Magnonics
Encyclopedia
Magnonics is an emerging field of modern magnetism
, which can be considered a sub-field of modern solid state physics. 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 moment
s. 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.
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. 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.
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.
Spin waves can propagate in magnetic media with magnetic ordering such 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 by to model the precessional motion of magnetization
in a solid with an effective magnetic field 
and with damping. Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,
The constant
is the Gilbert phenomenological damping parameter and depends on the solid, and 
is the electron gyromagnetic ratio. Here 
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. Prior to the start of the simulation, magnetic parameters of the sample and the initial groundstate magnetisation and bias field details are stated.
Experimentally, there are many techniques that exist to study magnetic phenomena, each with its own limitations and advantages. 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. Based on the magneto-optical 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 .
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
, which can be considered a sub-field of modern solid state physics. 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
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
of magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
s. Magnetic moments arise from the orbital and spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
moments of the electron, most often it is this spin moment that contributes to the net magnetic moment.
Following the success of the modern hard disk
Hard disk
A hard disk drive is a non-volatile, random access digital magnetic data storage device. It features rotating rigid platters on a motor-driven spindle within a protective enclosure. Data is magnetically read from and written to the platter by read/write heads that float on a film of air above the...
, there is much current interest in future magnetic data storage
Data storage
Data storage can refer to:* Computer data storage; memory, components, devices and media that retain digital computer data used for computing for some interval of time....
and using spin waves for things such as 'magnonic' logic and data storage. Similarly, spintronics
Spintronics
Spintronics , also known as magnetoelectronics, is an emerging technology that exploits both the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices.An additional effect occurs when a spin-polarized current is...
looks to utilize the inherent 'spin' degree of freedom to complement the already successful charge property of the electron used in contemporary electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
. 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.
A magnonic crystal is a magnetic metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
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
Relative permeability
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...
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.
Spin waves can propagate in magnetic media with magnetic ordering such 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
Group velocity
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....
on the order of a few km per second. The damping
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
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
A magnon is a collective excitation of the electrons' spin structure in a crystal lattice. In contrast, a phonon is a collective excitation of the crystal lattice atoms or ions. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. As a...
-magnon scattering
Scattering
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 localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
, magnon-phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
scattering and losses due to eddy currents. The Landau-Lifshitz-Gilbert equation is the 'equation of motion'
Equation of motion
Equations of motion are equations that describe the behavior of a system in terms of its motion as a function of time...
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 by to model the precessional motion of magnetization
Magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
in a solid with an effective magnetic field and with damping. Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,The constant
is the Gilbert phenomenological damping parameter and depends on the solid, and is the electron gyromagnetic ratio. Here 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. Prior to the start of the simulation, magnetic parameters of the sample and the initial groundstate magnetisation and bias field details are stated.
Experimentally, there are many techniques that exist to study magnetic phenomena, each with its own limitations and advantages. The experimental techniques can be distinguished by being time-domain (optical and field pumped TR-MOKE), field-domain (Ferromagnetic resonance
Ferromagnetic resonance
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)) 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. Based on the magneto-optical Kerr effect
Moke
Moke may refer to:* Moke - archaic British, Australian, and United States slang meaning Donkey* Mini Moke - a utility vehicle produced by the British Motor Corporation * Moke - a British rock band...
, 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 .