A spin density wave (SDW) is a phase in which a material suddenly shows a periodically modulated spin density $S_{\vec{q}}(\vec{r}) $ below a certain critical tempereature $T_C$.
Obviously some kind of symmetry is broken when a SDW forms, however I'm not exactly sure which one. Maybe translational symmetry? However that is already broken by simply forming a crystal and I don't know whether there is such a thing as further breaking a symmetry. Which symmetry exactly is broken in the case of an SDW?
My second question is: When a continuous symmetry is broken, one can associate a Goldstone mode to it in the ordered phase. What is the Goldstone mode of a spin density wave? Also, is it always true that the Goldstone modes are the same as the elementary excitations of the solid?
Answer
An ordered SDW phase breaks both the continuous $SU(2)$ spin-rotation symmetry and the time-reversal symmetry (because the presence of either of these two symmetries would force the order parameter of SDW vanishing). It is the spontaneously broken of continuous spin-rotation symmetry that leads to the gapless Goldstone mode. Here is a related issue.
The Goldstone mode of SDW is a gapless excitation of spin system, which is similar to that of phonons (the elementary excitations of oscillating crystals).
No comments:
Post a Comment