagation in a strictly one-dimensional wire has also been known for more than thirty years[6], but its experimental realization in nanowires was only achieved [1,2,3,4,5] in recent years when we are capable of fabricating various nano structures. Although much progress [9,10] has been made in understanding field-induced DW motion, it is still a formidable task to evaluate the DW propagation speed in a realistic magnetic nanowire even when the DW structure is obtained from various means like OOMMF simulator and/or other numerical software packages. A global picture about why and how a DW propagates in a magnetic nanowire is still lacking.In this report, we present a theory that reveals the origin of DW propagation. Firstly, we shall show that no static HH (TT...

The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using Noether's theorem, we prove that these conservation laws persist in the presence of dipole-dipole interactions. However, spin and orbital angular momentum are no longer conserved separately. We also define the linear momentum of ferromagnetic textures. We illustrate the general principles with special reference to spin transfer torques and identify the emergence of a nonadiabatic effective field acting on domain walls in ferromagnetic insulators. Mathematics can be very effective in guiding research when physical intuition fails, even in applied sciences such as condensed matter physics. An important tool is Noether's theorem 1 and its generalizations 2,3 that help identify invariants or continuity equations starting from the fundamental symmetry properties of a given system. In the field of spintronics, for instance, Noether's theorem has been used to express the spin current, i.e., the flow of spin angular momentum, 4 in spinorbit-coupled systems. 5 In metallic ferromagnets spin currents are carried by an imbalance between up-spin and down-spin electron currents and therefore accompanied by long-distance mass motion and strong Joule heating. Spin currents can also be carried by spin waves (magnons), thereby dissipating much less energy in some magnetic insulators with high crystal quality.4 Magnon-mediated spin transport in various systems has received some attention in recent years. [6][7][8][9] Schütz et al. 10demonstrated that magnons in a mesoscopic Heisenberg ring generate a persistent spin current under an inhomogeneous magnetic field. In magnetization textures particle-based [11][12][13] as well as magnonic spin currents 14-17 cause spin transfer torques that induce magnetization dynamics such as a domain wall (DW) motion. Direct imaging of a domain wall motion induced by thermally induced magnonic spin currents has been reported by Jiang et al. 18 The spin transfer torque in magnetic insulators is usually ascribed to conservation of spin angular momentum, implicitly assuming that the exchange interaction is isotropic. However, whereas a negative domain wall velocity, i.e., opposite to the spin-wave propagation direction, is the signature of a magnonic spin transfer torque, 15-17 positive domain wall velocities were found in micromagnetic simulations.19-23 A conclusive explanation of the latter observation is still lacking. Even the spin current and the corresponding continuity equation in Heisenberg magnets has not yet been properly formulated, 24,25 despite the proven angular momentum conservation in isolated magnetic systems. 25Tatara and Kohno 12 predicted domain wall motion by the force or (linear) momentum transfer experienced by narrow domain walls at which electron spins are reflected. But Volovik 26 noted that the linear momentum of magnetization dynamics is not in...

We show that parity-time (PT ) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the PT -broken phase, magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of environment, in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybridized system. As a comparison, neither PT -symmetry broken nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open a novel window to utilize magnonphoton entanglement as a resource for quantum technologies.