You " found noticeable increasing in coercivity" compared to what? I would say that's important to know in order to start guessing.

Why guessing? Well the M(H) curve itself is not quite telling about the reason why it looks the way it does. That is because the major influence is actually the mechanism or mode of magnetization reversal. And there exist quite a few. Each of them may be governed by different quantities.

Dear Kai Fauth,

Sorry if my question was not so clear.

The increasing of coercivity was a result of increasing the thickness of the layers, whether if the change in thickness of the upper layer or the middle layer or both of them.

Please, you can see the edit of my question.

Dear Hisham Hashim,

it remains nearly impossible (well , to me at least) to give you good answers or even suggestions without knowing more about

• your films (materials, thickness considered), role of surface/interface roughness, intermixing and chemistry (does oxidation play a role), relative magnitude of remnant magnetization compared to saturation magnetization, what is known about magnetocrystalline and interface anisotropies, are the films crystalline at all...
• The configuration of your experiment (what is the easy axis of magnetization), which configuration of Kerr magnetometry do you use [OK, just saw it's transverse Kerr effect].
• Seeing an example of the type of M(H) data change might also help to produce constructive ideas.

At the end of the day, as I wrote before, the "why and how" question may have many answers. What you need is a model for the process of magnetization reversal. This will have various parameters including magnetization, the diverse anisotropy terms, exchange stiffness etc.

"Simple" isothermal M(H) magnetization loops do not tell you where change in magnetization along the curve is reversible (rotation) or irreversible (switching). knowing about this provides you with insight about the mechanism of magnetization reversal. There are experimental protocols for determining that. Extending Kerr magetometry to Kerr microscopy may also provide additional insight into whats going on (formation and propagation of domain walls, in case this contributes significantly to the magnetization reversal in your films).

My bottom line: if you have idea what the mechanism of magnetization reversal is in your material(s) and some knowledge about intrinsic magnetic material parameters, then it may be possible to work out a scenario explaining your finding. If that is not the case, then additional experimental input is most probably required.

Agree with Kai Fauth , there is no single word/line to tell about the Coercivity variation in any material. The material need to be invetigated as independent/isolated/pristine/single ferromagentic layer. Its is also important to understand the crytalline effect on the coercivity.

I suggest you to do systematic study of these films by chaning the parameter such as under/top layer, thickness and crystallinity etc one by one.

Moreover, coercivity is function of defect and pining centers in isolated single FM thin film. If you put other layer neaby to it, several exchange interaction may influence your coercivity.

It seems that your system is a multilayer structure. Therefore, carefull and systematic study needed to explain the facts behind the coercivity variation.

Kai Fauth

Thanks for your reply. You highlighted for different factors I should take it into account.

I need to understand what do you mean by this sentience:

"The configuration of your experiment (what is the easy axis of magnetization)"??

This is an example of the type of M(H) data change of three layers thin film, and the change only in the thickness of the second layer

Dear Sajid Husain,

Thanks for your answer. Actually, I think that the investigation as an independent ferromagnetic layer and understanding the crystalline effect on the coercivity are good ideas. So, I need to go in this way.

OK, from your data and knowing it's T-MOKE we already learn quite a bit about the (probable) configuration of the experiment. The easy direction of magnetization in both films lies in the plane. The magnetic field also is in the plane. Having the two well aligned is actually a good reason for using T-MOKE despite the fact that the effect is smaller than L-MOKE (or P-MOKE) and is a pure intensity variation (when working with p-polarized light which I think is what you need to do).

Can you actually say

• what the precision of your angular alignments is
• what happens (if that's possible) when you rotate the sample by 90° about the surface normal? (and what is the overall shape?)

The next question would be to know how stable your signals are. This question is really about intensity drifts. Maybe you have a very stable laser and a chopped beam with Lock-in detection. If that's the case I can show you what you can do and find out in the next post. (I'll need a little bit of time, though).

Here comes kind of an idea.

The idea is based on the following: quite visibly there are kinks in your M(H) curves. Most probably, when moving the field from "negative" saturation up to the kink, the magnetization only rotates (coherently). That is a reversible process. So if true, the "going backward" curve will be exactly the same as the "going forward" curve. Actually, there appears to be already some loss of magnetization in the "going forward" curve when reaching zero field. That may be intrinsic, but could also indicate a slight misalignment of your sample.

(This is, where it gets interesting to know more about magnetization curves with rotated samples. Shape anisotropy may play a role. What are the lateral dimensions of the film and how large and how well centered is the illuminated area? Lots of questions...)

What is indicated here is the measurement of "partial demagnetization". Whether or not you can reliably do it depends on the capability of your apparatus. Maybe you have to do some programming first.

Maybe you have to do many cycles to get an averaged cycle with good statistics. That need not be a problem. As long as your M(H) major loop is well reproducible, you know where you have stopped in the curve. So you can normalize to whatever and rescale to the known major loop.

The magnetization on you "going backward" curve at zero field will show you for each "return (or stop) field", how much magnetization is being lost due to irreversible processes. All of the magnetization recovered between stopping the "forward curve" and returning to zero field is due to rotation.

Well, having done this you're not finished with thinking about what it means, but you have input to start modeling what's going on.

And you can look for literature on "partial demagnetization" measurements and their evaluation as well as magnetization reversal in general and study. This is going to take time!

My guess is that you have coherent rotation until the kink, where domain walls are being introduced into the film. Increasing that film thickness not only increases coercivity but also the field (and hence energy density) required to produce the domain wall. This might already be able to help finding out whether these should be Néel walls or Bloch walls. (You will have to find out about their energetics in decent magnetism books).

A. Huber's https://www.springer.com/de/book/9783540641087 is the resource about magnetic domains.

Now, knowing what domain configurations (in particular magnetization orientations in domains having switched) to expect depends on material properties and on crystallinity (and definedness of the overal crystal orientation). The more you know the better.

Since you have two different materials as films (or even three) are they all intrinsically magnetic? What is known about their interaction at interfaces? What is the homogeneity of film thickness? (All this will probably contribute to the details).

Do also watch out for literature on "FORC".

Kai Fauth

Thank you very much for your attention and your time. Actually, you gave me a lot of guidance and helpful information. So, I need to read it with care.

Kindly, can I contact with you if I have more questions?

Hisham Hashim,

my pleasure, thank you.

Added a reference to let you have a first idea about FORC (and what the acronym actually stands for).

There are a lot of factors, not one or two factors, as others also mentioned earlier. Like material, grain size, domain configuration, strain and in case of thin films, surface roughness also plays a role.

@Hafsa Khurshid

In my study I'm interested in thin films. Please, could you give me more information or recommend me a good and clear reference?