Spin spirals: Difference between revisions
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The above definition gives rise to the following magnetization density: | |||
:<math> | |||
{\bf m} ({\bf r} + {\bf R})= \left( | |||
\begin{array}{c} | |||
m_x({\bf r}) \cos({\bf q} \cdot {\bf R}) - m_y({\bf r}) \sin({\bf q} \cdot {\bf R}) \\ | |||
m_x({\bf r}) \sin({\bf q} \cdot {\bf R}) + m_y({\bf r}) \cos({\bf q} \cdot {\bf R}) \\ | |||
m_z({\bf r}) | |||
\end{array} | |||
\right) | |||
</math> |
Revision as of 12:21, 6 July 2018
Generalized Bloch condition
Spin spirals may be conveniently modeled using a generalisation of the Bloch condition:
- [math]\displaystyle{ \left[ \begin{array}{c} \Psi^{\uparrow}_{\bf k}(\bf r) \\ \Psi^{\downarrow}_{\bf k}(\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^{\uparrow}_{\bf k}(\bf r-R) \\ \Psi^{\downarrow}_{\bf k}(\bf r-R) \end{array} \right] }[/math]
The above definition gives rise to the following magnetization density:
- [math]\displaystyle{ {\bf m} ({\bf r} + {\bf R})= \left( \begin{array}{c} m_x({\bf r}) \cos({\bf q} \cdot {\bf R}) - m_y({\bf r}) \sin({\bf q} \cdot {\bf R}) \\ m_x({\bf r}) \sin({\bf q} \cdot {\bf R}) + m_y({\bf r}) \cos({\bf q} \cdot {\bf R}) \\ m_z({\bf r}) \end{array} \right) }[/math]