What Are Phonons, Magnons, and Their Applications to Spin Wave Theory?
The wonderful world of atomic physics is a landscape filled with amazing properties and complex dynamics that is a challenge for even the most experienced physicist. One has so many factors to consider in the interactions between objects in the molecular world that is a daunting prospect to gleam anything meaningful. So to aid us in this understanding, let’s take a look at the interesting properties of phonons and magnons and their relationship to spin waves. Oh yes, it’s getting real here, people.
Phonons and Magnons
Phonons are quasiparticles arising from a group behavior in which the vibrations act as if they were a particle moving through our system, transferring energy as they roll on. It’s a collective behavior with the shorter frequency range giving thermal conductive properties and the longer range resulting in noises (which is where the name comes from, for ‘phonos’ is a Greek word for voice). This vibrational transference is especially relevant in crystals where I have a regular structure that allows for a uniform phonon to develop. Otherwise, our phonon wavelengths become chaotic and difficult to map out. Magnons on the other hand are quasiparticles which arise from changes in the electron spin directions, impacting the magnetic properties of the material (and hence the magnet-like prefix to the word). If viewed from above, I would see the periodic rotation of the spin as it is altered, creating a wavelike effect (Kim, Candler, University).
Spin Wave Theory
To describe the behavior of magnons and phonons collectively, scientists developed the spin wave theory. With this, phonons and magnons should have harmonic frequencies that dampen out over time, becoming harmonic. This implies that the two do not impact each other, for if they did then we would lack the behavior of approaching our harmonic behavior, hence why we refer to this as the linear spin wave theory. If the two impact each other, then interesting dynamics would crop up. This would be the coupled spin wave theory, and it would be even more complex to handle. For one, given the right frequency the interactions of phonons and magnons would allow a phonon-to-magnon conversion as its wavelengths decreased (Kim).
Finding the Boundary
It is important to see how these vibrations impact molecules, especially crystals where their influence is most prolific. This is because of the regular structure of the material acting like a huge resonator. And sure enough, both phonons and magnons can impact each other and give rise to complex patterns just as the coupled theory predicted. To figure this out, scientists from IBS looked at (Y,Lu)MnO3 crystals to look at both atomic and molecular movement as a result of inelastic neutrons scattering. Essentially, they took neutral particles and had them impact their material, recording the results. And the theory of linear spin wave was unable to account for the results seen, but a coupled model worked great. Interestingly, this behavior is only present in certain materials with “a particular triangular atomic architecture.” Other materials do follow the linear model, but as far as the transition between the two remains to be seen in the hopes of generating the behavior on command (Ibid).
One area where spin waves may have a potential impact is with logic gates, a cornerstone of modern electronics. Like the name implies, they act like the logical operators used in math and provide a crucial step in determining pathways of information. But as one scales down electronics, the normal components we use get harder and harder to scale down. Enter research done by the German Research Foundation along with InSpin and IMEC, which has developed a spin-wave version of one type of logic gate known as a majority gate out of Yttrium-Iron-Garnet. It exploits magnon properties instead of current, with vibrations being used to change the value of the input going to the logic gate as interference between waves occurs. Based on the amplitude and phase of the interacting waves, the logic gate spits out one of its binary values in a predetermined wave. Ironically, this gate may perform better because of the propagation of the wave being faster than a traditional current, plus the ability to reduce noise could improve the performance of the gate (Majors).
However, not all potential uses of magnons have gone well. Traditionally, magnetic oxides provide a large amount of noise in magnons traveling through them which has limited their use. This is unfortunate because the benefits of using these materials in circuits include lower temperatures (because waves and not electrons are being processed), low loss of energy (similar reasoning), and can be transmitted further because of that. The noise is generated when the magnon transfers, for sometimes residual waves interfere. But researchers from the Spin Electronics Group of Toyohashi University in Technology found that by adding a thin layer of gold onto yttrium-iron-garnet reduces this noise depending on its placement near the transference point and the length of the thin gold layer. It allows for a smoothing-out effect that allows the transfer to blend in well enough as to prevent interference from occurring (Ito).
Hopefully our presentation on magnons has made it clear that spin is a way to carry information about a system. Attempts to exploit this for processing needs brings up the field of spintronics, and magnons are at the forefront of being the means to carry information via the spin state, allowing for more state to be carried through than just a simple electron could. We have demonstrated the logical aspects of magnons so this shouldn’t be a huge leap. Another such developmental step has come in the development of a magnon spin valve structure, which either allows a magnon to travel unimpeded or diminished “depending on the magnetic configuration of the spin valve.” This was demonstrated by a team from Johannes Gutenberg University Mainz and the University of Konstanz in Germany as well as the Tohoku University in Sendai, Japan. Together, they constructed a valve out of YIG/CoO/Co layered material. When microwaves were sent to the YIG layer, magnetic fields were created that send a magnon spin current to the CoO layer, and finally the Co provided the conversion from spin current to electrical current via an inverse spin Hall Effect. Yep. Isn’t physics just freakin’ awesome? (Giegerich)
An interesting physics concept I rarely hear talked about is a directional preference to photon movement inside a crystal. With the arrangement of the molecules inside the material come under an external magnetic field, a Faraday Effect takes hold which polarizes light going through the crystal, resulting in a rotating, circular motion for the direction of my polarization. Photons moving to the left will be affected differently than those to the right. Turns out, we can also apply circular birefringence to magnons, which are definitely susceptible to magnetic field manipulation. If we have ourselves an antiferromagnetic material (where magnetic spin directions alternate) with the right crystal symmetry, we can get nonreciprocal magnons which will also follow the directional preferences seen in photonic circular birefringence (Sato).
Heat transference seems basic enough on a macroscopic level but what about on the nanoscopic? Not everything is in physical contact with another to allow conduction to occur, nor is there always a viable way for our radiation to make contact, yet we still see heat transference occurring at this level. Work by MIT, the University of Oklahoma, and Rutgers University shows that a surprising element is at play here: phonon tunneling at a subnanometer size. Some of you may be wondering how this is possible because phonons are a collective behavior inside a material. As it turns out, electromagnetic fields at this scale allow our phonons to tunnel across the short span to our other material, allowing the phonon to continue on (Chu).
Phonons and Vibrating Heat Away
Could this nanoscale cooling yield interesting thermal properties? Depends on the composition of the material in which the phonons are traveling through. We need some regularity like in a crystal, we need certain atomic properties, and external fields to be conducive to the phonon’s existence. The location of the phonon in our structure will also be important, for interior phonons will be impacted differently than exterior ones. A team from the Institute of Nuclear Physics of the Polish Academy of Sciences, the Karlsruhe Institute of Technology, and the European Synchrotron in Grenoble looked at vibrating EuSi2 and examined the crystal structure. This looks like 12 silicon trapping the europium atom. When separate pieces of the crystal were put in contact while vibrating in a silicon sheet, the exterior portions vibrated differently than their interior ones mainly as a consequence of tetrahedronal symmetry impacting the direction of the phonons. This offered interesting ways to dissipate heat in some unconventional means (Piekarz).
We can alter the path of our phonons based on that result. Could we take it a step further and create a phonon source of desired properties? Enter the phonon laser, created using optical resonators whose photon frequency difference matches that of the physical frequency as it vibrates, according to work by Lan Yang (School of Engineering & Applied Science). This creates a resonance which permeates as a packet of phonons. How this relation can be further used for scientific purposes remains to be seen (Jefferson).
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© 2020 Leonard Kelley