In General > s.a. electromagnetism / effects and phenomenology; history of physics; magnetism in astrophysics and cosmology.
$ Magnetic Field: A pseudo-vector defined, in 3D terms, or on a spacelike hypersurface with unit normal na, by

B = ∇ × A,   Bi = εijkj Ak = \(1\over2\)εijk Fjk ,   or   Ba:= \(1\over2\)εabcd nb Fcd = \(1\over2\)εabc Fcd .

* Remark: One view of the magnetic field is that it is just a convenient device to encode the transformation law for the electric field, or the relativistic aspects of the interactions between moving charges, without using special relativity (<RMS).
* Ampère's law: In the SI system, and in the differential and integral forms, respectively,

∇ × B = μ0 j + μ0ε0 (∂E/∂t) ,    \(\int_C\)B · ds = μ0 I + μ0ε0 (d/dt) \(\int_S\) E · dA .

* Values: Earth's magnetic field is about 0.5 G or 5 × 10−5 T; The strongest fields obtained with permanent magnets have magnitudes above 5 T; 2011, The field with the largest magnitude so far, 91.4 T, has been produced at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR).
@ General references: Guimarães 05 [I]; Barbieri et al EJP(13) [vector potential, pedagogical]; Nishimura a1401 [Biot-Savart law, Ampère's law, and synthetic differential geometry]; Skomski 12 [simple models, IIb].
@ Ampère-Maxwell law: Heller AJP(92)jan; Monsivais AJP(04)sep [integral form, arbitrarily-moving surfaces]; Manogue et al AJP(06)apr [teaching].
@ Specific solutions: Behtouei et al a2004 [magnetic field of solenoid].
> Types of magnetic fields: see quantum systems [self-linking fields].

Magnetic Dipole Moment > s.a. angular momentum [bound on ratio?]; Gyromagnetic Ratio; solutions in general relativity.
* Models: The "Gilbert" model uses separated monopoles, the standard "Ampère" model uses a current loop; The latter constitutes an interesting manifestation of "hidden momentum".
* History: The electron (or muon) magnetic moment has been used as a precise check for QED predictions.
@ References: Hnizdo AJP(12)jul [for a moving electric dipole]; Bezerra et al EJP(12) [in introductory courses]; in Griffiths & Hnizdo AJP(13)aug [models]; Novello & Bittencourt IJMPA(14) [anomalous, proposal for origin].
> For specific types of particles: see electron; neutrino; particles [leptons, muons]; hadrons; supersymmetry [muons].

Magnetism in Matter > s.a. electricity [Faraday's law]; electromagnetism in matter; Hysteresis; Magnon; Susceptibility; technology [magnets].
* Permeability: The second-rank tensor μ (often isotropic, μij = diag(μ, μ, μ), and identified with a scalar) such that B = μ H.
* Diamagnetism: The phenomenon in which the induced magnetism in a substance tends to decrease the total magnetic field, and the induced one opposes the external field; It can happen with atoms that don't have a permanent dipole moment (Langevin diamagnetism) and with non-localized electrons in a metal (Landau diamagnetism); > s.a. Van Leeuwen's Theorem; Wikipedia page.
* Ferromagnetism: An extreme form of paramagnetism, occurring at T < TCurie, which corresponds to a phase transition (not in the Ehrenfest classification); Exhibited by, e.g., Fe and Ni; > s.a. coupled-spin models [including antiferromagnetism]; ising model; Nagaoka Model.
* Paramagnetism: The phenomenon in which the induced magnetism in a substance tends to enhance the total magnetic field – the atoms have a permanent magnetic moment and try to line up with the external field.
* Measurement: The most sensitive ones use muon spin rotation; Other methods include SQUIDs [high sensitivity], scanning Hall probe microscopes [high spatial resolution], and BECs [nT sensitivity, 3-micron resolution].
@ General references: Van Vleck RMP(78); Mattis 81, 85; De Masi et al PRL(85) [microscopic derivation]; Jiles 91; Craik 95; Mattis 06; Majlis 07; Furrer & Waldmann RMP(13) [magnetic clusters, excitations]; Subedi et al PRL(13) + Park & Paulsen Phy(13) [spin-reversal avalanche].
@ Ferromagnetism: Esposito AP(09)-a0805 [Majorana's theory]; Katsnelson et al RMP(08) [half-metallic]; Gholizade & Momeni JSP(10)-a1011 [electron gas]; Balk et al PRB(14) + news pt(14)nov [critical behavior of zero-field magnetic fluctuations].
@ Paramagnetism: Bethlem Phy(08) [and forces on atoms]; Vijayaraghavan & Gard AP(13) [Monte Carlo simulations of magnetization relaxation].
@ Measurement: news pn(06)jul [with BECs]; news Phys(19) [with quantum non-demolition measurements]; synopsis Phy(18)sep [diamond-defect magnetometers]; Ghosh et al a1912 [and precision tests of fundamental physics].
@ Related topics: news PT(00)may, news pw(07)mar [μ < 0]; news pw(07)feb [phase transition near 0 K]; news pw(13)apr [high-sensitivity atomic magnetometers]; Peng et al PRL(15) [Lee-Yang zeros and observation of imaginary magnetic fields].

@ References: Price et al PRL(14) [Berry curvature as a momentum-space magnetic field].

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