What is the spin Seebeck effect?

Thermoelectricity is an old story, and I've also discussed it here.  Take a length of some conductor, and hold one end of that conductor at temperature \(T_{\mathrm{hot}}\), and hold the other end of that conductor at temperature \(T_{\mathrm{cold}}\).  The charge carriers in the conductor will tend to diffuse from the hot end toward the cold end.  However, if the conductor is electrically isolated, that can't continue, and a voltage will build up between the ends of the conductor, so that in the steady state there is no net flow of charge.  The ratio of the voltage to the temperature difference is given by \(S\), the Seebeck coefficient.  

It turns out that spin, the angular momentum carried by electrons, can also lead to the generation of voltages in the presence of temperature differences, even when the material is an insulator and the electrons don't move.  

Let me describe an experiment for you.  Two parallel platinum wires are patterned next to each other on the surface of an insulator.  An oscillating current at angular frequency \(\omega\) is run through wire A,  while wire B is attached to a voltage amplifier feeding into a lock-in amplifier.  From everything we teach in first-year undergrad physics, you might expect some signal on the lock-in at frequency \(\omega\) because the two wires are capacitively coupled to each other - the oscillating voltage on wire A leads to the electrons on wire B moving back and forth because they are influenced by the electric field from wire A.  You would not expect any kind of signal on wire B at frequency \(2 \omega\), though, at least not if the insulator is ideal.

However, if that insulator is magnetically interesting (e.g., a ferrimagnet, an antiferromagnet, some kinds of paramagnet), it is possible to see a \(2 \omega\) signal on wire B.  

In the spin Seebeck effect, a temperature gradient leads to a build-up of a net spin density across the magnetic insulator.  This is analogous to the conventional Seebeck effect - in a magnetically ordered system, there is a flow of magnons from the hot side to the cold side, transporting angular momentum along.  This builds up a net spin polarization of the electrons in the magnetic insulator.  Those electrons can undergo exchange processes with the electrons in the platinum wire B, and if the spins are properly oriented, this causes a voltage to build up across wire B due to the inverse spin Hall effect.  

So, in the would-be experiment, the ac current in wire A generates a temperature gradient between wire A and wire B that oscillates at frequency \(2 \omega\).  An external magnetic field is used to orient the spins in the magnetic insulator, and if the transported angular momentum points the right direction, there is a \(2 \omega \) voltage signal on wire B.   

I think this is pretty neat - an effect that is purely due to the quantum properties of electrons and would just not exist in the classical electricity and magnetism that we teach in intro undergrad courses.

(On writing this, I realized that I've never written a post defining the spin Hall and related effects. I'll have to work on that....  Sorry for the long delay between postings.  The beginning of the semester has been unusually demanding of my time.)

More amazingly good harmonic oscillators

 Harmonic oscillators are key elements of the physicist's toolkit for modeling the world.  Back at the end of March I wrote about some recent results using silicon nitride membranes to make incredibly high quality (which is to say, low damping) harmonic oscillators.  (Remember, the ideal harmonic oscillator that gets introduced in undergrad intro physics is a mass on a spring, with no friction or dissipation at all.  An ideal oscillator would have a \(Q\) factor that is infinite, and it would keep ringing forever once started.) This past week, two papers appeared on the arxiv showing that it's possible to design networks of (again) silicon nitride beams that have resonances at room temperature (in vacuum) with \(Q > 10^{9}\).  

(a) A perimeter mode of oscillation. (b) a false-
color electron micrograph of such a device.

One of these papers takes a specific motif, a suspended polygon made from beams, supported by anchoring beams coming from its vertices, as shown in the figure.  The resonant modes with the really high \(Q\) factors are modes of the perimeter, with nodes at the vertices.  This minimizes "clamping losses", damping that occurs at anchoring points (where the strain tends to be large, and where phonons can leak vibrational energy out of the resonator and into whatever is holding it).  

The other paper gets to a very similar design, through a process that combines biological inspiration (spiderwebs), physics insight, and machine learning/optimization to really maximize \(Q\).  

With tools like this, it's possible to do quantum mechanics experiments  (that is, mechanics experiments where quantum effects are dominant) at or near room temperature with these.  Amazing.

Brief items

 It's been a busy week, so my apologies for the brevity, but here are a couple of interesting papers and sites that I stumbled upon:

• Back when I first started teaching about nanoscience, I said that you'd really know that semiconductor quantum dots had hit the big time when you occasionally saw tanker trucks full of them going down the highway.  I think we're basically there.  Here is a great review article that summarizes the present state of the art.
• Reaching back a month, I thought that this is an impressive piece of work.  They combine scanning tunneling microscopy, photoluminescence with a tunable optical source, and having the molecule sitting on a layer of NaCl to isolate it from the electronic continuum of the substrate.  The result is amazingly (to me) sharp spectral features in the emission, spatially resolved to the atomic scale.
• The emergence of python and the ability to embed it in web pages through notebooks has transformative educational potential, but it definitely requires a serious investment of time and effort.  Here is a fluid dynamics course from eight years ago that I found the other day - hey, it was new to me.
• For a more up-to-the-minute example, here is a new course about topology and condensed matter.  Now if I only had time to go through this.  The impending start of the new semester. 
• This preprint is also an important one.  There have been some major reports in the literature about quantum oscillations (e.g., resistivity or magnetization vs. magnetic field ) being observed in insulators.  This paper shows that one must be very careful, since the use of graphite gates can lead to a confounding effect that comes from those gates rather than the material under examination.
• This PNAS paper is a neat one.  It can be hard to grow epitaxial films of some "stubborn" materials, ones involving refractory metals (high melting points, very low vapor pressures, often vulnerable to oxidation).  This paper shows that instead one can use solid forms of precursor compounds containing those metals.  The compounds sublime with reasonably high vapor pressures, and if one can work out their decomposition properly, it's possible to grow nice films and multilayers of otherwise tough materials.  (I'd need to be convinced that the purity achieved from this comparatively low temperature approach is really good.)

Metallic water!

What does it take to have a material behave as a metal, from the physicist's perspective?  I've written about this before (wow, I've been blogging for a long time).  Fundamentally, there have to be "gapless" charge-carrying excitations, so that the application of even a tiny electric field allows those charge carriers to transition into states with (barely) higher kinetic energies and momenta.  

Top: a droplet of NaK 
alloy.  Bottom: That 
droplet coated with 
adsorbed water that 
has become a metal. 
From here.

In conventional band insulators, the electronic states are filled right up to the brim in an energy band.  Apply an electric field, and an electron has no states available into which it can go without somehow grabbing enough energy to make it all the way to the bottom of the next (conduction) band.  Since that band gap can be large (5.5 eV for diamond, 8.5 eV for NaCl), no current flows, and you have an insulator.

This is, broadly speaking, the situation in liquid water. (Even though it's a liquid, the basic concept of bands of energy levels is still helpful, though of course there are no Bloch waves as in crystalline solids.)  According to calculations and experiments, the band gap in ordinary water is about 7 eV.  You can dissolve ions in water and have those carry a current - that's the whole deal with electrolytes - but ordinarily water is not a conductor based on electrons.  It is possible to inject some electrons into water, and these end up "hydrated" or "solvated" thanks to interactions with the surrounding polar water molecules and the hydronium and hydroxyl ions floating around, but historically this does not result in a metal.  To achieve metallicity, you'd have to inject or borrow so many electrons that they could get up into that next band.

This paper from late last week seems to have done just that.  A few molecular layers of water adsorbed on the outside of a droplet of liquid sodium-potassium metal apparently ends up taking in enough electrons (\( \sim 5 \times 10^{21}\) per cc) to become metallic, as detected through optical measurements of its conductivity (including a plasmon resonance).   It's rather transient, since chemistry continues and the whole thing oxidizes, but the result is quite neat!