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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?

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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.

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  • $\begingroup$ 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
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    $\begingroup$ @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

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