  We define and study stacks which parametrize Lubin--Tate
$(\varphi,\Gamma)$-modules. By working at a perfectoid level, we compare these
with the Emerton--Gee stacks of cyclotomic $(\varphi,\Gamma)$-modules. As a
consequence, we deduce perfectness of the Herr complex in the Lubin--Tate
setting.
