!> Author: Jabir Ali Ouassou
!> Category: Materials
!>
!> This submodule is included by conductor.f, and contains the equations which model spin-orbit coupling in diffusive materials.
module spinorbit_m
use :: condmat_m
use :: material_m
private
! Public interface
public spinorbit, spinorbit_construct
! Type declarations
type :: spinorbit
class(material), pointer :: material => null() !! Pointer to the material modelled by this instance
type(spin), dimension(1:3) :: field !! Spin-orbit coupling field (SU(2) gauge field)
type(spin) :: Ax, Ay, Az, A2 !! Spin-orbit coupling matrices (the components and square)
type(spin) :: Axt, Ayt, Azt, A2t !! Spin-orbit coupling matrices (tilde-conjugated versions)
contains
procedure :: diffusion_equation => spinorbit_diffusion_equation !! Diffusion equation
procedure :: diffusion_equation_a => spinorbit_diffusion_equation_a !! Boundary condition (left)
procedure :: diffusion_equation_b => spinorbit_diffusion_equation_b !! Boundary condition (right)
procedure :: update_prehook => spinorbit_update_prehook !! Code to execute before updates
end type
! Type constructors
interface spinorbit
module procedure spinorbit_construct
end interface
contains
function spinorbit_construct(parent) result(this)
!! Constructs a spinorbit object with a given parent material.
type(spinorbit) :: this
class(material), target :: parent
! Save a pointer to the parent object
this % material => parent
! Ensure that the spin-orbit field is zero
this % field = spin(0)
end function
subroutine spinorbit_update_prehook(this)
!! Updates the internal variables associated with spin-orbit coupling.
class(spinorbit), intent(inout) :: this
! Spin-orbit coupling terms in the equations for the Riccati parameter γ
this % Ax = this % material % length * this % field(1)
this % Ay = this % material % length * this % field(2)
this % Az = this % material % length * this % field(3)
this % A2 = this % Ax**2 + this % Ay**2 + this % Az**2
! Spin-orbit coupling terms in the equations for the Riccati parameter γ~
this % Axt = conjg(this % Ax)
this % Ayt = conjg(this % Ay)
this % Azt = conjg(this % Az)
this % A2t = conjg(this % A2)
end subroutine
pure subroutine spinorbit_diffusion_equation(this, p)
!! Calculate the spin-orbit coupling terms in the diffusion equation,
!! and update the second derivatives of the Riccati parameters.
class(spinorbit), intent(in) :: this
type(propagator), intent(inout) :: p
associate( Ax => this % Ax, Axt => this % Axt, &
Ay => this % Ay, Ayt => this % Ayt, &
Az => this % Az, Azt => this % Azt, &
A2 => this % A2, A2t => this % A2t, &
N => p % N, Nt => p % Nt, &
g => p % g, gt => p % gt, &
dg => p % dg, dgt => p % dgt, &
d2g => p % d2g, d2gt => p % d2gt )
! Update the second derivatives of the Riccati parameters
d2g = d2g + (A2 * g - g * A2t) &
+ (2.0_wp,0.0_wp) * (Ax * g + g * Axt) * Nt * (Axt + gt * Ax * g) &
+ (2.0_wp,0.0_wp) * (Ay * g + g * Ayt) * Nt * (Ayt + gt * Ay * g) &
+ (2.0_wp,0.0_wp) * (Az * g + g * Azt) * Nt * (Azt + gt * Az * g) &
+ (0.0_wp,2.0_wp) * (Az + g * Azt * gt) * N * dg &
+ (0.0_wp,2.0_wp) * dg * Nt * (gt * Az * g + Azt)
d2gt = d2gt + (A2t * gt - gt * A2) &
+ (2.0_wp,0.0_wp) * (Axt * gt + gt * Ax) * N * (Ax + g * Axt * gt) &
+ (2.0_wp,0.0_wp) * (Ayt * gt + gt * Ay) * N * (Ay + g * Ayt * gt) &
+ (2.0_wp,0.0_wp) * (Azt * gt + gt * Az) * N * (Az + g * Azt * gt) &
- (0.0_wp,2.0_wp) * (Azt + gt * Az * g) * Nt * dgt &
- (0.0_wp,2.0_wp) * dgt * N * (g * Azt * gt + Az)
end associate
end subroutine
pure subroutine spinorbit_diffusion_equation_a(this, p, r, rt)
!! Calculate the spin-orbit coupling terms in the left boundary condition, and update the residuals.
class(spinorbit), target, intent(in) :: this
type(propagator), intent(in) :: p
type(spin), intent(inout) :: r, rt
associate( Az => this % Az, Azt => this % Azt, &
g => p % g, gt => p % gt )
! Update the residuals
r = r - (0.0_wp,1.0_wp) * (Az * g + g * Azt)
rt = rt + (0.0_wp,1.0_wp) * (Azt * gt + gt * Az )
end associate
end subroutine
pure subroutine spinorbit_diffusion_equation_b(this, p, r, rt)
!! Calculate the spin-orbit coupling terms in the right boundary condition, and update the residuals.
class(spinorbit), target, intent(in) :: this
type(propagator), intent(in) :: p
type(spin), intent(inout) :: r, rt
associate( Az => this % Az, Azt => this % Azt, &
g => p % g, gt => p % gt )
! Update the residuals
r = r - (0.0_wp,1.0_wp) * (Az * g + g * Azt)
rt = rt + (0.0_wp,1.0_wp) * (Azt * gt + gt * Az )
end associate
end subroutine
end module
