Fragmentation of a spin-1 mixture in a magnetic field

We study the ground state quantum fragmentation in a mixture of a polar condensate and a ferromagnetic condensate when subject to an external magnetic field. We pay more attentions to the polar condensate and find that it will be less fragile in the mixture when perturbed by the magnetic field. Both atom numbers and the number fluctuations in the spin-0 component will keep in a high magnitude of order of $N$ when the magnetization of the system is increased. The role of the ferromagnetic condensate is to provide a uniform and stable background which can delay the rapid shrink of the 0-component population and make it possible to capture the \textquotedblleft super-fragmentation \textquotedblright. Our method has potential applications in measuring the inter-species spin-coupling interaction through adjusting the magnetic field.