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We study magnetic behaviour of the Yb$^{3+}$ ions on a frustrated pyrochlorelattice in the spinel {\CYS}. The crystal-electric field parameters deducedfrom high-energy inelastic neutron scattering reveal well-isolated ytterbiumground state doublet with a weakly Ising character. Magnetic order studied bypowder neutron diffraction evolves from the $XY$-type antiferromagnetic$\Gamma_5$ state to a splayed ice-like ferromagnet (both with k=0) in appliedmagnetic field with $B_c$=3 T. Low-energy inelastic neutron scatteringidentifies weakly dispersive magnetic bands around 0.72 meV starting at$\mid\bf{Q}\mid$ = 1.1 \AA$^{-1}$~ at zero field, which diminish with field andvanish above 3 T. We explain the observed magnetic behaviour in framework ofthe nearest-neighbour anisotropic exchange model for effective $S=1/2$ Kramersdoublets on the pyrochlore lattice. The estimated exchanges position the {\CYS}spinel close to the phase boundary between the $\Gamma_5$ and splayedferromagnet states, similar to the Yb-pyrochlores suggesting an important roleof the competition between these phases.

Multi-phase competition in quantum $XY$ pyrochlore antiferromagnet CdYb$_{2}$Se$_{4}$: zero and applied magnetic field study