  Bose polarons are quasiparticles formed through the interaction between
impurities and Bose-Einstein condensates. In this paper, we derive an effective
Fr\"{o}hlich Hamiltonian using the generalized Bogoliubov transformation. The
effective Fr\"{o}hlich Hamiltonian encompasses two types of effective
interactions: impurity-density (ID) coupling and impurity-spin (IS) coupling.
Furthermore, we employ the Lee-Low-Pines variational approach to investigate
the relevant properties of Bose polarons induced by the ID and IS coupling.
These properties include the ground state energy, effective mass, and average
number of virtual phonons. Our findings reveal that the contribution resulting
from IS couplings to the ground energy decreases to zero near the
miscible-immiscible boundary. Additionally, the increase of the IS coupling
induces a greater number of virtual phonons, impeding the movement of
impurities and leading to a significant increase in the effective mass of Bose
polarons.
