  Using \textit{in situ} polarized neutron reflectometry, the depth resolved
evolution of the magnetism and structure in a Pd/Fe/Pd trilayer thin-film is
measured during growth. The initial film structure of Pd/Fe shows a small
proximity induced magnetism in the underlayer and a magnetization in the Fe
layer of $\approx1.6$\,$\mu_{\text{B}}$ per Fe atom, less than the expected
bulk value of $2.2$\,$\mu_{\text{B}}$. Deposition of the Pd capping layer
initially follows an island-like growth mode with subsequent coalescence. With
increasing Pd deposition the Fe moment and the proximity-induced magnetism in
the Pd capping layer decrease. After final deposition of the Pd capping layer,
the magnetic profile is structurally and magnetically symmetric across the Fe
layer, with magnetism induced in Pd up to 0.92 \,nm from the interface.
Throughout the Pd deposition the Pd/Fe/Pd trilayer structure is becoming
increasingly symmetric, a fact which points to a Dzyaloshinskii-Moriya
interaction as a likely cause of the observed magnetic behavior.
