// Finds the average exchange strength around each cell, for debugging.
func ExchangeDecode(dst *data.Slice, Aex_red SymmLUT, regions *Bytes, mesh *data.Mesh) {
c := mesh.CellSize()
wx := float32(2 * 1e-18 / (c[X] * c[X]))
wy := float32(2 * 1e-18 / (c[Y] * c[Y]))
wz := float32(2 * 1e-18 / (c[Z] * c[Z]))
N := mesh.Size()
pbc := mesh.PBC_code()
cfg := make3DConf(N)
k_exchangedecode_async(dst.DevPtr(0), unsafe.Pointer(Aex_red), regions.Ptr, wx, wy, wz, N[X], N[Y], N[Z], pbc, cfg)
}
// Add effective field of Dzyaloshinskii-Moriya interaction to Beff (Tesla).
// According to Bagdanov and Röβler, PRL 87, 3, 2001. eq.8 (out-of-plane symmetry breaking).
// See dmi.cu
func AddDMI(Beff *data.Slice, m *data.Slice, Aex_red, Dex_red SymmLUT, regions *Bytes, mesh *data.Mesh) {
cellsize := mesh.CellSize()
N := Beff.Size()
util.Argument(m.Size() == N)
cfg := make3DConf(N)
k_adddmi_async(Beff.DevPtr(X), Beff.DevPtr(Y), Beff.DevPtr(Z),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
unsafe.Pointer(Aex_red), unsafe.Pointer(Dex_red), regions.Ptr,
float32(cellsize[X]*1e9), float32(cellsize[Y]*1e9), float32(cellsize[Z]*1e9), N[X], N[Y], N[Z], mesh.PBC_code(), cfg)
}
// Set s to the toplogogical charge density s = m · (m/∂x ❌ ∂m/∂y)
// See topologicalcharge.cu
func SetTopologicalCharge(s *data.Slice, m *data.Slice, mesh *data.Mesh) {
cellsize := mesh.CellSize()
N := s.Size()
util.Argument(m.Size() == N)
cfg := make3DConf(N)
icxcy := float32(1.0 / (cellsize[X] * cellsize[Y]))
k_settopologicalcharge_async(s.DevPtr(X),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
icxcy, N[X], N[Y], N[Z], mesh.PBC_code(), cfg)
}
// Add Zhang-Li ST torque (Tesla) to torque.
// see zhangli.cu
func AddZhangLiTorque(torque, m, J *data.Slice, bsat, alpha, xi, pol LUTPtr, regions *Bytes, mesh *data.Mesh) {
c := mesh.CellSize()
N := mesh.Size()
cfg := make3DConf(N)
k_addzhanglitorque_async(torque.DevPtr(X), torque.DevPtr(Y), torque.DevPtr(Z),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
J.DevPtr(X), J.DevPtr(Y), J.DevPtr(Z),
float32(c[X]), float32(c[Y]), float32(c[Z]),
unsafe.Pointer(bsat), unsafe.Pointer(alpha), unsafe.Pointer(xi), unsafe.Pointer(pol),
regions.Ptr, N[X], N[Y], N[Z], mesh.PBC_code(), cfg)
}
// Add exchange field to Beff.
// m: normalized magnetization
// B: effective field in Tesla
// Aex_red: Aex / (Msat * 1e18 m2)
// see exchange.cu
func AddExchange(B, m *data.Slice, Aex_red SymmLUT, regions *Bytes, mesh *data.Mesh) {
c := mesh.CellSize()
wx := float32(2 * 1e-18 / (c[X] * c[X]))
wy := float32(2 * 1e-18 / (c[Y] * c[Y]))
wz := float32(2 * 1e-18 / (c[Z] * c[Z]))
N := mesh.Size()
pbc := mesh.PBC_code()
cfg := make3DConf(N)
k_addexchange_async(B.DevPtr(X), B.DevPtr(Y), B.DevPtr(Z),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
unsafe.Pointer(Aex_red), regions.Ptr,
wx, wy, wz, N[X], N[Y], N[Z], pbc, cfg)
}
// Add interlayer exchange field to Beff.
// see interlayer.cu
func AddInterlayerExchange(Beff, m *data.Slice, J1_red, J2_red, toplayer, bottomlayer LUTPtr, direc LUTPtrs, regions *Bytes, mesh *data.Mesh) {
cellsize := mesh.CellSize()
N := Beff.Size()
util.Argument(m.Size() == N)
cfg := make3DConf(N)
k_addinterlayerexchange_async(Beff.DevPtr(X), Beff.DevPtr(Y), Beff.DevPtr(Z),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
unsafe.Pointer(J1_red), unsafe.Pointer(J2_red),
unsafe.Pointer(toplayer), unsafe.Pointer(bottomlayer),
direc[X], direc[Y], direc[Z],
float32(cellsize[X])*1e9, float32(cellsize[Y])*1e9, float32(cellsize[Z])*1e9,
N[X], N[Y], N[Z],
regions.Ptr, cfg)
}
func compensateLRSurfaceCharges(m *data.Mesh, mxLeft, mxRight float64, bsat float64) *data.Slice {
h := data.NewSlice(3, m.Size())
H := h.Vectors()
world := m.WorldSize()
cell := m.CellSize()
size := m.Size()
q := cell[Z] * cell[Y] * bsat
q1 := q * mxLeft
q2 := q * (-mxRight)
prog, maxProg := 0, (size[Z]+1)*(size[Y]+1)
// surface loop (source)
for I := 0; I < size[Z]; I++ {
for J := 0; J < size[Y]; J++ {
prog++
util.Progress(prog, maxProg, "removing surface charges")
y := (float64(J) + 0.5) * cell[Y]
z := (float64(I) + 0.5) * cell[Z]
source1 := [3]float64{0, y, z} // left surface source
source2 := [3]float64{world[X], y, z} // right surface source
// volume loop (destination)
for iz := range H[0] {
for iy := range H[0][iz] {
for ix := range H[0][iz][iy] {
dst := [3]float64{ // destination coordinate
(float64(ix) + 0.5) * cell[X],
(float64(iy) + 0.5) * cell[Y],
(float64(iz) + 0.5) * cell[Z]}
h1 := hfield(q1, source1, dst)
h2 := hfield(q2, source2, dst)
// add this surface charges' field to grand total
for c := 0; c < 3; c++ {
H[c][iz][iy][ix] += float32(h1[c] + h2[c])
}
}
}
}
}
}
return h
}
// Add Zhang-Li ST torque (Tesla) to torque.
// see zhangli.cu
func AddZhangLiTorque(torque, m *data.Slice, Msat, J, alpha, xi, pol MSlice, mesh *data.Mesh) {
c := mesh.CellSize()
N := mesh.Size()
cfg := make3DConf(N)
k_addzhanglitorque2_async(
torque.DevPtr(X), torque.DevPtr(Y), torque.DevPtr(Z),
m.DevPtr(X), m.DevPtr(Y), m.DevPtr(Z),
Msat.DevPtr(0), Msat.Mul(0),
J.DevPtr(X), J.Mul(X),
J.DevPtr(Y), J.Mul(Y),
J.DevPtr(Z), J.Mul(Z),
alpha.DevPtr(0), alpha.Mul(0),
xi.DevPtr(0), xi.Mul(0),
pol.DevPtr(0), pol.Mul(0),
float32(c[X]), float32(c[Y]), float32(c[Z]),
N[X], N[Y], N[Z], mesh.PBC_code(), cfg)
}
// Kernel for the vertical derivative of the force on an MFM tip due to mx, my, mz.
// This is the 2nd derivative of the energy w.r.t. z.
func MFMKernel(mesh *d.Mesh, lift, tipsize float64) (kernel [3]*d.Slice) {
const TipCharge = 1 / Mu0 // tip charge
const Δ = 1e-9 // tip oscillation, take 2nd derivative over this distance
util.AssertMsg(lift > 0, "MFM tip crashed into sample, please lift the new one higher")
{ // Kernel mesh is 2x larger than input, instead in case of PBC
pbc := mesh.PBC()
sz := padSize(mesh.Size(), pbc)
cs := mesh.CellSize()
mesh = d.NewMesh(sz[X], sz[Y], sz[Z], cs[X], cs[Y], cs[Z], pbc[:]...)
}
// Shorthand
size := mesh.Size()
pbc := mesh.PBC()
cellsize := mesh.CellSize()
volume := cellsize[X] * cellsize[Y] * cellsize[Z]
fmt.Println("calculating MFM kernel")
// Sanity check
{
util.Assert(size[Z] >= 1 && size[Y] >= 2 && size[X] >= 2)
util.Assert(cellsize[X] > 0 && cellsize[Y] > 0 && cellsize[Z] > 0)
util.AssertMsg(size[X]%2 == 0 && size[Y]%2 == 0, "Even kernel size needed")
if size[Z] > 1 {
util.AssertMsg(size[Z]%2 == 0, "Even kernel size needed")
}
}
// Allocate only upper diagonal part. The rest is symmetric due to reciprocity.
var K [3][][][]float32
for i := 0; i < 3; i++ {
kernel[i] = d.NewSlice(1, mesh.Size())
K[i] = kernel[i].Scalars()
}
r1, r2 := kernelRanges(size, pbc)
progress, progmax := 0, (1+r2[Y]-r1[Y])*(1+r2[Z]-r1[Z])
for iz := r1[Z]; iz <= r2[Z]; iz++ {
zw := wrap(iz, size[Z])
z := float64(iz) * cellsize[Z]
for iy := r1[Y]; iy <= r2[Y]; iy++ {
yw := wrap(iy, size[Y])
y := float64(iy) * cellsize[Y]
progress++
util.Progress(progress, progmax, "Calculating MFM kernel")
for ix := r1[X]; ix <= r2[X]; ix++ {
x := float64(ix) * cellsize[X]
xw := wrap(ix, size[X])
for s := 0; s < 3; s++ { // source index Ksxyz
m := d.Vector{0, 0, 0}
m[s] = 1
var E [3]float64 // 3 energies for 2nd derivative
for i := -1; i <= 1; i++ {
I := float64(i)
R := d.Vector{-x, -y, z - (lift + (I * Δ))}
r := R.Len()
B := R.Mul(TipCharge / (4 * math.Pi * r * r * r))
R = d.Vector{-x, -y, z - (lift + tipsize + (I * Δ))}
r = R.Len()
B = B.Add(R.Mul(-TipCharge / (4 * math.Pi * r * r * r)))
E[i+1] = B.Dot(m) * volume // i=-1 stored in E[0]
}
dFdz_tip := ((E[0] - E[1]) + (E[2] - E[1])) / (Δ * Δ) // dFz/dz = d2E/dz2
K[s][zw][yw][xw] += float32(dFdz_tip) // += needed in case of PBC
}
}
}
}
return kernel
}