# Electron spin resonance in metals

In practice, ESR/EPR seems to concern only unpaired electrons in the outer layers of organic radicals or complexes. But what about the free electrons of metals? Does it also give rise to a signal? I can't find any information on the web.

Thanks

sophiecentaur
Gold Member
Off the top of my head I would say that, because there is a continuum of energy levels in the free electrons in a metal, there would be no identifiable 'lines' which could be seen to split. I read some mention of ESR in metal Ions but they would exhibit line structures.

...I am pretty sure that you would need discrete energy levels in order to be able to identify lines and the broadening due to applied fields.
It's an interesting lead, as I'm searching for an experimental protocol. I should have to "stabilize" the free electrons (I don't yet know how, but I don't need sharp lines, it's just to test a vague idea with the purpose of using it in classical electromagnetism).

sophiecentaur
Gold Member
It's an interesting lead, as I'm searching for an experimental protocol. I should have to "stabilize" the free electrons (I don't yet know how, but I don't need sharp lines, it's just to test a vague idea with the purpose of using it in classical electromagnetism).
As far as I'm aware, spin resonance is what happens to a single energy level when there is an applied magnetic field. If there is no 'single level' (i.e. vast numbers of electrons with the same level), then how can a split be detected?

marcusl
Gold Member
The relevant energy levels are the two Zeeman levels created by the magnetic field. The resonance condition is given by the energy difference between a spin aligned and anti-aligned with the field. The background behavior of the electrons can indirectly affect the resonance, mainly through coupling and its effect on relaxation time, but the resonance condition is set by the B field.

EDIT: Having said that, I imagine it would be hard to do EPR in an ordinary bulk metal due to the minuscule skin depth at micro- or millimeter-waves. You will be looking primarily at oxides and surface states.

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sophiecentaur
Gold Member
The relevant energy levels are the two Zeeman levels created by the magnetic field. The resonance condition is given by the energy difference between a spin aligned and anti-aligned with the field. The background behavior of the electrons can indirectly affect the resonance, mainly through coupling and its effect on relaxation time, but the resonance condition is set by the B field.

EDIT: Having said that, I imagine it would be hard to do EPR in an ordinary bulk metal due to the minuscule skin depth at micro- or millimeter-waves. You will be looking primarily at oxides and surface states.
Yes. I agree what the Zeeman effect is about but surely you need to have a population of atoms with defined energy levels in order to observe this. OR is the method to observe a transition between the two levels directly? That could make sense and the ΔE could correspond to a much lower (RF) frequency which would be similar for a whole range (band?) of energy states for the electrons. I am having a problem in identifying this as a 'Zeeman effect' because the original energy states of free electrons are extremely low magnitude.

You referred to "stabilising" free electrons, earlier on. Wouldn't that involve binding them to something and taking away their freedom.
This is starting to read like another thread for which the title is not really appropriate.

marcusl
Gold Member
Microwave photons induce transitions between the Zeeman states, or classically, the MW field causes the spins to process at the Larmor frequency set by the B field. As I said, the election energy is irrelevant to first order.

I never spoke of stabilizing electrons (whatever that may be), that was someone else.

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sophiecentaur
Gold Member
Microwave photons induce transitions between the Zeeman states, or classically, the MW field causes the spins to process at the Larmor frequency set by the B field. As I said, the election energy is irrelevant to first order.

I never spoke of stabilizing electrons (whatever that may be), that was someone else.
OK. You put the atoms in a cavity and look for a resonance at the Larmor Frequency. Have you done that? On the face of it, I guess it should work.

marcusl
Gold Member
On the face of it, I guess it should work.
There’s no need to guess; in the 74 years since EPR was first demonstrated, it has both been shown to “work” over and over, and been thoroughly explained using sound physics principles.

sophiecentaur
sophiecentaur
Gold Member
There’s no need to guess; in the 74 years since EPR was first demonstrated, it has both been shown to “work” over and over, and been thoroughly explained using sound physics principles.
Ah well. The only (afair) mention of this in my degree course was in the context of the Zeeman effect. I should not fire from the hip in these matters. Sorry.

f95toli
Gold Member
OK. You put the atoms in a cavity and look for a resonance at the Larmor Frequency. Have you done that? On the face of it, I guess it should work.

I'm not sure I follow. If the question is if you will see a defined peak in an ESR spectra from conduction electrons in an ordinary metal the answer is no (and I am speaking from experience here; I do ESR measurement as part of my work and my sample holders are made from metal ). You can (obviously) use ESR to study e.g. rare-earth ions in solids (typically the ions are impurities in some sort of dielectric) but the point is that these are quite well separated from each other.
Electrons that are completely free to move would as far as I understand never be spin active.

(btw the article i behind paywall so it is possible that I misunderstood what you meant)

sophiecentaur
Gold Member
Electrons that are completely free to move would as far as I understand never be spin active.
There’s no need to guess; in the 74 years since EPR was first demonstrated, it has both been shown to “work” over and over, and been thoroughly explained using sound physics principles.
Those two posts seem to be saying different things. what is the real situation?

marcusl
Gold Member
I'm not sure I follow. If the question is if you will see a defined peak in an ESR spectra from conduction electrons in an ordinary metal the answer is no (and I am speaking from experience here; I do ESR measurement as part of my work and my sample holders are made from metal ). You can (obviously) use ESR to study e.g. rare-earth ions in solids (typically the ions are impurities in some sort of dielectric) but the point is that these are quite well separated from each other.
Electrons that are completely free to move would as far as I understand never be spin active.
The fact that you do not incidentally see a signal in an apparatus that is not tuned for the purpose is not proof that the measurement is impossible. (A quadruple negative, oh dear...) On the contrary, there is a significant body of papers that present EPR data taken on conduction electrons in metals. The earliest complete experimental and theoretical report is from 1955, and it includes spectra on a variety of metals at temperatures from room temperature down to 4K.

Feher, George, and A. F. Kip. "Electron spin resonance absorption in metals. I. Experimental." Physical Review 98, no. 2 (1955): 337.
https://journals.aps.org/pr/abstract/10.1103/PhysRev.98.337
The companion paper, by no less a luminary than Freeman Dyson, analyzes how skin depth effects dramatically alter the Lorentzian line shape, making it asymmetric.
Dyson, Freeman J. "Electron spin resonance absorption in metals. II. Theory of electron diffusion and the skin effect." Physical Review 98, no. 2 (1955): 349.
https://journals.aps.org/pr/abstract/10.1103/PhysRev.98.349
These authors note that highly conductive metals have very short relaxation times that make them challenging to observe, which may be a factor in your null observation.

Dyson's computations correctly predict the asymmetric line shape. Of the many references online, I chose the following link to a recent article that describes observations of the Dysonian line shape in conduction electrons (though not of a common metal), in an article that can be downloaded for free.
https://cloudfront.escholarship.org/dist/prd/content/qt2wh158cn/qt2wh158cn.pdf
The opening paragraph references additional works where you can find conduction electron spin resonance (CESR) measurements of common metals.

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f95toli