Split-ring resonators (SRR) are metamaterials whose geometry (shaped like the letter 'C') induces a magnetic response from incident EM radiation.
At mm scale, these resonators show a magnetic response at GHz frequency.
When shrunk to nm scale, the SRRs that I've seen have their resonant frequencies increased to THz (1000s nm). This is because the frequency is defined by w~1/sqrt(LC), and the inductance L decreases as the SRR gets smaller.
I'm trying to think of some way to have a nanoscale SRR that operates at GHz frequency.
Is there something fundamental that would make this impossible?
What would happen if a conductive ferromagnetic material, say Fe, was nanofabricated into a SRR shape? Would it have a resonant magnetic response at GHz frequency?
Ferromagnetic resonance is a fundamental material property, and doesn't depend on the geometrical structure. A uniform thin film of Fe will also lead to FMR under the right experimental conditions.
You can increase both L and C of your SRRs to reduce its self resonance frequency by considering a dual SRR structure, such that there is a another smaller concentric "c" within the larger one, in the same plane. This will add "turns" to the planar resonator increasing its L, and there will be a self-capacitance between the two arms that increases C. With a more complicated fabrication method, you can add a dielectric on top of your SRR and carefully align and pattern another "c" SRR on top, probably rotated 180° so that the gaps don't line up. You can add as many such layers as you want. This creates a structure similar to a solenoidal coil and increases both L and C. You can use a high-K dielectric as the spacer to increase C even more.
Thanks for the thoughtful comment.
I wonder if FMR and the SRR resonances are different fundamentally though. FMR is a resonance of the precession of the spins of the electrons. Is the SRR resonance an electron current resonance? The magnetic nature of the resonance comes from the geometry of the current path right, not the dynamics of the electron spin?
If the two types of resonance are different, I wonder how they would interact with each other.
The split ring resonance is basically a half-wave resonance. When a wire is a half-wavelength long it will resonate. The resonance can be thought of in two ways, both of which are helpful sometimes. Either resonance of a signal bouncing between the ends of the wire at close to the speed of light, or a resonance of the inductance of the middle part of the wire resonating with the capacitance of the ends. If the wire is bent into a C shape the inductance of the middle part increases and the capacitance of the ends increases. Adding a tandem C can increase both of these. However, for a nanoscale wire (perhaps 300 nm long), the basic resonance scales to be at the frequency of orange light (600 nm) and the product of the inductance and capacitance will need to increase by a factor of a million to get resonance at 0.6 mm, which is 500 GHz.
Ferromagnetic resonance is to do with electrons spinning and their angular momentum, and not to do with the shape of the conductors, or the capacitance or inductance of parts of the structure. You get of lot of bang-for-your-buck with electrons, by which I mean that the resonance is at a much lower frequency than you would expect if you scaled an electrical circuits to the size of an atom (roughly the size of an electron).
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