Spin spirals: Difference between revisions
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Spin spirals may be conveniently modeled using a generalized Bloch condition: | Spin spirals may be conveniently modeled using a generalized Bloch condition: | ||
<span id="GeneralizedBlochTheorem"> | |||
:<math> | :<math> | ||
\left[ \begin{array}{c} \Psi^{\uparrow}_{\bf k}(\bf r) \\ | \left[ \begin{array}{c} \Psi^{\uparrow}_{\bf k}(\bf r) \\ | ||
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\Psi^{\downarrow}_{\bf k}(\bf r-R) \end{array} \right] | \Psi^{\downarrow}_{\bf k}(\bf r-R) \end{array} \right] | ||
</math> | </math> | ||
</span> | |||
Revision as of 10:58, 6 July 2018
Generalized Bloch condition
Spin spirals may be conveniently modeled using a generalized 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]](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3054f8bd4c27abc8ed2fe5951e9facb5ce4c25d)