Magnon
Encyclopedia
A magnon is a collective excitation of the electron
s' spin
structure in a crystal lattice. In contrast, a phonon
is a collective excitation of the crystal lattice atoms or ion
s. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave
. As a quasiparticle
, a magnon carries a fixed amount of energy
and lattice momentum. It also possesses a spin
of ħ (where ħ is the reduced Planck constant).
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s' spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
structure in a crystal lattice. In contrast, a phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
is a collective excitation of the crystal lattice atoms or ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave
Spin wave
Spin waves are propagating disturbances in the ordering of magnetic materials. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are boson modes of the spin lattice...
. As a quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
, a magnon carries a fixed amount of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
and lattice momentum. It also possesses a spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
of ħ (where ħ is the reduced Planck constant).
Brief history
- The concept of a magnon was introduced in 1930 by Felix BlochFelix BlochFelix Bloch was a Swiss physicist, working mainly in the U.S.-Life and work:Bloch was born in Zürich, Switzerland to Jewish parents Gustav and Agnes Bloch. He was educated there and at the Eidgenössische Technische Hochschule, also in Zürich. Initially studying engineering he soon changed to physics...
in order to explain the reduction of the spontaneous magnetizationSpontaneous magnetizationSpontaneous magnetization is the term used to describe the appearance of an ordered spin state at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or .-Overview:...
in a ferromagnet. At absolute zeroAbsolute zeroAbsolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
temperature, a ferromagnet reaches the state of lowest energy, in which all of the atomic spins (and hence magnetic momentMagnetic momentThe magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
s) point in the same direction. As the temperature increases, more and more spins deviate randomly from the common direction, thus increasing the internal energy and reducing the net magnetization. If one views the perfectly magnetized state at zero temperature as the vacuum stateVacuum stateIn quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
of the ferromagnet, the low-temperature state with a few spins out of alignment can be viewed as a gas of quasiparticles, in this case magnons. Each magnon reduces the total spin along the direction of magnetization by one unit of ħ and the magnetization itself by γħ , where γ is the gyromagnetic ratio.
- The quantitative theory of quantized spin waves, or magnons, was developed further by Theodore Holstein and Henry Primakoff (1940) and Freeman DysonFreeman DysonFreeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...
(1956). By using the formalism of second quantization they showed that the magnons behave as weakly interacting quasiparticles obeying the Bose-Einstein statistics (the bosons).
- For a brief outline of the theory see spin waveSpin waveSpin waves are propagating disturbances in the ordering of magnetic materials. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are boson modes of the spin lattice...
. A comprehensive treatment can be found in Kittel's textbook or in the article by Van Kranendonk and Van Vleck.
- A direct experimental detection of magnons by means of inelastic neutron scatteringNeutron scatteringNeutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
in ferrite was achieved in 1957 by Bertram BrockhouseBertram BrockhouseBertram Neville Brockhouse, was a Canadian physicist. He was awarded the Nobel Prize in Physics "for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter", in particular "for the development of neutron spectroscopy".-Life:Brockhouse was...
. Since then magnons have been detected in ferromagnets, ferrimagnets, and antiferromagnets.
- The fact that magnons obey the Bose-Einstein statistics was confirmed at latest by the light scattering experiments from magnons in 1960s-1980s. According to the classical theory the intensity of the Stokes and anti-Stokes lines in the light scattering spectrum should be the same. However, experimentally it was shown that if the energy of magnon ħω is comparable or smaller than the thermal energy
, the Stokes line becomes more intensive as it is followed from the Bose-Einstein statistics. The effect of Bose-Einstein condensation of magnons was proven recently in an antiferromagnet at low temperatures by Nikuni et al. and in a ferrimagnet by Demokritov et al. at room temperature. See the news report by Schewe and Stein and the scientific articles by Nikuni et al. and Demokritov et al. for more details.