Qualitatively, what fundamental physical property stops a paramagnetic material from reaching a high magnetic saturation under an applied field? This question is similar to the one asked here: Why do paramagnetic materials require large fields to achieve magnetic saturation?.

I am given to understand that it's thermal fluctuations that prevent the magnetic moments of a paramagnetic material aligning, i.e. thermal fluctuations at room temperature have a significantly larger effect on electron spin orientation than an applied field. Is that accurate, or is there another physical principle that causes paramagnets to have such low susceptibility?


1 Answer 1


While there may be other effects I don't know about, the thermal effects are certainly sufficient to explain it. The energy associated with a spin flip is on the order of the Bohr magneton times the applied magnetic field. For a magnetic field of 1 T this works out to be on the order of $\Delta E \approx 6 \times 10^{-5}$ eV. But in a thermal environment at temperature $T$, energy fluctuations with $\Delta E \ll k T$ happen pretty much at will; and $k T$ for a room-temperature sample is about 0.025 eV ("one-fortieth of an eV" is the mnemonic I was taught as a young physicist.)

To approach saturation, you would need $\Delta E \gtrsim k T$, which would require either reducing the temperature (in Kelvin) by a factor of about 500, increasing the magnetic field by a factor of 500, or some combination thereof.

  • $\begingroup$ Thanks very much! So the low magnetisation can be explained by the lack of field reinforcement by exchange interaction? $\endgroup$
    – Connor
    Dec 16, 2021 at 16:06
  • 1
    $\begingroup$ @Connor: The exchange interaction would be one of those "other effects I don't know about" (or at least am not familiar enough with to comment on meaningfully.) :-) $\endgroup$ Dec 16, 2021 at 16:09
  • $\begingroup$ So does this mean that if, say, I cooled down a block of Aluminum in liquid Helium, going to about 4 K, it would then become a bit sticky to a decently strong magnet? $\endgroup$ Dec 16, 2021 at 21:31
  • $\begingroup$ @The_Sympathizer: I suspect so. You probably don't even need to get it that cold, since you don't need to saturate the magnetization to get a noticeable effect. Famously, a 10-Tesla magnetic field can cause significant effects on water-based objects at room temperature; water is diamagnetic rather than paramagnetic, but the magnitudes of the forces would be the same. $\endgroup$ Dec 16, 2021 at 21:59
  • $\begingroup$ @Michael Seifert: Though getting access to a super powerful 10 T magnet is not easy, so cooling it down should be applied. If we want to be able to do it with 1 T, then we need 10x but that's still about 30 K which is cooler than liquid nitrogen. What do you do? $\endgroup$ Dec 16, 2021 at 22:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.