Magnetism: Causes of Susceptibility
What causes susceptibility?
Susceptibility is caused by interactions of electrons and nuclei with the externally applied magnetic field.
Nuclei and electrons each possess spin, a quantum mechanical property with no exact analogue in classical physics. Don't worry if you don't understand this. Not many people do. For now, it's OK just to think of nuclei and electrons as tiny spinning magnets. When nuclear and electron spins in a material orient in the same direction as the magnetic field, their individual magnetic moments locally augment the field. This augmentation of the external field is called paramagnetism. Subatomic particles may also create magnetic effects that oppose the applied field; this is called diamagnetism.
Electrons are much smaller than nuclei, so we can think of their spins being as being "concentrated" into smaller volumes. As a consequence of this spin/size discrepancy, electron-field interactions are thousands of times stronger than nuclear ones. Electrons, not nuclei, primarily determine overall magnetic susceptibility of a material.
In addition to having spin, electrons "orbit" the nucleus and possess a second quantum property - orbital angular momentum (L). How electrons are distributed among orbitals is critical in determining magnetic susceptibility. Orbitals containing paired electrons contribute to diamagnetism; orbitals with unpaired electrons contribute to paramagnetism.
In most substances there are several competing diamagnetic and paramagnetic effects whose net sum determines bulk susceptibility. The major mechanisms contributing to susceptibility are briefly described below:
1. Langevin (Larmor) diamagnetism. This phenomenon results from the angular momentum (L) of electrons in filled orbitals. Through a quantum process similar to Lenz' Law, the orbital motion of paired electrons generates an internal field that opposes the externally applied one. The effect is relatively weak, but because all molecules contain at least some filled orbitals, Langevin diamagnetism is present in all materials. Langevin diamagnetism dictates the overall susceptibility of a material unless it is overridden by a more powerful mechanism.
Water, most biological materials, nonmetallic atoms, stable salts, and covalently bonded molecules have no unpaired electrons, so their overall susceptibilities are dominated by Langevin diamagnetism. Their susceptibilities (χ) are weak and negative, typically with values close to −0.00001.
2. Van Vleck paramagnetism. This can be considered a minor counter-effect to Langevin diamagnetism, becoming important only for a few polyatomic molecules and certain atoms/ions with shells exactly one electron short of being half-filled. In water, for example, Van Vleck paramagnetism is only 10% the strength of Langevin diamagnetism.
3. Nuclear paramagnetism. Certain nuclei with non-zero spins (¹H, ¹³C, ²³Na, etc) - the same nuclei that undergo NMR - make a minimal positive contribution to the susceptibility of materials that contain them. As stated above, this effect is extremely small (typically < 0.01% of the already weak Langevin diamagnetism) so it can be largely disregarded except in the immediate vicinity of the nucleus.
4. Curie Paramagnetism. This important mechanism occurs in atoms and molecules with one or more unpaired electrons. It is moderately powerful -- a thousand times greater than Langevin diamagnetism. In such materials the unpaired electrons experience net "alignment" with the external field (similar to the net alignment of nuclei in NMR). This alignment augments the applied field and is therefore paramagnetic. Curie paramagnetism is important in:
Among the elements, gadolinium has one of the strongest Curie paramagnetic effects because it possesses 7 unpaired electrons in its 4f shells. For ions like gadolinium with partially filled shells whose magnetism comes purely from electron spin, the degree of expected paramagnetism is proportional to N(N + 2), where N = the number of unpaired electrons.
5. Mechanisms in simple metals (Pauli Paramagnetism and Landau Diamagnetism). Metals can be viewed as closed-shell cores surrounded by a "sea" of free conduction (valence) electrons. The cores have no unpaired electrons and thus exhibit only mild Langevin diamagnetism. The conduction electrons, however, interact more strongly with the external magnetic field. The usual dominant effect is to augment the applied field (Pauli paramagnetism), but they also generate an opposing field (Landau diamagnetism), which is usually smaller than the Pauli effect, but not always. Thus some metals with filled inner shells may demonstrate mild paramagnetism (Al, Ti), while others are weakly diamagnetic (Cu, Pb, Ag).
6. Exchange Coupling and Magnetic Domains. A few elemental and compound solids (containing transition metal and/or rare-earth atoms) demonstrate enormous positive susceptibilities that may even remain after the external magnetic field is removed. The resultant state is called ferromagnetism, whose origin is based on a quantum mechanical effect known as exchange coupling. These materials form magnetic domains - small regions whose spins become locked into orderly arrays and become spontaneously magnetized. Such phenomena are responsible for permanent magnetism of iron, nickel, cobalt and their alloys, and may manifest in different forms including ferromagnetism, ferrimagnetism, anti-ferromagnetism, and superparamagnetism, Ferromagnetism and its subtypes will be discussed more completely in several additional questions.
Nuclei and electrons each possess spin, a quantum mechanical property with no exact analogue in classical physics. Don't worry if you don't understand this. Not many people do. For now, it's OK just to think of nuclei and electrons as tiny spinning magnets. When nuclear and electron spins in a material orient in the same direction as the magnetic field, their individual magnetic moments locally augment the field. This augmentation of the external field is called paramagnetism. Subatomic particles may also create magnetic effects that oppose the applied field; this is called diamagnetism.
Electrons are much smaller than nuclei, so we can think of their spins being as being "concentrated" into smaller volumes. As a consequence of this spin/size discrepancy, electron-field interactions are thousands of times stronger than nuclear ones. Electrons, not nuclei, primarily determine overall magnetic susceptibility of a material.
In addition to having spin, electrons "orbit" the nucleus and possess a second quantum property - orbital angular momentum (L). How electrons are distributed among orbitals is critical in determining magnetic susceptibility. Orbitals containing paired electrons contribute to diamagnetism; orbitals with unpaired electrons contribute to paramagnetism.
In most substances there are several competing diamagnetic and paramagnetic effects whose net sum determines bulk susceptibility. The major mechanisms contributing to susceptibility are briefly described below:
1. Langevin (Larmor) diamagnetism. This phenomenon results from the angular momentum (L) of electrons in filled orbitals. Through a quantum process similar to Lenz' Law, the orbital motion of paired electrons generates an internal field that opposes the externally applied one. The effect is relatively weak, but because all molecules contain at least some filled orbitals, Langevin diamagnetism is present in all materials. Langevin diamagnetism dictates the overall susceptibility of a material unless it is overridden by a more powerful mechanism.
Water, most biological materials, nonmetallic atoms, stable salts, and covalently bonded molecules have no unpaired electrons, so their overall susceptibilities are dominated by Langevin diamagnetism. Their susceptibilities (χ) are weak and negative, typically with values close to −0.00001.
2. Van Vleck paramagnetism. This can be considered a minor counter-effect to Langevin diamagnetism, becoming important only for a few polyatomic molecules and certain atoms/ions with shells exactly one electron short of being half-filled. In water, for example, Van Vleck paramagnetism is only 10% the strength of Langevin diamagnetism.
3. Nuclear paramagnetism. Certain nuclei with non-zero spins (¹H, ¹³C, ²³Na, etc) - the same nuclei that undergo NMR - make a minimal positive contribution to the susceptibility of materials that contain them. As stated above, this effect is extremely small (typically < 0.01% of the already weak Langevin diamagnetism) so it can be largely disregarded except in the immediate vicinity of the nucleus.
4. Curie Paramagnetism. This important mechanism occurs in atoms and molecules with one or more unpaired electrons. It is moderately powerful -- a thousand times greater than Langevin diamagnetism. In such materials the unpaired electrons experience net "alignment" with the external field (similar to the net alignment of nuclei in NMR). This alignment augments the applied field and is therefore paramagnetic. Curie paramagnetism is important in:
- Atoms, molecules, and lattice defects with odd numbers of electrons (ions, NO, organic free radicals, charged molecules);
- Free atoms and ions with partly filled inner shells (transition metals, rare earth elements, actinides and lanthanides -- especially gadolinium);
- A few compounds with an even number of electrons but with unpaired spins in bonding or antibonding orbitals (O2).
Among the elements, gadolinium has one of the strongest Curie paramagnetic effects because it possesses 7 unpaired electrons in its 4f shells. For ions like gadolinium with partially filled shells whose magnetism comes purely from electron spin, the degree of expected paramagnetism is proportional to N(N + 2), where N = the number of unpaired electrons.
5. Mechanisms in simple metals (Pauli Paramagnetism and Landau Diamagnetism). Metals can be viewed as closed-shell cores surrounded by a "sea" of free conduction (valence) electrons. The cores have no unpaired electrons and thus exhibit only mild Langevin diamagnetism. The conduction electrons, however, interact more strongly with the external magnetic field. The usual dominant effect is to augment the applied field (Pauli paramagnetism), but they also generate an opposing field (Landau diamagnetism), which is usually smaller than the Pauli effect, but not always. Thus some metals with filled inner shells may demonstrate mild paramagnetism (Al, Ti), while others are weakly diamagnetic (Cu, Pb, Ag).
6. Exchange Coupling and Magnetic Domains. A few elemental and compound solids (containing transition metal and/or rare-earth atoms) demonstrate enormous positive susceptibilities that may even remain after the external magnetic field is removed. The resultant state is called ferromagnetism, whose origin is based on a quantum mechanical effect known as exchange coupling. These materials form magnetic domains - small regions whose spins become locked into orderly arrays and become spontaneously magnetized. Such phenomena are responsible for permanent magnetism of iron, nickel, cobalt and their alloys, and may manifest in different forms including ferromagnetism, ferrimagnetism, anti-ferromagnetism, and superparamagnetism, Ferromagnetism and its subtypes will be discussed more completely in several additional questions.
Susceptibilities of the Elements
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The table (above right) shows values of χ for various materials encountered in biological tissues and MRI. The videos below visibly demonstrate the diamagnetic properties of water and the paramagnetic properties of oxygen.
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References
Magnetic susceptibility of the elements and inorganic compounds. (Table from the Fermi National Accelerator Laboratory. Note these are molar susceptibilities given in the CGS-system units.)
Schenck JF. The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys 1996;23:815-850.
"Magnetic Susceptibility." Wikipedia, The Free Encyclopedia
Dresselhaus MS. MIT Course in Solid State Physics, Part III: Magnetic properties of Solids. (This publicly available document can also be obtained at web.mit.edu/course/6/6.732/www/6.732-pt3.pdf. A detailed, MIT-grad school level quantum mechanical explanation of susceptibility in its many forms.)
Magnetic susceptibility of the elements and inorganic compounds. (Table from the Fermi National Accelerator Laboratory. Note these are molar susceptibilities given in the CGS-system units.)
Schenck JF. The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys 1996;23:815-850.
"Magnetic Susceptibility." Wikipedia, The Free Encyclopedia
Dresselhaus MS. MIT Course in Solid State Physics, Part III: Magnetic properties of Solids. (This publicly available document can also be obtained at web.mit.edu/course/6/6.732/www/6.732-pt3.pdf. A detailed, MIT-grad school level quantum mechanical explanation of susceptibility in its many forms.)
Related Questions
I saw on the internet a video of a frog floating in a magnet. How does that happen? Did the frog become magnetized?
What is ferromagnetism?
What's so "super" about superparamagnetism?
I saw on the internet a video of a frog floating in a magnet. How does that happen? Did the frog become magnetized?
What is ferromagnetism?
What's so "super" about superparamagnetism?