Statics and dynamics of an incommensurate spin order in a geometrically frustrated antiferromagnet CdCr$_2$O$_4$

Using elastic and inelastic neutron scattering we show that a cubic spinel, CdCr$_2$O$_4$, undergoes an elongation along the c-axis ($c > a = b$) at its spin-Peierls-like phase transition at $T_N$ = 7.8 K. The N\'{e}el phase ($T < T_N$) has an incommesurate spin structure with a characteristic wave vector \textbf{Q}$_M$ = (0,$\delta$,1) with $\delta \sim$ 0.09 and with spins lying on the $ac$-plane. This is in stark contrast to another well-known Cr-based spinel, ZnCr$_2$O$_4$, that undergoes a c-axis contraction and a commensurate spin order. The magnetic excitations of the incommensurate N\'{e}el state has a weak anisotropy gap of 0.6 meV and it consists of at least three bands extending up to 5 meV.