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Paramagnetism is due to the presence of unpaired electrons in the material, so most atoms with incompletely filled atomic orbitals are paramagnetic, although exceptions such as copper exist. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. An external magnetic field causes the electrons' spins to ...
The magnitude of the paramagnetism is expressed as an effective magnetic moment, μ eff. For first-row transition metals the magnitude of μ eff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin–orbit coupling causes μ eff to deviate from the spin-only formula.
The difference between the chemical shift of a given nucleus in a diamagnetic vs. a paramagnetic environment is called the hyperfine shift.In solution the isotropic hyperfine chemical shift for nickelocene is −255 ppm, which is the difference between the observed shift (ca. −260 ppm) and the shift observed for a diamagnetic analogue ferrocene (ca. 5 ppm).
Due to the Pauli exclusion principle, each state is occupied by electrons of opposing spins, so that the charge density is compensated everywhere and the spin degree of freedom is trivial. Still, such materials typically do show a weak magnetic behaviour, e.g. due to diamagnetism or Pauli paramagnetism .
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons.The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei.
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field, assuming some simplifying assumptions (such as the sample system being ellipsoidal), one can derive a few compact thermodynamic relations. [4]
The Hamiltonian for an electron in a static homogeneous magnetic field in an atom is usually composed of three terms = + (+) + where is the vacuum permeability, is the Bohr magneton, is the g-factor, is the elementary charge, is the electron mass, is the orbital angular momentum operator, the spin and is the component of the position operator orthogonal to the magnetic field.
When Langevin published the theory paramagnetism in 1905 [12] [13] it was before the adoption of quantum physics. Meaning that Langevin only used concepts of classical physics. [17] Niels Bohr showed in his thesis that classical statistical mechanics can not be used to explain paramagnetism, and that quantum theory has to be used. [17]