Spin-wave Spectrum Research Articles

Spectrum of spin waves in cold polarized gases

The spin dynamics of cold polarized gases are investigated using the Boltzmann equation. The dispersion relation for spin waves (transverse component of the magnetic moment) and the spin diffusion coefficient of the longitudinal component of the magnetic moment are calculated without using fitting parameters. The spin wave frequency and the diffusion coefficient for rubidium atoms are estimated numerically.

Angular dependences of spin-wave resonance spectra of inhomogeneous films with orthorhombic anisotropy

Zero spin-wave mode in inhomogeneous magnetic films with orthorhombic anisotropy has been found to exhibit a change of its localization region in two of three typical angular dependences of resonance fields of high-intensity modes. It has been shown that the anisotropy fields on both sides of the film can be determined from the resonance fields of the zero and uppermost high-intensity spin-wave modes of spin-wave resonance spectra.

Bias field tunable magnetic configuration and magnetization dynamics in Ni80Fe20 nano-cross structures with varying arm length

Ferromagnetic nano-cross structures promise exotic static magnetic configurations and very rich and tunable magnetization dynamics leading towards potential applications in magnetic logic and communication devices. Here, we report an experimental study of external magnetic field tunable static magnetic configurations and magnetization dynamics in Ni80Fe20 nano-cross structures with varying arm lengths (L). Broadband ferromagnetic resonance measurements showed a strong variation in the number of spin-wave (SW) modes and mode frequencies (f) with bias field magnitude (H). Simulated static magnetic configurations and SW mode profiles explain the rich variation of the SW spectra, including mode softening, mode crossover, mode splitting, and mode merging. Such variation of SW spectra is further modified by the size of the nano-cross. Remarkably, with decreasing arm length of nano-cross structures, the onion magnetization ground state becomes more stable. Calculated magnetostatic field distributions support the above observations and revealed the non-collective nature of the dynamics in closely packed nano-cross structures. The latter is useful for their possible applications in magnetic storage and memory devices.

Excitations and magnetization density distribution in the dilute ferromagnetic semiconductorYb14MnSb11

While it is mostly well-known for its excellent thermoelectric properties at high temperatures, Yb${}_{14}$MnSb${}_{11}$ has also come to be characterized as a ferromagnetic semiconductor. Such systems support ferromagnetic correlations similar to metallic compounds, although with semiconducting electronic configurations. As such, they are promising materials for use in spintronic devices. The authors here use neutron scattering techniques to examine the distribution of the magnetization density and the energy scale of the magnetic exchange interactions in the Yb${}_{14}$MnSb${}_{11}$ compound. They find that there is a large ferromagnetic moment localized to the Mn site in the crystal structure with a `Kondo cloud' of negative moments distributed over the other atomic sites. The results provide long sought answers to questions regarding the valence, magnetization distribution, and energy scales of the magnetic interactions in this compound. The ferromagnetic spin-wave spectrum supports this premise and is well characterized by inclusion of nearest and next-nearest neighbor exchange interactions.

Optical excitation of spin waves in epitaxial iron garnet films: MSSW vs BVMSW.

In most of the previous studies of the spin wave optical generation in magnetic dielectrics, the backward volume spin waves were excited. Here we modified the parameters of the circularly polarized optical pump beams emitted by femtosecond laser to reveal surface spin waves in bismuth iron garnet thin film. Beams that are larger than 10 μm in diameter generate both surface and volume spin waves with only one spectral peak near the ferromagnetic resonance. On the contrary, narrower beams excite predominantly surface spin waves of higher frequency, providing an additional peak in the spin wave spectrum. Thus different interference patterns of the magnetization dynamics are achievable. This may significantly broaden the capabilities of spin wave based devices.

Spin-Wave Transport Along In-Plane Magnetized Laterally Coupled Magnonic Stripes

Dipolar spin-wave coupling in the lateral topology of adjacent magnonic stripes is studied. Two laterally parallel dipolarly coupled yttrium–iron garnet magnonic waveguides were considered. The periodic power transfer at a distance equal to the coupling length from one stripe to the other stripe was demonstrated. By means of finite-element and micromagnetic numerical simulation, the dispersion and transmission spectra of spin waves were obtained. The coupling length is determined by variation of the static magnetization angle. The lateral magnonic stripes can be used as a functional unit in planar magnonic networks as a directional coupler, spin-wave multiplexer, and microwave power divider.

Directional Spin Wave in Spin-Torque Oscillators Induced by Interfacial Dzyaloshinskii–Moriya Interaction

Spin-torque oscillators (STOs) have tunable frequencies, low energy consumption, and high-quality factor compared to traditional oscillators. Here, we report the characteristics of nanocontact-STOs in the presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) based on micromagnetic simulations. The DMI can decrease the STO frequency by about 2 GHz. More importantly, the DMI is able to break the isotropy of the spin-wave spectrum and turn the emitted microwave into directional spin-wave beams, potentially facilitating the synchronization of multiple STOs.

Ferromagnetic resonance study of interface coupling for spin waves in narrow NiFe/Ru/NiFe multilayer nanowires

A systematic investigation is presented for the magnetization dynamics in trilayer nanowires, consisting of two permalloy (${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$) layers separated by a nonmagnetic Ru spacer layer. The width of the wires ranges from 90 to 190 nm. By varying the Ru thickness between 0.7 and 2.0 nm, the interlayer coupling can be effectively controlled, modifying the corresponding magnetic ground state and the spin-wave dynamics. By contrast with previous work on coupled trilayer nanowires with larger widths (270 nm and more), the focus here is on nanowire arrays where the strong shape anisotropy competes with the Ruderman-Kittel-Kasuya-Yosida interactions and biquadratic exchange interactions across the Ru interface, as well as dipolar interactions and Zeeman energy. As a result, the spin-wave spectrum is found to be drastically modified. Ferromagnetic resonance and hysteresis loop measurements are reported over a wide range of applied magnetic fields, showing that the overall magnetization alignment between the permalloy layers may be parallel, antiparallel, or in a spin-flop state, depending on the overall interlayer coupling. The experimental results for different stripe widths are successfully analyzed using a microscopic dipole-dipole theory and micromagnetic simulations.

Band gap formation and control in coupled periodic ferromagnetic structures

We demonstrate theoretically and experimentally the formation of additional bandgaps in the spectrum of spin waves in coupled magnonic crystals. We present the analytical model, which reveals the mechanism of bandgaps formation in coupled structures. In particular, the formation of one, two, or three bandgaps in the region of the first Bragg resonance is demonstrated and control of its characteristics by the variation of the complex coupling coefficient between magnonic crystals is shown. The spatially-resolved Brillouin light scattering spectroscopy and microwave measurements demonstrate the bandgap splitting in the spin-wave spectrum. The main advantage of proposed coupled structure, as compared to the conventional magnonic crystal, is the tunability of multiple bandgaps in the spin-wave spectrum, which enables potential applications in the frequency selective magnonic devices.

Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour

We have studied the Heisenberg antiferromagnets characterized by the magnetic structures with the periods being two times larger than the lattice period. We have considered all the types of the Bravais lattices (simple cubic, bcc and fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4 classes denoted with symbols A and B correspondingly. The order parameter characterizing the degeneracies of the magnetic structures is an ordinary Neel vector for A classes and so-called 4-complex for B classes. We have taken into account the fluctuation corrections for these states within the spin-wave and large-N expansions ($N$ is the number of spin components). Below the Neel temperature $T_{\rm{N}}$ quantum and thermal fluctuations lift the degeneracy making simple one-wave vector collinear structure preferable for all the classes. A satellite of this effect is opening of the exchange gaps at certain wave vectors in the spin wave spectrum (there is an analogous effect for the nonuniform static transverse susceptibility). However, as the temperature approaches $T_{\rm{N}}$, the exchange gaps are closing. We have calculated the critical indices $\eta$ and $\nu$ to order of $1/N$ and found that they differ for A and B classes.

Surface effects on ferromagnetic resonance in magnetic nanocubes

We study the effect of surface anisotropy on the spectrum of spin-wave excitations in a magnetic nanocluster and compute the corresponding absorbed power. For this, we develop a general numerical method based on the (undamped) Landau–Lifshitz equation, either linearized around the equilibrium state leading to an eigenvalue problem or solved using a symplectic technique. For box-shaped clusters, the numerical results are favorably compared to those of the finite-size linear spin-wave theory. Our numerical method allows us to disentangle the contributions of the core and surface spins to the spectral weight and absorbed power. In regard to the recent developments in synthesis and characterization of assemblies of well defined nano-elements, we study the effects of free boundaries and surface anisotropy on the spin-wave spectrum in iron nanocubes and give orders of magnitude of the expected spin-wave resonances. For an iron nanocube, we show that the absorbed power spectrum should exhibit a low-energy peak around 10 GHz, typical of the uniform mode, followed by other low-energy features that couple to the uniform mode but with a stronger contribution from the surface. There are also high-frequency exchange-mode peaks around 60 GHz.

Thermal Spin Dynamics of Yttrium Iron Garnet.

The magnetic insulator yttrium iron garnet can be grown with near perfection and is therefore and ideal conduit for spin currents. It is a complex material with 20 magnetic moments in the unit cell. In spite of being a ferrimagnet, YIG is almost always modeled as a simple ferromagnet with a single spin wave mode. We use the method of atomistic spin dynamics to study the temperature evolution of the full spin wave spectrum, in quantitative agreement with neutron scattering experiments. The antiferromagnetic or optical mode is found to suppress the spin Seebeck effect at room temperature and beyond due to thermally pumped spin currents with opposite polarization to the ferromagnetic mode.

Spin-wave self-modulation instability in a perpendicularly magnetized magnonic crystal

Self-modulation instability of microwave spin waves monochromatically excited in a periodic magnetic film structure, a magnonic crystal, has been observed. The phenomena occurs only at the frequencies corresponding to the band gaps of the spin-wave spectrum of the magnonic crystal. Depending on the frequency within the band gap the nonlinear waveforms have a shape of bright or dark pulses.

Low Temperature Heat Capacity of polycrystalline MnSi

The itinerant helimagnet MnSi has been investigated by heat capacity using relaxation calorimetry in H=0. The paramagnetic to helimagnetic transition temperature Tc is found to be 29.6 K. Low temperature heat capacity data in the range 2-18 K is fitted with a usual electronic and phonon contribution. However, an additional magnetic term T 3/2 needs to be added to witness the role of spin wave excitations in the magnetically ordered state below Tc. As well the energy gap on the order A=1.29 meV in the spin wave spectrum is evidenced. Small value of magnetic coefficient δ = 1.66 mJmol-1K-5/2 hints the itinerant nature of the magnetism in MnSi. Obtained coefficients gives the Debye temperature θD = 534 K and the Sommerfeld coefficient of specific heat γ = 0.0367 Jmol-1K-2. Noteworthy observation is the negative trend in the magnetic part of the entropy after Tc.

Inelastic Neutron Scattering Investigations of an Anisotropic Hybridization Gap in the Kondo Insulators: CeT<sub>2</sub>Al<sub>10</sub> (T=Fe, Ru and Os)

The recent discovery of topological Kondo insulating behaviour in strongly correlated electron systems has generated considerable interest in Kondo insulators both experimentally and theoretically. The Kondo semiconductors CeT2Al10 (T=Fe, Ru and Os) possessing a c-f hybridization gap have received considerable attention recently because of the unexpected high magnetic ordering temperature of CeRu2Al10 (TN=27 K) and CeOs2Al10 (TN=28.5 K) and the Kondo insulating behaviour observed in the valence fluctuating compound CeFe2Al10 with a paramagnetic ground state down to 50 mK. We are investigating this family of compounds, both in polycrystalline and single crystal form, using inelastic neutron scattering to understand the role of anisotropic c-f hybridization on the spin gap formation as well as on their magnetic properties. We have observed a clear sign of a spin gap in all three compounds from our polycrystalline study as well as the existence of a spin gap above the magnetic ordering temperature in T=Ru and Os. Our inelastic neutron scattering studies on single crystals of CeRu2Al10 and CeOs2Al10 revealed dispersive gapped spin wave excitations below TN. Analysis of the spin wave spectrum reveals the presence of strong anisotropic exchange, along the c-axis (or z-axis) stronger than in the ab-plane. These anisotropic exchange interactions force the magnetic moment to align along the c-axis, competing with the single ion crystal field anisotropy, which prefers moments along the a-axis. In the paramagnetic state (below 50 K) of the Kondo insulator CeFe2Al10, we have also observed dispersive gapped magnetic excitations which transform into quasi-elastic scattering on heating to 100 K. We will discuss the origin of the anisotropic hybridization gap in CeFe2Al10 based on theoretical models of heavy-fermion semiconductors.

Direct Observation of Interfacial Dzyaloshinskii-Moriya Interaction from Asymmetric Spin-wave Propagation in W/CoFeB/SiO2 Heterostructures Down to Sub-nanometer CoFeB Thickness.

Interfacial Dzyaloshinskii-Moriya interaction (IDMI) is important for its roles in stabilizing the skyrmionic lattice as well as soliton-like domain wall motion leading towards new generation spintronic devices. However, achievement and detection of IDMI is often hindered by various spurious effects. Here, we demonstrate the occurrence of IDMI originating primarily from W/CoFeB interface in technologically important W/CoFeB/SiO2 heterostructures using Brillouin light scattering technique. Due to the presence of IDMI, we observe asymmetry in the peak frequency and linewidth of the spin-wave spectra in the Damon-Eshbach (DE) geometry at finite k wave-vectors. The DMI constant is found to scale as the inverse of CoFeB thickness, over the whole studied thickness range, confirming the presence of IDMI in our system without any extrinsic effects. Importantly, the W/CoFeB interface shows no degradation down to sub-nanometer CoFeB thickness, which would be useful for devices that aim to use pronounced interface effects.

Confined spin wave spectra of Kagome artificial spin ice arrays

The spin wave modes of elongated magnetic islands arranged in Kagome artificial spin-ice arrays are micromagnetically simulated in the frequency regime between 3 and 16GHz. The edge modes are more suitable in order to detect the signatures of various types of local order of the spin-ice lattice as they are much more sensitive to the magnetic configurations of neighboring elements. The spectra of arrays consisting up to 30 elements can be decomposed to those originating from local magnetic states of their vertices.

Confined states in photonic-magnonic crystals with complex unit cell

We have investigated multifunctional periodic structures in which electromagnetic waves and spin waves can be confined in the same areas. Such simultaneous localization of both sorts of excitations can potentially enhance the interaction between electromagnetic waves and spin waves. The system we considered has a form of one dimensional photonic-magnonic crystal with two types of magnetic layers (thicker and thinner ones) separated by sections of the dielectric photonic crystals. We focused on the electromagnetic defect modes localized in the magnetic layers (areas where spin waves can be excited) and decaying in the sections of conventional (nonmagnetic) photonic crystals. We showed how the change of relative thickness of two types of the magnetic layers can influence on the spectrum of spin waves and electromagnetic defect modes, both localized in magnetic parts of the system.

Spin excitations used to probe the nature of exchange coupling in the magnetically ordered ground state ofPr0.5Ca0.5MnO3

We have used time-of-flight inelastic neutron scattering to measure the spin wave spectrum of the canonical half-doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$, in its magnetic and orbitally ordered phase. The data, which cover multiple Brillouin zones and the entire energy range of the excitations, are compared with several different models that are all consistent with the CE-type magnetic order, but arise through different exchange coupling schemes. The Goodenough model, i.e. an ordered state comprising strong nearest neighbor ferromagnetic interactions along zig-zag chains with antiferromagnetic inter-chain coupling, provides the best description of the data, provided that further neighbor interactions along the chains are included. We are able to rule out a coupling scheme involving formation of strongly bound ferromagnetic dimers, i.e. Zener polarons, on the basis of gross features of the observed spin wave spectrum. A model with weaker dimerization reproduces the observed dispersion but can be ruled out on the basis of discrepancies between the calculated and observed structure factors at certain positions in reciprocal space. Adding further neighbor interactions results in almost no dimerization, i.e. recovery of the Goodenough model. These results are consistent with theoretical analysis of the degenerate double exchange model for half-doping, and provide a recipe for how to interpret future measurements away from half-doping, where degenerate double exchange models predict more complex ground states.

Shape- and Interface-Induced Control of Spin Dynamics of Two-Dimensional Bicomponent Magnonic Crystals.

Controlled fabrication of periodically arranged embedded nanostructures with strong interelement interaction through the interface between the two different materials has great potential applications in spintronics, spin logic, and other spin-based communication devices. Here, we report the fabrication of two-dimensional bicomponent magnonic crystals in form of embedded Ni80Fe20 nanostructures in Co50Fe50 thin films by nanolithography. The spin wave (SW) spectra studied by a broadband ferromagnetic resonance spectroscopy showed a significant variation as the shape of the embedded nanostructure changes from circular to square. Significantly, in both shapes, a minimum in frequency is obtained at a negative value of bias field during the field hysteresis confirming the presence of a strong exchange coupling at the interface between the two materials, which can potentially increase the spin wave propagation velocity in such structures leading to faster gigahertz frequency magnetic communication and logic devices. The spin wave frequencies and bandgaps show bias field tunability, which is important for above device applications. Numerical simulations qualitatively reproduced the experimental results, and simulated mode profiles revealed the spatial distribution of the SW modes and internal magnetic fields responsible for this observation. Development of such controlled arrays of embedded nanostructures with improved interface can be easily applied to other forms of artificial crystals.