Magnonic Band Research Articles

Control of magnonic spectra in cobalt nanohole arrays: the effects of density, symmetry and defects

Magnetic nanohole arrays are important systems for propagation of magnetic excitations and are among the potential candidates for magnonic crystals. A thorough investigation of magnonic band structures and the effect of the geometry of the array on them are important. Here, we present a systematic micromagnetic simulation study of magnonic modes in cobalt nanohole (antidot) arrays. In particular, we investigate the effects of the areal density and symmetry of the array and defects introduced in the array. The magnonic modes are strongly dependent on the density and the symmetry of the array but are weakly dependent on the defects. We have further investigated the modes in a tailored array consisting of equally wide hexagonal arrays with varying density. The magnonic spectrum of the tailored array contains additional modes above the modes of the constituent arrays due to the appearance of irregular domain structures at the regions joining arrays of two different types. This opens up the possibility of tuning the magnonic bands in magnetic nanohole arrays by careful design of the structure of the array.

Spectrum and reflection of spin waves in magnonic crystals with different interface profiles

Using the transfer-matrix method, we have developed a theory of exchange spin waves in a thin cylindrical magnonic crystal (periodically layered all-ferromagnetic nanowire) with diffuse interfaces. The magnonic spectrum and the frequency dependence of the reflection coefficient of spin waves from a junction between a homogeneous magnetic nanowire and a magnonic crystal have been calculated and compared. Diffuse interfaces with linear and sinusoidal profiles of variation in the uniaxial anisotropy value have been considered, also allowing for asymmetry in the relative thicknesses of either main layers, or interfaces, or both. We have found that, although the thickness and profile of interfaces have a significant effect on the size and position of the magnonic band gaps, the smoothing of interfaces does not lead to disappearance of the band gaps. At the same time, the profiles and relative thicknesses of interfaces might provide additional means by which to design magnonic crystals with a desired magnonic spectrum.

Phonon and magnon scattering of antiferromagneticBi2Fe4O9

The phonon structure of antiferromagnetic ${\text{Bi}}_{2}{\text{Fe}}_{4}{\text{O}}_{9}$ (space group $Pbnm$ No. 55, ${T}_{N}\ensuremath{\approx}240\text{ }\text{K}$) was studied theoretically by calculations of lattice dynamics and experimentally between 10 and 300 K by polarized Raman spectroscopy. Most of the $12{A}_{g}+12{B}_{1g}+9{B}_{2g}+9{B}_{3g}$ Raman modes were unambiguously identified. Strong second-order scattering was observed for $ab$-plane-confined incident and scattered light polarizations. In addition to the phonon-scattering, broad Raman bands with typical characteristics of magnon scattering appear below ${T}_{N}$. The magnon bands are analyzed on the basis of magnetic structure of ${\text{Bi}}_{2}{\text{Fe}}_{4}{\text{O}}_{9}$ and attributed to two-magnon excitations.

A gigahertz-range spin-wave filter composed of width-modulated nanostrip magnonic-crystal waveguides

We found a robust magnonic-crystal waveguide structure for use as an efficient gigahertz-range spin-wave filter that passes only spin waves of chosen narrow band frequencies and filters out the other frequencies. The structure consists of the serial combinations of various width modulations with different periodicities and motifs in planar-patterned thin-film nanostrips composed of a single soft magnetic material. The observed magnonic band gaps result from both the translation symmetry of the one-dimensional width modulation and the higher-quantized width-mode spin waves excited from scattering at the periodic edge-steps of the width modulation. This work brings us one step closer to practical implementations of spin waves in information transmission and processing devices.

Microscopic spin-wave theory for yttrium-iron garnet films

Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.

Physical Origin and Generic Control of Magnonic Band Gaps of Dipole-Exchange Spin Waves in Width-Modulated Nanostrip Waveguides

We report, for the first time, on a novel planar structure of magnonic-crystal waveguides, made of a single magnetic material, in which the allowed and forbidden bands of propagating dipole-exchange spin waves can be manipulated by the periodic modulation of different widths in thin-film nanostrips. The origin of the presence of several magnonic wide band gaps and the crucial parameters for controlling those band gaps of the order of approximately 10 GHz are found by micromagnetic numerical and analytical calculations. This work can offer a route to the potential application to broadband spin wave filters in the gigahertz frequency range.

Spin-wave spectrum of a magnonic crystal with an isolated defect

Real magnonic crystals—periodic magnetic media for spin-wave (magnon) propagation—may contain some defects. We report theoretical spin-wave spectra of a one-dimensional magnonic crystal with an isolated defect. The latter is modeled by insertion of an additional layer with thickness and magnetic anisotropy values different from those of the magnonic crystal constituent layers. The defect layer leads to appearance of several localized defect modes within the magnonic band gaps. The frequency and the number of the defect modes may be controlled by varying parameters of the constituent layers of the magnonic crystal.

Interaction of an external impurity with the surface intrinsic mode in a Heisenberg chain

In this paper we have demonstrated the existence of surface intrinsic localized modes in one-dimensional classical spin systems. These modes have frequencies above the top of the magnon band and are more localized than the corresponding modes that were found in the lattice dynamics. By numerical methods we have studied the forward evolution in time. These entities are stable in time for many time steps. Also, we consider the interaction of these surface excitations with an external dipolar field. We have first considered the case in which the external dipole is parallel to the spins of the bulk. According to the distance of the impurity from the surface we find that at a particular distance a new surface mode appears, that we have called a mixed mode because it is formed by a localized state at the surface plus a plane wave. At large distances the dipole traps the surface mode, while at small distances the external impurity potential is so strong that all the spins are forced to be aligned in the $z$ direction. For the case in which the external magnetic dipole is antiparallel to the bulk spins there are no mixed modes and the external impurity is so strong that the surface modes are trapped at large distances, and the bulk modes are trapped at very short distances.

Spin wave spectrum of a magnonic crystal with an internally structured defect

We report a theoretical investigation of the spin wave spectrum of a magnonic crystal with a defect. The latter is considered as either a single or double layer with parameters (the values of the uniaxial anisotropy and/or layer thickness) different from those of the constituent layers of the magnonic crystal. It is shown that, depending upon the parameters of the defect, the spectrum may contain either one or several additional discrete (localized) modes within the magnonic band gaps, or even a mini-band of those.

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

We investigate the low-energy properties of N-leg integer-spin ladders and tubes with an antiferromagnetic (AF) intrachain coupling. In the odd-leg tubes, the AF rung coupling causes the frustration. To treat all ladders and tubes systematically, we apply S\'en\'echal's method [Phys. Rev. B 52, 15319 (1995)], based on the nonlinear sigma model. This strategy is valid in the weak interchain (rung) coupling regime. We show that all frustrated tubes possess six-fold degenerate spin-1 magnon bands, as the lowest excitations, while other ladders and tubes have a standard triply degenerate bands. We also consider effects of four kinds of Zeeman terms: uniform, staggered only along the rung, only along the chain, or both directions. The above prediction of the no-field case implies that a sufficiently strong uniform field yields a two-component Tomonaga-Luttinger liquid (TLL) due to the condensation of doubly degenerate lowest magnons in frustrated tubes. In contrast, the field induces a standard one-component TLL in all other systems. This is supported by symmetry and bosonization arguments based on the Ginzburg-Landau theory. The bosonization also suggests that the two-component TLL vanishes and a one-component TLL appears, when the uniform field becomes larger for the second lowest magnon bands to touch the zero-energy line. This transition could be observed as a cusp singularity in the magnetization process. All the analyses for the systems with a staggered Zeeman term suggest that the emergence of the doubly degenerate transverse magnons and the single longitudinal one is universal for the one-dimensional AF spin systems with weak staggered field.

Spectrum of dynamic magnetic susceptibility of a randomized f–d magnet with spin–lattice coupling. II. “Opening” of the spin excitation bands

The transformation of the magnetic absorption spectra of a narrow-band ferromagnetic conductor containing local f and quasilocal d magnetic moments under conditions of weak spin–lattice coupling and spatial randomization of the g factors of the quasilocal and local spin subsystems is investigated. It is shown that randomization of the g factors (e.g., as a result of the introduction of an impurity) leads mainly to the “opening” (i.e., to the appearance in the magnetic absorption spectrum) of acoustic and optical magnon bands formed in the system while not affecting the position and shape of the narrow magnetic resonance lines comprising the spectrum of the impurity-free crystal. The effects of spin–lattice coupling, besides the “opening” of the phonon and magnon bands, lead to a shift and a temperature smearing of the narrow resonance lines. The relative corrections to the effective magnon masses generated by the spin–lattice coupling in a 4f–5d metal amount to ∼2×10−4 for an acoustic mode and to ∼4×10−4 for an optical mode.

Spin excitation spectrum in striped bilayer compounds

The spin dynamics of bilayer cuprate compounds are studied in a basic model. The magnetic spectral properties are calculated in linear spin-wave theory for several stripe configurations which differ by the relative location of the stripes in the layers. We focus on the bilayer splitting of the magnon bands near the incommensurate low energy peaks as well as near the $\pi$ resonance, distinguishing between the odd and even channel. We find that a x-shaped dispersion near the $\pi$ resonance is generic for stripes. By comparison of our results to neutron scattering data for $\mathrm{YBa_2Cu_3O_{6+x}}$ we conclude that the stripe model is consistent with characteristic features of bilayer high-$T_c$ compounds.

Identification of features in the powder pattern of the antiferromagnet FePS 3 using polarization analysis with energy analysis

Recent powder patterns of the antiferromagnet FePS 3 below its Néel temperature show unusual magnetic diffuse intensity in the Q range 0.5–0.8 Å −1. This was initially thought to be a group of unresolved magnetic Bragg peaks. However subsequent powder patterns taken with longer wavelengths and better resolution have failed to resolve the peaks except to confirm the existence of a Bragg peak at Q=0.61 Å −1. In particular the powder pattern taken with λ=5 Å neutrons shows a marked diminution of the rest of the diffuse intensity with respect to this Bragg peak. To test whether the diffuse intensity is due to magnon scattering, the low Q region of the scattering from the powder sample of FePS 3 was measured on LONGPOL at 100 K with both polarization and energy analysis. The diffuse intensity was confirmed as magnetic but energy analysis showed that it is at least overwhelmingly elastic with no suggestion of scattering with an energy gain of 13 meV, the energy expected for the magnon band gap in this highly anisotropic antiferromagnet.

Magneto-transport in asymmetric serial loop structures

In the frame of the long-wavelength Heisenberg model, the magnonic band structures and transmission spectra of asymmetric serial loop structures (ASLS), made of asymmetric loops pasted together with segments of finite length, are examined theoretically. These monomode structures, composed of one-dimensional ferromagnetic materials, may exhibit large stop bands where the propagation of spin waves is forbidden. The width of these band gaps depends on the geometrical parameters of the structure and may be drastically increased in a tandem geometry made of several successive ASLS which differ by their geometrical characteristics. These ASLS's may have potential applications in spin-injection devices.

Coupled Solitons in Alternating Heisenberg FerromagneticChains with a Small Magnon Band Gap

The coupled soliton excitations in an alternating Heisenbergferromagnetic chain with a small magnon band gap are considered. Based ona quasi-discrete multiple scale approach, a set of coupled mode equationsis derived which describes the dynamics of strongly coupled acoustic uppercut-off and optical lower cut-off modes. Coupled magnetic band gapsoliton solutions are explicitly provided and their frequency propertiesare discussed.

Giant magnonic band gaps and defect modes in serial stub structures: application to the tunneling between two wires

In the frame of the long-wavelength Heisenberg model, we investigate the existence of giant gaps in the band structure of a comblike geometry composed of a one-dimensional magnonic waveguide along which N ′ dangling side branches are grafted at N equidistant sites. These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted branches (which play the role of resonators). The width of these gaps is sensitive to the length of the side branches as well as to the numbers N and N ′. The presence of defect branches in the comblike structure can give rise to localized states inside the gaps. These states may have useful applications in the band structure engineering of nanostructure materials. In the second part of this work, we consider the tunneling between two monomode quantum wires through a coupling device. We give the conditions for selective transfer of a single propagating magnon from one wire to the other, leaving all the neighbor states unaffected. The magnon channel drop tunneling in this system is due to one localized state situated within a gap of the coupling device.

Optical evidence for compatibility of antiferromagnetism and superconductivity in YBa2Cu3O6+x

The evolution of the spectral composition of the absorption in the 1.25–2.6 eV region for metallic films of YBa2Cu3O6+x with superconducting transition temperatures of Tc=51 and 74 K is measured as the films are cooled from 180 to 20 K. Particular attention is paid to the temperature effects in two absorption bands: the A band (≃1.8 eV), which reflects the appearance of holes dressed in antiferromagnetic (AFM) fluctuations, and the (A+J) band (≃2.15 eV), which reflects an additional (magnon) excitation of the short-range AFM order. It is found that the changes of these bands begin in the normal phase at T<T* in the temperature region corresponding to the opening of the pseudogap state, and the (A+J) magnon band arises in the pseudogap state even in the case when it is absent at room temperatures. At the superconducting transition the parameters of the bands stop changing, and the (A+J) magnon band is preserved in the superconducting state. The results are interpreted as evidence of a magnetic nature of the pseudogap state and for the compatibility of AFM short-range order with superconductivity.

Large magnonic band gaps and defect modes in one-dimensional comblike structures

We report the existence of large gaps in the band structure of a comblike structure composed of a one-dimensional magnonic waveguide along which ${N}^{\ensuremath{'}}$ dangling side branches are grafted at N equidistant sites. These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted branches (which play the role of resonators). The width of these gaps is sensitive to the length of the side branches as well as to the numbers N and ${N}^{\ensuremath{'}}.$ The presence of defect branches in the comblike structure can give rise to localized states inside the gaps. We show that these states are very sensitive to the length of the side branches, to the periodicity, to N or/and ${N}^{\ensuremath{'}}$ and to the length of the defect branches. Analytic expressions are given for the band structure of combs for large N and for the transmission coefficient for an arbitrary value of N and ${N}^{\ensuremath{'}}$ with and without defects.

Internal oscillations of kink-type solitons in one-dimensional antiferromagnets like TMMC

The problem of internal oscillations of kink-type solitons in a one-dimensional easy-plane antiferromagnet is studied by analytical methods. Apart from the Goldstone mode a second local mode which is due to the coupling between in-plane and out-of-plane spin components has been derived. For typical experimental conditions in a model system like (TMMC) the frequency of this mode is very close to the bottom of the magnon band. Considering both a twofold and a weak sixfold in-plane crystal field anisotropy we found that close to the spin-flop transition the separation of this local mode from the magnon band is increased and dramatically affected by the sixfold anisotropy. We show that quantum properties of this mode are not important.

POLARIZED ABSORPTION SPECTRA OF NICKEL ION IN MAGNETIC TRIMETHYL AMMONIUM NICKEL TRICHLORIDE DIHYDRATE (NiTAC) [(CH3)3NH]NiCl3.2H2O SINGLE CRYSTALS

The low temperature polarized absorption spectra of the Ni2+ ions in the orthorhombic [(CH3)3NH]NiCl3.2H2O NiTAC single crystal have been reported at 300 K and 15 K. The polarization spectra show the presence of a lower field (D4) which is rather small to split the levels. A moiety vibration of 370 cm−1 has been observed. No magnon or magnon-phonon side bands are observed. © 1997 Elsevier Science Ltd. All rights reserved