Clarification on Interlayer Exchange Prefactor for SAF with One Spacer Layer in MuMax3

[Sandhya Ravi]

Hi Sir,

Thank you very much for your valuable comments regarding my implementation of the interlayer antiferromagnetic exchange coupling.

My implementation is based on the official MuMax3 custom field tutorial, where the interlayer exchange is implemented as:

cellsize := 1e-9 

AFMAex := -5e-13 

Ms := 580e3

prefactorZ := Const((2 * AFMAex) / (cellsize * cellsize * Ms)) 

up := Mul(prefactorZ, Mul(Add(Mul(Const(-1), m), Shifted(m, 0, 0, 2)), Shifted(Const(1),0, 0, 2))) 

down := Mul(prefactorZ, Mul(Add(Mul(Const(-1), m), Shifted(m, 0, 0, -2)), Shifted(Const(1), 0, 0, -2))) 

Bc := Add(up, down) 

AddFieldTerm(Bc) 

AddEdensTerm(Mul(Const(-0.5), Dot(Bc, M_full)))

In my simulation, I have modified this implementation for a synthetic antiferromagnet consisting of:

1. Layer 2: Top ferromagnetic layer(1 nm)
2. Layer 1: Nonmagnetic spacer (1 nm)
3. Layer 0: Bottom ferromagnetic layer(1 nm)

The two ferromagnetic layers are therefore separated by one spacer cell, and I use Shifted(m, 0, 0, ±2) exactly as in the tutorial.

After reading your comment,

"The prefactor is the distance between the cells that are exchange coupled. So if there is a spacer layer of thickness cellsize, the cells are 2 cellsizes apart, not just one."

I wanted to confirm my understanding.

Should the prefactor be modified to account for the actual center-to-center distance between the coupled magnetic cells, i.e.,

distance := 2 * cellsize prefactorZ := Const((2 * AFMAex) / (distance * distance * Ms_eff))

which is equivalent to

prefactorZ := Const(AFMAex / (2 * cellsize * cellsize * Ms_eff))

Or should I continue using the original tutorial expression,

prefactorZ := Const((2 * AFMAex) / (cellsize * cellsize * Ms_eff))

even though the magnetic layers are separated by one spacer layer?

I would be grateful if you could clarify which expression is physically correct for this geometry. I want to ensure that my implementation is consistent before using it .

Thank you very much for your time and assistance.

Kind regards,

Sandhya R