Effects of Disorder on Quantum Phase Transitions and Quantum Dynamics

We present experimental studies of the effects of disorder on the quantum phase transitions of antiferromagnetic LiErF₄ and of the dynamic behavior of LiHo0.2Y0.8F₄, which hosts a spin glass ground state due to the combination of substitutional disorder and magnetic frustration. Both compounds are insulating dipolar-coupled magnets that can be effectively treated as spin ½ systems. Two distinct quantum phase transitions can be induced in the easy-plane antiferromagnet LiErF₄, applying a magnetic field in the plane or perpendicular to it. The isotopic distribution of natural Er permits us to probe these transitions in the clean and dirty regimes. 167Er has a natural abundance of 23% and is the only stable isotope with a non-zero nuclear spin. At low temperatures, the nuclear spin slaves to the electronic spin and reduces the effective field felt by the electronic spin, thereby inducing random mass disorder in the dirty (low-temperature) regime. We use specific heat measurements to identify the temperature scale of the crossover between the dirty and clean regime as T=150 mK, and make ac magnetic susceptibility measurements to characterize the effects of disorder on the two quantum phase transitions. When the field is applied along the c-axis, the critical behavior is consistent with a violation of the Harris criterion in the clean regime and a change of universality class in the dirty regime. When the field is applied along the a-axis, the critical behavior is unchanged by the crossover between clean and dirty regimes. We use ac susceptibility measurements to conduct thermal memory dip experiments on the spin glass state of LiHo0.2Y0.8F₄ in zero magnetic field and find no apparent rejuvenation or memory. We perform an analogous “quantum memory dip” measurement which uses a transverse magnetic field rather than temperature to enter the spin glass state, and we find strong rejuvenation. The relaxation rate of the susceptibility decreases as the transverse field increases. This counterintuitive result is attributed to an increase in the variance of the random longitudinal field associated with increasing the transverse field and is supported by simulations. Finally, we perform a "negative field cycle" experiment which finds erasure of memory in the spin glass state. We establish a theoretical framework of quantum resonant tunneling to explain our results, rather than the conventional picture of a hierarchical free energy landscape associated with classical spin glasses.