# Magnetic susceptibility in 1/eV

In this paper the authors refer to

transverse susceptibility $\chi_{ \perp}$ [meV $^{−1}$]

I was taught that the magnetic susceptibility is dimensionless.

How do I get $\chi$ in the above units??

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In one place it is given in emu/mol, whatever that may be. – Georg Mar 23 '11 at 22:06
Excellent question :) – David Zaslavsky♦ Mar 23 '11 at 23:12
At any rate, whatever you were taught, it's clear that $\chi_\perp$, defined as a coefficient in equation 2 of that paper, has the unit of inverse energy, just like they indicate. $\int d^3 x$ cancels against $abc$, one time derivative cancels against  $\partial_t$, the other $\partial_t$ combined with one $\hbar$ gives one energy which has to be cancelled for $S$ to have the right dimension of the other $\hbar$. So maybe you should have already asked a different question about the previous texts such as eqn 2. $\chi_\perp$ is apparently normalized differently than you think. – Luboš Motl May 4 '11 at 11:40

## 1 Answer

Magnetic susceptibility is a static constant relating the amount of magnetization to the applied magnetic field; it is dimensionless. Transverse susceptibility is a measure of the magnetic response of a material to an alternating field; it is not dimensionless. The transverse susceptibility is often used when talking to the ferromagnetic resonance (like I think they are doing in the paper you cite) of a material.

So the short answer is that MS is dimensionless and TS is not.

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Ok, this is something I didn't know. Anyway, as Georg already mentioned, the authors use the value given in emu/mol to evaluate $\chi _{\perp}$. How should I convert between these units? – Pie86 Mar 24 '11 at 8:37
I could not find the TS given in emu/mol. emu/mol are the units of molar susceptibility.  Molar susceptibility is postulated in Curie's law for paramagnetic material.  Though I must admit this is a dense paper (and not in my field) so in order to keep it from taking up my morning I've just been skimming it. – AOA Mar 24 '11 at 16:34
It's in the caption of "Table 1" (near the end). Anyway I want to thank you for your help and the precious information about TS. – Pie86 Mar 24 '11 at 20:10
'emu' should only be used as a shorthand IMHO.  It is difficult to convert without context, and is an unfortunate cgs anachronism.  It stands for "electromagnetic unit" and can mean simply the volume of a field (here it usually means cm^3) or it can mean magnetic moment (erg/G).  I suspect that if I was more familiar with operating an NMR I would be able to give you a better crafted answer. – AOA Mar 25 '11 at 3:44
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