FM/I/FM Magnetic Tunnel Junction
In this example, we demonstrate transport calculations for a ferromagnetic/insulator/ferromagnetic (FM/I/FM) magnetic tunnel junction (MTJ), where an insulating (I) barrier is sandwiched between two semi-infinite ferromagnetic (FM) electrodes. This example reproduces the results from Phys. Rev. B 81, 054437 (2010).
Import Necessary Libraries
import matplotlib.pyplot as plt
import numpy as np
import junpy as jp
from junpy.factory import stack
%config InlineBackend.figure_format = 'svg'
%config InlineBackend.rc = {'font.size': 12}
Build Device
In this device, the chemical potentials (uL and uR) and spin angles (sL and sR) of the left and right FM regions are adjustable. The onsite energy of the non-magnetic insulator is set to 5.4, with the number of sites defined as NB=5. A linear potential drop, np.arange(NB)*dV, is applied across the insulator. To simulate the properties of a 3D solid, translation symmetry along the $x$ and $y$ directions is enabled.
def build_device(uL=0, uR=0, sL=0, sR=0, NB=5):
# energy parameters
eL = ( 1.2, 2.0) # [eV] onsite energy of the left lead
eB = ( 5.4, 5.4) # [eV] onsite energy of the insulator
eR = ( 1.2, 2.0) # [eV] onsite energy of the right lead
t = (-0.4,-0.4) # [eV] hopping energy in all regions
# potential drop in the barrier
dV = (uR-uL)/(NB-1)
# define the two-probe device
builder = stack.TwoProbeDeviceBuilder()
builder.L.set(chemicalPotential=uL, temperature=0)
builder.L.add(eL, t, nsites=1, spin=sL, bias=uL)
builder.C.add(eL, t, nsites=1, spin=sL, bias=uL)
builder.C.add(eB, t, nsites=NB, spin=0, bias=np.arange(NB)*dV)
builder.C.add(eR, t, nsites=1, spin=sR, bias=uR)
builder.R.add(eR, t, nsites=1, spin=sR, bias=uR)
builder.R.set(chemicalPotential=uR, temperature=0)
# define coupling between layers
builder.set_layer_coupling(all=t)
# define translation symmetry
builder.set_translationSymmetry(x=True, y=True)
# create device
return builder.create_device()
Calculate Bias-Dependent Interfacial Spin Current
We define a function to create and return a bias-dependent jp.SpinCurrent calculation. In this setup, the spin angle of the left FM material is fixed to np.pi/2.
def build_calculation_of_bias(bias):
calcr = jp.SpinCurrent(
device=build_device(uR=bias, sL=np.pi/2, NB=5),
kpoints=jp.SymmetryKspaceSampling((15,15,1)),
nonequilibriumEnergies=jp.BiasWindow(interval=0.01),
equilibriumEnergies=dict(
circlePoints=30,
lowestEnergy=-30))
return calcr
Since there are multiple biases to calculate, the jp.BiasBatchRunner class is used to perform batch calculations efficiently. The bias is applied over the range from -0.6 to 0.6.
runner_bias = jp.BiasBatchRunner(
biases=np.linspace(-0.6, 0.6, 13),
factory=build_calculation_of_bias)
jp.run(runner_bias, savefile=False)
Show code cell output
<<< Batch 1/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:46)
Device information
bias (mu2-mu1)--------------------------: -0.6
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.6
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.2463e-02j, -3.0018e-01+7.2463e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.3
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-6.0000e-01, 0.0000e+00]
number----------------------------------: 61
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -2.513124e-12 -1.694950e-12 1.061590e-12 6.415641e-13
1.000000e+00 -5.357303e-20 -2.222565e-20 1.331533e-19 1.111690e-19
2.000000e+00 2.887581e-21 4.169859e-22 5.441176e-23 1.124787e-19
3.000000e+00 -6.603126e-20 -1.062249e-24 -1.932040e-24 -1.979048e-20
4.000000e+00 1.232773e-20 2.100263e-26 -1.716561e-26 2.451146e-20
5.000000e+00 -1.430997e-19 0.000000e+00 0.000000e+00 -2.154602e-20
6.000000e+00 2.513124e-12 1.694950e-12 -1.061590e-12 -6.415643e-13
Calculation of spin current finished (2024-08-16 14:16:49)
Elapsed time----------------------------: 0:00:03.213149
<<< Batch 2/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:49)
Device information
bias (mu2-mu1)--------------------------: -0.5
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.5
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.2585e-02j, -2.5018e-01+7.2585e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.25
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-5.0000e-01, 0.0000e+00]
number----------------------------------: 51
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -2.183100e-12 -1.344848e-12 8.889235e-13 3.102726e-13
1.000000e+00 -8.438477e-20 1.142858e-20 -5.007853e-20 -1.437316e-19
2.000000e+00 -1.927671e-20 1.782316e-22 -3.512486e-22 5.309507e-20
3.000000e+00 1.457840e-20 2.803851e-24 2.831720e-24 -7.465170e-20
4.000000e+00 3.608394e-20 1.777146e-26 -7.795208e-26 -4.929949e-20
5.000000e+00 -6.981907e-20 4.038968e-28 -5.048710e-28 2.740244e-20
6.000000e+00 2.183101e-12 1.344848e-12 -8.889235e-13 -3.102725e-13
Calculation of spin current finished (2024-08-16 14:16:52)
Elapsed time----------------------------: 0:00:02.912608
<<< Batch 3/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:52)
Device information
bias (mu2-mu1)--------------------------: -0.4
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.4
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.2707e-02j, -2.0018e-01+7.2707e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.2
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-4.0000e-01, 0.0000e+00]
number----------------------------------: 41
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -1.814547e-12 -9.883695e-13 7.205824e-13 8.256437e-14
1.000000e+00 -1.217078e-20 5.917087e-20 -3.492170e-20 -3.381722e-21
2.000000e+00 -1.145862e-19 -1.342129e-22 -2.697049e-22 3.473442e-20
3.000000e+00 2.194554e-20 5.066885e-24 -3.958390e-24 2.233574e-20
4.000000e+00 3.714129e-20 -1.211690e-26 -3.826922e-26 8.171925e-21
5.000000e+00 -1.094413e-19 2.019484e-28 -2.019484e-28 -7.530165e-20
6.000000e+00 1.814547e-12 9.883694e-13 -7.205823e-13 -8.256435e-14
Calculation of spin current finished (2024-08-16 14:16:55)
Elapsed time----------------------------: 0:00:02.550405
<<< Batch 4/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:55)
Device information
bias (mu2-mu1)--------------------------: -0.3
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.3
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.2829e-02j, -1.5018e-01+7.2829e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.15
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-3.0000e-01, 0.0000e+00]
number----------------------------------: 31
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000023)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000078)
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.073413)
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--> 100.0% finished (Elapsed time: 0:00:00.048736)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000041)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000090)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -1.399090e-12 -6.488006e-13 5.670127e-13 -4.374049e-14
1.000000e+00 -6.247855e-20 -1.590725e-20 2.856995e-20 3.040669e-20
2.000000e+00 5.253509e-20 6.010198e-22 -2.205404e-22 -6.612449e-20
3.000000e+00 5.304147e-20 8.096111e-25 -4.014835e-24 5.621373e-21
4.000000e+00 -8.878704e-20 -6.169523e-26 8.178910e-27 3.925589e-20
5.000000e+00 7.377281e-20 3.029226e-28 -2.019484e-28 1.042385e-21
6.000000e+00 1.399090e-12 6.488006e-13 -5.670127e-13 4.374048e-14
Calculation of spin current finished (2024-08-16 14:16:57)
Elapsed time----------------------------: 0:00:02.311114
<<< Batch 5/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:57)
Device information
bias (mu2-mu1)--------------------------: -0.2
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.2
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.2951e-02j, -1.0018e-01+7.2951e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.1
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-2.0000e-01, 0.0000e+00]
number----------------------------------: 21
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.068708)
--> 10.0% finished (Elapsed time: 0:00:00.054019)
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--> 100.0% finished (Elapsed time: 0:00:00.051636)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000007)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000049)
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.046738)
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--> 100.0% finished (Elapsed time: 0:00:00.049380)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000011)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000245)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -9.449093e-13 -3.626318e-13 4.346190e-13 -9.412239e-14
1.000000e+00 -6.437143e-20 9.814692e-20 5.324176e-21 -3.035175e-19
2.000000e+00 4.850027e-20 -6.084745e-23 3.166993e-22 3.179656e-20
3.000000e+00 -6.926002e-22 6.889974e-25 -2.043970e-24 -6.655296e-20
4.000000e+00 -3.334906e-20 2.332504e-26 -1.019839e-26 9.932090e-20
5.000000e+00 1.003669e-19 0.000000e+00 0.000000e+00 -1.623960e-19
6.000000e+00 9.449092e-13 3.626317e-13 -4.346190e-13 9.412279e-14
Calculation of spin current finished (2024-08-16 14:16:59)
Elapsed time----------------------------: 0:00:01.910603
<<< Batch 6/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:16:59)
Device information
bias (mu2-mu1)--------------------------: -0.10000000000000003
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: -0.10000000000000003
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3073e-02j, -5.0178e-02+7.3073e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: -0.05000000000000002
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [-1.0000e-01, -2.7756e-17]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.093403)
--> 10.0% finished (Elapsed time: 0:00:00.055372)
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--> 100.0% finished (Elapsed time: 0:00:00.041443)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000008)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000172)
Integrate over energy and k-space...
Start MPI execution...
--> 5.1% finished (Elapsed time: 0:00:00.025500)
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--> 100.0% finished (Elapsed time: 0:00:00.020457)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000011)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000154)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 -4.885728e-13 -1.459852e-13 3.440551e-13 -7.593856e-14
1.000000e+00 -9.129794e-20 -3.578327e-20 4.764134e-20 9.489017e-20
2.000000e+00 8.366025e-20 -6.951503e-22 -5.510300e-22 6.303013e-20
3.000000e+00 3.234143e-20 -3.586200e-24 4.078853e-25 -2.646744e-20
4.000000e+00 7.501790e-21 -2.170945e-27 4.316647e-26 -7.919541e-20
5.000000e+00 -1.696179e-19 -7.573065e-29 7.573065e-28 1.919076e-20
6.000000e+00 4.885730e-13 1.459852e-13 -3.440551e-13 7.593849e-14
Calculation of spin current finished (2024-08-16 14:17:01)
Elapsed time----------------------------: 0:00:01.577957
<<< Batch 7/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:01)
Device information
bias (mu2-mu1)--------------------------: 0.0
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.0
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3195e-02j, -1.7859e-04+7.3195e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.0
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 0.0000e+00]
number----------------------------------: 1
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.058945)
--> 10.0% finished (Elapsed time: 0:00:00.054911)
--> 15.0% finished (Elapsed time: 0:00:00.054810)
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--> 100.0% finished (Elapsed time: 0:00:00.043069)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000007)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000122)
Integrate over energy and k-space...
Start MPI execution...
--> 5.6% finished (Elapsed time: 0:00:00.002526)
--> 11.1% finished (Elapsed time: 0:00:00.003720)
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--> 100.0% finished (Elapsed time: 0:00:00.001861)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000010)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000051)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 6.506358e-20 1.166044e-20 3.213901e-13 4.938513e-20
1.000000e+00 -4.214243e-20 -1.218096e-20 1.177026e-19 -7.968641e-20
2.000000e+00 3.002677e-20 5.153259e-22 8.813088e-23 4.630523e-20
3.000000e+00 -6.067230e-20 5.222641e-24 -1.296701e-23 -3.462583e-20
4.000000e+00 -6.622437e-20 -3.159230e-26 -5.200171e-27 -1.372761e-20
5.000000e+00 1.454442e-19 4.291403e-28 -3.029226e-28 1.073811e-19
6.000000e+00 -7.149544e-20 7.888609e-29 -3.213902e-13 -7.503162e-20
Calculation of spin current finished (2024-08-16 14:17:02)
Elapsed time----------------------------: 0:00:01.319681
<<< Batch 8/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:02)
Device information
bias (mu2-mu1)--------------------------: 0.09999999999999998
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.09999999999999998
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.04999999999999999
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 9.0000e-02]
number----------------------------------: 10
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.062566)
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Wait for other processes...
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Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000049)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
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Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000108)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 4.294330e-13 6.871229e-14 3.459493e-13 1.324539e-13
1.000000e+00 1.172719e-20 8.621434e-20 -7.205928e-20 1.162986e-19
2.000000e+00 -1.042061e-19 1.042347e-22 -1.654723e-22 3.768859e-20
3.000000e+00 6.822145e-20 -3.538767e-25 -3.156201e-24 -7.931464e-20
4.000000e+00 1.185648e-20 7.497334e-27 -3.453317e-26 7.456362e-21
5.000000e+00 3.117353e-20 -1.009742e-28 -6.058452e-28 1.934649e-19
6.000000e+00 -4.294330e-13 -6.871237e-14 -3.459493e-13 -1.324542e-13
Calculation of spin current finished (2024-08-16 14:17:04)
Elapsed time----------------------------: 0:00:01.573163
<<< Batch 9/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:04)
Device information
bias (mu2-mu1)--------------------------: 0.19999999999999996
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.19999999999999996
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3439e-02j, 9.9821e-02+7.3439e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.09999999999999998
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.9000e-01]
number----------------------------------: 20
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.063085)
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000024)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000178)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000013)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000200)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 8.938125e-13 9.295623e-14 4.315111e-13 3.497573e-13
1.000000e+00 1.729758e-19 5.192161e-20 -3.706407e-20 -9.896428e-20
2.000000e+00 -1.340903e-19 2.628585e-22 6.002790e-22 1.680724e-19
3.000000e+00 6.681995e-20 -2.239986e-25 -8.699937e-25 -9.643025e-20
4.000000e+00 1.385936e-19 2.448624e-26 -3.498756e-26 2.087720e-20
5.000000e+00 -1.579975e-19 2.398137e-28 -6.058452e-28 9.040847e-20
6.000000e+00 -8.938126e-13 -9.295628e-14 -4.315111e-13 -3.497574e-13
Calculation of spin current finished (2024-08-16 14:17:06)
Elapsed time----------------------------: 0:00:01.932849
<<< Batch 10/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:06)
Device information
bias (mu2-mu1)--------------------------: 0.29999999999999993
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.29999999999999993
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3561e-02j, 1.4982e-01+7.3561e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.14999999999999997
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 2.9000e-01]
number----------------------------------: 30
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.131423)
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000010)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000127)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000007)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000044)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 1.340883e-12 4.869356e-14 5.622496e-13 6.323459e-13
1.000000e+00 -1.509821e-19 -1.697417e-20 -1.034047e-19 -2.695439e-19
2.000000e+00 -4.984723e-20 -4.717366e-22 -6.964335e-22 5.216137e-20
3.000000e+00 5.319902e-20 -2.301700e-24 1.743420e-24 -2.426105e-20
4.000000e+00 -5.550943e-20 -6.456038e-27 1.615587e-26 4.455135e-20
5.000000e+00 -4.047612e-20 -3.155444e-28 0.000000e+00 -3.202762e-20
6.000000e+00 -1.340883e-12 -4.869355e-14 -5.622495e-13 -6.323457e-13
Calculation of spin current finished (2024-08-16 14:17:08)
Elapsed time----------------------------: 0:00:02.253262
<<< Batch 11/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:08)
Device information
bias (mu2-mu1)--------------------------: 0.3999999999999999
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.3999999999999999
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3683e-02j, 1.9982e-01+7.3683e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.19999999999999996
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 3.9000e-01]
number----------------------------------: 40
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.151839)
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000016)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000052)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000025)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000079)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 1.751498e-12 -7.000098e-14 7.136596e-13 9.687758e-13
1.000000e+00 -3.723728e-19 -2.575493e-20 -1.005228e-19 -1.771334e-19
2.000000e+00 -6.883626e-20 -6.623877e-23 -3.918612e-22 -1.195980e-20
3.000000e+00 -4.103865e-21 1.638344e-24 7.752799e-25 -5.264152e-21
4.000000e+00 -9.878755e-20 -5.171141e-26 1.605490e-26 5.659738e-20
5.000000e+00 2.653733e-19 1.767048e-28 1.009742e-28 -1.475387e-19
6.000000e+00 -1.751498e-12 7.000101e-14 -7.136595e-13 -9.687755e-13
Calculation of spin current finished (2024-08-16 14:17:11)
Elapsed time----------------------------: 0:00:02.639710
<<< Batch 12/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:11)
Device information
bias (mu2-mu1)--------------------------: 0.4999999999999999
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.4999999999999999
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3805e-02j, 2.4982e-01+7.3805e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.24999999999999994
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 4.9000e-01]
number----------------------------------: 50
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 2.117201e-12 -2.860784e-13 8.791859e-13 1.320998e-12
1.000000e+00 -1.054968e-19 -3.363674e-20 -7.062041e-22 -5.527542e-20
2.000000e+00 -1.008698e-19 2.204681e-22 -1.084792e-21 3.214923e-21
3.000000e+00 1.291744e-19 -2.444282e-24 -7.643343e-24 8.706235e-21
4.000000e+00 2.223754e-20 1.418687e-26 -1.241983e-26 6.566334e-20
5.000000e+00 1.013192e-19 -3.534097e-28 2.019484e-28 8.069056e-20
6.000000e+00 -2.117201e-12 2.860784e-13 -8.791859e-13 -1.320998e-12
Calculation of spin current finished (2024-08-16 14:17:14)
Elapsed time----------------------------: 0:00:02.866075
<<< Batch 13/13 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:17:14)
Device information
bias (mu2-mu1)--------------------------: 0.6
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.6
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3927e-02j, 2.9982e-01+7.3927e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.3
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 6.0000e-01]
number----------------------------------: 61
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 2.511824e-12 -6.413220e-13 1.061880e-12 1.693479e-12
1.000000e+00 3.354903e-20 -7.545648e-20 8.124138e-20 -2.197330e-20
2.000000e+00 8.487429e-20 6.136389e-22 7.293043e-23 -2.001582e-20
3.000000e+00 -8.643968e-20 -2.050786e-25 -9.567103e-24 -2.771770e-20
4.000000e+00 4.950295e-20 -1.221788e-26 5.654555e-27 8.162410e-20
5.000000e+00 5.523834e-20 -1.009742e-28 2.019484e-28 -7.326941e-20
6.000000e+00 -2.511824e-12 6.413221e-13 -1.061880e-12 -1.693478e-12
Calculation of spin current finished (2024-08-16 14:17:17)
Elapsed time----------------------------: 0:00:03.152324
In our device, the number of sites in the central region is 7, so the number of interfaces is 6. To retrieve the interfacial spin current between the barrier and the right FM material, we set interface = 5 to get the 6th interface.
# shape: (#biases, #interfaces, #spin)
interfacial_current = runner_bias.get_by_attribute('interfacial_spin_current')
# 6th interface
interface = 5
interfacial_current_n = interfacial_current[:,interface,:]
plt.plot(runner_bias.biases, interfacial_current_n, '.-')
plt.title(f'interface = {interface}')
plt.xlabel('Bias (V)')
plt.ylabel('Spin current (eV)')
plt.legend(['Q0', 'Qx', 'Qy', 'Qz'])
plt.grid()
plt.show()
Calculate Angle-Dependent Interfacial Spin Current
For angular dependency, we keep the bias 0.1 fixed while rotating the spin angle of the left FM material.
def build_calculation_of_angle(angle):
calcr = jp.SpinCurrent(
device=build_device(uR=0.1, sL=angle, NB=5),
kpoints=jp.SymmetryKspaceSampling((15,15,1)),
nonequilibriumEnergies=jp.BiasWindow(interval=0.01),
equilibriumEnergies=dict(
circlePoints=30,
lowestEnergy=-30))
return calcr
Similarly, we use jp.AngleBatchRunner to construct the batch calculations.
runner_angle = jp.AngleBatchRunner(
angles=np.linspace(0, np.pi, 7),
factory=build_calculation_of_angle)
jp.run(runner_angle, savefile=False)
Show code cell output
<<< Batch 1/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:42)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 5.582895e-13 0.000000e+00 0.000000e+00 2.167971e-13
1.000000e+00 5.173637e-20 0.000000e+00 0.000000e+00 -9.218853e-20
2.000000e+00 6.492787e-20 0.000000e+00 0.000000e+00 -2.772991e-20
3.000000e+00 -9.635374e-20 0.000000e+00 0.000000e+00 2.034876e-20
4.000000e+00 -3.001578e-20 0.000000e+00 0.000000e+00 -5.418350e-20
5.000000e+00 4.783156e-20 0.000000e+00 0.000000e+00 -3.073218e-21
6.000000e+00 -5.582895e-13 0.000000e+00 0.000000e+00 -2.167970e-13
Calculation of spin current finished (2024-08-16 14:18:44)
Elapsed time----------------------------: 0:00:01.905177
<<< Batch 2/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:44)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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--> 100.0% finished (Elapsed time: 0:00:00.017222)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000014)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000163)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 5.469346e-13 3.707976e-14 1.733449e-13 2.068611e-13
1.000000e+00 -3.569644e-20 7.043073e-23 -8.333430e-21 2.912015e-19
2.000000e+00 4.645202e-20 -5.342230e-23 -6.044497e-23 7.821313e-20
3.000000e+00 -9.759004e-22 7.999554e-25 -1.919898e-24 4.416242e-20
4.000000e+00 3.402788e-20 1.514613e-27 2.307260e-26 -2.797914e-20
5.000000e+00 -3.842844e-20 1.514613e-28 -2.524355e-29 1.209607e-19
6.000000e+00 -5.469346e-13 -3.707976e-14 -1.733449e-13 -2.068616e-13
Calculation of spin current finished (2024-08-16 14:18:45)
Elapsed time----------------------------: 0:00:01.441027
<<< Batch 3/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:45)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.057661)
--> 10.0% finished (Elapsed time: 0:00:00.054328)
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--> 100.0% finished (Elapsed time: 0:00:00.045561)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000007)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000081)
Integrate over energy and k-space...
Start MPI execution...
--> 5.1% finished (Elapsed time: 0:00:00.031045)
--> 10.1% finished (Elapsed time: 0:00:00.036673)
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--> 100.0% finished (Elapsed time: 0:00:00.020355)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000042)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000191)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 5.159126e-13 6.422405e-14 3.002422e-13 1.797173e-13
1.000000e+00 -2.005374e-19 -2.160365e-20 -4.497676e-20 -7.856306e-20
2.000000e+00 1.626044e-21 7.021342e-23 4.054458e-22 2.779517e-20
3.000000e+00 1.182163e-19 -1.688932e-24 -4.339770e-24 3.152766e-20
4.000000e+00 -7.142782e-20 4.815207e-26 3.034275e-26 -4.659987e-20
5.000000e+00 -1.879379e-19 -4.038968e-28 -5.048710e-29 -2.225738e-20
6.000000e+00 -5.159123e-13 -6.422403e-14 -3.002422e-13 -1.797172e-13
Calculation of spin current finished (2024-08-16 14:18:47)
Elapsed time----------------------------: 0:00:01.744983
<<< Batch 4/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:47)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.065511)
--> 10.0% finished (Elapsed time: 0:00:00.060571)
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--> 100.0% finished (Elapsed time: 0:00:00.044602)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000011)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000078)
Integrate over energy and k-space...
Start MPI execution...
--> 5.1% finished (Elapsed time: 0:00:00.027261)
--> 10.1% finished (Elapsed time: 0:00:00.024435)
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--> 100.0% finished (Elapsed time: 0:00:00.018557)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000007)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000112)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 4.735355e-13 7.415943e-14 3.466899e-13 1.426374e-13
1.000000e+00 5.165075e-21 8.673070e-20 -6.511707e-20 1.226236e-19
2.000000e+00 -1.041544e-19 1.069009e-22 -2.361245e-22 3.769699e-20
3.000000e+00 6.818535e-20 -4.206333e-25 -3.239909e-24 -7.929312e-20
4.000000e+00 5.653618e-21 5.654555e-27 -3.332148e-26 6.434569e-22
5.000000e+00 -7.987074e-20 6.310887e-29 -4.543839e-28 1.052036e-19
6.000000e+00 -4.735354e-13 -7.415952e-14 -3.466898e-13 -1.426375e-13
Calculation of spin current finished (2024-08-16 14:18:49)
Elapsed time----------------------------: 0:00:01.558732
<<< Batch 5/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:49)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.055972)
--> 10.0% finished (Elapsed time: 0:00:00.055318)
--> 15.0% finished (Elapsed time: 0:00:00.057500)
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--> 100.0% finished (Elapsed time: 0:00:00.042032)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000006)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000053)
Integrate over energy and k-space...
Start MPI execution...
--> 5.1% finished (Elapsed time: 0:00:00.024783)
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--> 100.0% finished (Elapsed time: 0:00:00.018755)
Wait for other processes...
--> finished (Elapsed time: 0:00:00.000009)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000117)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 4.311586e-13 6.422410e-14 3.002423e-13 1.055577e-13
1.000000e+00 -8.189539e-20 -7.329410e-20 -1.271824e-19 -2.044216e-20
2.000000e+00 -1.202232e-19 1.580644e-22 -1.491822e-22 6.982849e-20
3.000000e+00 1.714045e-19 -5.606895e-24 -3.002973e-25 -3.201327e-20
4.000000e+00 -1.813803e-19 9.844984e-27 4.609472e-26 -1.720126e-20
5.000000e+00 -1.707496e-19 1.767048e-28 3.029226e-28 -2.092236e-20
6.000000e+00 -4.311582e-13 -6.422403e-14 -3.002422e-13 -1.055576e-13
Calculation of spin current finished (2024-08-16 14:18:50)
Elapsed time----------------------------: 0:00:01.450626
<<< Batch 6/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:50)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
--> 5.0% finished (Elapsed time: 0:00:00.055612)
--> 10.0% finished (Elapsed time: 0:00:00.139435)
--> 15.0% finished (Elapsed time: 0:00:00.043806)
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Wait for other processes...
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Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000212)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
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Gather results from other processes...
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Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 4.001362e-13 3.707977e-14 1.733448e-13 7.841342e-14
1.000000e+00 7.005097e-20 -9.717656e-21 7.190677e-20 4.446103e-20
2.000000e+00 4.075664e-20 -9.852199e-23 -3.428085e-22 -3.814385e-21
3.000000e+00 4.947991e-20 -4.053609e-25 -2.277271e-24 -1.529442e-20
4.000000e+00 1.129408e-19 3.407879e-27 -4.624618e-26 -8.378697e-20
5.000000e+00 -1.316586e-19 -6.310887e-30 -1.514613e-28 -4.790714e-20
6.000000e+00 -4.001363e-13 -3.707976e-14 -1.733449e-13 -7.841331e-14
Calculation of spin current finished (2024-08-16 14:18:52)
Elapsed time----------------------------: 0:00:01.769522
<<< Batch 7/7 >>>
JunPy version---------------------------: 0.15.0.post29+ga5b3260
Parallelization information
BLAS Vendor-----------------------------: MKL
Total number of MPI processes-----------: 1
OMP_NUM_THREADS-------------------------: 1
MKL_NUM_THREADS-------------------------: unset
OPENBLAS_NUM_THREADS--------------------: unset
Calculating spin current... (2024-08-16 14:18:52)
Device information
bias (mu2-mu1)--------------------------: 0.1
central.numberOfSites-------------------: 7
central.spinType------------------------: SpinType.GeneralSpin
lead1.numberOfSites---------------------: 1
lead1.spinType--------------------------: SpinType.GeneralSpin
lead1.direction-------------------------: -3
lead1.temperature-----------------------: 0
lead1.chemicalPotential-----------------: 0
lead2.numberOfSites---------------------: 1
lead2.spinType--------------------------: SpinType.GeneralSpin
lead2.direction-------------------------: 3
lead2.temperature-----------------------: 0
lead2.chemicalPotential-----------------: 0.1
Energy sampling (equilibrium)
samplingName----------------------------: SemiCircleContourEnergySampling
range-----------------------------------: [-3.0000e+01+7.3317e-02j, 4.9821e-02+7.3317e-02j]
number----------------------------------: 30
temperature-----------------------------: 0.0
chemicalPotential-----------------------: 0.05
circlePoints----------------------------: 30
lowestEnergy----------------------------: -30
Energy sampling (non-equilibrium)
samplingName----------------------------: CustomSampling
range-----------------------------------: [0.0000e+00, 1.0000e-01]
number----------------------------------: 11
K-space sampling
samplingName----------------------------: SymmetryKspaceSampling
gridNumber------------------------------: (15, 15, 1)
isTimeReversalSymmetry------------------: True
numReducedKpoints-----------------------: 36
Runtime message
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
--> finished (Elapsed time: 0:00:00.000010)
Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000102)
Integrate over energy and k-space...
Start MPI execution...
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Wait for other processes...
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Gather results from other processes...
--> finished (Elapsed time: 0:00:00.000158)
Report of the intra-atomic spin current accumulation
Site A0_intra_eV Ax_intra_eV Ay_intra_eV Az_intra_eV
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
Report of the inter-atomic spin current accumulation
Site A0_inter_eV Ax_inter_eV Ay_inter_eV Az_inter_eV
0.000000e+00 3.887814e-13 9.081927e-30 4.245725e-29 6.847783e-14
1.000000e+00 6.755973e-20 -5.043559e-36 6.497792e-38 9.921997e-20
2.000000e+00 1.082051e-20 9.433059e-39 1.221562e-38 1.929087e-20
3.000000e+00 -2.249925e-20 -2.202183e-40 7.417017e-40 6.833349e-20
4.000000e+00 1.043564e-20 3.365919e-42 1.345247e-42 -8.441159e-20
5.000000e+00 -3.248664e-20 4.484155e-44 2.802597e-44 1.151540e-20
6.000000e+00 -3.887814e-13 -9.081922e-30 -4.245725e-29 -6.847794e-14
Calculation of spin current finished (2024-08-16 14:18:54)
Elapsed time----------------------------: 0:00:01.587309
# shape: (#biases, #interfaces, #spin)
interfacial_current = runner_angle.get_by_attribute('interfacial_spin_current')
# 6th interface
interface = 5
interfacial_current_n = interfacial_current[:,interface,:]
plt.plot(runner_angle.angles/np.pi*180, interfacial_current_n, '.-')
plt.title(f'interface = {interface}')
plt.xlabel('Angle (deg.)')
plt.ylabel('Spin current (eV)')
plt.legend(['Q0', 'Qx', 'Qy', 'Qz'])
plt.xticks(runner_angle.angles/np.pi*180)
plt.grid()
plt.show()