Robust spin-ice freezing in magnetically frustrated Ho₂Ge_xTi_2-xO₇pyrochlore

Structural analysis of spin frustrated Ho₂Ge_xTi_2-xO₇(x= 0, 0.1, 0.15 & 0.25) pyrochlore oxides has been performed using high resolution x-ray diffraction pattern and low temperature synchrotron x-ray diffraction pattern. The effect of positive chemical pressure on the spin dynamics of Ho₂Ge_xTi_2-xO₇has been analysed through the study of static (M-TandM-H; magnetisation against temperature & magnetisation against magnetic field) and dynamical (ac susceptibility) magnetic measurements. In lower temperature regime (∼2 K), such systems are predominantly governed by competing exchange (J_nn) and dipolar (D_nn) magnetic interactions. Magnetic measurements indicate that the application of increased chemical pressure in Ho₂Ti₂O₇matrix propels the system towards diminished ferromagnetic interaction. Dipolar coupling constant remains almost unchanged but Curie-Weiss temperature (θ_cw) reduces to -0.04 K from 0.33 K (for an applied magnetic field;H= 100 Oe) with increasingxin Ho₂Ge_xTi_2-xO₇. Positive chemical pressure establishes the dominance of Ho-Ho antiferromagnetic interactionJ_nnover dipolar interactionD_nn. Spin relaxation feature corresponding to thermally activated single ion freezing (T_s∼15 K) is shifted towards lower temperature. This chemical pressure-drivenT_sshift is ascribed to the alteration in crystal field effect, which reduces the activation energy for singe ion spin freezing. The reduction in the activation energy indicates crystal field-phonon coupling in Ho₂Ge_xTi_2-xO₇system. The robustness in spin ice freezing (second spin relaxation feature in ac susceptibility curve) remains unaffected with increasingly chemical pressure. This spin freezing ('2 in-2 out' spin arrangement in tetrahedra) is related to quantum tunnelling phenomenon, atT_ice∼ 2 K. It indicates that majority of spins still follows the 'ice rule' in Ho₂Ge_xTi_2-xO₇even after the application of chemical pressure.