Magnetocaloric effect and electron energy levels

[potatowhisperer]

i am trying to understand the magnetocaloric effect from another point of view (besides thermodynamics ) , i know that under the influence of an external field , a zeeman splitting happens , and the electrons will have different levels of energy , those with + 1/2 spin will have a higher energy than those with -1/2 . is this separation what causes an increase in temperature ? , i know that after the zeeman splitting, a variation in the distribution will occur , the electrons with + 1/2 spin , will try to lower their energy to the same level as -1/2 electrons , by releasing releasing thermal energy . doesn't that mean they will get cooler ?
can someone please enlighten me ? thank you very much in advance .

 

[Charles Link]

I needed to google the topic, but I think I at least partially understand the explanation that was given. A magnetic field is introduced to a magnetic material and because the energy shift is $E=-\mu*B$, (magnetic moment $\mu$ is proportional to the spin), when thermal equilibrium is reached the lower energy spin state will have excess population. A state with aligned spins is also lower in energy without the magnetic field (presumably because of the Heisenberg exchange effect). When the magnetic field is removed, (in a material that exhibits this effect), the spins will once again become more randomized (from entropy effects). The system has now gone to a higher energy state, and in order to do this, thermal energy must be supplied by the material-thereby a cooling results. I'm on a learning curve here to, but I think I got it correct...editing...additional item is when the magnetic field is first applied, heat will be given off that needs to be dissipated as the system goes to a lower energy state. The cycle of applying the magnetic field, dissipating the heat and then removing the field can be repeated multiple times...

 

[potatowhisperer]

thank you very much for going through the trouble . so if i understand correctly :
when an external magnetic field is applied to a magnetic material an energy shift happens , electrons with spin moment parallel to the applied field will have a lower energy , those with a spin moment opposed to the applied field will be at a higher energy level . so far the temperature of the material does not change , right ? , to decrease its energy , the electrons will go from the higher energy level to the lower energy level , be releasing energy , this magnetic energy will be proportional to the difference between the levels , this magnetic energy that was released will be converted to a thermal energy , thus increasing the temperature of the system . so the alignment of the spins is what causes the increase in temperature. am i understanding this correctly ?

 

[Charles Link]

thank you very much for going through the trouble . so if i understand correctly :
when an external magnetic field is applied to a magnetic material an energy shift happens , electrons with spin moment parallel to the applied field will have a lower energy , those with a spin moment opposed to the applied field will be at a higher energy level . so far the temperature of the material does not change , right ? , to decrease its energy , the electrons will go from the higher energy level to the lower energy level , be releasing energy , this magnetic energy will be proportional to the difference between the levels , this magnetic energy that was released will be converted to a thermal energy , thus increasing the temperature of the system . so the alignment of the spins is what causes the increase in temperature. am i understanding this correctly ?

So far, you have it correct. Heat is released at this point and the temperature will of course rise until it is dissipated. If I understand it correctly, there will also be an exchange energy $E_s=-J s_1*s_2$ (where J is an exchange energy factor) that works between adjacent spins that results in a lowering of the energy for the aligned state. The externally applied field gives the system a push to go to this state. When the externally applied field is removed, and the spins randomize, both the change in $E=-\mu*B$ and $E_s=-J s_1*s_2$ terms will result in heat being absorbed (and resulting cooling of the material) to take the spins to the higher (randomized) energy state. (Note: The exchange effect adds an extra term, but it is likely to play an important role, just as it does with ferromagnetism and permanent magnets. The exchange effect makes it possible for the magnetism in permanent magnets to persist at temperatures as high as 1000 C. Without the exchange effect, thermal effects would disrupt the ferromagnetism except at extremely low temperatures.)

 

[potatowhisperer]

thank you so much . may i ask if you have a book/website that i can read or use as a reference ?

 

[Charles Link]

For the exchange effect and ferromagnetism, F. Reif's "Statistical and Thermal Physics" does a good job with ferromagnetism and the Weiss mean field theory (Heisenberg exchange effect), along with the Curie temperature (above which thermal effects disrupt the ferromagnetism.) . He might also treat the magnetocaloric effect in his book. I can also offer a suggestion: the magnetocaloric effect is a somewhat specialized topic. An important and part of magnetism in materials is introduced in a homework problem that a physics student posted a couple of weeks ago. The magnetic surface currents in this problem are a very important concept. (Griffith's mentions them in his E&M textbook, but they can easily be overlooked.) Here is a "link" to that homework problem:
https://www.physicsforums.com/threads/magnetic-field-of-a-ferromagnetic-cylinder.863066/ I gave the student a thorough response and I think he found it helpful. It is a good problem that illustrates some of the basic concepts.

 

[potatowhisperer]

thank you soo much for your help , it is immensely, immensely! appreciated .

 

[Charles Link]

I could mention one additional item involving the exchange effect which my prove useful. The exchange effect results in electron spins clustering together (in the same direction) and behaving as a unit. It should be noted that the magnetic field in materials comes from applied fields (such as from the current in a solenoid) along with the fields from magnetic surface currents. The exchange effect makes it much more energetically favorable for the spins to align and make the magnetized state much more stable and not so easily disrupted by thermal effects. It would take very little thermal energy to flip the spin of a single isolated electron that is held in the lower spin state by the magnetic field inside a permanent magnet. When coupled to a cluster of its neighbors (where each experiences a strong exchange coupling to its nearest neighbors), the aligned spin is not so easily disrupted by thermal effects, making for very high Curie temperatures. The magnetocaloric effect is similar to ferromagnetism in that it involves the alignment of spins in the same direction. Just like with magnets, not all materials would be expected to behave similarly. In some ferromagnetic materials, upon removal of the applied magnetic field, small domains of magnetization occur, with a somewhat random direction of the magnetization of the individual domains. In other materials, the alignment of the spins persists upon removal of the applied field (without the formation of all kinds of individual domains), making for a good permanent magnet. (Incidentally, it is the magnetic surface currents from the magnetization that are the source of the magnetic field that maintains the magnetization in a permanent magnet once the external applied field is removed). In the magnetocaloric effect, it is necessary that the spins randomize themselves in some form (rather than staying in alignment) upon removal of the applied field to achieve the cooling that occurs. Hopefully this extra info was helpful.

 

[potatowhisperer]

i seriously can not thank you enough for adding this little bit . i have a question ,does this mean that the magnetocaloric effect is stronger in paramagnetic materials ?

 

[Charles Link]

i seriously can not thank you enough for adding this little bit . i have a question ,does this mean that the magnetocaloric effect is stronger in paramagnetic materials ?

This I will need to research further. I have seen "soft" iron as a type of iron that makes a lot of domains with net zero bulk magnetization upon removal of the applied field as being useful for transformers because it doesn't form a permanent magnet when a field is applied. The permanent magnet state would not be wanted in an ac transformer (with a high level of DC magnetization), because the susceptibility curve (of M vs. H) (H=applied field) levels off and it would then have weaker ac response. Paramagnetism I think would also imply low magnetic susceptibility, but I'm still learning the details...

 

[potatowhisperer]

so sorry for bothering you , you have already given me more than enough help . saying'' working with para is better than ferro '' is a bit hard,i imagine . as you yourself said , not all materials would be expected to behave similarly . thank you