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Einstein–de Haas effect

The Einstein-de Haas effect is a physical phenomenon in which a change in the magnetic moment of a free body causes this body to rotate.The effect is a consequence of the conservation of angular momentum. It isstrong enough to be observable in ferromagnetic materials. The experimental observation and accurate measurement of the effect demonstratedthat the phenomenon of magnetization is caused by the alignment (polarization)of the angular momenta of the electrons in the material along the axis of magnetization. These measurements also allow the separation of the two contributions to themagnetization: that which is associated with the spin and with the orbital motion of theelectrons. The effect also demonstrated the close relation between the notions of angular momentumin classical and in quantum physics.52. Experimenteller Nachweis der Ampereschen Molekularströme , Deutsche Physikalische Gesellschaft, Verhandlungen 17 (1915): 152-170.Considering Ampère's hypothesis that magnetism is caused by the microscopic circular motions of electric charges, the authors proposed a design to test Lorentz's theory that the rotating particles are electrons. The aim of the experiment was to measure the torque generated by a reversal of the magnetisation of an iron cylinder.53. Experimental Proof of the Existence of Ampère's Molecular Currents (in English), Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings 18 (1915-16).Einstein wrote three papers with Wander J. de Haas on experimental work they did together on Ampère's molecular currents, known as the Einstein–de Haas effect. He immediately wrote a correction to paper 52 (above) when Dutch physicist H. A. Lorentz pointed out an error. In addition to the two papers above Einstein and de Haas cowrote a 'Comment' on paper 53 later in the year for the same journal. This topic was only indirectly related to Einstein's interest in physics, but, as he wrote to his friend Michele Besso, 'In my old age I am developing a passion for experimentation.' The Einstein-de Haas effect is a physical phenomenon in which a change in the magnetic moment of a free body causes this body to rotate.The effect is a consequence of the conservation of angular momentum. It isstrong enough to be observable in ferromagnetic materials. The experimental observation and accurate measurement of the effect demonstratedthat the phenomenon of magnetization is caused by the alignment (polarization)of the angular momenta of the electrons in the material along the axis of magnetization. These measurements also allow the separation of the two contributions to themagnetization: that which is associated with the spin and with the orbital motion of theelectrons. The effect also demonstrated the close relation between the notions of angular momentumin classical and in quantum physics. The effect was predicted by O.W.Richardson in 1908. It is named after Albert Einstein and Wander Johannes de Haas, who published two papers in 1915 claiming the first experimental observation of the effect. The orbital motion of an electron (or any charged particle) around a certain axis producesa magnetic dipole with the magnetic moment of μ = e / 2 m ⋅ j , {displaystyle {oldsymbol {mu }}=e/2mcdot mathbf {j} ,} where e {displaystyle e} and m {displaystyle m} are the charge and the mass of the particle, while j {displaystyle mathbf {j} } is the angular momentum of the motion. In contrast, the intrinsic magneticmoment of the electron is related to its intrinsic angular momentum (spin) as μ ≈ 2 ⋅ e / 2 m ⋅ j {displaystyle {oldsymbol {mu }}approx {}2cdot {}e/2mcdot mathbf {j} } (see Landé g-factor and anomalous magnetic dipole moment).If a number of electrons in a unit volume of the material have a total orbital angular momentum of J o {displaystyle mathbf {J_{o}} } with respect to a certain axis, their magnetic moments would produce the magnetization of M o = e / 2 m ⋅ J o {displaystyle mathbf {M_{o}} =e/2mcdot mathbf {J_{o}} } .For the spin contribution the relation would be M s ≈ e / m ⋅ J s {displaystyle mathbf {M_{s}} approx e/mcdot mathbf {J_{s}} } .A change in magnetization, Δ M , {displaystyle Delta mathbf {M} ,} implies a proportional change in the angular momentum, Δ J ∝ Δ M , {displaystyle Delta mathbf {J} propto {}Delta mathbf {M} ,} of the electrons involved. Provided that there is no externaltorque along the magnetization axis applied to the body in the process, the rest of the body (practically all its mass) should acquire an angular momentum − Δ J {displaystyle -Delta mathbf {J} } due to the law of conservation of angular momentum. The experiments involve a cylinder of a ferromagnetic material suspended with the aid of a thin string inside a cylindrical coil which is used to provide an axial magnetic field that magnetizes the cylinder alongits axis. A change in the electric current in the coil changes themagnetic field the coil produces, which changes the magnetization of the ferromagnetic cylinder and, due to the effect described, its angular momentum. A change in the angular momentum causes a change in the rotational speed ofthe cylinder, monitored using optical devices. The external field B {displaystyle mathbf {B} } interacting with a magnetic dipole μ {displaystyle {oldsymbol {mu }}} can not produce any torque ( τ = μ × B {displaystyle {oldsymbol { au }}={oldsymbol {mu }} imes mathbf {B} } )along the field direction.In these experiments the magnetization happens along the direction of the fieldproduced by the magnetizing coil, therefore, in absence of other external fields,the angular momentum along this axis must be conserved.In spite of the simplicity of such a layout, the experiments are not easy. The magnetizationcan be measured accurately with the help of a pickup coil around the cylinder,but the associated change in the angular momentum is small. Furthermore,the ambient magnetic fields, such as the Earth field, can provide a 107 - 108times larger mechanical impact on the magnetized cylinder. Thelater accurate experiments were done in a specially constructed demagnetizedenvironment with active compensation of the ambient fields.The measurement methods typically use the properties of the torsion pendulum,providing periodic current to the magnetization coil at frequencies close to thependulum's resonance. The experiments measure directly the ratio: λ = Δ J / Δ M {displaystyle lambda =Delta mathbf {J} /Delta mathbf {M} } and derive the dimensionless gyromagnetic factor g ′ {displaystyle g'} (see g-factor) of the material from the definition: g ′ ≡ 2 m e 1 λ {displaystyle g'equiv {}{frac {2m}{e}}{frac {1}{lambda }}} .The quantity γ ≡ 1 λ ≡ e 2 m g ′ {displaystyle gamma equiv {frac {1}{lambda }}equiv {frac {e}{2m}}g'} is called gyromagnetic ratio. The expected effect and a possible experimental approach was first described by Owen Willans Richardson in a paper published in 1908. The electronspin was discovered in 1925, therefore only the orbital motion of electronswas considered before that. Richardson derived the expected relationof M = e / 2 m ⋅ J {displaystyle mathbf {M} =e/2mcdot mathbf {J} } .The paper mentioned the ongoing attempts to observe the effect at Princeton. In that historical context the idea of the orbital motion of electronsin atoms contradicted classical physics. This contradiction wasaddressed in the Bohr model in 1913, and later was removed withthe development of quantum mechanics. S.J. Barnett, motivated by the Richardson's paper realized that the oppositeeffect should also happen - a change in rotation should cause a magnetization (the Barnett effect). He published the idea in 1909,after which he pursued the experimental studies of the effect. Einstein and de Haas published two papersin April 1915 containing adescription of the expected effect and the experimental results. Inthe paper 'Experimental proof of the existence of Ampere's molecularcurrents' they described in details the experimental apparatus andthe measurements performed. Their result for the ratio of the angularmomentum of the sample to its magnetic moment (the authors called it λ {displaystyle lambda } ) was very close (within3%) to the expected value of 2 m / e {displaystyle 2m/e} . It was realized later that theirresult with the quoted uncertainty of 10% was not consistentwith the correct value which is close to m / e {displaystyle m/e} . Apparently, the authorsunderestimated the experimental uncertainties. S.J. Barnett reported the results of his measurements at several scientificconferences in 1914. In October 1915 he published the first observation of theBarnett effect in a paper titled 'Magnetization by Rotation'.His result for λ {displaystyle lambda } was close to the right value of m / e {displaystyle m/e} , which was unexpected at that time.

[ "Total angular momentum quantum number", "Magnetic field", "Electron", "Angular momentum", "Dipole" ]
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