`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, theta_H=None, phi_H=None, Nd=None, Na=None)#

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

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

The laboratory coordinate frame of reference is z || to film normal and x || to in-plane wavevector.

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: (T ) external magnetic field.
materialMaterial: Instance of Material describing the magnetic layer material. Its properties are saved as attributes, but this object is not.
dfloat: (m ) layer thickness (in z direction).
kxifloat or ndarray, optional: (rad/m) in-plane k-vector (wavenumber), usually a vector.
thetafloat, optional: (rad) out of plane angle of static M. Measured from film normal, i.e. pi/2 is totally in-plane magnetization.
phifloat or ndarray, optional: (rad) in-plane angle of M from kxi, 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.
theta_Hfloat or None, optional: (rad) polar angle of external field wrt. film normal. If None, field is taken as collinear with M. Default is None.
phi_Hfloat, optional: (rad) azimuthal angle of external field wrt. kxi. If None, field is taken as collinear with M. Default is None.
Nd(3,3) array or None, optional: Shape demag tensor in lab frame. If None, taken as for an infinite thin film np.diag([0,0,1]). Default is None.
Na(3,3) array or None, optional: () anisotropy tensor in lab frame. If None, np.zeros((3, 3)) is used. Default is None.

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: (T ) inhomogeneous broadening.
w0float: (rad*Hz) parameter in Kalinikos-Slavin equation. w0 = MU0*gamma*Hext
wMfloat: (rad*Hz) parameter in Kalinikos-Slavin equation. wM = MU0*gamma*Ms
Afloat: (m^2) parameter in Kalinikos-Slavin 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.
`set_DE`()	Changes angles theta and phi to match the Damon Eshbach geometry, i.e. M \|\| y, Bext \|\| y.
`set_BV`()	Changes angles theta and phi to match the backward volume geometry, i.e. M \|\| x, Bext \|\| x.
`set_FV`()	Changes angles theta and phi to match the forward volume geometry, i.e. M \|\| z, Bext \|\| z.

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: (m ) 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: (s ) 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: (T ) 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.

set_BV()#: Changes angles theta and phi to match the backward volume geometry, i.e. M || x, Bext || x.

set_DE()#: Changes angles theta and phi to match the Damon Eshbach geometry, i.e. M || y, Bext || y.

set_FV()#: Changes angles theta and phi to match the forward volume geometry, i.e. M || z, Bext || z.

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

property Bext#: External field value (T).

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

property Na#: Anisotropy tensor in lab frame.

property Nd#: Shape demag tensor in lab frame.

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

property phi_H#: Azimuthal angle of external field wrt. M (rad).

property theta#: Out-of-plane angle of static M (rad).

property theta_H#: Polar angle of external field wrt. film normal (rad).

SpinWaveToolkit.SingleLayer#

`SpinWaveToolkit.SingleLayer`#