Spin spirals

Generalized Bloch condition

Spin spirals may be conveniently modeled using a generalisation of the Bloch condition:

$\left[{\begin{array}{c}\Psi _{\bf {k}}^{\uparrow }({\bf {r)}}\\\Psi _{\bf {k}}^{\downarrow }({\bf {r)}}\end{array}}\right]=\left({\begin{array}{cc}e^{-i{\bf {q\cdot {\bf {R/2}}}}}&0\\0&e^{+i{\bf {q\cdot {\bf {R/2}}}}}\end{array}}\right)\left[{\begin{array}{c}\Psi _{\bf {k}}^{\uparrow }({\bf {r-R)}}\\\Psi _{\bf {k}}^{\downarrow }({\bf {r-R)}}\end{array}}\right]$