Spin density wave and soft phonon mode from nesting Fermi surfaces

The problems of spin density wave and of soft phonon mode leading to periodic lattice distortion as a consequence of nesting Fermi surfaces have been investigated. By examining the changes in the energy functional of the electron-lattice system as small amplitude spin density wave and periodic lattice distortion develop, the necessary and sufficient criteria for the existence of each kind of instability and for the coexistence of the two kinds have been derived. These results are expressed in terms of the generalized susceptibility function of the electron system, the Coulomb and exchange interactions between the electrons, the electron-phonon coupling and the phonon frequency.