A magnon is a
quasiparticle, a
collective excitation of the
electrons'
spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
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 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 new ...
in order to explain the reduction of the
spontaneous magnetization in a
ferromagnet. 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 vibratio ...
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), in which all of the atomic spins (and hence
magnetic moments) 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 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, , gamma. Its ...
. This leads to Bloch's law for the temperature dependence of spontaneous magnetization: