# I Saturation magnetization of iron as a function of temperature

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1. Jun 26, 2018

### umby

Hi, I am looking for the temperature dependence of the saturation magnetization of Fe. Any help?

2. Jun 26, 2018

Here is a previous thread on Physics Forums about the temperature dependence of the magnetization and the Curie temperature. The formula of interest is contained in posts 2 and 3: https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/ The saturation magnetization is approximately the same as the magnetization of a permanent magnet, but they are not exactly the same thing. $\\$ If the material does not make a permanent magnet, I think the same formula may still be applicable to give the approximate magnetization that occurs for relatively high applied magnetic fields.

Last edited: Jun 26, 2018
3. Jun 27, 2018

### umby

many thanks!

4. Jun 27, 2018

### essenmein

Isn't saturation defined as all magnetic dipoles aligned? Ie a further increase of external magnetic field does not increase the magnetic flux beyond that of vacuum. Short of the change in density due to temperature the number of dipoles doesn't significantly change, therefore Bsat should be ~ temp independent?

Now its willingness to hold onto that magnetization does depend on temp.

5. Jun 27, 2018

I agree, and this is why I told the OP that saturation and the level of magnetization $M$ in a permanent magnet are not exactly the same thing.

6. Jun 28, 2018

### umby

Approaching the Curie temperature, the saturation magnetization (the magnetic moment per unit volume at saturation) of a ferromagnetic material should not go to zero?

7. Jun 28, 2018

### umby

Is there a law to describe this phenomenon?

8. Jun 28, 2018

You can try to google "the temperature dependence of magnetic permeability". I was able to find this: https://www.google.com/search?q=magnetic+permeability+vs+temperature&sa=X&rlz=1CASMAI_enUS803&biw=1366&bih=654&tbm=isch&source=iu&ictx=1&fir=AX4ierIuB_aX3M%3A%2CqbHqX83I7tNh9M%2C_&usg=__Uij0rI2Ck0_GwdbgMw2GBQFmFcM=&ved=0ahUKEwi5uIWFvfbbAhUEEqwKHdWkAGEQ9QEILTAC#imgrc=AX4ierIuB_aX3M: $\\$ Also see: https://physics.stackexchange.com/questions/293737/magnetic-susceptibility-of-ferromagnets $\\$ One complicating feature here is that there are basically two types of ferromagnetic magnetic materials: Those that make permanent magnets, and those that have high permeability but do not make permanent magnets. $\\$ And two or three terms are used to describe basically the same phenomenon: Permeabiity $\mu$ and susceptibility $\chi$ and relative permeability $\mu_r$:$\\$ $B=\mu_r \mu_o H$ with $B=\mu_o H+M$, while $M=\mu_o \chi H$ gives $\mu_r=1+\chi$. The permeability $\mu$ and relative permeability $\mu_r$ are related by $\mu=\mu_o \mu_r$, so that $B=\mu H$. $\\$ The temperature dependence of the susceptibility and its dramatic fall off at the Curie temperature as the material goes from ferromagnetic to paramagnetic is quite interesting. This is the subject of the graph in the second "link" above.

Last edited: Jun 28, 2018
9. Jun 28, 2018

### essenmein

Have to be careful with terminology here.

Saturation = all magnetic dipoles aligned, this is a physical property based on the number of atoms in the material that have a magnetic moment. This changes only with density (with in the constraints of classical physics at least, I assume you could change this property with extremes of gravity or radiation).

Saturation B max does not change with temperature, however the external applied field needed to reach this does (magnetic susceptibility).

Now basically all magnetic materials have some level of hysteresis, ie apply an external field, and remove it, and some level of internal magnetization remains if the forces due to the now aligned dipoles is not enough to disorder them again. All magnets will self demagnetize to some extent based on this, if you go look lat the load lines of neo materials, this is very shape dependent (and temperature dependent). The field the moments induce wants to undo those aligned moments, and if the shape (and external reluctance) is such that the induced field is enough to demag, they will demag to that point.

The currie temperature is where thermal agitation is overcoming the "stickiness" of those magnetic moments within the material, and they spontaneous fall back into disorder (currie point). Ie the material will no longer hold a magnetic field once an external field is removed.

This thermal agitation also affects how the dipoles want to align to an external field, ie they are vibrating now and take more force to hold in place, the hotter a material gets the more the thermal "vibrations" over power the aligning forces of the external field on the magnetic dipole. So while its harder to align the individual atoms, they can still be aligned with enough field.

So as I understand it Bmax does not change, but susceptibility does, ie permeability is temp dependent.

10. Jun 28, 2018

### essenmein

Oh the law you are looking for is the "Currie-Weiss law".

11. Jun 28, 2018

### umby

Can i try to summarize with a picture?

So, the saturation is always the same, but the higher the temperature is, the higher the field needed to reach it; then, at a given external field, the same material can be at saturation at a certain temperature but can be not at saturation at an higher temperature.

12. Jun 28, 2018

The curve does not show the tremendously dramatic change that occurs at the Curie temperature (below the Curie temperature, the susceptibility is much higher), but otherwise, I think it has the right idea. Also, be sure and see my post 8 including a couple additions to it.

13. Jun 28, 2018

### essenmein

Yup, so the slope of T1, T2 etc is the permeability of the material, if you plotted this value over a wide range of temp above and below the currie temp, it would be high below the currie temp, and nose dive to barely above u0, which is the dramatic effect Charles Link is referring too.

14. Jun 28, 2018

### umby

I forgot to tell that the picture was depicting the situation below the curie point.

15. Jun 28, 2018

### umby

essenmein, Charles Link, now all is much more clear. Thank you so much.

16. Jun 29, 2018

### umby

Dear essenmein, could you please clarify this point? I think this explains why some material loose the magnetization as the external field is removed.

17. Jun 30, 2018

### essenmein

Permanent magnets do not want to remain magnetised, being magnetised is a higher energy state for the material and it will try to release that energy to go back to its lower unmagnetised energy state.

The mechanism is the internal (demagnetising) field a permanent magnet generates opposes the external (stray) magnetic field (note we are not talking about flux density B, but the H field). If you look at the ohms law equivalent for magnetic circuits, V (or EMF) = MMF (A/m), reluctance = resistance and flux density = current. So around a magnetic circuit, the sum of H around the loop = 0, since the magnet has external field, it must generate an identical but opposite internal field, much like a AA battery, when you measure it you see the external EMF of 1.5V, which means internally it has generated -1.5V, other wise Kirchoff would get upset.

There is nothing magical about permanent magnets or ferro magnetic materials, they all have an unpaired electron in the outer shell, so they have lots of little amperian loops which you can "turn" or align within the structure of the material and they either stay there (hard magnetic materials) or they change willingly with changing external field (soft magnetic materials). Important is that with moving charge (ie one electron orbiting its atom) you generate H, and B happens as a result of the magnetic path, one does not exist without the other. Also important is that a moving charge experiences a force due to flux density B, not H.

So a permanent magnet is a source of H field generated by all the little internal current loops being aligned and adding together. Then since magnetic insulation is not a thing, a magnet in free space will have magnetic flux dependant on the total reluctance path in the outer loop (ie not the magnet), importantly the reluctance of the magnet itself and the strength of the internal H field. Vaccum will always complete the loop around the magnet, but adding magnetic conductors (ie the soft magnetic materials) reduces this reluctance, producing more B for a given H.

Demagnetization happens when the total reluctance path is low enough that a given H generates more B than the magnetic dipoles can "hold" before they are forced to align with the new H field. Remember its flux density that ultimately puts a force on a moving charge (ie the dipole), and its exceeding a certain flux density that causes that dipole to move. All thats happening is the total reluctance path and the internally generated H causes the magnet it self to exceed the flux density and therefore the forces needed to re-align the dipoles.

Self demagnetisation of a permanent magnet of a given material in free space is entirely driven by the shape of the magnet, more specifically the ratio of its length to area. Larger length to area ratio is more resistant to demagnetisation.

18. Jun 30, 2018

This subject of why one ferromagnetic material makes a permanent magnet while another goes to a state of zero net magnetization, but where there are microscopic domains, each of which has perhaps a rather random orientation, can get very complicated, and I have yet to see a good simple model that explains all of these details. For a permanent magnet, the magnetized state is, in fact, one of lower energy. $\\$ Calculation of the magnetic fields of permanent magnets by computing the magnetic surface currents and using Biot-Savart does lend some insight into what is going on in these permanent magnets. A couple threads that you might find of interest are https://www.physicsforums.com/threads/magnetic-field-of-a-ferromagnetic-cylinder.863066/ and https://www.physicsforums.com/threa...thin-magnetized-cylinder.949570/#post-6013061 $\\$ The magnetic surface current approach can be very useful in getting some understanding of the magnetic field of a permanent magnet. The magnetic fields from the magnetic surface currents that are a result of the boundary of the magnetization of the material is what supplies the mechanism to maintain the magnetization in a permanent magnet at a level that is very near the saturation level in the absence of externally applied fields. $\\$ One very complicating factor in all of this is the exchange effect, and the result is that the magnetization $\vec{M}$ is no longer simply a function of the magnetic field $\vec{B}$ at a given point, but is also influenced by the magnetization (magnetic moments) that occur in the vicinity of the point in question.

19. Jul 2, 2018

I would like to make a couple additional comments to the previous post, in regard to the exchange effect, which is quite strong in ferromagnetic materials, and the magnetization $M$ at a given point is affected by the magnetization that is in the vicinity of a point under consideration. A good portion of the literature uses $M=\chi H$, where $H$ is the applied field in the case of a long cylindrical geometry in a solenoid. Because of hysteresis, $\chi$ is, in general, not a constant, and $M=M(H)$ is only partially valid, because, if you look at a hysteresis curve, you will see that $M$ can take on different values for a given $H$, and is not a single-valued function. $\\$ In studying the problem, it occurred to me that perhaps it might be an improvement to write $M=M(B)$, so that $M=\chi' B$ might offer an improved description in the response of the materials. The $B$ would include the magnetic field from magnetic surface currents, besides the $H$ from the applied field of the solenoid. For some materials, particularly permanent magnets, this does offer an improved description of the response. It does not offer an improved description though for materials that do not make permanent magnets. The equation would predict that, with the inclusion of the magnetic surface currents, in general, you would get a permanent magnet state from most or even all ferromagnetic materials. It puzzled me why this new description of $M=M(B)$ and $M=\chi' B$ was particularly deficient in the case of materials that do not form permanent magnets. The reason seems to involve the exchange effect. These equations attempt to link together the effects at the same location, i.e. $M(x)=\chi' B(x)$, when in fact, with the exchange effect, $M(x)$ depends not only on $B(x)$, but also on $M(x')$ for locations $x' \neq x$, so that $M(x)=M((B(x), M(x'))$, etc.. This exchange effect that needs to take into account the state of neighboring locations puts a monkey wrench into the works of any and all attempts to describe the magnetic system with a simple mathematical description. $\\$ In these magnetic systems, in many cases, individualized domains are forming, each with their own specific orientation of the vector $\vec{M}$. The resulting system is mathematically quite complex. $\\$ One of the better theories that incorporates the effects of neighboring atoms is the Weiss molecular field approach. See e.g. https://www.tcd.ie/Physics/research/groups/magnetism/files/lectures/5006/5006-5.pdf