我們利用自恰的格林函數方法求出自旋波在稀磁半導體內的生命週期，並且發現當溫度升高時，自旋波的生命週期居然隨之增長。我們試圖以減少量子震盪的方式來看看是否自旋波生命週期會隨著溫度上升而縮短，但是似乎生命週期增長的趨勢並不是由量子震盪導致的。

The Self-consistent Green's function method satis‾es Goldstone's theorem and preserves spin kinematics, whereas mean-field theory does not satisfy Goldstone's theory which predicts gapless spin-wave excitation, and the independent spin-wave theory using Holstein-Primakov boson (HP boson) in
path integral formulism fails to preserve spin kinematics. The dilute impurity limit provides the nice translational invariance and allowing Fourier transform. Random Phase Approximation(RPA) lowers the order of Green's function and therefore the spin-wave Green's function can be extracted from two equations of motion. In isotropic coupling case, we've found the atypical phenomena of spin-wave lifetime increasing as temperature raises. Obviously, this spectral function narrowing can not due to thermal fluctuation. We then wonder if this awkward behavior comes from quantum fluctuation and whether this would be corrected to match our common sense that lifetime shortens at higher temperature when anisotropy being introduced, in other words, quantum fluctuation being suppressed. It turns out that neither thermal nor quantum fluctuation is to blame on the trend of the increase of spin-wave lifetime at high temperature. And at the same time we are also eager to look for experimental evidence that'll support our prediction.

Ohno, H. et al., Phys. Rev. Lett. 68, 2664-2667(1992)
Ohno, H. et al., Appl. Phys. Lett. 69, 363-365(1996)
Ku, K. C. et al., Appl. Phys. Lett. 82, 2302-2304(2003)
A. H. MacDonald, P. Schiffer and N. Samarth, Nature Materials 4, 195-202(2005)
J. Konig, H.-H. Lin, and A. H. MacDonald Phys. Rev. Lett. 84, 5628(2000)
M.-F. Yang, S.-J. Sun, and M.-C. Chang Phys. Rev. Lett.
96, 5636(2001)
J. Konig, H.-H. Lin, and A. H. MacDonald Phys. Rev. Lett. 86, 5637(2001)
J.E. Bunder, Shih-Jye Sun, and Hsiu-Hau Lin, Appl. Phys. Lett. 89, 072101(2006)
H. B. Callen, Phys. Rev. 130, 890(1963)
R. Akimoto, K. Ando, F. Sasaki, S. Kobayashi, and T. Tani,
Phys. Rev. B 56, 9726(1997)