| Condensed matter physics |
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A magnon is a quasiparticle, a collective excitation of the spin structure of an electron in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, indicating they obey boson behavior.
The concept of a magnon was introduced in 1930 by Felix Bloch [1] in order to explain the reduction of the spontaneous magnetization in a ferromagnet. At absolute zero temperature (0 K), a Heisenberg ferromagnet 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 (the reduced Planck constant) and the magnetization by , where is the gyromagnetic ratio. This leads to Bloch's law for the temperature dependence of spontaneous magnetization:
where is the (material dependent) critical temperature, and is the magnitude of the spontaneous magnetization.
The quantitative theory of magnons, quantized spin waves, was developed further by Theodore Holstein and Henry Primakoff, [2] and then by Freeman Dyson. [3] Using the second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose–Einstein statistics (bosons). A comprehensive treatment can be found in the solid state textbook by Charles Kittel [4] or the early review article by Van Kranendonk and Van Vleck. [5]
Direct experimental detection of magnons by inelastic neutron scattering in ferrite was achieved in 1957 by Bertram Brockhouse. [6] Since then magnons have been detected in ferromagnets, ferrimagnets, and antiferromagnets.
The fact that magnons obey the Bose–Einstein statistics was confirmed by the light scattering experiments done during the 1960s through the 1980s. Classical theory predicts equal intensity of Stokes and anti-Stokes lines. However, the scattering showed that if the magnon energy is comparable to or smaller than the thermal energy, or , then the Stokes line becomes more intense, as follows from Bose–Einstein statistics. Bose–Einstein condensation of magnons was proven in an antiferromagnet at low temperatures by Nikuni et al. [7] and in a ferrimagnet by Demokritov et al. at room temperature. [8] In 2015 Uchida et al. reported the generation of spin currents by surface plasmon resonance. [9]
Paramagnons are magnons in magnetic materials which are in their high temperature, disordered (paramagnetic) phase. For low enough temperatures, the local atomic magnetic moments (spins) in ferromagnetic or anti-ferromagnetic compounds will become ordered. Small oscillations of the moments around their natural direction will propagate as waves (magnons). At temperatures higher than the critical temperature, long range order is lost, but spins will still align locally in patches, allowing for spin waves to propagate for short distances. These waves are known as a paramagnon, and undergo diffusive (instead of ballistic or long range) transport.
The concept was first proposed based on the spin fluctuations in transition metals, by Berk and Schrieffer [10] and Doniach and Engelsberg, [11] to explain additional repulsion between electrons in some metals, which reduces the critical temperature for superconductivity.
Magnon behavior can be studied with a variety of scattering techniques. Magnons behave as a Bose gas with no chemical potential. Microwave pumping can be used to excite spin waves and create additional non-equilibrium magnons which thermalize into phonons. At a critical density, a condensate is formed, which appears as the emission of monochromatic microwaves. This microwave source can be tuned with an applied magnetic field.
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero, i.e., 0 K. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which microscopic quantum-mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. More generally, condensation refers to the appearance of macroscopic occupation of one or several states: for example, in BCS theory, a superconductor is a condensate of Cooper pairs. As such, condensation can be associated with phase transition, and the macroscopic occupation of the state is the order parameter.
Spintronics, also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices. The field of spintronics concerns spin-charge coupling in metallic systems; the analogous effects in insulators fall into the field of multiferroics.
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas, and why other properties differ.
Tunnel magnetoresistance (TMR) is a magnetoresistive effect that occurs in a magnetic tunnel junction (MTJ), which is a component consisting of two ferromagnets separated by a thin insulator. If the insulating layer is thin enough, electrons can tunnel from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly quantum mechanical phenomenon, and lies in the study of spintronics.
In condensed matter physics, 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, which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice. As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization. The energies of spin waves are typically only μeV in keeping with typical Curie points at room temperature and below.
Spin pumping is the dynamical generation of pure spin current by the coherent precession of magnetic moments, which can efficiently inject spin from a magnetic material into an adjacent non-magnetic material. The non-magnetic material usually hosts the spin Hall effect that can convert the injected spin current into a charge voltage easy to detect. A spin pumping experiment typically requires electromagnetic irradiation to induce magnetic resonance, which converts energy and angular momenta from electromagnetic waves to magnetic dynamics and then to electrons, enabling the electronic detection of electromagnetic waves. The device operation of spin pumping can be regarded as the spintronic analog of a battery.
In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was first predicted by Lars Onsager in 1949 in connection with superfluid helium. Onsager reasoned that quantisation of vorticity is a direct consequence of the existence of a superfluid order parameter as a spatially continuous wavefunction. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.
The Gross–Pitaevskii equation describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model.
Spin-polarized scanning tunneling microscopy (SP-STM) is a type of scanning tunneling microscope (STM) that can provide detailed information of magnetic phenomena on the single-atom scale additional to the atomic topography gained with STM. SP-STM opened a novel approach to static and dynamic magnetic processes as precise investigations of domain walls in ferromagnetic and antiferromagnetic systems, as well as thermal and current-induced switching of nanomagnetic particles.
In a standard superconductor, described by a complex field fermionic condensate wave function, vortices carry quantized magnetic fields because the condensate wave function is invariant to increments of the phase by . There a winding of the phase by creates a vortex which carries one flux quantum. See quantum vortex.
Discovered only as recently as 2006 by C.D. Stanciu and F. Hansteen and published in Physical Review Letters, this effect is generally called all-optical magnetization reversal. This magnetization reversal technique refers to a method of reversing magnetization in a magnet simply by circularly polarized light and where the magnetization direction is controlled by the light helicity. In particular, the direction of the angular momentum of the photons would set the magnetization direction without the need of an external magnetic field. In fact, this process could be seen as similar to magnetization reversal by spin injection. The only difference is that now, the angular momentum is supplied by the circularly polarized photons instead of the polarized electrons.
A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions were originally envisioned in the context of the fractional quantum Hall effect, but subsequently took on a life of their own, exhibiting many other consequences and phenomena.
Spin engineering describes the control and manipulation of quantum spin systems to develop devices and materials. This includes the use of the spin degrees of freedom as a probe for spin based phenomena. Because of the basic importance of quantum spin for physical and chemical processes, spin engineering is relevant for a wide range of scientific and technological applications. Current examples range from Bose–Einstein condensation to spin-based data storage and reading in state-of-the-art hard disk drives, as well as from powerful analytical tools like nuclear magnetic resonance spectroscopy and electron paramagnetic resonance spectroscopy to the development of magnetic molecules as qubits and magnetic nanoparticles. In addition, spin engineering exploits the functionality of spin to design materials with novel properties as well as to provide a better understanding and advanced applications of conventional material systems. Many chemical reactions are devised to create bulk materials or single molecules with well defined spin properties, such as a single-molecule magnet. The aim of this article is to provide an outline of fields of research and development where the focus is on the properties and applications of quantum spin.
In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids. The term "orbital" distinguishes it from the contribution of spin degrees of freedom, Mspin, to the total magnetization. A nonzero orbital magnetization requires broken time-reversal symmetry, which can occur spontaneously in ferromagnetic and ferrimagnetic materials, or can be induced in a non-magnetic material by an applied magnetic field.
The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher, in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It was observed in a gravitational neutron interferometer in 1989 and later by fluxon interference of magnetic vortices in Josephson junctions. It has also been seen with electrons and atoms.
Bose–Einstein condensation can occur in quasiparticles, particles that are effective descriptions of collective excitations in materials. Some have integer spins and can be expected to obey Bose–Einstein statistics like traditional particles. Conditions for condensation of various quasiparticles have been predicted and observed. The topic continues to be an active field of study.
The term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself was formulated for fermions, the quasi-particles present within Dirac matter can be of any statistics. As a consequence, Dirac matter can be distinguished in fermionic, bosonic or anyonic Dirac matter. Prominent examples of Dirac matter are graphene and other Dirac semimetals, topological insulators, Weyl semimetals, various high-temperature superconductors with -wave pairing and liquid helium-3. The effective theory of such systems is classified by a specific choice of the Dirac mass, the Dirac velocity, the gamma matrices and the space-time curvature. The universal treatment of the class of Dirac matter in terms of an effective theory leads to a common features with respect to the density of states, the heat capacity and impurity scattering.
Spinor condensates are degenerate Bose gases that have degrees of freedom arising from the internal spin of the constituent particles . They are described by a multi-component (spinor) order parameter. Since their initial experimental realisation, a wealth of studies have appeared, both experimental and theoretical, focusing on the physical properties of spinor condensates, including their ground states, non-equilibrium dynamics, and vortices.
In condensed matter physics, the quantum dimer magnet state is one in which quantum spins in a magnetic structure entangle to form a singlet state. These entangled spins act as bosons and their excited states (triplons) can undergo Bose-Einstein condensation (BEC). The quantum dimer system was originally proposed by Matsubara and Matsuda as a mapping of the lattice Bose gas to the quantum antiferromagnet. Quantum dimer magnets are often confused as valence bond solids; however, a valence bond solid requires the breaking of translational symmetry and the dimerizing of spins. In contrast, quantum dimer magnets exist in crystal structures where the translational symmetry is inherently broken. There are two types of quantum dimer models: the XXZ model and the weakly-coupled dimer model. The main difference is the regime in which BEC can occur. For the XXZ model, the BEC occurs upon cooling without a magnetic field and manifests itself as a symmetric dome in the field versus temperature phase diagram centered about H = 0. The weakly-coupled dimer model does not magnetically order in zero magnetic field, but instead orders upon the closing of the spin gap, where the BEC regime begins and is a dome centered at non-zero field.
YuryMikhailovich Bunkov is a Russian experimental physicist, specializing in condensed matter physics. He is known as one of the co-discoverers of the quantum spin liquid state.
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