Every day we use dozens of electromagnetic devices, from a simple water heater to brew a cup of coffee to cell phones, office computers, light bulbs, elevators, air conditioners and so on. What all of these devices have in common is that they use either electricity or magnetism or, in many cases, both.

None of these technologies would exist today had it not been for decades worth of painstaking experimental and theoretical work by people like Coulomb, Faraday, Gauss, Ampère and others who made it possible for James Maxwell in 1861 to explain all known experimental results in the form of four elegant differential equations. The behavior of all electric and magnetic fields is described very accurately by what we now refer to as Maxwell’s Equations.

For many of us, our very first encounter with the basic properties of electrical charges and bar magnets was likely in a middle- or high-school science lab. The instructor would give students interesting hairdos using a static electricity generator or make visible the field lines that surround a bar magnet by pouring iron filings on top of a sheet of paper covering the magnet. Who hasn’t played, as a child or even as an adult, with a couple of magnets and wondered about the invisible forces that make poles attract or repel each other?

Over the last century, physicists and engineers have managed to put these forces to good use, first with the development of powerful electromagnets, transformers and electric motors. More recently, the development of high-density magnetic recording media makes it possible for all of us to preserve for eternity long videos of cute kitties. In the future, we can hopefully harness the power of atomic fusion, for which magnetic containment of an ultra-hot plasma appears to be one of the viable technologies.

The use of magnetic fields and magnets in data recording started in the mid-1950s. Over the years, the size of the “bar magnets” used to store information has steadily decreased, and the latest drives have individual data bits that are formed by magnetic regions of only a few nanometers across.

Developing such technology requires (among many other things) the ability to produce images of the individual bits as well as the magnetic fields surrounding them (i.e., the equivalent of the iron-filings experiment) but at a length scale that is about 10 million times smaller than the classic science-class demonstration. Obviously, this requires the use of advanced materials-characterization tools, and our Materials Characterization Facility (MCF) at Carnegie Mellon University is one of only a handful of labs worldwide that specializes in the use of Lorentz microscopy – a technique that measures the tiny deflections in the trajectories of electrons as they pass through the magnetic fields surrounding magnetic nanoparticles. Typical deflection angles are well below 1/10,000th of a degree!

Lorentz microscopy allows us to determine a 2-D projection of the magnetic-field distribution in and around a small magnetic object or a collection of such objects. These projections cannot be observed directly but must be extracted from experimental images through extensive post-processing of the data. Our research group has contributed significantly to the development of these algorithms over the past two decades, and it is now almost a routine operation to obtain magnetic induction maps with a spatial resolution of a few nanometers.

A Deeper Dive into Professor De Graef’s Research

Prof. De Graef’s research group has contributed extensively to the field of Lorentz microscopy. In recent research, we have successfully reconstructed the magnetic vector potential (a fundamental vector field from which other magnetic quantities can be derived) in 3-D based on a tilt series of regular Lorentz images. The sample was a patterned array of flat nanoscale Permalloy (Fe-Ni) islands that have their magnetic north-south axis aligned with their longest dimension.

A 2-D array of such islands reveals an interesting interplay between all these magnetic poles. The figure shows a reconstruction of the vector potential field. Several planar sections through the 3-D volume are shown. Note how the vectors, represented by arrows, form closed loops around many of the islands, in agreement with theoretical predictions.

What is even more interesting is that we can use the 3-D tomographic techniques described in an earlier edition of this column to reconstruct the magnetic induction in and around a series of magnetic nanoparticles. In other words, we can perform the equivalent of the iron-filings experiment in 3-D and at a length scale that is 10 million times smaller than the science-lab demonstration!

Perhaps it should not be too surprising that the tools we use for these observations (i.e., transmission electron microscopes) are based on the laws of electromagnetism. There is something strangely satisfying about the fact that we can use the magnetic fields of the microscope lenses along with an electrical current (the electron beam) to study other, often really tiny, magnetic fields. Whether we work at the lab scale or at the nanoscale, Maxwell’s equations guide us through all the fields and their interactions with the materials we investigate.


Dr. Marc De Graef is Professor of Materials Science and Engineering at Carnegie Mellon University. Over the past two decades, Prof. De Graef’s research group has been at the forefront of developing the numerical tools that allow us to convert raw experimental data from serial sectioning experiments into accurate 3D reconstructions. The group has developed a simulation technique that relies on basic physics to model the scattering of electrons in materials and the subsequent formation of an EBSD pattern. Ongoing work involves machine-learning approaches to speed up the new technique and turn it into a near-real-time indexing engine. De Graef’s research group has also contributed extensively to the field of Lorentz microscopy.