Your first IETS spectrum¶

Tunneling electrons can excite a spin when their available energy exceeds a level splitting. Opening this transport channel produces steps in differential conductance, $dI/dV$.

We calculate a spin-half at 5 T, first with thermal populations and then with tunneling-induced pumping of the state populations.

In [1]:

import numpy as np
import plotly.graph_objects as go
import plotly.io as pio

from spinfinity import SpinSys, dIdV, hamil, plotting

pio.renderers.default = "plotly_mimetype+notebook"
# Use "fixed" for compact plots, or "no" to suppress display.
plotting.set_display_mode("responsive")

import numpy as np import plotly.graph_objects as go import plotly.io as pio from spinfinity import SpinSys, dIdV, hamil, plotting pio.renderers.default = "plotly_mimetype+notebook" # Use "fixed" for compact plots, or "no" to suppress display. plotting.set_display_mode("responsive")

Hamiltonian and scattering parameters¶

For $g=2$ and a field along $z$, the splitting is approximately $0.579 \mathrm{meV}$. Excitation thresholds are therefore near $\pm0.579 \mathrm{mV}$.

G_st sets the transport conductance scale. G_ss controls substrate scattering without transferring charge between tip and sample. We disable tip-tip scattering with G_tt=0. U=0 removes potential scattering; b0=0 removes the separate spin-independent background.

In [2]:

spin = SpinSys([0.5])
spin.B = [0.0, 0.0, 5.0]  # T
spin.BTip = [0.0, 0.0, 0.0]  # T
spin.gfactorvector = [2.0]

# Tunneling parameters
spin.T = 0.5  # K
spin.G_st = 1e-9  # S
spin.G_ss = [0.1e-9]  # S
spin.G_tt = 0  # can be 0 to disable or 1 to enable
spin.TipPolarization = [0.0, 0.0, 0.0]
spin.U = np.array([0.0])
spin.b0 = 0.0

hamil.calc_EigEnergies(spin, rebuildH=True)
gap = spin.E_All[1] - spin.E_All[0]
voltage = np.linspace(-1.5, 1.5, 601)  # mV

print(f"Relative eigenenergies: {spin.E_All} meV")
print(f"Excitation thresholds: +/-{gap:.4f} mV")

spin = SpinSys([0.5]) spin.B = [0.0, 0.0, 5.0] # T spin.BTip = [0.0, 0.0, 0.0] # T spin.gfactorvector = [2.0] # Tunneling parameters spin.T = 0.5 # K spin.G_st = 1e-9 # S spin.G_ss = [0.1e-9] # S spin.G_tt = 0 # can be 0 to disable or 1 to enable spin.TipPolarization = [0.0, 0.0, 0.0] spin.U = np.array([0.0]) spin.b0 = 0.0 hamil.calc_EigEnergies(spin, rebuildH=True) gap = spin.E_All[1] - spin.E_All[0] voltage = np.linspace(-1.5, 1.5, 601) # mV print(f"Relative eigenenergies: {spin.E_All} meV") print(f"Excitation thresholds: +/-{gap:.4f} mV")

Relative eigenenergies: [0.         0.57883818] meV
Excitation thresholds: +/-0.5788 mV

Thermal second-order spectrum¶

plot_IETS(order="2nd") calculates a thermal spectrum and constructs its Plotly figure. Finite temperature broadens the steps.

With norm=False, conductance is returned in $\mathrm{S}$.

In [3]:

dIdV.plot_IETS(
    spin, V_array=voltage, order="2nd", norm=False,
);

dIdV.plot_IETS( spin, V_array=voltage, order="2nd", norm=False, );

Tunneling-induced pumping¶

The order 2ndR solves voltage-dependent population rate equations and numerically differentiates the current. Population redistribution changes the conductance and can produce an overshoot.

In [4]:

dIdV.plot_IETS(
    spin, V_array=voltage, order="2ndR", norm=False,
);

dIdV.plot_IETS( spin, V_array=voltage, order="2ndR", norm=False, );