Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld

Gerlāch, Wālther; Stern, O.

doi:10.1007/bf01326983

Cited by 672 publications

(396 citation statements)

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“…That year can be regarded as the debut of what is called the old quantum theory of atomic structure, which utilized classical mechanics supplemented by quantum conditions. In particular it quantized angular momentum and hence the magnetic moment of the atom, as was verified experimentally in the molecular beam experiments of Stern and Gerlach (5). H ence there was no longer the statistical continuous distribution of values of the dipole moment which was essential to the proof of zero magnetism in classical theory.…”

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confidence: 89%

Quantum mechanics-The key to understanding magnetism

Vleck

1978

Rev. Mod. Phys.

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The existence of magnetic materials has been known almost since prehistoric times, but only in the 20th century has it been understood how and why the magnetic susceptibility is influenced by chemical composition or crystallographic structure. In the 19th century the pioneer work of Oersted, Ampere, Faraday and Joseph Henry revealed the intimate connection between electricity and magnetism. Maxwell's classical field equations paved the way for the wireless telegraph and the radio. At the turn of the present century Zeeman and Lorentz received the second Nobel Prize in physics for respectively observing and explaining in terms of classical theory the so-called normal Zeeman effect. The other outstanding early attempt to understand magnetism at the atomic level was provided by the semi-empirical theories of Langevin and Weiss. To account for paramagnetism, Langevin (1) in 1905 assumed in a purely ad hoc fashion that an atomic or molecular magnet carried a permanent moment µ, whose spatial distribution was determined by the Boltzmann factor. It seems today almost incredible that this elegantly simple idea had not occurred earlier to some other physicist inasmuch as Boltzmann had developed his celebrated statistics over a quarter of a century earlier. With the Langevin model, the average magnetization resulting from N elementary magnetic dipoles of strength µ in a field H is given by the expression (1) At ordinary temperatures and field strengths, the argument x of the Langevin function can be treated as small compared with unity. Then L(x) = :x, and Eq. (1) becomes perature, a relation observed experimentally for oxygen ten years earlier by Pierre Curie (2) and hence termed Curie's law.To explain diamagnetism, Langevin took into account the Larmor precession of the electrons about the magnetic field, and the resulting formula for the diamagnetic susceptibility is

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confidence: 89%

Quantum mechanics-The key to understanding magnetism

Vleck

1978

Rev. Mod. Phys.

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“…DOI: 10.1103/PhysRevLett.99.057203 PACS numbers: 75.45.+j, 75.50.Dd, 75.50.Lk, 76.30.Kg A basic feature of quantum mechanics is the superposition of states and the projection of these superpositions into observable quantities. From the Stern-Gerlach experiment of 1922, where quantum projection was first demonstrated with angular momentum states in silver atoms [1], to spin echoes in nuclear magnetic resonance [2], where a series of radio frequency pulses induce the precession of nuclear spins projected into classically inaccessible states, strict experimental protocols have been derived for quantum manipulation at the atomic level. For quantum information purposes, it would be advantageous to extend these techniques to coherent clusters of atoms and to explore such effects in solids.…”

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confidence: 99%

Quantum Projection in an Ising Spin Liquid

et al. 2007

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A transverse magnetic field is used to scan the diagonal and off-diagonal susceptibility of the uniaxial quantum magnet, LiHo 0:045 Y 0:955 F 4 . Clusters of strongly coupled spins act as the primary source for the response functions, which result from a field-induced quantum projection of the system into a classically forbidden (meaning non-Ising) regime. Calculations based on spin pairs reproduce only some features of the data and fail to predict the measured off-diagonal response, providing evidence of a multispin collective state. DOI: 10.1103/PhysRevLett.99.057203 PACS numbers: 75.45.+j, 75.50.Dd, 75.50.Lk, 76.30.Kg A basic feature of quantum mechanics is the superposition of states and the projection of these superpositions into observable quantities. From the Stern-Gerlach experiment of 1922, where quantum projection was first demonstrated with angular momentum states in silver atoms [1], to spin echoes in nuclear magnetic resonance [2], where a series of radio frequency pulses induce the precession of nuclear spins projected into classically inaccessible states, strict experimental protocols have been derived for quantum manipulation at the atomic level. For quantum information purposes, it would be advantageous to extend these techniques to coherent clusters of atoms and to explore such effects in solids. In this Letter, we pioneer measurements of the off-diagonal susceptibility to observe quantum mixing effects in a uniaxial magnetic salt, where we are able to rotate clusters of spins into a classically forbidden (meaning non-Ising) state, transverse to the spin axis. The spins can be manipulated by a combination of ac and dc magnetic fields, detected by a multiaxis susceptometer, and parsed for their quantum-mechanical (xy) or classical (polarized along z, the Ising axis) nature by sweeping transverse magnetic field or temperature, respectively. Our technique takes full advantage of the tensor nature of the magnetic susceptibility, revealing the fundamental role played by the off-diagonal terms [3] in the Hamiltonian.Comparison of the results with calculations including only single ions and pairs of ions shows that the off-diagonal response is not only large, but that it also displays the characteristics of a quantum spin liquid [3].The results of the technique depend crucially on two properties of our system: (i) the ability to introduce quantum mechanics via a controllable, external tuning parameter, and (ii) the predilection of disorder to form spin clusters that may occur rarely but can dominate the physics. In particular, the random distribution of magnetic Ho ions in the diluted, spin-1=2 Ising system LiHo 0:045 Y 0:955 F 4 gives rise to regions where the local density of Ho is comparable to that of the pure compound, and hence are locally ferromagnetic or antiferromagnetic depending on the displacement between nearest neighbors. The Ising spins are constrained to point up or down along the crystallographic c axis, and can be controllably mixed with the application of a magnetic field H t tr...

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“…First ideas of utilizing electrostatic deflection for the separation of quantum states were introduced by Stern in 1926 20 . While early experiments were conducted on small molecules at high temperatures, we demonstrate the application of this technique to large polar molecules and clusters at low temperatures 16,21 .…”

Section: Introductionmentioning

confidence: 99%

Spatial Separation of Molecular Conformers and Clusters

Horke

Trippel

Chang

et al. 2014

JoVE

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Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules. Video LinkThe video component of this article can be found at

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Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld

Cited by 672 publications

References 2 publications

Quantum mechanics-The key to understanding magnetism

Quantum mechanics-The key to understanding magnetism

Quantum Projection in an Ising Spin Liquid

Spatial Separation of Molecular Conformers and Clusters

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