## Saturday, February 03, 2024

### Large magnetic fields as a scientific tool

When I was at Berkeley at the beginning of the week to give a seminar, I was fortunate enough to overlap with their departmental physics colloquium by Greg Boebinger, an accomplished scientist who is also an extremely engaging and funny speaker.  Since 2004 he has been the director of the National High Magnetic Field Lab in Tallahassee, Florida, the premier user facility for access to large magnetic fields for scientific research.  He gave a great talk that discussed both the challenges in creating very large magnetic fields and a sampling of the cool science that can be done using these capabilities.

Leaving aside spin for a moment, magnetic fields* in some reference frame are generated by currents of moving charges and changing electric fields, as in AmpĂ¨re's law, $\nabla \times \mathbf{B} = \mu_{0}\mathbf{J} + \epsilon_{0}\mu_{0}\partial_{t}\mathbf{E}$, where $\mathbf{J}$ is the current density.  Because materials have collective responses to magnetic fields, generating within themselves some magnetization (magnetic dipole moment per volume $\mathbf{M}$), we can think of the magnetic field as a thermodynamic variable, like pressure.  Just as all kinds of interesting physics can be found by using pressure to tune materials between competing phases (because pressure tunes interatomic spacing, and thus things like the ability of electrons to move from atom to atom, and hence the magnitude of magnetic exchange), a magnetic field can tune materials across phase transitions.

It's worth remembering some physically relevant scales.  The earth's magnetic field at the surface is around 30-50 microTesla.  The magnetic field at the surface of a rare earth magnet is around 1 Tesla.  The field in a typical MRI machine used for medical imaging is 1.5 or 3 T.  The energy levels for the spin of an electron in a magnetic field are set by the Zeeman effect and shift by an amount around $\mu_{\mathrm{B}}B$, where $\mu_{\mathrm{B}}$ is the Bohr magneton, $9.27 \times 10^{-24}$ J/T.  A 10 T magnetic field, about what you can typically get in an ordinary lab, leads to a Zeeman energy comparable to the thermal energy scale at about 6.7 K, or compared to an electron moving through a voltage of 0.6 mV.   In other words, magnetic fields are weak in that it generally takes a lot of current to generate a big field, and the associated energies are small compared to room temperature ($k_{\mathrm{B}}T$ at 300 K is equivalent to 26 mV) and the eV scales relevant to chemistry.  Still, consequences can be quite profound, and even weak fields can be very useful with the right techniques. (The magnetic field at the surface of a neutron star can be $10^{11}$ T, a staggering number in terms of energy density.)

Generating large magnetic fields is a persistent technological challenge.  Superconductors can be great for driving large currents without huge dissipation, but they have their own issues of critical currents and critical fields, and the mechanical forces on the conductors can be very large (see here for a recent review).  The largest steady-state magnetic field that has been achieved with a (high-Tc) superconducting coil combined with a resistive magnet is around 45.5 T (see here as well).  At the Los Alamos outpost of the Magnet Lab, they've achieved non-destructive pulsed fields as large as 101 T (see this video).  A huge limiting factor is the challenge of making joints between superconducting wires, so that the joint itself remains superconducting at the very large currents and fields needed.

The science that can be done with large fields extends well beyond condensed matter physics.  One example from the talk that I liked:  Remarkable resolution is possible in ion cyclotron resonance mass spectroscopy, so that with a single drop of oil, it is possible to identify the contribution of the many thousands of hydrocarbon molecules in there and "fingerprint" where it came from.

Fun stuff, and a great example of an investment in technology that would very likely never have been made by private industry alone.

* I know that $\mathbf{B}$ is technically the magnetic induction or magnetic flux density in SI units, but colloquially everyone calls it the magnetic field, so I'll do the same here.