
Magnetic fields induce changes in materials, cooling, transitions, or structural patterns.Magnetic field effects encompass a wide range of phenomena where magnetic fields alter the physical properties of materials, including inducing phase transitions, cooling (magnetocaloric effect), changing electrical resistance (magnetoresistance), or organizing particles into structured patterns. These effects arise from the interaction between the magnetic field and the spins or orbital motion of electrons, which can lead to macroscopic changes in a material's behavior.
The foundational effects were discovered in the 19th century (e.g., Faraday's magneto-optical effect, 1845) and the Zeeman effect (1896). The magnetocaloric effect was discovered by Emil Warburg in 1881, and giant magnetoresistance (GMR) was found in 1988 by Albert Fert and Peter Grünberg, leading to the 2007 Nobel Prize in Physics.
A magnetic field exerts a torque on magnetic moments (electron spins) and affects the motion of charged particles via the Lorentz force. In materials, this can align spins, suppress or enhance superconductivity, shift energy levels (Zeeman effect), or modify the density of states near the Fermi level. In magnetic fluids, the field induces dipole-dipole interactions that cause particles to chain into filaments. In magnetocaloric materials, changing the field alters the magnetic entropy, which is compensated by heat absorption or release from the lattice, leading to temperature changes.
Magnetic fields are used in magnetic resonance imaging (MRI), magnetic refrigeration, hard disk read heads (GMR), and controlling the behavior of magnetic nanoparticles in targeted drug delivery.
The Meissner effect, where a superconductor expels all magnetic fields, can be observed at room temperature in certain high-temperature superconductors, though still requiring very low temperatures compared to everyday life.
| Δφ | variable | Difference in work functions — work function difference joule |
| φ₁ | variable | Work function of material 1 — work function joule |
| φ₂ | variable | Work function of material 2 — work function joule |
| B | variable | Magnetic field strength — magnetic field strength tesla |
| v | variable | Characteristic velocity of plasma flow — velocity metre per second |
| ρ | variable | Mass density of the plasma — mass density kilogram per cubic metre |
| √ | operator | Takes the square root of the argument — square root |
| l_B | variable | Magnetic length — length metre |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| ħ | constant | Reduced Planck constant, fundamental quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second |
| e | constant | Elementary charge, the magnitude of charge of an electron — elementary charge = 1.602176634e-19 coulomb |
| √ | operator | Square root of the argument — square root |
| B_{\mathrm{sat}} | variable | saturated magnetic field strength — magnetic flux density tesla |
| v_{\mathrm{rms}} | variable | root-mean-square turbulent velocity — velocity metre per second |
| f_{\mathrm{sat}} | variable | fraction of turbulent energy converted to magnetic energy |
| \rho | variable | mass density of the medium — mass density kilogram per cubic metre |
| \sqrt{} | operator | takes the square root of the argument — square root |
| Δn | variable | Change in refractive index — refractive index change |
| E | variable | Applied electric field — electric field volt per metre |
| r | constant | Pockels coefficient (linear electro-optic coefficient) — pockels coefficient = varies by material (e.g., 30.8e-12 for L metre per volt |
| \theta | variable | Angle between the magnetic moments of two interacting spins — angle radian |
| J | variable | Exchange coupling strength between the two magnetic moments — exchange coupling joule |













