Magnetic#
The magnetic module contains functions for working with magnetic moments required for setting up a magnetic refinement.
- cartesian(mu1, mu2, mu3, C)[source]#
Components of magnetic moment in Cartesian coordiantes \(\mu_x\), \(\mu_x\), and \(\mu_x\).
- Parameters:
- mu1, mu2, mu3float or 1d array
Components of magnetic momenet \(\mu_1\), \(\mu_2\), and \(\mu_3\).
- C2d array, 3x3
Transform matrix from crystal axis to Cartesian coordiante system.
- Returns:
- mu_x, mu_y, mu_z1d array
Magnetic moment components in Cartesian coordinates. Has same size as input magnetic moment components.
- f(Q, j0, j2=0, K2=0)[source]#
Magnetic form factor \(f(Q)\).
- Parameters:
- Q1d array.
Magnitude of wavevector.
- j0, j21d array
\(j_0\) and \(j_2\) constant with same shape as wavevector.
- K21d array, optional
Coupling constant, defualt
K2=0.
- Returns:
- f1d array
Form factor. Has the same shape as the input wavevector.
- form(Q, ions, g=2)[source]#
Magnetic form factor \(f(Q)\).
- Parameters:
- Q1d array
Magnitude of wavevector.
- ions1d array, str
Magnetic ions.
- gfloat, 1d array, optional
\(g\) factor of the spins, defualt
g=2.
- Returns:
- f1d array
Form factor. Has the same shape as the input wavevector.
- intensity(Qx_norm, Qy_norm, Qz_norm, Sx_k, Sy_k, Sz_k, i_dft, factors)[source]#
Magnetic scattering intensity.
- Parameters:
- Qx_norm, Qy_norm, Qz_norm1d array
Normalized wavevector component \(\hat{Q}_x\), \(\hat{Q}_y\), and \(\hat{Q}_z\).
- Sx_k, Sy_k, Sz_k1d array
Fourier transform of the spin vector component \(S_x\), \(S_y\), and \(S_z\) component.
- i_dft1d array, int
Array indices of Fourier transform corresponding to reciprocal space.
- factors1d array
Prefactors of form factors and phase factors.
- Returns:
- I1d array
Intensity. Array has a flattened shape of size
i_dft.shape[0].
- j0(Q, A, a, B, b, C, c, D)[source]#
Appoximation of the integral with the zeroth-order spherical Bessesl function \(j_0(Q)\).
- Parameters:
- Q1d array
Magnitude of wavevector \(Q\).
- A, a, B, b, C, c, Dfloat
Constants \(A_0\), \(a_0\), \(B_0\), \(b_0\), \(C_0\), \(c_0\) and \(D_0\).
- Returns:
- j01d array
Approximation of \(\langle j_0(Q)\rangle\). Has the same shape as the input wavevector.
- j2(Q, A, a, B, b, C, c, D)[source]#
Appoximation of the integral with the second-order spherical Bessesl function \(j_2(Q)\).
- Parameters:
- Q1d array
Magnitude of wavevector \(Q\).
- A, a, B, b, C, c, Dfloat
Constants \(A_2\), \(a_2\), \(B_2\), \(b_2\), \(C_2\), \(c_2\) and \(D_2\).
- Returns:
- j21d array
Approximation of \(\langle j_2(Q)\rangle\). Has the same shape as the input wavevector.
- magnitude(mu1, mu2, mu3, C)[source]#
Magnitude of magnetic moment \(\mu\).
- Parameters:
- mu1, mu2, mu31d array
Components of magnetic momenet \(\mu_1\), \(\mu_2\), and \(\mu_3\).
- C2d array, 3x3
Transform matrix from crystal axis to Cartesian coordiante system.
- Returns:
- mu1d array
Magnetic moment magnitude. Has same size as input magnetic moment components.
- spin(nu, nv, nw, n_atm, value=1, fixed=True)[source]#
Generate random spin vectors.
- Parameters:
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- n_atmint
Number of atoms in the unit cell.
- Returns:
- Sx, Sy, Sz1d array
Spin vector components. Each array has a flattened shape of size
nu*nw*nv*n_atm.
- structure(Qx_norm, Qy_norm, Qz_norm, Sx_k, Sy_k, Sz_k, i_dft, factors)[source]#
Partial magnetic structure factor.
- Parameters:
- Qx_norm, Qy_norm, Qz_norm1d array
Normalized wavevector component \(\hat{Q}_x\), \(\hat{Q}_y\), and \(\hat{Q}_z\).
- Sx_k, Sy_k, Sz_k1d array
Fourier transform of the spin vector component \(S_x\), \(S_y\), and \(S_z\) component.
- i_dft1d array, int
Array indices of Fourier transform corresponding to reciprocal space.
- factors1d array
Prefactors of form factors and phase factors.
- Returns:
- Fx, Fy, Fz1d array
Magnetic structure factor components. Each array has a flattened shape of size
i_dft.shape[0].- prod_x, prod_y, prod_z1d array
Magnetic partial structure factor components. Each array has a flattened shape of size
i_dft.shape[0]*n_atm.
- transform(Sx, Sy, Sz, H, K, L, nu, nv, nw, n_atm)[source]#
Discrete Fourier transform of spin vectors.
- Parameters:
- Sx, Sy, Sz1d array
Spin vector component \(S_x\), \(S_y\), and \(S_z\) in Cartesian components along the \(x\), \(y\), and \(z\)-direction.
- H, K, L1d array, int
Supercell index along the \(a^*\), \(b^*\), and \(c^*\)-axis in reciprocal space.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- n_atmint
Number of atoms in the unit cell.
- Returns:
- Sx_k, Sy_k, Sz_k1d array
Fourier transform of spin vector components. Each array has a flattened shape of size
nu*nw*nv*n_atm.- i_dft1d array, int
Fourier transform indices. Array has a flattened shape of size
nu*nw*nv*n_atm.