What Is a Magnetic Moment and Its Significance?

[Priyadarshini]

Hi! I recently learned about magnetic moments of atoms and their ions. I understand the formula and the calculations. However, what exactly IS a magnetic moment? What does the value in Bohr Magnetons give us? How does this value affect the properties of the atom/ion?
Thanks in advance!

 

[blue_leaf77]

Magnetic (dipole) moment is just the first term in the multipole expansion of a current distribution. In an atom, electron moves with some velocity around the nucleus, therefore there must be a net current associated with this movement. The magnetic moment of a free atom does nothing upon itself, however its influence to the electronic states begins to emerge when the atom interacts with external magnetic fields. See also "Zeeman effect".

 

[Priyadarshini]

Magnetic (dipole) moment is just the first term in the multipole expansion of a current distribution. In an atom, electron moves with some velocity around the nucleus, therefore there must be a net current associated with this movement. The magnetic moment of a free atom does nothing upon itself, however its influence to the electronic states begins to emerge when the atom interacts with external magnetic fields. See also "Zeeman effect".

What do you mean by "the multipole expansion of a current distribution"? Magnetic moments are the same as dipole moments? (excuse my ignorance, but I'm not exactly sure what dipole moments are... In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right? But where and what exactly is the dipole moment?)

 

[blue_leaf77]

This subject might be more of a physics subject rather than chemistry. First of all, it's important to realize that there are in general two groups of multipole expansion: multipole expansion of charge distribution and multipole expansion of current distribution. To go further you must go through the related chapter which I don't really recommend if you are only interested in the practical aspect of it. Anyway, I hope this link http://www.pas.rochester.edu/~dmw/phy217/Lectures/Lect_20b.pdf can give you a more graphical picture about multipole expansion for charge distribution, especially in the first slide bottom part where there are 4 different charge configuration. The left most one is the so-called monopole, as we go to the right: dipole, quadrupole, and octopole. They are just the first 4 of infinite number of expansion terms, however as we go to higher terms, the contribution to the expanded quantity (e.g. electric potential) will usually die down and we can simply take the first few terms.

The same goes for current distribution which will generate magnetic multipole expansion. Likewise there are also monopole, dipole, quadrupole terms and so on, however it had been shown that the monopole term for magnetic expansion is always zero, leaving the dipole term to be the most important term in the expansion.

Magnetic moments are the same as dipole moments?

As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.

In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right?

The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.

 

[Priyadarshini]

This subject might be more of a physics subject rather than chemistry. First of all, it's important to realize that there are in general two groups of multipole expansion: multipole expansion of charge distribution and multipole expansion of current distribution. To go further you must go through the related chapter which I don't really recommend if you are only interested in the practical aspect of it. Anyway, I hope this link http://www.pas.rochester.edu/~dmw/phy217/Lectures/Lect_20b.pdf can give you a more graphical picture about multipole expansion for charge distribution, especially in the first slide bottom part where there are 4 different charge configuration. The left most one is the so-called monopole, as we go to the right: dipole, quadrupole, and octopole. They are just the first 4 of infinite number of expansion terms, however as we go to higher terms, the contribution to the expanded quantity (e.g. electric potential) will usually die down and we can simply take the first few terms.

The same goes for current distribution which will generate magnetic multipole expansion. Likewise there are also monopole, dipole, quadrupole terms and so on, however it had been shown that the monopole term for magnetic expansion is always zero, leaving the dipole term to be the most important term in the expansion.

As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.

The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.

The maths on the pdf link you provided was a wee bit confusing (I haven't learned integration or limits yet :/ ) But I get the general idea about the differences between monopoles, dipoles, quadrupoles and octopoles. The pdf talks about just the multipole expansion of charge distribution only, right? Is the graphical idea of current distribution similar/the same? Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right? Besides charge, electric and magnetic, are there any other sorts of dipole moments?

 

[blue_leaf77]

The pdf talks about just the multipole expansion of charge distribution only, right?

Yes it does.

Is the graphical idea of current distribution similar/the same?

Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.

Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right?

The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.

Besides charge, electric and magnetic, are there any other sorts of dipole moments?

Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.

 

[Priyadarshini]

Yes it does.

Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.

The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.

Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.

Thank you for your help! :)