A magnon is a
quasiparticle
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For exam ...
, a
collective excitation
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For ex ...
of the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s'
spin structure in a
crystal lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized
spin wave
A spin wave is a propagating disturbance in the ordering of a magnetic material. 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 carry a fixed amount of
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
and
lattice momentum, and are spin-1, indicating they obey
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
behavior.
Brief history
The concept of a magnon was introduced in 1930 by
Felix Bloch
Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of ne ...
in order to explain the reduction of the
spontaneous magnetization
Spontaneous magnetization is the appearance of an ordered spin state ( magnetization) at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or .
Overview
Heated to tempe ...
in a
ferromagnet
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...
. At
absolute zero
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
temperature (0 K), a
Heisenberg ferromagnet
A spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as ...
reaches the state of lowest energy (so-called
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
), in which all of the atomic spins (and hence
magnetic moment
In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...
s) point in the same direction. As the temperature increases, more and more spins deviate randomly from the alignment, increasing the internal energy and reducing the net magnetization. If one views the perfectly magnetized state at zero temperature as the
vacuum state
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as ...
of the ferromagnet, the low-temperature state with a few misaligned spins 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
(reduced Planck's constant) and the magnetization by
, where
is the
gyromagnetic ratio
In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...
. This leads to Bloch's law for the temperature dependence of spontaneous magnetization: