# Magnonics

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Magnonics is an emerging field of modern magnetism, which can be considered a sub-field of modern solid state physics. [1] Magnonics combines waves and magnetism, its main aim is to investigate the behaviour of spin waves in nano-structure elements. In essence, spin waves are a propagating re-ordering of the magnetisation in a material and arise from the precession of magnetic moments. Magnetic moments arise from the orbital and spin moments of the electron, most often it is this spin moment that contributes to the net magnetic moment.

Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the most common ones are iron, nickel and cobalt and their alloys such as steel. The prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4.

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

The magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects.

## Contents

Following the success of the modern hard disk, there is much current interest in future magnetic data storage and using spin waves for things such as 'magnonic' logic and data storage. [2] Similarly, spintronics looks to utilize the inherent 'spin' degree of freedom to complement the already successful charge property of the electron used in contemporary electronics. Modern magnetism is concerned with furthering the understanding of the behaviour of the magnetisation on very small (sub-micrometre) length scales and very fast (sub-nanosecond) timescales and how this can be applied to improving existing or generating new technologies and computing concepts.

Computer data storage, often called storage or memory, is a technology consisting of computer components and recording media that are used to retain digital data. It is a core function and fundamental component of computers.

Spintronics, also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices. The field of spintronics concerns spin-charge coupling in metallic systems; the analogous effects in insulators fall into the field of multiferroics.

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. The identification of the electron in 1897, along with the invention of the vacuum tube, which could amplify and rectify small electrical signals, inaugurated the field of electronics and the electron age.

A magnonic crystal is a magnetic metamaterial with alternating magnetic properties. Like conventional metamaterials, their properties arise from geometrical structuring, rather than their bandstructure or composition directly. Small spatial inhomogeneities create an effective macroscopic behaviour, leading to properties not readily found in nature. By alternating parameters such as the relative permeability or saturation magnetisation, there exists the possibility to tailor 'magnonic' bandgaps in the material. By tuning the size of this bandgap, only spin wave modes able to cross the bandgap would be able to propagate through the media, leading to selective propagation of certain spin wave frequencies.

A metamaterial is a material engineered to have a property that is not found in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals or plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

In multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio of the effective permeability of that phase to the absolute permeability. It can be viewed as an adaptation of Darcy's law to multiphase flow.

## Theory

Spin waves can propagate in magnetic media with magnetic ordering such as ferromagnets and antiferromagnets. The frequencies of the precession of the magnetisation depend on the material and its magnetic parameters, in general precession frequencies are in the microwave from 1–100 GHz, exchange resonances in particular materials can even see frequencies up to several THz. This higher precession frequency opens new possibilities for analogue and digital signal processing.

Spin waves themselves have group velocities on the order of a few km per second. The damping of spin waves in a magnetic material also causes the amplitude of the spin wave to decay with distance, meaning the distance freely propagating spin waves can travel is usually only several 10's of μm. The damping of the dynamical magnetisation is accounted for phenomenologically by the Gilbert damping constant in the Landau-Lifshitz-Gilbert equation (LLG equation), the energy loss mechanism itself is not completely understood, but is known to arise microscopically from magnon-magnon scattering, magnon-phonon scattering and losses due to eddy currents. The Landau-Lifshitz-Gilbert equation is the 'equation of motion' for the magnetisation. All of the properties of the magnetic systems such as the applied bias field, the sample's exchange, anisotropy and dipolar fields are described in terms of an 'effective' magnetic field that enters the Landau–Lifshitz–Gilbert equation. The study of damping in magnetic systems is an ongoing modern research topic. The LL equation was introduced in 1935 by Landau and Lifshitz to model the precessional motion of magnetization ${\displaystyle \mathbf {M} }$ in a solid with an effective magnetic field ${\displaystyle \mathbf {H} _{\mathrm {eff} }}$ and with damping. [3] Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.

A magnon is a quasiparticle, a collective excitation of the electrons' spin structure in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, indicating they obey boson behavior.

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more paths due to localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections.

${\displaystyle {\frac {\partial {\textbf {m}}}{\partial t}}\,=\,-\gamma \,{\textbf {m}}\times {\textbf {H}}_{\mathrm {eff} }\,+\,\alpha \,{\textbf {m}}\times {\frac {\partial {\textbf {m}}}{\partial t}}\,.\qquad }$

The constant ${\displaystyle \alpha }$ is the Gilbert phenomenological damping parameter and depends on the solid, and ${\displaystyle \gamma }$ is the electron gyromagnetic ratio. Here ${\displaystyle {\textbf {m}}={\textbf {M}}/{\mathrm {M} _{S}}\,.}$

In physics, the gyromagnetic ratio of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma. Its SI unit is the radian per second per tesla (rad⋅s−1⋅T−1) or, equivalently, the coulomb per kilogram (C⋅kg−1).

Research in magnetism, like the rest of modern science, is conducted with a symbiosis of theoretical and experimental approaches. Both approaches go hand-in-hand, experiments test the predictions of theory and theory provides explanations and predictions of new experiments. The theoretical side focuses on numerical modelling and simulations, so called micromagnetic modelling. Programs such as OOMMF or NMAG are micromagnetic solvers that numerically solve the LLG equation with appropriate boundary conditions. [4] Prior to the start of the simulation, magnetic parameters of the sample and the initial groundstate magnetisation and bias field details are stated. [5]

## Experiment

Experimentally, there are many techniques that exist to study magnetic phenomena, each with its own limitations and advantages.[ citation needed ] The experimental techniques can be distinguished by being time-domain (optical and field pumped TR-MOKE), field-domain (ferromagnetic resonance (FMR)) and frequency-domain techniques (Brillouin light scattering (BLS), vector network analyser - ferromagnetic resonance (VNA-FMR)). Time-domain techniques allow the temporal evolution of the magnetisation to be traced indirectly by recording the polarisation response of the sample. The magnetisation can be inferred by the so-called 'Kerr' rotation. Field-domain techniques such as FMR tickle the magnetisation with a CW microwave field. By measuring the absorption of the microwave radiation through the sample, as an external magnetic field is swept provides information about magnetic resonances in the sample. Importantly, the frequency at which the magnetisation precesses depends on the strength of the applied magnetic field. As the external field strength is increased, so does the precession frequency. Frequency-domain techniques such as VNA-FMR, examine the magnetic response due to excitation by an RF current, the frequency of the current is swept through the GHz range and the amplitude of either the transmitted or reflected current can be measured.

Modern ultrafast lasers allow femtosecond (fs) temporal resolution for time-domain techniques, such tools are now standard in laboratory environments.[ citation needed ] Based on the magneto-optic Kerr effect, TR-MOKE is a pump-probe technique where a pulsed laser source illuminates the sample with two separate laser beams. The 'pump' beam is designed to excite or perturb the sample from equilibrium, it is very intense designed to create highly non-equilibrium conditions within the sample material, exciting the electron, and thereby subsequently the phonon and the spin system. Spin-wave states at high energy are excited and subsequently populate the lower lying states during their relaxation path's. A much weaker beam called a 'probe' beam is spatially overlapped with the pump beam on the magnonic material's surface. The probe beam is passed along a delay line, which is a mechanical way of increasing the probe path length. By increasing the probe path length, it becomes delayed with respect to the pump beam and arrives at a later time on the sample surface. Time-resolution is built in the experiment by changing the delay distance. As the delay line position is stepped, the reflected beam properties are measured. The measured Kerr rotation is proportional to the dynamic magnetisation as the spin-waves propagate in the media. The temporal resolution is limited by the temporal width of the laser pulse only. This allows to connect ultrafast optics with a local spin-wave excitation and contact free detection in magnonic metamaterials, photomagnonics. [6] [7]

## Related Research Articles

Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than μ0, the permeability of vacuum. In most materials diamagnetism is a weak effect which can only be detected by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it repels a magnetic field entirely from its interior.

In physics, Landau damping, named after its discoverer, the eminent Soviet physicist Lev Davidovich Landau (1908–68), is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomenon was occurring in galactic dynamics, where the gas of electrons interacting by electrostatic forces is replaced by a "gas of stars" interacting by gravitation forces. Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation. It was proved to exist experimentally by Malmberg and Wharton in 1964, almost two decades after its prediction by Landau in 1946.

In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is of the order of a picosecond or less. Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. They are commonly referred to as ultrafast events. Amplification of ultrashort pulses almost always requires the technique of chirped pulse amplification, in order to avoid damage to the gain medium of the amplifier.

Magnetostatics is the study of magnetic fields in systems where the currents are steady. It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory. Magnetostatic focussing can be achieved either by a permanent magnet or by passing current through a coil of wire whose axis coincides with the beam axis.

The Classical Heisenberg model is the case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.

Spin waves are propagating disturbances in the ordering of magnetic materials. These low-lyingcollective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice. As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization. The energies of spin waves are typically only μeV in keeping with typical Curie points at room temperature and below. The discussion of spin waves in antiferromagnets is beyond the scope of this article.

In physics, Larmor precession is the precession of the magnetic moment of an object about an external magnetic field. Objects with a magnetic moment also have angular momentum and effective internal electric current proportional to their angular momentum; these include electrons, protons, other fermions, many atomic and nuclear systems, as well as classical macroscopic systems. The external magnetic field exerts a torque on the magnetic moment,

Ferromagnetic resonance, or FMR, is a spectroscopic technique to probe the magnetization of ferromagnetic materials. It is a standard tool for probing spin waves and spin dynamics. FMR is very broadly similar to electron paramagnetic resonance (EPR), and also somewhat similar to nuclear magnetic resonance (NMR), except that FMR probes the sample magnetization resulting from the magnetic moments of dipolar-coupled but unpaired electrons, while NMR probes the magnetic moment of atomic nuclei that are screened by the atomic or molecular orbitals surrounding such nuclei of non-zero nuclear spin.

Micromagnetics is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored, yet small enough to resolve magnetic structures such as domain walls or vortices.

Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970s, and developed in collaboration with John Hayter. In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.

In physics, the Landau–Lifshitz–Gilbert equation, named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the precessional motion of magnetization M in a solid. It is a modification by Gilbert of the original equation of Landau and Lifshitz.

In physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a name used for several different differential equations

In physics, magnetization dynamics is the branch of solid-state physics that describes the evolution of the magnetization of a material.

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong static magnetic field are perturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics, crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI).

In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. A material where such a coupling is intrinsically present is called a magnetoelectric.

Single domain, in magnetism, refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle. Such particles are very small. They are also very important in a lot of applications because they have a high coercivity. They are the main source of hardness in hard magnets, the carriers of magnetic storage in tape drives, and the best recorders of the ancient Earth's magnetic field.

Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational acceleration and any other accelerations.

Neutrons are spin 1/2 particles that interact with magnetic induction fields via the Zeeman interaction. This interaction is both rather large and simple to describe. Several neutron scattering techniques have been developed to use thermal neutrons to characterize magnetic micro and nanostructures.

## References

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