Einstein–de Haas effect

• 1. A Passion for Experiments

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  In a letter to his friend Michele Besso, Albert Einstein admitted that in his old age he was developing a passion for experimentation. The Einstein-de Haas effect is one result of that passion. Suspend a ferromagnetic cylinder from a thin string, change its magnetism, and the whole cylinder begins to turn. The effect carries the names of Einstein and the physicist Wander Johannes de Haas, who published two papers on it in 1915.

  Yet the idea did not begin with them, and their celebrated measurement did not hold up. Why should magnetism make a solid object rotate? What is really moving inside the metal? And how did a famous experiment end up with the wrong answer while another physicist's work turned out right?

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• 2. Spinning Inside Iron

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  A single electron circling an axis behaves like a tiny magnet. Its orbital motion produces a magnetic dipole, and the strength of that dipole depends on the electron's charge, its mass, and the angular momentum of its motion. The electron also carries an intrinsic angular momentum called spin, which has its own magnetic moment.

  Add up these tiny magnets across a unit volume of material, and the total is the magnetization. Careful measurement of the effect showed that magnetization comes from electrons lining up their angular momenta along the axis of magnetization. A change in magnetization must therefore change the angular momentum of those electrons, in proportion.

  Here the law of conservation of angular momentum takes over. If no outside torque acts along the axis, the rest of the body must pick up the opposite angular momentum. That rest of the body is practically all of its mass, so the whole object turns. The effect also revealed how closely the idea of angular momentum in classical physics matches the same idea in quantum physics.

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• 3. The Hanging Cylinder

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  The experiment uses a cylinder of ferromagnetic material dangling from a thin string inside a cylindrical coil. Current in the coil creates a magnetic field along the cylinder's axis and magnetizes the metal. When the current changes, the magnetization changes, and so does the cylinder's angular momentum. Optical devices watch the resulting change in rotational speed.

  The layout works because an external field cannot push a magnetic dipole along the direction of the field itself. The cylinder is magnetized along the coil's axis, so angular momentum about that axis must be conserved unless some other field interferes.

  Simple as it sounds, the experiments are hard. A pickup coil around the cylinder can measure the magnetization accurately, but the matching change in angular momentum is tiny. Ambient fields such as the Earth's can shove a magnetized cylinder roughly ten million to a hundred million times harder.

  Later precise versions were run in a specially built demagnetized environment, with active compensation of the surrounding fields. They treated the cylinder as a torsion pendulum and fed the coil a periodic current at frequencies close to the pendulum's resonance. What they measured directly was a ratio, and from it they derived the dimensionless gyromagnetic factor of the material.

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• 4. A Prediction from 1908

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  Owen Willans Richardson described the expected effect, and a possible way to test it, in a paper published in 1908. Electron spin was not discovered until 1925, so he considered only the orbital motion of electrons. His paper also noted that attempts to observe the effect were already under way at Princeton University.

  At that time the picture of electrons orbiting inside atoms contradicted classical physics. The Bohr model addressed the contradiction in 1913, and quantum mechanics later removed it.

  Samuel Jackson Barnett, motivated by Richardson's paper, realized that the opposite should also happen. A change in rotation should cause magnetization, a phenomenon now called the Barnett effect. He published the idea in 1909 and then turned to experiments. He reported his measurements at several scientific conferences in 1914, a year before the Einstein-de Haas papers appeared.

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• 5. Einstein in the Laboratory

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  In April 1915, Einstein and de Haas published two papers describing the expected effect and their experimental results. One was titled "Experimental proof of the existence of Ampere's molecular currents," and it laid out the apparatus and measurements in detail. Ampere's hypothesis held that magnetism comes from microscopic circular motions of electric charge. The authors set out to test Hendrik Lorentz's theory that the circling particles are electrons, by measuring the torque produced when an iron cylinder's magnetization is reversed.

  On the 7th of May 1915, Einstein reported to the German Physical Society that he had done the experiments jointly with de Haas over the previous three months at the Imperial Physicotechnical Institute. In his opinion they had "firmly established the existence of Ampère molecular currents."

  Lorentz was close to the project in more ways than one. He communicated the second paper to the Proceedings of the Royal Netherlands Academy of Arts and Sciences. When he pointed out an error in the first paper, Einstein immediately wrote a correction. Later that year the pair also wrote a comment on the English-language paper for the same journal.

  De Haas was married to Geertruida de Haas-Lorentz, a theoretical physicist and Lorentz's daughter. The numbers in those papers carried a flaw that took years to expose.

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• 6. The Wrong Number

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  Einstein and de Haas found a ratio of angular momentum to magnetic moment within 3% of the value that theory expected. They quoted an uncertainty of 10%. Even so, it was later realized that their result was inconsistent with the correct value. Apparently the authors had underestimated their experimental uncertainties.

  Barnett published the first observation of his own effect in October 1915, in a paper titled "Magnetization by Rotation." His number landed close to the right value, which nobody expected at the time. In 1918, John Quincy Stewart published measurements that confirmed Barnett's result. Stewart called the phenomenon the "Richardson effect."

  Later experiments showed that the gyromagnetic ratio for iron is indeed close to the surprising value rather than the predicted one. Physicists dubbed the mismatch the "gyromagnetic anomaly." It was finally explained after the discovery of spin and the introduction of the Dirac equation in 1928.

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• 7. What Iron Reveals

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  Once the physics was settled, the effect became a measuring tool for various ferromagnetic elements and alloys. The key to better accuracy was improved magnetic shielding, while the methods stayed essentially the same as in the first experiments.

  The measured g-factor lets physicists split magnetization into two parts. One part comes from electron spin, and the other comes from the orbital motion of the electrons. For pure iron, the numbers show that 96% of the magnetization comes from the polarization of electron spins. The remaining 4% comes from the polarization of orbital angular momenta.

  The orbital motion that Richardson had in mind in 1908 turns out to be the junior partner in iron.

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• 8. Lost and Found

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  In 1961, Geertruida de Haas-Lorentz donated the original experimental equipment to the Ampère Museum in Lyon, France. The apparatus later went missing. It was rediscovered in 2023.

  The museum that received it is named for André-Marie Ampère, the physicist whose molecular currents the experiment had set out to prove.

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