Low-energy Spin-wave Excitations 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.

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.

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.

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.

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.

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.

Similar zone-center gaps in the low-energy spin-wave spectra of Na1−δFeAs and BaFe2As2

We report results of inelastic-neutron-scattering measurements of low-energy spin-wave excitations in two structurally distinct families of iron-pnictide parent compounds: Na${}_{1\ensuremath{-}\ensuremath{\delta}}$FeAs and BaFe${}_{2}$As${}_{2}$. Despite their very different values of the ordered magnetic moment and N\'eel temperatures, ${T}_{\mathrm{N}}$, in the antiferromagnetic state both compounds exhibit similar spin gaps of the order of 10 meV at the magnetic Brillouin-zone center. The gap opens sharply below ${T}_{\mathrm{N}}$, with no signatures of a precursor gap at temperatures between the orthorhombic and magnetic phase transitions in Na${}_{1\ensuremath{-}\ensuremath{\delta}}$FeAs. We also find a relatively weak dispersion of the spin-wave gap in BaFe${}_{2}$As${}_{2}$ along the out-of-plane momentum component, ${q}_{z}$. At the magnetic zone boundary (${q}_{z}=0$), spin excitations in the ordered state persist down to $\ensuremath{\sim}$20 meV, which implies a much smaller value of the effective out-of-plane exchange interaction, ${J}_{\mathrm{c}}$, as compared to previous estimates based on fitting the high-energy spin-wave dispersion to a Heisenberg-type model.

Low Ordered Magnetic Moment by Off-Diagonal Frustration in Undoped Parent Compounds to Iron-Based High-TcSuperconductors

A Heisenberg model over the square lattice recently introduced by Si and Abrahams to describe local-moment magnetism in the new class of Fe-As high-T(c) superconductors is analyzed in the classical limit and on a small cluster by exact diagonalization. In the case of spin-1 iron atoms, large enough Heisenberg exchange interactions between neighboring spin-1/2 moments on different iron 3d orbitals that frustrate true magnetic order lead to hidden magnetic order that violates Hund's rule. It accounts for the low ordered magnetic moment observed by elastic neutron diffraction in an undoped parent compound to Fe-As superconductors. We predict that low-energy spin-wave excitations exist at wave numbers corresponding to either hidden Néel or hidden ferromagnetic order.

Anisotropic itinerant magnetism and spin fluctuations inBaFe2As2: A neutron scattering study

Neutron scattering measurements were performed to investigate magnetic excitations in a single-crystal sample of the ternary iron arsenide ${\text{BaFe}}_{2}{\text{As}}_{2}$, a parent compound of a recently discovered family of Fe-based superconductors. In the ordered state, we observe low energy spin-wave excitations with a gap energy $\ensuremath{\Delta}=9.8(4)\text{ }\text{meV}$. The in-plane spin-wave velocity ${v}_{ab}$ and out-of-plane spin-wave velocity ${v}_{c}$ measured at 12 meV are 280(150) and $57(7)\text{ }\text{meV}\text{ }\text{\AA{}}$, respectively. At high energy, we observe anisotropic scattering centered at the antiferromagnetic wave vectors. This scattering indicates two-dimensional spin dynamics, which possibly exist inside the Stoner continuum. At ${T}_{N}=136(1)\text{ }\text{K}$, the gap closes and quasielastic scattering is observed above ${T}_{N}$, indicative of short-range spin fluctuations. In the paramagnetic state, the scattering intensity along the $L$ direction becomes ``rodlike,'' characteristic of uncorrelated out-of-plane spins, attesting to the two-dimensionality of the system.

Magnetic ordering and spin excitations in Mn(dca) 2 (pyz) [dca = N(CN) 2 - , pyz = pyrazine

We have studied the T- and H-dependent magnetism in Mn(dca)2(pyz) [dca = N(CN)2-, pyz = pyrazine] using neutron-scattering methods. The crystal structure can be viewed as a molecular analog of ReO3, where 1D Mn–pyz–Mn chains connect 2D Mn(dca)2 square sheets to form a 3D network. In zero field, the Mn2+ moments order antiferromagnetically below 2.53(2) K along the ac diagonal with a magnitude of 4.15(6) μB at 1.35 K. The field-dependent response of the [111] magnetic reflection is consistent with spin-flop and induced ferromagnetic phase transitions as previously observed in magnetization measurements. Diffuse-scattering studies indicated no evidence for low-dimensional spin correlations. Using quasielastic neutron scattering, a low-energy spin-wave excitation was observed at ∼0.23 meV, which is ∼1/6 the momentum transfer observed in Mn(dca)2 owing to a reduced number of magnetic nearest neighbors.

Direct evidence of spin frustration in the fcc antiferromagnet NiS 2

NiS2 is a well-known Mott insulator with anomalous antiferromagnetic long-range order of coexistent type I (Q M=(1,0,0), TN1=40 K) and type II (Q M= $\frac\Box1\Box\Box2\Box$ , $\frac\Box1\Box\Box2\Box$ , $\frac\Box1\Box\Box2\Box$ , TN2=30 K). Extensive neutron-scattering measurements reveal that magnetism in NiS2 is governed by geometrical spin frustration, resulting in magnetic diffuse scattering extending along the fcc zone boundary. Although the diffuse scattering exists at temperatures as high as 250 K (6TN1), it disappears rapidly below TN2, associated with minor crystal distortion. We observed a clear energy gap in addition to the low-energy spin-wave excitation at significantly below 30 K, and obtain evidence that degeneracy due to the coexistence of the two types of antiferromagnetism is relieved in the ground state via the reduction in symmetry due to distortion.

First-order phase transition inUO2:235Uand17ONMR study

A nuclear magnetic resonance (NMR) study is reported for a $5f$-cooperative Jahn-Teller (JT) system with antiferromagnetic ordering, ${\mathrm{UO}}_{2},$ where we have performed magnetic actinide ${(}^{235}\mathrm{U})$ as well as nonmagnetic ligand ${(}^{17}\mathrm{O})$ NMR studies in a $5f$-electron system. The observed ${}^{235}\mathrm{U}$ hyperfine interaction is consistent with an axially symmetric $5f$-wave-function character for ${\mathrm{U}}^{4+}$ below a first-order transition temperature ${T}_{\mathrm{N}}=30.8\mathrm{K}.$ Thus, the orbital degeneracy in the cubic crystalline field is lifted by a magnetic ordering combined with a JT distortion. On the other hand, modulation phenomena in the ${}^{17}\mathrm{O}$ spin-echo decay provide evidence of a lattice distortion just below ${T}_{\mathrm{N}},$ which gives rise to an axially symmetric electric-field gradient at the oxygen sites. These results indicate that, in a cooperative JT transition which occurs as a result of coupling between $5f$ quadrupoles and lattice distortion, the behavior of the $5f$ quadrupoles can be investigated using uranium NMR, while the lattice distortion can be studied with the nonmagnetic ligand NMR. Among magnetic structures and JT distortions, proposed on the basis of neutron scattering experiments and theoretical work, the noncollinear $3\mathit{k}$-type structure is the most likely, because either the $1\mathit{k}$ or $2\mathit{k}$ would cause an orthorhombic distortion. With respect to low-energy spin-wave excitations, nuclear spin-lattice relaxation rates ${T}_{1}^{\ensuremath{-}1}$ at both sites show a ${T}^{7}$ behavior below ${T}_{\mathrm{N}},$ which suggests the presence of gapless excitations due to strong magnon-phonon coupling.

Low-energy spin-wave excitations in the bilayer manganite La1.2Sr1.8Mn2O7

Inelastic neutron scattering experiments were performed on a single crystal of the bilayer manganite La1.2Sr1.8Mn2O7. Low-energy spin-wave excitations were observed along the c direction with a maximum energy of ∼ 0.5 meV at the zone boundary. The dispersion of these acoustic spin wave modes is modeled by a nearest-neighbor Heisenberg model with an interbilayer exchange interaction between neighboring spins in different bilayers of 0.048(1) meV and an anisotropy gap of Δ = 0.077(3) meV. These results confirm the two-dimensional nature of the spin correlations in the bilayer manganites, with a ratio of the in-plane to interbilayer interaction of ∼ 200. The temperature dependence of the energies and intensities of the spin wave excitations are in agreement with our earlier conclusion that the ferromagnetic transition is second order.

Effective single-particle potentials for MnO in light of interatomic magnetic interactions: Existing theories and perspectives

It is shown that the fundamental gauge-symmetry constraints superimposed on the admissible form of the exchange-correlation energy functional lead to the generalized local force theorem for small nonuniform rotations of the spin magnetic moments near equilibrium. The theorem suggests that the magnetic interactions responsible for the low-energy spin-wave excitations near the ground state can be expressed in terms of the effective single-particle potential designed for the ground-state spin-magnetization density. The theorem allows us to obtain an empirical effective potential for MnO by fitting the experimental low-temperature spin-wave dispersion curve. The theorem is further applied to investigate abilities of several different first-principles techniques: local-(spin)-density approximation, LDA plus ``Hubbard $U$'' $(\mathrm{LDA}+U)$ and optimized effective potential (OEP). None of these approaches treats the magnetic interactions in MnO properly. Limitations of the one-electron band picture underlying the failure are elucidated in each case. As one of the perspective techniques to deal with the electronic structure of narrow-band materials, we propose to combine the $\mathrm{LDA}+U$ form of the single-particle equations with the variational principles of the OEP approach. Several possible approximations along this line are discussed.

Itinerant electron magnetism in the quantum Hall regime

The two-dimensional interacting electron gas at Landau level filling factor f=1 at temperature T = 0 is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on a theoretical study of its thermodynamic properties, particularly the temperature dependence of the spin magnetization. Our study is based on an approximation in which the self-energy includes contributions obtained by summing up particle-hole ladders which take into account the presence of low-energy collective spin-wave excitations. The emission and absorption of spin waves is accompanied by electronic spin flips. In our approximation the spin-wave bands narrow with increasing temperature leading eventually to an abrupt decrease of the spin magnetization. We compare our results with recent magnetization data from NMR measurements by Barrett et al.

Low-energy spin-wave theory for disordered Pd3Fe

Low-energy spin-wave excitations in the partially ordered ferromagnetic alloy Pd3Fe have been studied using a Heisenberg model. A long-range order (LRO) parameter has been introduced to Murray's spin-wave theory and the order dependence of the stiffness constant to the first-order approximation is given. The nearest- and next-nearest-neighbour exchange integrals have been estimated from a neutron diffraction experiment performed by Menzinger et al (1971). The results the authors obtained are different from the values given by them.

The double-crystal small angle scattering technique for inelastic scattering for neutrons: Spin-waves in Fe and FeNi

In this paper we describe, in detail, the application of the double-crystal small angle scattering technique to the observation of very low energy spin-wave excitations. We present data on the small angle spin-wave scattering in Fe and FeNi single crystals using this technique and also a multiple detector system. The studies on Fe, which are more extensive, include investigations of the effects of temperature and applied magnetic field on the long wavelenght spin-wave scattering.