Floating magnets to sense magnetic fields

We've all seen a traditional compass.  A ferromagnetic, magnetized needle is mounted on a rotating bearing (or floated on the surface of a liquid) so that it can rotate in the \(x-y\) plane.  If there is an in-plane magnetic field \(\mathbf{B}\), the needle will rotate to align with that component of the field.  (It stops in the aligned state because of friction; otherwise it would "librate", oscillating back and forth about the field direction.)  In first-year undergrad physics, we learn a simple model of why this happens.  The magnetized needle can be modeled as a magnetic dipole \(\mathbf{m}\).  We learn that a magnetic dipole in a uniform magnetic field generates a torque \(\boldsymbol{\tau} = \mathbf{m}\times \mathbf{B}\).  If both \(\mathbf{m}\) and \(\mathbf{B}\) are in the \(x-y\) plane, any torque must be directed along \(z\), and the torque goes to zero when \(\mathbf{m} || \mathbf{B}\).  The simplest result of \(\boldsymbol{\tau} || z\) is an angular acceleration that would cause an otherwise at-rest compass needle to rotate in the plane counterclockwise about the \(z\) axis. 

Left: A compass needle out of alignment with an in-plane 
magnetic field produces a torque along \(z\), and angularly
accelerates to reorient toward the field . Right: Under the 
right circumstances, the spin angular momentum of the 
needle could also precess around the field.

So, how sensitive of a magnetic field detector could you make using this basic approach?  This week I came upon this paper from a few years ago, which looks at this problem from the theoretical modeling side, and then this paper from last year that does the experiment.  The magnet in question is a little (21 \(\mu\)m diameter) sphere of Nd2Fe14B, a rare-earth magnet.  The authors put that inside a lead chamber with a rounded bottom, and they cool the lead down to 4.2 K, well below its superconducting transition temperature.  As a result, the sphere is magnetically levitated inside thanks to the Meissner effect, with its magnetization lying in the \(x-y\) plane.  There is some residual magnetic flux trapped in the setup that does lead to a preferred field direction.  The authors can use cleverly wound pickup coils inside the chamber to detect the orientation of the sphere, as well as apply AC magnetic fields.  The authors are primarily concerned in thinking about energy resolution of detection, because they are thinking about detecting unusual particles (e.g. dark matter, axions), but they point out that it should be possible to achieve tens of atto-Tesla per Hz\(^{1/2}\) field sensitivity per unit bandwidth - pretty wild.

But wait, there's more!  The magnetic moment of the magnetized needle originates from the spins of electrons in there.  This is gyromagnetism, so \(\mathbf{m} \propto \mathbf{S}\), the total spin angular momentum of the electrons in the magnet.  This means that in the presence of \(\boldsymbol{\tau} || z\), if mechanically possible the needle could start swinging up out of the \(x-y\) plane to project a component of \(\mathbf{S}\) along \(z\).  This is gyroscopic precession.  For macroscopic magnets, it's hard to be in the regime where this is the dominant effect, because that would require the precessional angular momentum to be small compared to \(\mathbf{S}\), and that's tough to achieve.  Maxwell (!) tried to do it in 1861 (!!), with no success.

In a very recent paper, this precessional response was finally observed, again in Nd2Fe14B microspheres.  (For a uniformly magnetized sphere of radius \(R\), the moment of inertia \(I \propto R^{5}\), and \(|\mathbf{S}| \propto R^{3}\), so it's easier to get into the precessional regime with smaller \(R\).)  This precession approach is a pathway to even higher sensitivity measurements of magnetic fields.

I think this is very cool, and it is a strong reminder that spin angular momentum is just as real as any "mechanical rotation of solids" angular momentum.  

Disorder and illumination

No, this is not another grim post about the chaotic US research funding environment.  Instead I wanted to write a bit about a good example of empiricism in experimental condensed matter physics, the use of illumination to (somewhat but not entirely mysteriously) improve electronic transport in 2D electronic systems.  

This story goes back decades, and it's all about the role of "disorder" and its effects on electronic conduction.  It's been appreciated since the 1930s that, at low temperatures so that lattice vibrations are frozen out, conduction in ordinary crystalline metals and semiconductors is limited by the charge carriers (let's work with electrons rather than holes to make discussion simpler) scattering from disorder, deviations from an infinite periodic crystal lattice.  Grain boundaries, vacancies, impurities - these all can scatter electrons that would otherwise propagate ballistically through the material, and this is often modeled as a "disorder potential", a spatially varying potential energy \(V(\mathbf{r})\).  If you want the best transport properties (longest elastic mean free path), you want \(V(\mathbf{r})\) to be small in magnitude and as smooth as possible.  This is even more important if you want to study some delicate many-body state that is expected to arise at very low temperatures - you need the disorder potential to be small compared to the energy scale of that state to avoid messing it up.

In semiconductors, where the carrier density is low and screening is therefore not as good, charged defects are particularly effective at scattering.  In modulation doping, the dopants that are the source of the charge carriers in some nearby semiconductor 2D interface or quantum well are spatially distant from where the current is going to be flowing, to minimize the scattering from those ionized donors.  

For decades it has been known that, to get the best transport properties in GaAs-based (and other) semiconductor structures, it can be good to illuminate the devices at cryogenic temperatures with a red LED.  See, for example, this paper trying to explore the upper limits of charge mobility in GaAs 2D electron gas (2DEG), where the authors say "For measurement, our samples are loaded into a 3He cryostat, where a red light-emitting diode (LED) is used to illuminate the samples for 5 min at \(T \sim \) 10 K. Following illumination, we wait for 30 min at \(T  \sim \) 10 K after the LED has been turned off before resuming the cool down to base temperature."   The qualitative explanation for this is that the photons provide enough energy to excite charge carriers, and those mobile carriers can occupy trap states, rearrange themselves, and generally set up a better screened disorder potential.  In GaAs 2DEG, the result is higher mobilities (as inferred from conductivity + Hall effect) and much cleaner fractional quantum Hall effect data, showing that the post-illumination disorder is now sufficiently weak that more delicate states can form - see Fig. 1 of this paper (arXiv version) for the before/after.  As far as I know, there is not a deep, rigorous theory of how this works, but it is known empirically.  

Fig. 2 from this paper, showing electronic magnetotransport

before/after illumination by a UV LED at low temperatures.

This preprint on the arXiv this week shows that a similar improvement in transport properties can be found in structures where graphene is encapsulated by hexagonal boron nitride (hBN).  Sandwiching graphene and other 2D materials in hBN has been known since 2010 as a way of drastically improving the charge disorder situation compared to just putting 2D materials on top of SiO2.  (That paper has 8800+ citations on google scholar btw.)  Now, it is shown that if you shine 5 eV photons (deep UV = 248 nm wavelength) on such a sandwiched structure, the already-good charge environment can become even better.  Even though that energy scale is below the band gap of hBN, the light is able to kick enough charges around to smooth out some residual disorder.  Very cool.  

FY27 Presidential budget request

To the surprise of no one at all, the 2027 presidential budget request is extremely bad for science.  Remember, this is largely a political document, and Congress does not have to follow this.  In the past year, Congress largely ignored the recommendations and appropriated a much flatter budget (though agency priorities are still set by the PBR for executive agencies).  This new request shows that Vought et al. still would prefer to kill much public funding for science.

• NSF: request to cut from $8.8B (FY26 enacted) to $4B, a 56% cut that would eviscerate the agency.
• DOE: request to cut $1.1B from $8.4B (FY26 enacted) Office of Science budget.
• NASA: request to cut $5.6B from $24.4B (FY26 enacted), including $3.7B from science programs and $1.1B from the ISS.
• Commerce: This one shocks me. Request to cut $993M from NIST's $1.184B (FY26 enacted) budget. That would be an 84% cut (!!), seemingly destroying NIST. This needs to get headlines.  Either the people making this recommendation have no idea what NIST does (seems plausible), or someone has a personal grudge against the standard kilogram. Update:  Dan Garisto on bluesky points out that the enormous cut topline number is not consistent with the budget appendix, which implies a much smaller cut.  Unclear what the answer is here - it'd be quite a goof to have a topline number that far off.
• NIH: Proposed $5.5B cut from $47.2B (FY26 enacted).
• DOD: It's very hard to tell, especially since they're proposing hundreds of billions of dollars in additional spending including for missile defense. The proposed DOD increases vastly outweigh the cuts described above. 

These cuts are proposed despite constant fretting that China is surpassing the US scientifically. This past year it took aggressive lobbying to ensure that Congress pushed back against these kinds of cuts. For those who favor continued public investment in science and engineering research in the US, the task of arguing against these kinds of cuts begins again now.  As I've written before, this is a marathon not a sprint, and this will be an annual exercise under this administration.