Low-energy Spin Waves Research Articles

Charged magnons on the surface of a topological insulator

We study a system of two-dimensional Dirac electrons (as is realized on the surface of a 3D topological insulator) coupled to an array of localized spins. The spins are coupled ferromagnetically to each other, forming an ordered ground state with low-energy spin-wave excitations (magnons). The Dirac electrons couple to the spins through a spin-dependent effective Zeeman field. The out-of-plane effective Zeeman field therefore serves as a Dirac mass that gaps the electronic spectrum. Once a spin is flipped, it creates a surrounding domain in which the sign of the Dirac mass is opposite to that of the rest of the sample. Therefore, an electronic bound state appears on the domain wall, as predicted by Jackiw and Rebbi. However, in a quantum magnet, a localized spin flip does not produce an eigenstate. Instead, the eigenstates correspond to delocalized spin waves (magnons). As in the case of the single flipped spin, the delocalized magnon also binds an in-gap electronic state. We name this excitation a `Jackiw-Rebbi-Magnon' (JRM) and study its signature in the dynamic spin susceptibility. When the sample is tunnel-coupled to an electronic reservoir, a magnon produced in a system without any electrons hybridizes with a JRM (which binds a single electron), producing magnon-JRM polaritons. For such a system, we identify a quantum phase transition when the magnon-JRM polariton energy falls below that of the fully polarized ferromagnetic ground state.

Neutron scattering sum rules, symmetric exchanges, and helicoidal magnetism in MnSb2O6

MnSb$_{2}$O$_{6}$ is based on the noncentrosymmetric $P321$ space group with magnetic Mn$^{2+}$ ($S={5/2}$, $L\approx 0$) spins ordering below $T_{\mathrm{N}}=12$ K in a helicoidal structure. The ground state magnetic structure, expected to be built and originate from 7 Heisenberg exchange constants, has been shown to be coupled to the underlying crystallographic chirality with polar domain switching being reported. We apply neutron spectroscopy to extract these symmetric exchange constants. Given the high complexity of the magnetic exchange network, crystallographic structure and complications fitting linear spin-wave models, we take advantage of multiplexed neutron instrumentation to use the first moment sum rule of neutron scattering to estimate the 7 exchange constants. We then use these parameters to calculate the low-energy spin-waves in the N\'eel state to reproduce the neutron response without strong antisymmetric coupling. Using Green's response functions, the stability of long-wavelength excitations in the context of proposed magnetic structures is then discussed. The results show the presence of strong exchange constants for the chiral exchange pathways and illustrate an underlying coupling between crystallographic and magnetic ``chirality" through predominantely symmetric exchange.

Handedness filter and Doppler shift of spin waves in ferrimagnetic domain walls

Excitation and propagation of spin waves inside magnetic domain walls (DWs) have received attention because of their potentials in spintronic and communication applications. In addition to wave amplitude and frequency, spin waves have a third character: handedness, whose manipulation is certainly of interest. We propose in this paper that the handedness of low-energy spin-wave excitations can be controlled by tuning the net angular momentum ${\ensuremath{\delta}}_{s}$ in a ferrimagnetic (FiM) DW, attributing to the inequivalent magnetic sublattices. The results indicate that the spin-wave dispersion depends on both ${\ensuremath{\delta}}_{s}$ and wave handedness. For a positive (negative) ${\ensuremath{\delta}}_{s}$, a gapless dispersion is observed for left-handed (right-handed) spin waves, while a frequency gap appears for right-handed (left-handed) spin waves. Thus, a FiM wall could serve as a filter of low-energy spin waves in which only spin waves with a specific handedness can propagate. Furthermore, the energy consumption loss for spin-wave excitation in the wall is much lower than that inside the domain, while the group velocity is much faster too, demonstrating the advantages of DWs serving as spin waveguides. Moreover, the current-induced spin-wave Doppler shift in the FiM wall is also revealed and can be controlled by ${\ensuremath{\delta}}_{s}$. In this paper, we unveil the interesting spin-wave dynamics in FiM DWs, benefiting future spin-wave applications.

Anisotropic spin-wave excitations in multiferroic BiFeO3

Polarized inelastic neutron-scattering experiments have been performed to elucidate the anisotropic behavior of the low-energy spin-wave excitations in a multiferroic ${\mathrm{BiFeO}}_{3}$, which shows a cycloidal spin structure below 640 K. Using neutron polarization analysis for single magnetic domain crystals, magnetic excitation modes in and out of the cycloidal plane below 6 meV were separated successfully. The magnetic excitation spectra were analyzed using linear spin-wave theory. The low-energy magnon density of states consist of several magnon modes, including the two anisotropic modes, $\mathrm{\ensuremath{\Phi}}$ and $\mathrm{\ensuremath{\Psi}}$ modes, distributed in and out of the cycloidal plane, respectively, which were previously observed using optical spectroscopies. Furthermore, there are other magnon modes that are not active in optical measurements. A model spin Hamiltonian, which reproduces the spin-wave frequencies observed using optical spectroscopies, explains the overall spectra reasonably well.

Neutron Spectroscopy Evidence on the Dual Nature of Magnetic Excitations in a van der Waals Metallic Ferromagnet Fe2.72GeTe2

In the local or itinerant extreme, magnetic excitations can be described by the Heisenberg model which treats electron spins as localized moments, or by the itinerant-electron model where the exchange interaction between electrons leads to unequal numbers of electrons with up and down spins. However, it has been elusive when both local moments and itinerant electrons are present in the intermediate range. Using inelastic neutron scattering, we provide direct spectroscopic evidence on the coexistence of and interplay between local moments and itinerant electrons in a van der Waals metallic ferromagnet Fe$_{2.72}$GeTe$_{2}$, which can sustain tunable room-temperature ferromagnetism down to the monolayer limit. We find that there exist ferromagnetic spin-wave excitations dispersing from the zone center at low energies resulting from local moments, and a column-like broad continuum at the zone boundary at high energies up to over 100 meV resulting from itinerant electrons. Unlike the two-dimensional crystal structure, the low-energy mode exhibits a three-dimensional nature, and the high-energy mode also has an out-of-plane dependence. Both modes persist well above the Curie temperature of 160 K. Our neutron spectroscopic data reveal that the low-energy spin waves at 100 K are more coherent than those at 4 K, which is evidence of the weakening of the Kondo screening at high temperatures. These results unambiguously demonstrate the coexistence of local moments and itinerant electrons, and the Kondo effect between these two components in Fe$_{2.72}$GeTe$_{2}$. Such behaviors are generally expected in heavy-fermion systems with heavy $f$ electrons but rarely clearly observed in materials with light $d$ electrons. These findings shed light on the understanding of magnetism in transition-metal compounds.

Conceptual design of magnonic majority-logic gate based on channeling of spin waves in domain walls

A three-input majority gate, which operates on the basis of majority decisions, can function as multifunctional Boolean logic gates. Here, we report a micromagnetic simulation study of a specially devised magnonic majority-logic gate that utilizes channeling of spin waves into narrow domain walls. Our model system is a four-armed cross structure where low-energy spin waves are guided and channeled along Néel-type domain walls and then interact with a single magnetic vortex positioned at the cross-point. After exciting spin waves simultaneously from the ends of three individual arms where input binary digits are encoded using spin-wave phase information, the phases of spin waves passing through the cross-point (after being scattered from the vortex) are measured as output binary digits at the end of the remaining single output arm. Consequently, the majority of the input variables determines the output signal, which is a clear sign of a majority gate. Furthermore, by setting a control input, our proposed single structure can perform multiple operations of AND-, OR-, NAND-, and NOR-gates. Finally, the gate structure and channeling spin waves into domain walls/their interaction with a vortex core have the additional merits of being free of the Joule heating typically encountered in conventional electronic devices and of having long coherence lengths.

Spin-orbit torque-mediated spin-wave excitation as an alternative paradigm for femtomagnetism

Laser-induced femtosecond demagnetization, femtomagnetism, offers a potential route to develop faster magnetic storage devices. It is generally believed that the traditional spin-wave theory, which is developed for thermally driven slow demagnetization, cannot explain this rapid demagnetization by design. Here, we show that this traditional spin-wave theory, once augmented by laser-induced spin–orbit torque, provides a highly efficient paradigm for demagnetization, by capturing low-energy spin-wave excitation that is absent in existing mechanisms. Our paradigm is different from existing ones but does not exclude them. Microscopically, we find that optical spin–orbit torque generates massive spin waves across several hundred lattice sites, collapsing the long-range spin-spin correlation within 20 fs. Our finding does not only explain new experiments but also establishes an alternative paradigm for femtomagnetism. It is expected to have far-reaching impacts on future research.

Excitations in the field-induced quantum spin liquid state of \u03b1-RuCl3

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl3. In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations. However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase.

Spin-density fluctuations and the fluctuation-dissipation theorem in 3d ferromagnetic metals

Spatial and time scales of spin density fluctuations (SDF) were analyzed in 3d ferromagnets using ab initio linear response calculations of complete wavevector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDF are spread continuously over the entire Brillouin zone and while majority of them reside within the 3d bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin wave contribution and a much larger high-energy component from more localized excitations. Using the fluctuation-dissipation theorem (FDT), the on-site spin correlator (SC) and the related effective fluctuating moment were properly evaluated and their universal dependence on the 3d band population is further discussed.

Direct observation of magnon-phonon coupling in yttrium iron garnet

The magnetic insulator yttrium iron garnet (YIG) with a ferrimagnetic transition temperature of $\sim$560 K has been widely used in microwave and spintronic devices. Anomalous features in the spin Seeback effect (SSE) voltages have been observed in Pt/YIG and attributed to the magnon-phonon coupling. Here we use inelastic neutron scattering to map out low-energy spin waves and acoustic phonons of YIG at 100 K as a function of increasing magnetic field. By comparing the zero and 9.1 T data, we find that instead of splitting and opening up gaps at the spin wave and acoustic phonon dispersion intersecting points, magnon-phonon coupling in YIG enhances the hybridized scattering intensity. These results are different from expectations of conventional spin-lattice coupling, calling for new paradigms to understand the scattering process of magnon-phonon interactions and the resulting magnon-polarons.

Investigation of Feshbach resonances in ultracold 40K spin mixtures.

Magnetically tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on 37 thus far unpublished Feshbach resonances and four further probable Feshbach resonances in spin mixtures of ultracold fermionic 40K with temperatures well below 100 nK. In particular, we locate a broad resonance at B = 389.7G with a magnetic width of 26.7 G. Here 1 G = 10-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40K quantum gases.

Dynamics of linarite: Observations of magnetic excitations

Here we present inelastic neutron scattering measurements from the frustrated, quantum spin-1/2 chain material linarite, PbCuSO_4(OH)_2. Time of flight data, taken at 0.5K and zero applied magnetic field reveals low-energy dispersive spin wave excitations below 1.5meV both parallel and perpendicular to the Cu-chain direction. From this we confirm that the interchain couplings within linarite are around 10% of the nearest neighbour intrachain interactions. We analyse the data within both linear spin-wave theory and density matrix renormalisation group theories and establish the main magnetic exchange interactions and the simplest realistic Hamiltonian for this material.

Electrical detection of spiral spin structures inPt|Cu2OSeO3heterostructures

The interaction between the itinerant spins in metals and localized spins in magnetic insulators thus far has only been explored in collinear spin systems, such as garnets. Here, we report the spin-Hall magnetoresistance (SMR) sensitive to the surface magnetization of the spin-spiral material, Cu_2OSeO_3. We experimentally demonstrate that the angular dependence of the SMR changes drastically at the transition between the helical spiral and the conical spiral phases. Furthermore, the sign and magnitude of the SMR in the conical spiral state are controlled by the cone angle. We show that this complex behaviour can be qualitatively explained within the SMR theory initially developed for collinear magnets. In addition, we studied the spin Seebeck effect (SSE), which is sensitive to the bulk magnetization. It originates from the conversion of thermally excited low-energy spin waves in the magnet, known as magnons, into the spin current in the adjacent metal contact (Pt). The SSE displays unconventional behavior where not only the magnitude but also the phase of the SSE vary with the applied magnetic field.

Low-energy spin-wave excitations in amplitude-modulated magnetic structure of PrNi2Si2

Inelastic neutron scattering (INS) experiments and random phase approximation calculations have been used to investigate the low-energy spin-wave excitations in PrNi2Si2. The modulated magnitude of the ordered magnetic moments of Pr3+ ions implies that the associate, longitudinally polarized magnetic excitations are more intense and dispersive than the usual transverse spin waves. Within the random phase approximation the results are in good overall agreement with the predictions made by the model determined previously from the paramagnetic excitations. The most unusual observation is the well-defined amplitude mode detected close to the magnetic Bragg point existing simultaneously with the phason mode. At low energies, an extra mode is observed to hybridize with the magnetic phasons in the neighborhood of the magnetic Brillouin zone center. A magnetoelastic interaction between the magnetic excitations and the longitudinal phonons is able to explain part of the disturbances, but it is concluded that the extra mode must be of some other, unknown origin.

Quantum Hall bilayer as pseudospin magnet

We revisit the physics of electron gas bilayers in the quantum Hall regime (MacDonald A. and Eisenstein J., Nature, 432 (2004) 691; Eisenstein J., Science, 305 (2004) 950), where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation of a BEC of excitons in the half-filled electron bilayers, where empty states play the role of holes. We discuss the fundamental difficulties with this scenario, and propose an alternative approach based on a treatment of the system as a pseudospin magnet. We show that the experimentally observed tunneling peak can be linked to the XY ferromagnet (FM) to Ising antiferromagnet (AFM) phase transition of the S = 1/2 XXZ pseudospin model, driven by the change in total electron density. This transition is accompanied by a qualitative change in the nature of the low-energy spin wave dispersion from a gapless linear mode in the XY-FM phase to a gapped, quadratic mode in the Ising AFM phase.

Complementary terahertz absorption and inelastic neutron study of the dynamic anisotropy contribution to zone-center spin waves in a canted antiferromagnetNdFeO3

We employ a combination of pulsed- and continuous-wave polarized terahertz spectroscopy techniques to probe temperature-dependent spin waves in the antiferromagnet $\mathrm{Nd}\mathrm{Fe}{\mathrm{O}}_{3}$. Our optical data span 1.6--467 K and reveal a conspicuous spin reorientation between 110 and 170 K, during which the lower-energy mode softens completely. Complementary inelastic neutron scattering reveals that the frequencies of the optically excited spin waves are consistent with a temperature-variable spin gap in the low-energy spin-wave dispersion of $\mathrm{Nd}\mathrm{Fe}{\mathrm{O}}_{3}$. The result links the temperature dependence of the spin waves to a dynamic in-plane anisotropy. The magnetic anisotropy is calculated based on the results of the optical measurements. The change observed in the anisotropy energy along the $a$ and $c$ crystal axes suggests that the spin reorientation evident in $\mathrm{Nd}\mathrm{Fe}{\mathrm{O}}_{3}$ is driven by temperature-dependent in-plane anisotropy.

Observation of spin-wave dispersion in Nd-Fe-B magnets using neutron Brillouin scattering

The low-energy spin-wave dispersion in polycrystalline Nd-Fe-B magnets was observed using neutron Brillouin scattering (NBS). Low-energy spin-wave excitations for the lowest acoustic spin-wave mode were clearly observed. From the spin-wave dispersion, we were able to determine the spin-wave stiffness constant Dsw (100.0 ± 4.9 meV.Å2) and the exchange stiffness constant A (6.6 ± 0.3 pJ/m).

Magnetic orders, excitations, and phase transitions in Fe1+yTe

We study the magnetic properties of Fe_1+y Te, a parent compound of the iron-based high-temperature superconductors. Motivated by recent neutron scattering experiments, we show that a spin-1 exchange model, supplemented by a single-ion spin anisotropy, accounts well for the experimentally observed low temperature magnetic phase diagram, that exhibits a commensurate bicollinear order at low Fe dopings (y < 0.12) and an incommensurate spin-spiral order at high Fe dopings (y > 0.12). We suggest that the commensurate-incommensurate transition at y = 0.12 is due to the competition between the exchange interaction and the local spin anisotropy. At low Fe dopings, the single-ion spin anisotropy is strong and pins the spins along the easy axis, which, together with the spatially anisotropic exchanges, induces a unusual bicollinear commensurate magnetic order. The low-energy spin-wave excitation is gapped due to the explict breaking of spin-rotational symmetry by the local spin anisotropy. At high Fe dopings, the single-ion anisotropy is weak, and the exchange favors an incommensurate coplanar state. The incommensurate magnetic wavevector averages out the spin anisotropy so that a gapless low-energy spin-wave excitation is obtained. We also analyze the low-energy hydrodynamic model and use it to describe the magneto-structural transition and the static and dynamical spin structure factors across the magnetic ordering transitions.

Magnetic anisotropic energy gap and low-energy spin wave excitation in the antiferromagnetic block phase of K2Fe4Se5

Neutron scattering experiments were performed to investigate magnetic order and magnetic excitations in ternary iron chalcogenide K2Fe4Se5. The formation of a superlattice structure below 580 K together with the decoupling between the Fe-vacancy order-disorder transition and the antiferromagnetic order transition appears to be a common feature in the A2Fe4Se5 family. The study of spin dynamics of K2Fe4Se5 reveals two distinct energy gaps at the magnetic Brillouin zone center, which indicates the presence of magnetic anisotropy and the decrease of local symmetry due to electronic and orbital anisotropy. The low-energy spin wave excitations of K2Fe4Se5 can be properly described by linear spin wave theory within a Heisenberg model. Compared to iron pnictides, K2Fe4Se5 exhibits a more two-dimensional magnetism as characterized by large differences not only between out-of-plane and in-plane spin wave velocities, but also between out-of-plane and in-plane exchange interactions.

Spin-wave excitations and superconducting resonant mode in CsxFe2−ySe2

We report neutron inelastic scattering measurements on the normal and superconducting states of single-crystalline Cs0.8Fe1.9Se2. Consistent with previous measurements on Rb(x)Fe(2-y)Se2, we observe two distinct spin excitation signals: (i) spin-wave excitations characteristic of the block antiferromagnetic order found in insulating A(x)Fe(2-y)Se2 compounds, and (ii) a resonance-like magnetic peak localized in energy at 11 meV and at an in-plane wave vector of (0.25, 0.5). The resonance peak increases below Tc = 27 K, and has a similar absolute intensity to the resonance peaks observed in other Fe-based superconductors. The existence of a magnetic resonance in the spectrum of Rb(x)Fe(2-y)Se2 and now of Cs(x)Fe(2-y)Se2 suggests that this is a common feature of superconductivity in this family. The low energy spin-wave excitations in Cs0.8Fe1.9Se2 show no measurable response to superconductivity, consistent with the notion of spatially separate magnetic and superconducting phases.