#include <spinAccumulationSolver.h>

Inheritance diagram for spinAcc:

Public Member Functions
	spinAcc (const Settings &mySettings, Mesh::mesh &_msh, const double _tol, const int max_iter)

void	boundaryConditions (void)

bool	compute (const Nodes::step k=Nodes::NEXT)

std::vector< double >	potential (const double factor) const

void	checkBoundaryConditions (void) const override

Public Member Functions inherited from solver< DIM_PB_SPIN_ACC >
	solver (Mesh::mesh &_msh, const std::vector< Tetra::prm > &_pTetra, const std::vector< Triangle::prm > &_pTri, const std::string &name, const double _tol, const bool v, const int max_iter, const std::function< bool(Mesh::Edge)> &edge_filter=[](Mesh::Edge) { return true;})

Public Attributes
double	jn_multiplier = 1.0

std::vector< Eigen::Vector3d >	s

Private Member Functions
void	fillDirichletData (const int k, Eigen::Vector3d &s_value)

double	getMs (const Tetra::Tet &tet) const

double	getSigma (const Tetra::Tet &tet) const

double	getPolarizationRate (const Tetra::Tet &tet) const

double	getDiffusionCst (const Tetra::Tet &tet) const

double	getLsd (const Tetra::Tet &tet) const

double	getLsf (const Tetra::Tet &tet) const

Eigen::Matrix< double, Nodes::DIM, Tetra::N >	calc_u_nod (const Tetra::Tet &tet) const

void	prepareExtraField (void) const

bool	solve (void)

void	integrales (const Tetra::Tet &tet, Eigen::Matrix< double, DIM_PB Tetra::N, DIM_PB Tetra::N > &AE) const

void	integrales (const Tetra::Tet &tet, std::vector< double > &BE) const

Private Attributes
std::vector< double >	valDirichlet

std::vector< int >	idxDirichlet

std::vector< double >	V

double	V_D = 0.0

const int	precision = 8

Nodes::step	uStep = Nodes::NEXT

Additional Inherited Members
Protected Member Functions inherited from solver< DIM_PB_SPIN_ACC >
algebra::MatrixShape	build_shape (const std::function< bool(Mesh::Edge)> &edge_filter) const

void	buildMat (std::array< int, N > &ind, Eigen::Matrix< double, DIM_PROBLEM N, DIM_PROBLEM N > &Ke)

void	buildVect (std::array< int, N > &ind, std::vector< double > &Le)

Protected Attributes inherited from solver< DIM_PB_SPIN_ACC >
Mesh::mesh *	msh

const int	NOD

const std::vector< Tetra::prm > &	paramTet

const std::vector< Triangle::prm > &	paramTri

const bool	verbose

algebra::iteration< double >	iter

algebra::SparseMatrix	K

std::vector< double >	L_rhs

Static Protected Attributes inherited from solver< DIM_PB_SPIN_ACC >
static const int	DIM_PB

Detailed Description

container for Spin Accumulation constants, solver and related datas. The model obeys the diffusive spin equation. User has to provide through mesh and settings at least one surface where spin diffusion vector s is a constant (zero recommended): Dirichlet boundary condition, and at least one surface where the current density jn is defined; if a spin polarization uP is also given on such a surface (and no s), the spin injection is a flux (Neumann) boundary condition. These surfaces are the ones given to the potential solver for its own boundary conditions. A surface may have both jn and s (s is then imposed on it).

Constructor & Destructor Documentation

◆ spinAcc()

spinAcc::spinAcc	(	const Settings &	mySettings,
		Mesh::mesh &	_msh,
		const double	_tol,
		const int	max_iter
	)

spin accumulation constructor if mySettings.spin_acc bool is false it is a do nothing constructor

Parameters

[in]	mySettings
[in]	_msh	ref to the mesh
[in]	_tol	tolerance for bicg_dir solver
[in]	max_iter	maximum number of iterations

Member Function Documentation

◆ boundaryConditions()

void spinAcc::boundaryConditions ( void )

Dirichlet boundary conditions: all the surfaces with a fixed s (the surface with fixed normal current density J and polarization vector P, without s, is a flux condition, added to the RHS in solve()) set valDirichlet values and fill vector of indices idxDirichlet

◆ calc_u_nod()

Eigen::Matrix< double, Nodes::DIM, Tetra::N > spinAcc::calc_u_nod ( const Tetra::Tet & tet ) const

private

nodal magnetization of the tetrahedron (step uStep, see compute()) used by the spin diffusion problem, columns are the nodes

◆ checkBoundaryConditions()

void spinAcc::checkBoundaryConditions ( void ) const

overridevirtual

check boundary conditions: mesh and settings have to define at least one surface with a normal current density jn and at least one surface where the spin diffusion s is given

Implements solver< DIM_PB_SPIN_ACC >.

◆ compute()

bool spinAcc::compute ( const Nodes::step k = Nodes::NEXT )

call solver and update spin diffusion solution, with the magnetization of step k: NEXT (the latest one, default) or CURRENT (the one of the start of the time step, u_n, used at each attempt of a time step: a rejected attempt leaves its own u_{n+1} in NEXT); returns true if solver succeeded

◆ fillDirichletData()

void spinAcc::fillDirichletData	(	const int	k,
		Eigen::Vector3d &	s_value
	)

private

fill valDirichlet and idxDirichlet vectors with k, a node index from tri.ind and the corresponding spin diffusion s value

◆ getDiffusionCst()

double spinAcc::getDiffusionCst ( const Tetra::Tet & tet ) const

private

diffusion constant, units: s^-1 m^2

◆ getLsd()

double spinAcc::getLsd ( const Tetra::Tet & tet ) const

private

length s-d : only in magnetic material

◆ getLsf()

double spinAcc::getLsf ( const Tetra::Tet & tet ) const

private

spin flip length : exists in both non-magnetic and magnetic metals

◆ getMs()

double spinAcc::getMs ( const Tetra::Tet & tet ) const

private

returns Ms

◆ getPolarizationRate()

double spinAcc::getPolarizationRate ( const Tetra::Tet & tet ) const

private

\( P \) is polarization rate of the current density

◆ getSigma()

double spinAcc::getSigma ( const Tetra::Tet & tet ) const

private

returns sigma of the tetraedron, (conductivity in (Ohm.m)^-1

◆ integrales() [1/2]

void spinAcc::integrales	(	const Tetra::Tet &	tet,
		Eigen::Matrix< double, DIM_PB Tetra::N, DIM_PB Tetra::N > &	AE
	)		const

private

computes all contributions to matrix AE from tetrahedron tet (LHS) all = non magnetic metal + magnetic metal

◆ integrales() [2/2]

void spinAcc::integrales	(	const Tetra::Tet &	tet,
		std::vector< double > &	BE
	)		const

private

computes magnetic metal contributions to spin diffusion from tetrahedron tet (RHS)

Parameters

[in]	tet
[out]	BE

◆ potential()

std::vector< double > spinAcc::potential ( const double factor ) const

electrostatic potential on the nodes [V], indexed as s: V_D + factor V, V being solved with V = 0 on the surface with V and V_D the imposed V (the electrokinetics being linear, the potential at time t follows the current density); factor is Settings::jnMultiplier(t) at the time t of the potential

◆ prepareExtraField()

void spinAcc::prepareExtraField ( void ) const

private

affect extraField member function of all tetrahedrons extraField is computing the contribution from the spin diffusion s to llg

◆ solve()

bool spinAcc::solve ( void )

private

solver, using biconjugate stabilized gradient, with diagonal preconditionner and Dirichlet boundary conditions

Member Data Documentation

◆ idxDirichlet

std::vector<int> spinAcc::idxDirichlet

private

list of the indices for Dirichlet boundary conditions, it contains the indices of the nodes where s is given by the user to be a constant on a surface

◆ jn_multiplier

double spinAcc::jn_multiplier = 1.0

dimensionless multiplier of all the normal current densities jn at the time of the solve (Settings::jnMultiplier, 1 by default). The electrokinetics being linear, the potential is solved once with the jn of the settings, and grad V -> jn_multiplier grad V, jn -> jn_multiplier jn (the constant imposed V does not change grad V). It multiplies the source terms (polarized current, injection through the surfaces with jn and uP), not the imposed s

◆ precision

const int spinAcc::precision = 8

private

number of digits in the optional output file

◆ s

std::vector<Eigen::Vector3d> spinAcc::s

solution of the spin diffusion vector s over the nodes

◆ uStep

Nodes::step spinAcc::uStep = Nodes::NEXT

private

step of the magnetization read by the solve (calc_u_nod()), set by compute()

◆ V

std::vector<double> spinAcc::V

private

electrostatic potential on the nodes, solved once with V = 0 on the surface with V (V_D is added by potential()), for the jn of the settings; grad V -> jn_multiplier grad V at time t unit [V] = Volt = kg A^-1 s^-3

◆ V_D

double spinAcc::V_D = 0.0

private

potential imposed on the surface with V (Dirichlet condition of the electrostatic problem) [V]

◆ valDirichlet

std::vector<double> spinAcc::valDirichlet

private

Dirichlet values of the components of s on the nodes, it is zero if the node is not in idxDirichlet

The documentation for this class was generated from the following files:

src/spinAccumulationSolver.h
src/spinAccumulationSolver.cpp

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ spinAcc()

Member Function Documentation

◆ boundaryConditions()

◆ calc_u_nod()

◆ checkBoundaryConditions()

◆ compute()

◆ fillDirichletData()

◆ getDiffusionCst()

◆ getLsd()

◆ getLsf()

◆ getMs()

◆ getPolarizationRate()

◆ getSigma()

◆ integrales() [1/2]

◆ integrales() [2/2]

◆ potential()

◆ prepareExtraField()

◆ solve()

Member Data Documentation

◆ idxDirichlet

◆ jn_multiplier

◆ precision

◆ s

◆ uStep

◆ V

◆ V_D

◆ valDirichlet