The pyrochlore oxides Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$ are well studied spin ice systems and have shown the evidences of magnetic monopole excitations. Unlike these, Dy$_{2}$Zr$_{2}$O$_{7}$ is reported to crystallize in a distorted fluorite structure. We present here the magnetic and heat capacity studies of La substituted Dy$_{2}$Zr$_{2}$O$_{7}$. Our findings suggest the absence of spin ice state in Dy$_{2}$Zr$_{2}$O$_{7}$ but the emergence of the magnetic field induced spin freezing near T $approx$ 10 K in ac susceptibility measurements which is similar to Dy$_{2}$Ti$_{2}$O$_{7}$. The magnetic heat capacity of Dy$_{2}$Zr$_{2}$O$_{7}$ shows a shift in the peak position from 1.2 K in zero field to higher temperatures in the magnetic field, with the corresponding decrease in the magnetic entropy. The low temperature magnetic entropy at 5 kOe field is Rln2 - (1/2)Rln(3/2) which is same as for the spin ice state. Substitution of non-magnetic, isovalent La$^{3+}$ for Dy$^{3+}$ gradually induces the structural change from highly disordered fluorite to weakly ordered pyrochlore phase. The La$^{3+}$ substituted compounds with less distorted pyrochlore phase show the spin freezing at lower field which strengthens further on the application of magnetic field. Our results suggest that the spin ice state can be stabilized in Dy$_{2}$Zr$_{2}$O$_{7}$ either by slowing down of the spin dynamics or by strengthening the pyrochlore phase by suitable substitution in the system.
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