The Raman spectroscopy and AC and DC magnetization of Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$ have been investigated. In Raman Spectroscopy, the systematic shift in all phonon modes with Eu content in Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$ confirms that Dy$^{3+}$ ion is substituted by Eu3+ ions. High concentration of Eu induces the dipolar exchange interactions and crystal-field interactions in Dy$_{2-x}$Eu$_x$Ti$_2$O$_7$. Rich Eu content samples (x=1.8 and 1.9) show the existence of wasp-waisted hysteresis loop and that can be attributed to the coexistence of dipolar field and anisotropy exchange interaction. AC susceptibility shows two single ion spin freezing transitions corresponding to Dy$^{3+}$ and Eu$^{3+}$ ions respectively in x = 1.5, 1.8, 1.9 samples.
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