`SpinWaveToolkit.SingleLayer`#

class SpinWaveToolkit.SingleLayer(Bext, material, d, kxi=array([1.00000000e-12, 1.25628141e+05, 2.51256281e+05, 3.76884422e+05, 5.02512563e+05, 6.28140704e+05, 7.53768844e+05, 8.79396985e+05, 1.00502513e+06, 1.13065327e+06, 1.25628141e+06, 1.38190955e+06, 1.50753769e+06, 1.63316583e+06, 1.75879397e+06, 1.88442211e+06, 2.01005025e+06, 2.13567839e+06, 2.26130653e+06, 2.38693467e+06, 2.51256281e+06, 2.63819095e+06, 2.76381910e+06, 2.88944724e+06, 3.01507538e+06, 3.14070352e+06, 3.26633166e+06, 3.39195980e+06, 3.51758794e+06, 3.64321608e+06, 3.76884422e+06, 3.89447236e+06, 4.02010050e+06, 4.14572864e+06, 4.27135678e+06, 4.39698492e+06, 4.52261307e+06, 4.64824121e+06, 4.77386935e+06, 4.89949749e+06, 5.02512563e+06, 5.15075377e+06, 5.27638191e+06, 5.40201005e+06, 5.52763819e+06, 5.65326633e+06, 5.77889447e+06, 5.90452261e+06, 6.03015075e+06, 6.15577889e+06, 6.28140704e+06, 6.40703518e+06, 6.53266332e+06, 6.65829146e+06, 6.78391960e+06, 6.90954774e+06, 7.03517588e+06, 7.16080402e+06, 7.28643216e+06, 7.41206030e+06, 7.53768844e+06, 7.66331658e+06, 7.78894472e+06, 7.91457286e+06, 8.04020101e+06, 8.16582915e+06, 8.29145729e+06, 8.41708543e+06, 8.54271357e+06, 8.66834171e+06, 8.79396985e+06, 8.91959799e+06, 9.04522613e+06, 9.17085427e+06, 9.29648241e+06, 9.42211055e+06, 9.54773869e+06, 9.67336683e+06, 9.79899497e+06, 9.92462312e+06, 1.00502513e+07, 1.01758794e+07, 1.03015075e+07, 1.04271357e+07, 1.05527638e+07, 1.06783920e+07, 1.08040201e+07, 1.09296482e+07, 1.10552764e+07, 1.11809045e+07, 1.13065327e+07, 1.14321608e+07, 1.15577889e+07, 1.16834171e+07, 1.18090452e+07, 1.19346734e+07, 1.20603015e+07, 1.21859296e+07, 1.23115578e+07, 1.24371859e+07, 1.25628141e+07, 1.26884422e+07, 1.28140704e+07, 1.29396985e+07, 1.30653266e+07, 1.31909548e+07, 1.33165829e+07, 1.34422111e+07, 1.35678392e+07, 1.36934673e+07, 1.38190955e+07, 1.39447236e+07, 1.40703518e+07, 1.41959799e+07, 1.43216080e+07, 1.44472362e+07, 1.45728643e+07, 1.46984925e+07, 1.48241206e+07, 1.49497487e+07, 1.50753769e+07, 1.52010050e+07, 1.53266332e+07, 1.54522613e+07, 1.55778894e+07, 1.57035176e+07, 1.58291457e+07, 1.59547739e+07, 1.60804020e+07, 1.62060302e+07, 1.63316583e+07, 1.64572864e+07, 1.65829146e+07, 1.67085427e+07, 1.68341709e+07, 1.69597990e+07, 1.70854271e+07, 1.72110553e+07, 1.73366834e+07, 1.74623116e+07, 1.75879397e+07, 1.77135678e+07, 1.78391960e+07, 1.79648241e+07, 1.80904523e+07, 1.82160804e+07, 1.83417085e+07, 1.84673367e+07, 1.85929648e+07, 1.87185930e+07, 1.88442211e+07, 1.89698492e+07, 1.90954774e+07, 1.92211055e+07, 1.93467337e+07, 1.94723618e+07, 1.95979899e+07, 1.97236181e+07, 1.98492462e+07, 1.99748744e+07, 2.01005025e+07, 2.02261307e+07, 2.03517588e+07, 2.04773869e+07, 2.06030151e+07, 2.07286432e+07, 2.08542714e+07, 2.09798995e+07, 2.11055276e+07, 2.12311558e+07, 2.13567839e+07, 2.14824121e+07, 2.16080402e+07, 2.17336683e+07, 2.18592965e+07, 2.19849246e+07, 2.21105528e+07, 2.22361809e+07, 2.23618090e+07, 2.24874372e+07, 2.26130653e+07, 2.27386935e+07, 2.28643216e+07, 2.29899497e+07, 2.31155779e+07, 2.32412060e+07, 2.33668342e+07, 2.34924623e+07, 2.36180905e+07, 2.37437186e+07, 2.38693467e+07, 2.39949749e+07, 2.41206030e+07, 2.42462312e+07, 2.43718593e+07, 2.44974874e+07, 2.46231156e+07, 2.47487437e+07, 2.48743719e+07, 2.50000000e+07]), theta=1.5707963267948966, phi=1.5707963267948966, weff=3e-06, boundary_cond=1, dp=0)#

Compute spin wave characteristic in dependance to k-vector (wavenumber) such as frequency, group velocity, lifetime and propagation length.

The model uses the famous Slavin-Kalinikos equation from https://doi.org/10.1088/0022-3719/19/35/014

Most parameters can be specified as vectors (1d numpy arrays) of the same shape. This functionality is not guaranteed.

Functions related to parametric pumping are based on: A.G. Gurevich and G.A. Melkov. Magnetization Oscillations and Waves. CRC Press, 1996.

Parameters:

Bextfloat

external magnetic field.

materialMaterial

Instance of Material describing the magnetic layer material. Its properties are saved as attributes, but this object is not.

dfloat

layer thickness (in z direction).

kxifloat or ndarray, optional

(rad/m) k-vector (wavenumber), usually a vector.

thetafloat, optional

(rad) out of plane angle of static M, pi/2 is totally in-plane magnetization.

phifloat or ndarray, optional

(rad) in-plane angle of kxi from M, pi/2 is DE geometry.

wefffloat, optional

(m) effective width of the waveguide (not used for zeroth order width modes).

boundary_cond{1, 2, 3, 4}, optional

boundary conditions (BCs), 1 is totally unpinned and 2 is totally pinned BC, 3 is a long wave limit, 4 is partially pinned BC. Default is 1.

dpfloat, optional

(rad/m) pinning parameter for 4 BC, ranges from 0 to inf, 0 means totally unpinned. Can be calculated as dp=Ks/Aex, see https://doi.org/10.1103/PhysRev.131.594.

Attributes:

[same as Parameters (except `material`), plus these]

Msfloat

Saturation magnetization (A/m).

gammafloat

Gyromagnetic ratio (rad*Hz/T).

Aexfloat

Exchange stiffness constant (J/m).

alphafloat

() Gilbert damping.

mu0dH0float

inhomogeneous broadening.

w0float

(rad*Hz) parameter in Slavin-Kalinikos equation. w0 = MU0*gamma*Hext

wMfloat

(rad*Hz) parameter in Slavin-Kalinikos equation. wM = MU0*gamma*Ms

Afloat

(m^2) parameter in Slavin-Kalinikos equation. A = Aex*2/(Ms**2*MU0)

Methods

`GetPartiallyPinnedKappa`(n)	Gives kappa from the transverse equation (in rad/m).
`GetDispersion`([n, nT])	Gives frequencies for defined k (Dispersion relation).
`GetGroupVelocity`([n, nT])	Gives (tangential) group velocities for defined k.
`GetLifetime`([n, nT])	Gives lifetimes for defined k.
`GetDecLen`([n, nT])	Give decay lengths for defined k.
`GetSecondPerturbation`(n, nc)	Give degenerate dispersion relation based on the secular equation (54).
`GetDensityOfStates`([n, nT])	Give density of states for given mode.
`GetBlochFunction`([n, nT, Nf])	Give Bloch function for given mode.
`GetExchangeLen`()	Calculate exchange length in meters from the parameter A.
`GetEllipticity`()	Calculate ellipticity of the precession ellipse for all kxi.
`GetCouplingParam`()	Calculate coupling parameter of the parallel pumped spin wave modes.
`GetThresholdField`()	Calculate threshold field for parallel pumping.
`GetThresholdFieldNonAdiabatic`([L])	Threshold field for parallel pumping including radiative losses in the non-adiabatic case.

See also

SingleLayerNumeric, DoubleLayerNumeric, Material, SingleLayerSCcoupled

Examples

Example of calculation of the dispersion relation f(k_xi), and other important quantities, for the lowest-order mode in a 30 nm thick NiFe (Permalloy) layer.

kxi = np.linspace(1e-6, 150e6, 150)

PyChar = SingleLayer(Bext=20e-3, kxi=kxi, theta=np.pi/2,
                     phi=np.pi/2, d=30e-9, weff=2e-6,
                     boundary_cond=2, material=SWT.NiFe)
DispPy = PyChar.GetDispersion()*1e-9/(2*np.pi)  # GHz
vgPy = PyChar.GetGroupVelocity()*1e-3  # km/s
lifetimePy = PyChar.GetLifetime()*1e9  # ns
decLen = PyChar.GetDecLen()*1e6  # um

GetBlochFunction(n=0, nT=0, Nf=200)#

Give Bloch function for given mode. Bloch function is calculated with margin of 10% of the lowest and the highest frequency (including Gilbert broadening).

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.
Nfint, optional: Number of frequency levels for the Bloch function.

Returns:

wndarray: (rad*Hz) frequency axis for the 2D Bloch function.
blochFuncndarray: () 2D Bloch function for given kxi and w.

GetCouplingParam()#

Calculate coupling parameter of the parallel pumped spin wave modes.

Vk = gamma * Bk / (2 * wk)

Returns:

Vkfloat: (rad*Hz/T) coupling parameter for parallel pumping.

GetDecLen(n=0, nT=0)#

Give decay lengths for defined k. Decay length is computed as lambda = v_g*tau. The result is given in m.

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.

Returns:

declenndarray

decay length.

GetDensityOfStates(n=0, nT=0)#

Give density of states for given mode. Density of states is computed as DoS = 1/v_g. Output is density of states in 1D for given dispersion characteristics.

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.

Returns:

dosndarray: (s/m) value proportional to density of states.

GetDispersion(n=0, nT=0)#

Gives frequencies for defined k (Dispersion relation). The returned values are in rad*Hz.

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.

GetEllipticity()#

Calculate ellipticity of the precession ellipse for all kxi. It is defined such that it falls within [0, 1].

Returns:

ellipticityndarray: () ellipticity for all kxi.

GetExchangeLen()#: Calculate exchange length in meters from the parameter A.

GetGroupVelocity(n=0, nT=0)#

Gives (tangential) group velocities for defined k. The group velocity is computed as vg = dw/dk. The result is given in m/s.

Warning

Works only when kxi.shape[0] >= 2.

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.

Returns:

vgndarray: (m/s) tangential group velocity.

GetLifetime(n=0, nT=0)#

Gives lifetimes for defined k. Lifetime is computed as tau = (alpha*w*dw/dw0)^-1. The result is given in s.

Parameters:

nint: Quantization number.
nTint, optional: Waveguide (transversal) quantization number.

Returns:

lifetimendarray

lifetime.

GetPartiallyPinnedKappa(n)#

Gives kappa from the transverse equation (in rad/m).

Parameters:

nint: Quantization number.

GetSecondPerturbation(n, nc)#

Give degenerate dispersion relation based on the secular equation (54). Output is dispersion relation in the vicinity of the crossing of the two different modes.

Parameters:

nint: Quantization number.
ncint: Quantization number of the crossing mode.

Returns:

wdn, wdnctuple[ndarray]: (rad*Hz) frequencies of corresponding kxi for the two crossing modes.

GetThresholdField()#

Calculate threshold field for parallel pumping.

mu_0 * h_th = w_r / Vk (relaxation frequency / coupling parameter)

Returns:

mu_0 * h_thfloat

threshold field for parallel pumping.

GetThresholdFieldNonAdiabatic(L=1e-06)#

Threshold field for parallel pumping including radiative losses in the non-adiabatic case.

This is an approximation which only works when radiative losses are greater than intrinsic, i.e. when: v_g / L >> w_r (relaxation frequency).

Parameters:

Lfloat: (m) pumping field localization length. (i.e. width of the excitation antenna)

Returns:

mu_0 * h_thfloat: (T) threshold field for parallel pumping including radiative losses.

property Aex#: Exchange stiffness constant (J/m).

property Bext#: External field value (T).

property Ms#: Saturation magnetization (A/m).

property gamma#: Gyromagnetic ratio (rad*Hz/T).

SpinWaveToolkit.SingleLayer#

`SpinWaveToolkit.SingleLayer`#