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Multipolar Exchange Interaction
Magnetic materials with strong spin-orbit interaction, such as: LaFeAsO, PrFe4P12, YbRu2Ge2, UO2, NpO2, Ce1−xLaxB6, URu2Si2 and many other compounds, are found to have magnetic ordering constituted by high rank multipoles, e.g. quadruple, octople, etc. Due to the strong spin-orbit coupling, multipoles are automatically introduced to the systems when the total angular momentum quantum number J is larger than 1/2. If those multipoles are coupled by some exchange mechanisms, those multipoles could tend to have some ordering as conventional spin 1/2 Heisenberg problem. Except the multipolar ordering, many hidden order phenomena are believed closely related to the multipolar interactions Tensor operator expansion Basic concepts Consider a quantum mechanical system with Hilbert space spanned by , j,m_ \rangle , where j is the total angular momentum and m_ is its projection on the quantization axis. Then any quantum operators can be represented using the basis set \lbrace , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Angular Momentum Quantum Number
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is \mathbf j = \mathbf s + \boldsymbol ~. The associated quantum number is the main total angular momentum quantum number ''j''. It can take the following range of values, jumping only in integer steps: , \ell - s, \le j \le \ell + s where ''ℓ'' is the azimuthal quantum number (parameterizing the orbital angular momentum) and ''s'' is the spin quantum number (parameterizing the spin). The relation between the total angular momentum vector j and the total angular momentum quantum number ''j'' is given by the usual relation (see angular momentum quantum number) \Vert \mathbf j \Vert = \sqrt \, \hbar The vector's ''z''-projection is given b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Operator
In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are very useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory. Operators in classical mechanics In classical mechanics, the movement of a particle (or system of particles) is completely determined by the Lagrangian L(q, \dot, t) or equivalently the Hamiltonian H(q, p, t), a function of the generalized coordinates ''q'', generalized velocities \dot = \mathrm q / \mathrm t and its conjugate momenta: :p = \frac If either ''L'' or ''H'' is independent of a generalized coordinate ''q'', meaning the ''L'' and ''H'' do not change when ''q'' is changed, which in turn means the dynamics of the particle are still the same e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Operator
In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. The general notion of scalar, vector, and tensor operators In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3-j Symbol
In quantum mechanics, the Wigner 3-j symbols, also called 3''-jm'' symbols, are an alternative to Clebsch–Gordan coefficients for the purpose of adding angular momenta. While the two approaches address exactly the same physical problem, the 3-''j'' symbols do so more symmetrically. Mathematical relation to Clebsch–Gordan coefficients The 3-''j'' symbols are given in terms of the Clebsch–Gordan coefficients by : \begin j_1 & j_2 & j_3 \\ m_1 & m_2 & m_3 \end \equiv \frac \langle j_1 \, m_1 \, j_2 \, m_2 , j_3 \, (-m_3) \rangle. The ''j'' and ''m'' components are angular-momentum quantum numbers, i.e., every (and every corresponding ) is either a nonnegative integer or half-odd-integer. The exponent of the sign factor is always an integer, so it remains the same when transposed to the left, and the inverse relation follows upon making the substitution : : \langle j_1 \, m_1 \, j_2 \, m_2 , j_3 \, m_3 \rangle = (-1)^ \sqrt \begin j_1 & j_2 & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multipolar Exchange Interactions
Multipolar or multipolarity can refer to: * Polarity (international relations) * Multipolar neuron A multipolar neuron is a type of neuron that possesses a single axon and many dendrites (and dendritic branches), allowing for the integration of a great deal of information from other neurons. These processes are projections from the neuron cell ... See also * Tripolar (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flipping The Phases Of Multipoles
Flipping is a term used to describe purchasing a revenue-generating asset and quickly reselling (or "flipping") it for profit. Within the real estate industry, the term is used by investors to describe the process of buying, rehabbing, and selling properties for profit. In 2017, 207,088 houses or condos were flipped in the US, an 11-year high. In the United Kingdom, "flipping" is used to describe a technique whereby Members of Parliament were found to be switching their second home between several houses, which had the effect of allowing them to maximize their taxpayer funded allowances. Types Wholesaling and assigning a contract Wholesalers make a profit by signing a contract to purchase a property from a seller and then entering into an agreement with a third party to sell their role of buyer in the contract to an end buyer. All rights to the original purchase contract are assigned to the new buyer and the new buyer pays an "assignment fee" to the wholesaler in order to gain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AFM Multipole Chain
AFM may refer to: Organizations * AFM Records, a German record label * Africa Fighting Malaria, a health campaign in Africa * Alex von Falkenhausen Motorenbau, a German racing car constructor * American Federation of Motorcyclists, a road racing club in the US * American Federation of Musicians, a labor union of musicians in North America * American Film Market, an annual event for the financing of film production and distribution * American Freedom Mortgage, Inc., a corporation based in Georgia, U.S. * Apostolic Faith Mission of South Africa, a Pentecostal Christian denomination in South Africa * Australia First Movement, an Australian fascist organisation during the second world war. * Autoriteit Financiële Markten, Netherlands financial markets regulator * Macau Football Association, the governing body of football in Macau * Armed Forces of Malta, the name given to the combined armed services of Malta Publications * ''Aquarium Fish Magazine'', a North American monthly mag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933. Generally, antiferromagnetic order may exist at sufficiently low temperatures, but vanishes at and above the Néel temperature – named after Louis Néel, who had first identified this type of magnetic ordering. Above the Néel temperature, the material is typically paramagnetic. Measurement When no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. In an external magnetic field, a kind of ferrimagnetic behavior may be displayed in the antiferromagnetic phase, with the absolute value of one of the sublattice magneti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnetic
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 are the familiar metals noticeably attracted to a magnet, a consequence of their large magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an ''external'' magnetic field, and it is this temporarily induced magnetization inside a steel plate, for instance, which accounts for its attraction to the permanent magnet. Whether or not that steel plate acquires a permanent magnetization itself, depends not only on the strength of the applied field, but on the so-called coercivity of that material, which varies greatly among ferromagnetic materials. In physics, several different types of material magnetism are distinguished. Ferromagnetism (along with the similar effect ferrimagneti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Ordering
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Magnetism is one aspect of the combined phenomena of electromagnetism. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones are iron, cobalt, and nickel and their alloys. The rare-earth metals neodymium and samarium are less common examples. The prefix ' refers to iron because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4. All substances exhibit some type of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
