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| '''Magnonics''' is an emerging field of modern [[magnetism]], which can be considered a sub-field of modern [[solid state physics]].<ref>Kruglyak V.V, Demokritov S.O, Grundler D Magnonics J. Phys. D Appl. Phys. 43 264001 (2010), {{doi|10.1088/0022-3727/43/26/264001}}</ref> 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 (physics)|spin]] moments of the electron, most often it is this spin moment that contributes to the net magnetic moment. | | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
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| 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.
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
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| 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' [[bandgap]]s 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.
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| ==Theory== | | '''MathML''' |
| Spin waves can propagate in magnetic media with magnetic ordering such [[ferromagnet]]s and [[antiferromagnet]]s. 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.
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| Spin waves themselves have [[group velocity|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|'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.
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| The LL equation was introduced in 1935 by Landau and Lifshitz to model the precessional motion of [[magnetization]] <math>\mathbf{M}</math> in a solid with an effective magnetic field <math>\mathbf{H}_\mathrm{eff}</math> and with damping.<ref>{{citation|authorlink1=Lev Landau|authorlink2=Evgeny Lifshitz|first=L.D. |last=Landau|first2= E.M.|last2= Lifshitz|title= Theory of the dispersion of magnetic permeability in ferromagnetic bodies|journal= Phys. Z. Sowietunion|volume= 8, 153 |year=1935}}</ref> Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,
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| :<math>\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 </math> | | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
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| The constant <math>\alpha</math> is the Gilbert phenomenological damping parameter and depends on the solid, and <math>\gamma</math> is the electron [[gyromagnetic ratio]]. Here <math>\textbf m={\textbf M}/{\mathrm M_S}\,.</math>
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| 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 [[micromagnetics|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.
| | ==Demos== |
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| ==Experiment==
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
| 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 [[polarization (waves)|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.
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| Modern [[ultrafast laser]]s allow femtosecond (fs) temporal resolution for time-domain techniques, such tools are now standard in laboratory environments. Based on the [[MOKE|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]].<ref>B. Lenk, H. Ulrichs, F. Garbs, M. Münzenberg, The building blocks of magnonics, Physics Reports 507, 107-136 (2011), {{doi|10.1016/j.physrep.2011.06.003}}or arXiv:cond-mat/1101.0479v2</ref><ref>{{cite journal|last=Nikitov|first=Sergey|coauthors=Tailhades, Tsai|title=Spin waves in periodic magnetic structures—magnonic crystals|journal=Journal of Magnetism and Magnetic Materials|date=3|year=2001|month=November|volume=236|issue=3|pages=320–330|doi=10.1016/S0304-8853(01)00470-X|bibcode = 2001JMMM..236..320N }}</ref>
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| ==References==
| | * accessibility: |
| {{Reflist}}
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
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| [[Category:Magnetic ordering]] | | ==Test pages == |
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| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
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| | *[[Styling]] |
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| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
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| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | *[[Url2Image|Url2Image (private Wikis only)]] |
| | ==Bug reporting== |
| | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.
If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]
- Only registered users will be able to execute this rendering mode.
- Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.
Registered users will be able to choose between the following three rendering modes:
MathML
Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.
Demos
Here are some demos:
- accessibility:
- Safari + VoiceOver: video only, File:Voiceover-mathml-example-1.wav, File:Voiceover-mathml-example-2.wav, File:Voiceover-mathml-example-3.wav, File:Voiceover-mathml-example-4.wav, File:Voiceover-mathml-example-5.wav, File:Voiceover-mathml-example-6.wav, File:Voiceover-mathml-example-7.wav
- Internet Explorer + MathPlayer (audio)
- Internet Explorer + MathPlayer (synchronized highlighting)
- Internet Explorer + MathPlayer (braille)
- NVDA+MathPlayer: File:Nvda-mathml-example-1.wav, File:Nvda-mathml-example-2.wav, File:Nvda-mathml-example-3.wav, File:Nvda-mathml-example-4.wav, File:Nvda-mathml-example-5.wav, File:Nvda-mathml-example-6.wav, File:Nvda-mathml-example-7.wav.
- Orca: There is ongoing work, but no support at all at the moment File:Orca-mathml-example-1.wav, File:Orca-mathml-example-2.wav, File:Orca-mathml-example-3.wav, File:Orca-mathml-example-4.wav, File:Orca-mathml-example-5.wav, File:Orca-mathml-example-6.wav, File:Orca-mathml-example-7.wav.
- From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
Test pages
To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:
Bug reporting
If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .
