Magnetic Structure Factors

The magnetic structure factor M(k) can be defined as the Fourier transform of the magnetisation distribution.

The intensity of neutron scattering is proportional to the square of the component of M(k)perpendicular to the scattering vector k. This is the magnetic interaction vector $\mathbf{Q(k)}$. Thus

$$\Qk=\sv\times\Mk\times\sv$$

Using the description of a magnetic structure just given the magnetic structure factor is written:

$$\begin{eqnarray*} \Mk & = & \sum_l^{\mathit{crystal}}\sum_{n=-\infty}^\infty p(n... ...ath[\sv\cdot\tilde R_s(\tilde R_p{\bf r}_i+{\bf t}_p)+{\bf t}_s] \end{eqnarray*}$$

$f_i(\sv)$ is the magnetic form factor and $p(n)$ the Fourier transform of the modulating function $\mbox{\rm fn}(x)$. The sum over the lattice vectors is zero unless $\sv=\rl\pm n\kv$ where g is a reciprocal lattice vector. At present CCSL only recognises sinusiodal modulations so that $p(n)=0$ unless $n=1$. The rest of the equation defines the unit cell magnetic structure factor; its projection on the plane perpendicular to the scattering vector is the quantity calculated by the magnetic structure factor routines FMCALC and LMCALC.