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calculate_spin_CPU.cpp
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calculate_spin_CPU.cpp
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/********************************************************************************
*
* Copyright (C) 2015 Culham Centre for Fusion Energy,
* United Kingdom Atomic Energy Authority, Oxfordshire OX14 3DB, UK
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
********************************************************************************
*
* Program: SPILADY - A Spin-Lattice Dynamics Simulation Program
* Version: 1.0
* Date: Aug 2015
* Author: Pui-Wai (Leo) MA
* Contact: [email protected]
* Address: Culham Centre for Fusion Energy, OX14 3DB, United Kingdom
*
********************************************************************************/
#if (defined SDH || defined SDHL || defined SLDH || defined SLDHL || defined SLDNC) && defined CPU
#include "spilady.h"
void calculate_spin(atom_struct *atom_ptr, double dt){
#ifdef extfield
atom_ptr->Heff_H = atom_ptr->Hext;
#else
atom_ptr->Heff_H = vec_zero();
#endif
#if defined SDHL || defined SLDHL
atom_ptr->Heff_L = vec_zero();
#endif
inner_spin(atom_ptr); //calculate the effective field of current atom
#ifndef spinlang
//exact solution; no thermostat; PRL 86, 898 (2001) I. P. Omelyan
atom_ptr->s = spin_rotation(atom_ptr->Heff_H, atom_ptr->s, dt);
#endif /*no spin langevin*/
#ifdef spinlang
double dt_half = dt/2e0;
#if defined SDH || defined SLDH
//Pui-Wai Ma and S. L. Dudarev, PHYSICAL REVIEW B 83, 134418 (2011)
//There are 3 parts. Deterministic -> Stochastic -> Deterministic
vector s_temp = atom_ptr->s;
//1st part
vector s_cross_Heff = vec_cross(s_temp, atom_ptr->Heff_H);
double Heff_H0 = vec_length(atom_ptr->Heff_H);
double cos_a = cos(Heff_H0*(dt_half/hbar));
double sin_a = sin(Heff_H0*(dt_half/hbar));
double exp_b = exp(-Heff_H0*atom_ptr->s0*gamma_S_H*(dt_half/hbar));
double exp_2b = exp_b*exp_b;
double normalized_S_dot_H = 0e0;
if (atom_ptr->s0 > 0e0 && Heff_H0 > 0e0)
normalized_S_dot_H = vec_dot(s_temp, atom_ptr->Heff_H)/atom_ptr->s0/Heff_H0;
double denominator = (1e0 + exp_2b + normalized_S_dot_H*(1e0 - exp_2b))*Heff_H0;
double factor = (1e0 - exp_2b + normalized_S_dot_H*(1e0 + exp_2b - 2e0*cos_a*exp_b))*atom_ptr->s0;
atom_ptr->s = vec_divide( vec_add(vec_add(vec_times(2e0*cos_a*exp_b*Heff_H0, s_temp),
vec_times(2e0*sin_a*exp_b, s_cross_Heff)),
vec_times(factor, atom_ptr->Heff_H)), denominator);
//2nd part
#ifdef eltemp
double random_h = sqrt(2e0*(first_cell_ptr+(atom_ptr->new_cell_index))->Te*gamma_S_H*hbar/dt);
#else
double random_h = sqrt(2e0*temperature*gamma_S_H*hbar/dt);
#endif
int thread_index = omp_get_thread_num();
vector dh;
dh.x = random_h*normal_rand(thread_index);
dh.y = random_h*normal_rand(thread_index);
dh.z = random_h*normal_rand(thread_index);
atom_ptr->s = spin_rotation(dh, atom_ptr->s, dt);
//3rd part
s_temp = atom_ptr->s;
s_cross_Heff = vec_cross(s_temp, atom_ptr->Heff_H);
normalized_S_dot_H = 0e0;
if (atom_ptr->s0 > 0e0 && Heff_H0 > 0e0)
normalized_S_dot_H = vec_dot(s_temp, atom_ptr->Heff_H)/atom_ptr->s0/Heff_H0;
denominator = (1e0 + exp_2b + normalized_S_dot_H*(1e0 - exp_2b))*Heff_H0;
factor = (1e0 - exp_2b + normalized_S_dot_H*(1e0 + exp_2b -2e0*cos_a*exp_b))*atom_ptr->s0;
atom_ptr->s = vec_divide( vec_add(vec_add(vec_times(2e0*cos_a*exp_b*Heff_H0, s_temp),
vec_times(2e0*sin_a*exp_b, s_cross_Heff)),
vec_times(factor, atom_ptr->Heff_H)), denominator);
#endif
#if defined SDHL || defined SLDHL
// In 5 parts.
//part 1
atom_ptr->s = spin_rotation(atom_ptr->Heff_H, atom_ptr->s, dt_half);
//part 2
double dt_quad = dt/4e0;
#ifdef SLDHL
double A = LandauA(atom_ptr->rho);
double B = LandauB(atom_ptr->rho);
double C = LandauC(atom_ptr->rho);
double D = LandauD(atom_ptr->rho);
#endif
#ifdef SDHL
double A = LandauA(1);
double B = LandauB(1);
double C = LandauC(1);
double D = LandauD(1);
#endif
double s_sq;
double s0;
//RK2
s_sq = vec_sq(atom_ptr->s);
atom_ptr->Heff_L = vec_times(-(2e0*A + 4e0*B*s_sq + 6e0*C*pow(s_sq,2) + 8e0*D*pow(s_sq,3)), atom_ptr->s);
#ifdef SLDHL
atom_ptr->sum_Jij_sj = 0e0;
inner_sum_Jij_sj(atom_ptr);
s0 = sqrt(s_sq);
atom_ptr->Heff_HC = vec_zero();
if (s0 > 0e0) atom_ptr->Heff_HC = vec_times(-atom_ptr->sum_Jij_sj/s0, atom_ptr->s);
atom_ptr->Heff_L = vec_add(atom_ptr->Heff_L, atom_ptr->Heff_HC);
#endif
vector s_temp = vec_add(atom_ptr->s, vec_times(gamma_S_HL*dt_quad, vec_add(atom_ptr->Heff_H, atom_ptr->Heff_L)));
s_sq = vec_sq(s_temp);
atom_ptr->Heff_L = vec_times(-(2e0*A + 4e0*B*s_sq + 6e0*C*pow(s_sq,2) + 8e0*D*pow(s_sq,3)), s_temp);
#ifdef SLDHL
s0 = sqrt(s_sq);
atom_ptr->Heff_HC = vec_zero();
if (s0 > 0e0) atom_ptr->Heff_HC = vec_times(-atom_ptr->sum_Jij_sj/s0, s_temp);
atom_ptr->Heff_L = vec_add(atom_ptr->Heff_L, atom_ptr->Heff_HC);
#endif
atom_ptr->s = vec_add(atom_ptr->s, vec_times(gamma_S_HL*dt_half, vec_add(atom_ptr->Heff_H, atom_ptr->Heff_L)));
//part 3
#ifdef eltemp
double random_S = sqrt(2e0*(first_cell_ptr+(atom_ptr->new_cell_index))->Te*gamma_S_HL/dt);
#else
double random_S = sqrt(2e0*temperature*gamma_S_HL/dt);
#endif
int thread_index = omp_get_thread_num();
vector dS;
dS.x = random_S*normal_rand(thread_index);
dS.y = random_S*normal_rand(thread_index);
dS.z = random_S*normal_rand(thread_index);
atom_ptr->s = vec_add(atom_ptr->s, vec_times(dt, dS));
//part 4; RK2
s_sq = vec_sq(atom_ptr->s);
atom_ptr->Heff_L = vec_times(-(2e0*A + 4e0*B*s_sq + 6e0*C*pow(s_sq,2) + 8e0*D*pow(s_sq,3)), atom_ptr->s);
#ifdef SLDHL
s0 = sqrt(s_sq);
atom_ptr->Heff_HC = vec_zero();
if (s0 > 0e0) atom_ptr->Heff_HC = vec_times(-atom_ptr->sum_Jij_sj/s0, atom_ptr->s);
atom_ptr->Heff_L = vec_add(atom_ptr->Heff_L, atom_ptr->Heff_HC);
#endif
s_temp = vec_add(atom_ptr->s, vec_times(gamma_S_HL*dt_quad, vec_add(atom_ptr->Heff_H, atom_ptr->Heff_L)));
s_sq = vec_sq(s_temp);
atom_ptr->Heff_L = vec_times(-(2e0*A + 4e0*B*s_sq + 6e0*C*pow(s_sq,2) + 8e0*D*pow(s_sq,3)), s_temp);
#ifdef SLDHL
s0 = sqrt(s_sq);
atom_ptr->Heff_HC = vec_zero();
if (s0 > 0e0) atom_ptr->Heff_HC = vec_times(-atom_ptr->sum_Jij_sj/s0, s_temp);
atom_ptr->Heff_L = vec_add(atom_ptr->Heff_L, atom_ptr->Heff_HC);
#endif
atom_ptr->s = vec_add(atom_ptr->s, vec_times(gamma_S_HL*dt_half, vec_add(atom_ptr->Heff_H, atom_ptr->Heff_L)));
//part 5
atom_ptr->s = spin_rotation(atom_ptr->Heff_H, atom_ptr->s, dt_half);
#endif
#endif /*spinlang*/
atom_ptr->s0 = vec_length(atom_ptr->s);
}
void inner_spin(atom_struct *atom_ptr){
struct atom_struct *work_ptr;
struct cell_struct *ccell_ptr;
struct cell_struct *wcell_ptr;
ccell_ptr = first_cell_ptr + atom_ptr->new_cell_index;
for (int i = 0; i <= 26; ++i){
if (i == 26)
wcell_ptr = ccell_ptr;
else
wcell_ptr = first_cell_ptr + (ccell_ptr->neigh_cell[i]);
work_ptr = wcell_ptr->head_ptr;
while (work_ptr != NULL){
vector rij = vec_sub(atom_ptr->r, work_ptr->r);
//find image of j closest to i
find_image(rij);
double rsq = vec_sq(rij);
if (rsq < rcut_mag_sq && atom_ptr != work_ptr){
double rij0 = sqrt(rsq);
double Jij_rij = Jij(rij0);
atom_ptr->Heff_H = vec_add(atom_ptr->Heff_H, vec_times(Jij_rij, work_ptr->s));
}
work_ptr = work_ptr->next_atom_ptr;
}
}
}
#ifdef SLDHL
void inner_sum_Jij_sj(atom_struct *atom_ptr){
struct atom_struct *work_ptr;
struct cell_struct *ccell_ptr;
struct cell_struct *wcell_ptr;
ccell_ptr = first_cell_ptr + atom_ptr->new_cell_index;
for (int i = 0; i <= 26; ++i){
if (i == 26)
wcell_ptr = ccell_ptr;
else
wcell_ptr = first_cell_ptr + (ccell_ptr->neigh_cell[i]);
work_ptr = wcell_ptr->head_ptr;
while (work_ptr != NULL){
vector rij = vec_sub(atom_ptr->r, work_ptr->r);
//find image of j closest to i
find_image(rij);
double rsq = vec_sq(rij);
if (rsq < rcut_mag_sq && atom_ptr != work_ptr){
double rij0 = sqrt(rsq);
double Jij_rij = Jij(rij0);
double sj = vec_length(work_ptr->s);
atom_ptr->sum_Jij_sj += Jij_rij*sj;
}
work_ptr = work_ptr->next_atom_ptr;
}
}
}
#endif
#endif