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[1]: 117 The formula above is known as the Langevin paramagnetic equation. Pierre Curie found an approximation to this law that applies to the relatively high temperatures and low magnetic fields used in his experiments. As temperature increases and magnetic field decreases, the argument of the hyperbolic tangent decreases.
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} .
The Curie temperature of nanoparticles is also affected by the crystal lattice structure: body-centred cubic (bcc), face-centred cubic (fcc), and a hexagonal structure (hcp) all have different Curie temperatures due to magnetic moments reacting to their neighbouring electron spins. fcc and hcp have tighter structures and as a results have ...
An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of 1 / H . This behaviour is known as the De Haas–Van Alphen effect and relates the period of the susceptibility with the Fermi surface of the material.
Here μ 0 is the permeability of free space; M the magnetization (magnetic moment per unit volume), B = μ 0 H is the magnetic field, and C the material-specific Curie constant: = (+), where k B is the Boltzmann constant, N the number of magnetic atoms (or molecules) per unit volume, g the Landé g-factor, μ B the Bohr magneton, J the angular ...
A useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequencies in a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other through some scalar permeability, at high frequencies these quantities will react to each other with some lag time. [36]
The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q m (Wb) = μ 0 q m (Am).
The effect is weak because it depends on the magnitude of the induced magnetic moment. It depends on the number of electron pairs and the chemical nature of the atoms to which they belong. This means that the effects are additive, and a table of "diamagnetic contributions", or Pascal's constants, can be put together.