Repeated magnetic layers not implemented

[acaruana2009]

Currently it is not possible to define a magnetic multilayer in the same way you can specify a non-magnetic multilayer. E.g.:

Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer = Slab(material=Ni, thickness=100, interface=5)
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML = (Ni_layer(magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1"))
      | Si_layer)

sample = (Si_sub
          | ML*2
          | air
          )

Raises: NotImplementedError("Repeated magnetic layers not implemented") from line 162 in refl1d/profile.py

The work around is to define the magnetism in the Slab instantiation, and define the multilayer as a list/tuple: ML = (Ni_layer, Si_layer)
This has the disadvantage that if you are doing multi-fits (say multiple fields), unlinking the magnetism between fits becomes tedious.

[bmaranville]

Can you provide your counterexample as code here, where you define the magnetism in the Slab and then define the multilayer as a list?

[acaruana2009]

# Set materials/SLDs
Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer = Slab(material=Ni, thickness=100, interface=5,
                magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1"))
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML = (Ni_layer, Si_layer)

sample = (Si_sub
          | ML*2
          | air
          )

The above should work.

[bmaranville]

Ok - I can see the difference clearly - but I still don't completely understand the problem. How do you want to unlink the magnetism between fits, vs. how you have to do it now?

[acaruana2009]

Currently I would define a separate Slab for each field. Then later on in the code I would have to make all of the thicknesses/interfaces for the different Slabs equal to each other. I am sure this could be solved with FreeVars but I have never got my head around that.

Also, if users are expecting to put together a repeating stack in a certain way for XRR or NR, it is confusing then to extend it to a magnetic layer to then find it doesn't work.

for example the code below also fails in the same way:

# Set materials/SLDs
Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer = Slab(material=Ni, thickness=100, interface=5,
                magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1"))
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML = (Ni_layer | Si_layer)

sample = (Si_sub
          | ML*2
          | air
          )

[bmaranville]

I think what I am not understanding is how the problem would be solved if the above code worked, instead of throwing an error. How would you be able to unlink the magnetism between fits more easily for repeated Stack vs. the same Slab object many times?

[acaruana2009]

No problem, let me put together an example in both cases:

If it worked:

# Set materials/SLDs
Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer = Slab(material=Ni, thickness=100, interface=5)
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML_1T = (Ni_layer(magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1.0T"))
      | Si_layer)

sample_1T = (Si_sub
          | ML_1T*2
          | air
          )

ML_0p1T = (Ni_layer(magnetism=Magnetism(rhoM=0.2, interface_above=5, interface_below=5, name="Ni Layer Sample 0.1T"))
      | Si_layer)

sample_0p1T = (Si_sub
          | ML_0p1T*2
          | air
          )

Ni_layer.thickness.range(0, 1500)

And currently:

# Set materials/SLDs
Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer_1T = Slab(material=Ni, thickness=100, interface=5,
                magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1T"))
Ni_layer_0p1T = Slab(material=Ni, thickness=100, interface=5,
                magnetism=Magnetism(rhoM=0.2, interface_above=5, interface_below=5, name="Ni Layer Sample 0.1T"))
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML_1T = (Ni_layer_1T, Si_layer)

sample_1T = (Si_sub
          | ML_1T*2
          | air
          )

ML_0p1T = (Ni_layer_0p1T, Si_layer)

sample_0p1T = (Si_sub
          | ML_0p1T*2
          | air
          )

Ni_layer_0p1T.thickness = Ni_layer_1T.thickness
Ni_layer_0p1T.thickness.range(0, 1500)

Code above not fully tested in both cases.

This isn't too bad for one magnetic layer, and two fields, but it could quickly get messy with a larger number of both. Equally I think you can define the ML within the sample object as well if you want to make it slightly more compact or want to put it in a loop.

[bmaranville]

I think the main purpose of the Repeat structure is to make the calculation go faster, and magnetic Repeat would take quite a bit of effort to implement correctly.

On the other hand, even though it's a bit weird that a Slab object is callable, that particular trick works the same whether you're using a tuple or making a stack, so the code below works just fine. Note that __call__ method in Slab is just calling copy.copy() on itself and then replacing any attribute of thickness, interface or magnetism that is present in the kwargs (not deepcopy) - so that thickness and interface attributes are linked in the new instance by default.

If you wanted to be more explicit and not rely on the __call__ magic, you could just call copy(Ni_layer) directly in your scripts and replace the magnetism attr on the copies.

from refl1d.names import *

# Set materials/SLDs
Si = Material(formula="Si")
Ni = Material(formula="Ni[58]")
Si_ml = Material(formula="Si")


Si_sub = Slab(material=Si, thickness=0, interface=5)
Ni_layer = Slab(material=Ni, thickness=100, interface=5)
Si_layer = Slab(material=Si_ml, thickness=100, interface=5)

# Sample construction/Stack

ML_1T = (Ni_layer(magnetism=Magnetism(rhoM=2.0, interface_above=5, interface_below=5, name="Ni Layer Sample 1.0T"))
      , Si_layer)

sample_1T = (Si_sub
          | ML_1T*2
          | air
          )

ML_0p1T = (Ni_layer(magnetism=Magnetism(rhoM=0.2, interface_above=5, interface_below=5, name="Ni Layer Sample 0.1T"))
      , Si_layer)

sample_0p1T = (Si_sub
          | ML_0p1T*2
          | air
          )

Ni_layer.thickness.range(0, 1500)

# Make a simple PolarizedNeutronProbe
probe = PolarizedNeutronProbe(pp = NeutronProbe(T=np.linspace(0.001, 0.10, 101), dT=0.001, L=4.75, dL=0.1))

experiment_1T = Experiment(sample=sample_1T, probe=probe, name="Ni/Si Multilayer 1.0T")
experiment_0p1T = Experiment(sample=sample_0p1T, probe=probe, name="Ni/Si Multilayer 0.1T")

assert experiment_1T.sample[0].thickness is experiment_0p1T.sample[0].thickness, "Thickness parameter not shared!"
assert experiment_1T.sample[1].magnetism.rhoM is not experiment_0p1T.sample[1].magnetism.rhoM, "Magnetism parameter is shared!"

[acaruana2009]

Thanks for this. Yes I must admit I hadn't thought to try that in the list (or if I had I have forgotten!). Yes that would work. I still feel that at some point we should sort out the magnetic repeat even if it is a lot of work, just to make it consistent with the non-magnetic repeat - especially if it speed up the calculation. But I understand that this may not be where we want to put our resources right now.