ソフトモード

$$\mbox{\boldmath$u$}_{nj} = {1 \over{sqrt{Nm_{j}}}}\sum_{\mbox{\bo... ...dmath$k$}\cdot\mbox{\boldmath$R$}_{n} - {\rm i}\omega_{\mbox{\boldmath$k$}s}t),$$ (2.5.67)

$${1 \over{2}}\omega_{\mbox{\boldmath$k$}s}^{2}\langle Q_{\mbox{\bo... ...\mbox{\boldmath$k$}s}\rangle + {1 \over{2}})\hbar\omega_{\mbox{\boldmath$k$}s},$$ (2.5.68)

$$\langle n_{\mbox{\boldmath$k$}s}\rangle = {1 \over{{\rm exp}({\hbar\omega_{\mbox{\boldmath$k$}s} \over{k_{\rm B}T}}) - 1}},$$ (2.5.69)

ある特別のフォノンモード $(\mbox{\boldmath$k$}_{0},\ s_{0})$の振動数 $\omega_{\mbox{\boldmath$k$}_{0}s_{0}}$の減少 $\longrightarrow$ $\mbox{\boldmath$Q$}_{\mbox{\boldmath$k$}_{0}s_{0}}$の減少， $\mbox{\boldmath$u$}_{nj}$の増加
$\omega_{\mbox{\boldmath$k$}_{0}s_{0}} = 0$ $\longrightarrow$ $(\mbox{\boldmath$k$}_{0},\ s_{0})$フォノンの凍結：静的原子変位
$\omega_{\mbox{\boldmath$k$}_{0}s_{0}}^{2} = A(T-T_{\rm c})$
$T \longrightarrow T_{\rm c}$, $\omega_{\mbox{\boldmath$k$}_{0}s_{0}} \longrightarrow 0$：ソフトモード
↓
変位型相転移

図 2.5: 古典的磁石と電子スピン磁石