= Einstein-de Haas experiment
{c}
In 1915, <Albert Einstein> and <Wander Johannes de Haas> suspended a soft-<iron> cylinder by glass fibre between coaxial coils. Alternating <magnetization> drove torsional <resonance>; a mirror reflected lamplight onto a scale. They compensated Earth's <magnetic field>, tilted the coils, and rotated the suspension attachment to test unwanted <magnetic dipole torques>. Added known <moment of inertia> calibrated the mechanical response.<Experimental proof of the existence of Ampère's molecular currents by Albert Einstein and Wander Johannes de Haas>[§§4–5, pp. 702–706: apparatus, controls, calibration]{ref}
\Image[/einstein-de-haas-suspended-magnet-apparatus.png]
{title=<Einstein-de Haas experiment>: suspended magnet, drive and optical readout}
{description=Original functional schematic of the first apparatus, rather than a scale reconstruction. The split coaxial coils leave an optical gap. The enlarged plan view explains the <optical lever>; the calibration bar is attached for a separate calibration run. Compensation windings are represented by their function.}
Their paper acknowledges a failed <phase> determination and claims only ten-percent precision for the revised measurement. Its agreement with the orbital <gyromagnetic ratio> prediction was not a direct discovery of <spin>.<Experimental proof of the existence of Ampère's molecular currents by Albert Einstein and Wander Johannes de Haas>[§6, pp. 706–707: phase failure; §7, pp. 707–711: resonance, precision]{ref} Comparing that orbital <gyromagnetic ratio> prediction with the <electron spin g-factor> explains why a successful qualitative demonstration of <angular momentum> transfer can coexist with an inadequate quantitative interpretation. The stated precision is the authors' estimate; it does not establish that all <systematic errors> were bounded by that amount.
The general control problem follows directly from the model. Unwanted <magnetic dipole torque> can drive the same mechanical <resonance> as the desired reaction <torque>. In the ideal geometry $m_z$ and $B_z$ alone produce no axial <cross product>, but transverse <magnetic dipole moments>, stray transverse <magnetic fields> and imperfect alignment can. Nulling stray <magnetic fields> and deliberately varying alignment test this contribution. Merely observing a large resonant twist cannot identify its cause.
For a nearly instantaneous magnetic response, a sinusoidal <magnetization> makes $m_z$ follow the drive while $-\dot m_z/\gamma$ is in <phase quadrature>. An ordinary magnetic contribution proportional to $m_z$ is then distinguishable by <phase>, after removing the mechanical <frequency response>. <Hysteresis> or delayed magnetic response can spoil this simple separation. The measured <magnetization>, rather than the coil <electric current> alone, must set the reference. Mechanical vibration, <magnetostriction> coupled through imperfect geometry, and changing suspension properties require separate checks; none is eliminated simply by reversing the coil <electric current>.
Back to article page
