Magnon Dispersion Research Articles

Spin Waves in Two and Three Dimensional Magnetic Materials

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

Theoretical Study of Magnetic Excitation in Interacting Inequivalent Spin Dimer System NH4CuCl3

Magnetic excitation in the interacting spin dimer system NH4CuCl3 is investigated on the basis of an extended spin-wave theory, assuming a doubled unit cell with four dimer sublattices of inequivalent intradimer interactions as suggested by neutron scattering measurements. In the magnetically ordered phase, there are both transverse (Nambu–Goldstone) and longitudinal (Higgs) excitation modes as in the pressure-induced ordered phase of the isostructural spin dimer compounds TlCuCl3 and KCuCl3. The inequivalent dimer model is consistent with the magnon dispersion relation at zero magnetic field and with the field dependence of the excitation energies obtained by neutron scattering and ESR measurements. This supports the existence of four dimer sublattices with inequivalent dimers in NH4CuCl3.

Lifetimes of magnons in two-dimensional diluted ferromagnetic systems

Spin dynamics in low dimensional magnetic systems has been of fundamental importance for a long time and has currently received an impetus owing to the emerging field of nanoelectronics. Knowledge of the spin wave lifetimes, in particular, can be favorable for future potential applications. We investigate the low-temperature spin wave excitations in two-dimensional disordered ferromagnetic systems, with a particular focus on the long wavelength magnon lifetimes. A semi-analytical Green's functions based approach is used to determine the dynamical spectral functions, for different magnetic impurity concentrations, from which the intrinsic linewidth is extracted. We obtain an unambiguous $q^4$ scaling of the magnon linewidth which is ascribed to the disorder induced damping of the spin waves, thereby settling a longstanding unresolved issue on the wave-vector dependence. Our findings are also in good agreement with previous theoretical studies on Heisenberg ferromagnets. Additionally, we demonstrate the futility of using the low moments associated with the spectral densities to evaluate the magnon dispersions and lifetimes.

Spin Waves in One Dimensional Magnetic Material

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

Spin Waves in One Dimensional Magnetic Material

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

Direct observation of the Dzyaloshinskii-Moriya interaction in a Pt/Co/Ni film.

The interfacial Dzyaloshinskii-Moriya interaction in an in-plane anisotropic Pt(4 nm)/Co(1.6 nm)/Ni(1.6 nm) film has been directly observed by Brillouin spectroscopy. It is manifested as the asymmetry of the measured magnon dispersion relation, from which the Dzyaloshinskii-Moriya interaction constant has been evaluated. Linewidth measurements reveal that the lifetime of the magnons is asymmetric with respect to their counter-propagating directions. The lifetime asymmetry is dependent on the magnon frequency, being more pronounced, the higher the frequency. Analytical calculations of the magnon dispersion relation and linewidth agree well with experiments.

Magnetic excitation spectrum ofLuFe2O4measured with inelastic neutron scattering

We report neutron inelastic scattering measurements and analysis of the spectrum of magnons propagating within the Fe2O4 bilayers of LuFe2O4. The observed spectrum is consistent with six magnetic modes and a single prominent gap, which is compatible with a single bilayer magnetic unit cell containing six spins. We model the magnon dispersion by linear spin-wave theory and find very good agreement with the domain-averaged spectrum of a spin-charge bilayer superstructure comprising one Fe3+ -rich monolayer and one Fe2+ -rich monolayer. These findings indicate the existence of polar bilayers in LuFe2O4, contrary to recent studies that advocate a charge-segregated non-polar bilayer model. Weak scattering observed below the magnon gap suggests that a fraction of the bilayers contain other combinations of charged monolayers not included in the model. Refined values for the dominant exchange interactions are reported.

Magnetic order and electromagnon excitations inDyMnO3studied by neutron scattering experiments

Magnetic order and excitations in multiferroic ${\mathrm{DyMnO}}_{3}$ were studied by neutron scattering experiments using a single crystal prepared with an enriched $^{162}\mathrm{Dy}$ isotope. The ordering of Mn moments exhibits pronounced hysteresis arising from the interplay between Mn and Dy magnetism, which has a strong impact on the ferroelectric polarization. The magnon dispersion resembles that reported for ${\mathrm{TbMnO}}_{3}$. We identify the excitations at the magnetic zone center and near the zone boundary in the $b$ direction, which can possess electromagnon character. The lowest frequency of the zone-center magnons is in good agreement with a signal in a recent optical measurement, so this mode can be identified as the electromagnon coupled by the same Dzyaloshinskii-Moriya interaction as the static multiferroic phase.

Effect of Magnetic Field on Spin Excitations in the Kondo Lattice Antiferromagnet

The properties of spin excitations in the antiferromagnetic ordered phase of the Kondo lattice model in a magnetic field are investigated by the S−1 expansion method with S being the magnitude of localized spins. It is shown that the field dependence of magnon dispersion is different from that in the Heisenberg antiferromagnet, showing an enhancement of excitation energy in the entire Brillouin zone. As a result, the magnon states are found to be unstable and to decay into particle–hole excitations in a high magnetic field.

Direct evidence of antiferromagnetic exchange interaction in Fe(001) films: Strong magnon softening at the high-symmetryM¯point

We report on the direct observation of a large unusual antiferromagnetic exchange interaction in Fe(001) films. By measuring the magnon dispersion relation over the entire Brillouin zone of an ultrathin Fe(001) film on Rh(001), we demonstrate that the signature of this unusual antiferromagnetic exchange interaction can be observed at the high-symmetry $\overline{\mathrm{M}}$ point. The exchange parameters are quantified by comparing the measured magnon dispersion relation with the results of our first-principles calculations. We suggest a way of examining the existence of an antiferromagnetic exchange interaction in layered magnetic structures and also a way of quantifying its strength.

Bandgaps and Demagnetizing Effects in a Py/Co Magnonic Crystal

The magnonic mode dispersion in a bi-component ferromagnetic system composed by a periodic arrangement of cobalt cylindrical nanodots of diameter 310 nm totally etched into a permalloy film 16 nm thick is theoretically investigated. The array lattice constant of the 2-D magnonic crystal is 600 nm and the in-plane magnetic field is applied along the y-direction and perpendicularly to the in-plane Bloch wave vector. The simulations are based on a finite-difference micromagnetic approach, the so-called dynamical matrix method (DMM). The calculated frequency bandgaps for the most relevant magnonic modes according to the DMM are discussed and compared with the ones obtained by means of an analytical approach based on the plane wave method. An analytical expression of the effective static demagnetizing field experienced by localized collective modes whose spatial profiles are mainly concentrated in the horizontal rows containing cobalt cylindrical nanodots is derived and its dependence on the modulus of the Bloch wave vector of the magnonic modes is studied.

Weyl fermions induced magnon electrodynamics in a Weyl semimetal

Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the so-called Weyl semimetals, this anomaly gives rise to topological electromagnetic response of magnetic fluctuations, which takes the form of non-local interaction between magnetic fluctuations and electromagnetic fields. We study the physical consequences of this non-local interaction, including electric field assisted magnetization dynamics, an extra gapless magnon dispersion, and polariton behaviors that feature "sibling" bands in small magnetic fields.

Magnon dispersion in thin magnetic films

Although the dispersion of magnons has been measured in many bulk materials, few studies deal with the changes in the dispersion when the material is in the form of a thin film, a system that is of interest for applications. Here we review inelastic tunneling spectroscopy studies of magnon dispersion in Mn/Cu3Au(1 0 0) and present new studies on Co and Ni thin films on Cu(1 0 0). The dispersion in Mn and Co films closely follows the dispersion of bulk samples with negligible dependence on thickness. The lifetime of magnons depends slightly on film thickness, and decreases considerably as the magnon energy increases. In Ni/Cu(1 0 0) films the thickness dependence of dispersion is much more pronounced. The measurements indicate a considerable mode softening for thinner films. Magnon lifetimes decrease dramatically near the edge of the Brillouin zone due to a close proximity of the Stoner continuum. The experimental study is supported by first-principles calculations.

Temperature-Dependent Interplay of Dzyaloshinskii-Moriya Interaction and Single-Ion Anisotropy in MultiferroicBiFeO3

Low-energy magnon excitations in multiferroic BiFeO3 were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fit an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO3.

Magnetic excitations in ultrathin magnetic films: Temperature effects

The idea of investigating large wave-vector magnetic excitations in ultrathin films by spin-polarized electron spectroscopy is briefly reviewed. The historical background of the paper is based on the personal experience of the authors who collaborated and discussed with Douglas Mills regarding this subject. Douglas Mills' impact on the understanding of fundamental mechanisms involved in the excitation process and the development of the theory of magnetic excitations is outlined.In addition, the temperature effects on the large wave-vector magnetic excitations in ultrathin Fe films are addressed. The experimental results of magnon excitations in the pseudomorphic Fe monolayer on W(110) are presented. The temperature dependence of the magnon dispersion relation is discussed.

Spin-liquid phase in a spatially anisotropic frustrated antiferromagnet: A Schwinger boson mean-field approach

We explore the effect of the third-nearest neighbors on the magnetic properties of the Heisenberg model on an anisotropic triangular lattice. We obtain the phase diagram of the model using Schwinger boson mean-field theory. Competition between N\'eel, spiral, and collinear magnetically ordered phases is found as we vary the ratios of the nearest ${J}_{1}$, next-nearest ${J}_{2}$, and third-nearest ${J}_{3}$ neighbor exchange couplings. A spin-liquid phase is stabilized between the spiral and collinear ordered states when ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}1.8$, for rather small ${J}_{3}/{J}_{1}\ensuremath{\lesssim}0.1$. The lowest-energy two-spinon dispersions relevant to neutron scattering experiments are analyzed and compared to semiclassical magnon dispersions finding significant differences in the spiral and collinear phases between the two approaches. The results are discussed in the context of the anisotropic triangular materials: Cs${}_{2}$CuCl${}_{4}$ and Cs${}_{2}$CuBr${}_{4}$ and layered organic materials, $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}X$, and $Y$[Pd(dmit)${}_{2}$]${}_{2}$.

S-duality and the giant magnon dispersion relation

We use S-duality and planarity to propose an argument for the non-renormalization of the dispersion relation of giant magnon solutions in type IIB string theory on AdS_5 x S^5. We compute the spectrum of giant magnons for (p,q)-strings from field theory at strong coupling by using the central charge properties of electrically and magnetically charged supersymmetric states in the Coulomb branch of N=4 super Yang-Mills. We argue that the coupling dependence of the giant magnon dispersion relation conjectured in the literature using integrability assumptions is in fact the only functional dependence compatible with S-duality.

High-energy continuum of magnetic excitations in the two-dimensional quantum antiferromagnetSr2CuO2Cl2

We have measured the magnetic excitation spectrum of the model square-lattice spin-1/2 antiferromagnet $\rm Sr_2CuO_2Cl_2$ over a broad range of energy and momentum using high-resolution inelastic neutron scattering (INS). The magnon dispersion along the zone boundary was accurately measured to be a 43 meV between (1/2,0) and (3/4,1/4) indicating the importance of coupling beyond nearest neighbors in the spin Hamiltonian. We observe a strong momentum dependent damping of the zone-boundary magnons at (1/2,0) revealing a high energy continuum of magnetic excitations. A direct comparison between our INS measurements and resonant inelastic X-ray scattering (RIXS) measurements shows that the RIXS spectrum contains significant contributions from higher energy excitations not previously considered. Our observations demonstrate that this high-energy continuum of magnetic fluctuations is a ubiquitous feature of insulating monolayer cuprates, apparent in both inelastic neutron and light scattering measurements.

Magnetic properties and magnon excitations in Fe(001) films grown on Ir(001)

We present a comprehensive study of magnetic properties and high wave-vector magnon excitations in epitaxial Fe(001) films grown on Ir(001) substrate. The magnetic properties are investigated by magneto-optical Kerr effect for various thicknesses of Fe film from 4 up to 27 monolayers. The magnon dispersion relation is obtained by means of spin-polarized electron energy loss spectroscopy. By comparing the experimental and theoretical results, we comment on the effect of the strain induced tetragonal distortion in the Fe film and the electronic hybridizations between the film and the substrate on the exchange interaction and magnon dispersion relation. The thickness-dependent measurements show that the magnon dispersion relation does not change significantly while changing the film thickness in the regime, where the film is uniformly strained. In addition, the measurements are also performed on thicker Fe films, where the films are relaxed into a bulklike structure. The magnon energies close to the zone boundary differ from the ones measured on thick Fe(110) films on W(110). However, the magnon dispersion relation measured for both systems can be well described within the Heisenberg model by using the same effective exchange parameters.

Magnon Hall effect and topology in kagome lattices: A theoretical investigation

Ferromagnetic insulators with Dzyaloshinskii-Moriya interaction show the magnon Hall effect, i.e., a transverse heat current upon application of a temperature gradient. In this theoretical investigation we establish a close connection of the magnon Hall effect in two-dimensional kagome lattices with the topology of their magnon dispersion relation. From the topological phase diagram we predict systems which show a change of sign in the heat current in dependence on temperature. Furthermore, we derive the high-temperature limit of the thermal Hall conductivity; this quantity provides a figure of merit for the maximum strength of the magnon Hall effect. Eventually, we compare the temperature and field dependence of the magnon Hall conductivity of the three-dimensional pyrochlore ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ with experimental results.