Tikalon Blog by Dev Gualtieri

Unusual Hall Effect

April 5, 2021

Just as the baking soda and vinegar reaction demonstrates a chemical principle with household items, there are household items that can be used in many physics demonstrations. Rubbing together dissimilar materials will create an electric charge that will attract small pieces of paper. Refrigerator magnets will attract and repel each other and act to attract some materials like steel paper clips, but not other materials like plastic.

Reaction of baking soda (sodium bicarbonate) and vinegar (acetic acid) to produce sodium acetate, water and carbon dioxide. I did this reaction often as an elementary school student. (Created using Inkscape. Click for larger image.)

While there doesn't appear to be a commonality of the attraction of paper to a plastic drinking straw and the magnet holding a child's artwork on the steel door of a refrigerator, James Clerk Maxwell (1831-1879) in 1873 deduced that electricity and magnetism were manifestations of the same force now called electromagnetism. Electromagnetism is one of the fundamental forces of nature, the others being gravity, the strong nuclear force, and the weak nuclear force.

As its name implies, the strong nuclear force is indeed strong, but it operates only at a length scale around the size of an atomic nucleus. Gravity operates over an infinite range, but it's strength is nearly forty orders of magnitude (10⁴⁰) weaker than the nuclear force. Electromagnetism likewise has infinite range, but it's much stronger than gravity. It has a strength that's 1/137 that of the strong nuclear force. This strange constant, 1/137, is the fine structure constant that I wrote about in an earlier article (The Fine Structure Constant, June 8, 2020).

The electromagnetic coupling between electric charge and magnetism was the principle behind the operation of cathode ray tubes (CRTs) in early television and computer displays. Magnetic deflection of moving electrons ("cathode rays") allowed images to be "painted" onto a phosphor screen (see figure). The scanning electron microscope is another device that uses magnetic fields to raster scan an electron beam.

A cathode ray tube along with the right-hand rule describing the magnetic force on its electron beam.

Movement of electrons in cathode rays is the equivalent of an electric current. When an electric current is acted upon by a magnetic field, the direction of the force is given by the so-called "right-hand rule," as shown on the left. The force is the cross product of the current and magnetic field. Magnetic deflection of electrons in a cathode ray tube is shown on the right. (Left image (modified) by Tokamac and right image (modified), both from Wikimedia Commons. Click for larger image.)

Magnetic fields also affect electron movement in electrical conductors in a response known as the Hall effect, discovered in 1879 by American physicist, Edwin Hall (1855-1938). Hall observed that when an electric current was passed through a gold leaf conductor, a magnetic field perpendicular to the current produced a voltage (now known as the Hall Voltage) transverse to the current.[1] His experiment was a demonstration that electric currents were carried by electrons and not by protons. The effect is caused by the Lorentz force acting to pile more electrons on one side of the metal strip than on the other, leading to a potential difference between the two sides.

Excerpt from Edwin Hall's 1879 paper about the Hall effect. I always enjoy reading honestly written research accounts like this. Today, a paper written in this style would never be accepted for publication. (Archive.org image.[1])

Hall effect research has been celebrated by the Nobel Prize in Physics in 1885 for the discovery of the Quantum Hall effect by Klaus von Klitzing (b. 1943); and in 1998 for the discovery of the fractional quantum Hall effect. The quantum Hall effect has given us a fundamental unit of electrical resistance with the value 25812.80745 ohms.

A recent open access paper at the Proceedings of the National Academy of Sciences reports on the discovery of an unusual manifestation of the Hall effect in a crystal of a compound of cerium, bismuth and palladium in which no magnetism is involved.[2-4] This research was conducted by an international team of physicists and materials scientists from the Vienna University of Technology (Vienna, Austria), the Swiss Federal Institute of Technology (ETH, Zürich, Switzerland), the Paul Scherrer Institut (Villigen, Switzerland), McMaster University (Hamilton, Ontario, Canada), and Rice University (Houston, Texas).[2]

Not only was the Hall effect observed without an applied magnetic field, it was especially strong.[2-4] It's reasoned that the electrons in this material behave as if it also contained magnetic monopoles. According to Maxwell's electromagnetic equations, magnetic monopoles should not exist. In analogy with electric charge that exists as individual positive and negative units, a magnetic monopole would exist as an isolated north or south pole. As everyone knows, when you break a magnetic in half, you always get two new magnets with both poles, no monopoles.

This unusual non-magnetic Hall effect was discovered by Sami Dzsaber, a doctoral student at the Vienna University of Technology who was doing careful measurements on Ce₃Bi₄Pd₃, a noncentrosymmetric crystal, for his thesis.[2-3] The non-magnetic Hall effect wasn't just present, but it was huge, being orders of magnitude larger than expected.[2-3] It's been said that extraordinary claims require extraordinary evidence, so further work was undertaken at the Paul Scherrer Institute in Switzerland using muons as a probe for magnetism in the material at a microscopic scale.[4] Such magnetism was not found, and this suggested that the effect was topological.[4]

Sami Dzsaber and Silke Bühler-Paschen, TUW

Left, Sami Dzsaber and Silke Bühler-Paschen in the laboratory at Vienna University of Technology. Right, a single crystal of the topological cerium, bismuth and palladium compound prepared for measurement of the novel Hall effect. (TU Wien images.[3] Click for larger image.)

Electrons in topological materials enter into immutable quantum entanglement.[4] One class of topological materials are the Weyl semimetals that contain a type of quasiparticle known as a Weyl fermion, and this new material appears to be a member of this class.[4] Some layered semiconductors have demonstrated this kind of spontaneous Hall effect, but at a level that's a thousand times smaller.[4] Says Professor Silke Bühler-Paschen of the the Institute of Solid State Physics at the Vienna University of Technology in whose laboratory this discovery was made, "It's also important to note that you can't look at the electrons individually here - there are strong quantum mechanical interactions between them."[3]

Although magnetic monopoles do not exist, this material behaves as if they are present and act upon the electrons.[3] The large Hall effect of this topological quantum device might be technologically useful.[2] Such quantum devices might be used as non-reciprocal elements to steer electrons in different directions.[3] This research was funded by the Austrian Science Fund, the European Union's Horizon 2020 Research and Innovation Program, the Swiss National Science Foundation, the National Science Foundation, the Welch Foundation and Los Alamos National Laboratory.[4]

Artist's conception of electron motion in the Ce₃Bi₄Pd₃ Hall effect material. The material behaves as if magnetic monopoles are present.

(TU Wien image, also found here.)

Unusual Hall Effect

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