Your first ESR spectrum¶

This model combines transition frequencies, thermal population differences and tip-field-weighted transition strengths with Lorentzian lines.

The linewidth is supplied by the user. The model does not calculate absolute current contrast, saturation or driven time evolution.

In [1]:

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

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

Build the spin Hamiltonian¶

Use an external field of 0.5 T and a small tilted tip field. For tip="f", the fields add on the readout spin.

BTip affects the static Hamiltonian and the phenomenological transition/detection weighting. It is not an independently specified RF amplitude B1.

In [2]:

spin = SpinSys([0.5])
spin.B = [0.0, 0.0, 0.5]  # T
spin.BTip = [0.01, 0.0, 0.01]  # T
spin.tip = "f"
spin.gfactorvector = [2.0]
spin.T = 0.2  # K

hamil.calc_EigEnergies(spin, rebuildH=True)
resonance = spin.E_All_inGHz[1] - spin.E_All_inGHz[0]

print(f"Transition frequency: {resonance:.6f} GHz")

spin = SpinSys([0.5]) spin.B = [0.0, 0.0, 0.5] # T spin.BTip = [0.01, 0.0, 0.01] # T spin.tip = "f" spin.gfactorvector = [2.0] spin.T = 0.2 # K hamil.calc_EigEnergies(spin, rebuildH=True) resonance = spin.E_All_inGHz[1] - spin.E_All_inGHz[0] print(f"Transition frequency: {resonance:.6f} GHz")

Transition frequency: 14.278914 GHz

Calculate the spectrum¶

lw is the Lorentzian full width at half maximum (FWHM), in GHz. We prescribe 0.02 GHz = 20 MHz.

The package plotting function returns a figure, the frequency grid and the calculated signal. We use thermal populations and keep the raw signal with norm=False; its scale is phenomenological, not a current in A.

In [3]:

linewidth = 0.02  # GHz
frequency = np.linspace(resonance - 0.25, resonance + 0.25, 1001)

ESR.plot_FreqSweep(
    spin,
    freq_array=frequency,
    AllowPumping=False,
    lw=linewidth,
    norm=False,
    output=False,
);

linewidth = 0.02 # GHz frequency = np.linspace(resonance - 0.25, resonance + 0.25, 1001) ESR.plot_FreqSweep( spin, freq_array=frequency, AllowPumping=False, lw=linewidth, norm=False, output=False, );