Activated quantum criticality of complex systems

Magnetization measurements performed on single crystals of Ho$_{x}$Y$_{1-x}$LiF$_{4}$ with x = 16.5{\%} and 4.5{\%} show the same behavior for both compositions: (i) absence of divergence of the non-linear susceptibility in a transverse field (ii) same absence of divergence in zero field. These results are in sharp contrast with earlier studies of Ho$_{x}$Y$_{1-x}$LiF$_{4}$. In (i) the observed lack divergence results from the presence of random fields induced by the applied transverse field (no spin-glass phase transition, as predicted by Schechter, Laflorencie and Stamp). In (ii) it results from important slowing down of the dynamics due to huge energy barriers. Excellent fits are obtained for the linear and non-linear susceptibilities with ln($M)$ = -$T$f($H,T)$ (f is a functional form), suggesting the possibility of a dynamical phase transition involving thermally activated tunneling states. This model may also be useful for more general quantum dynamics of complex systems at finite temperatures. \newline \newline Scaling of non-linear susceptibility in MnCu and GdAl spin-glasses, B. Barbara, A. P. Malozemoff, and Y. Imry, PRL, 7, 1852 (1981). \newline Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo$_{x}$Y$_{1-x}$F$_{4}$, P. E. J\"{o}nsson, R. Mathieu, W. Wernsdorfer, A. M. Tkachuk, and B. Barbara, PRL, 98, 256403 (2007). \newline Nuclear spin driven quantum relaxation in LiHo$_{0.002}$Y$_{0.998}$F$_{4}$, R. Giraud, W. Wernsdorfer, A. M. Tkachuk, D. Mailly, and B. Barbara, PRL, 87, 057203 (2001). \newline Significance of the hyperfine interactions in the phase diagram of LiHo$_{x}$Y$_{1-x}$F$_{4}$, M. Schechter and P. C. E. Stamp, PRL, 95, 267208 (2005). \newline Quantum spin-glass and the dipolar interactions, M. Schechter and N. Laflorencie, PRL, 97,137204 (2006). \newline Induced Random Fields in the LiHo$_{x}$Y$_{1-x}$F$_{4}$ Quantum Ising Magnet in a Transverse Magnetic Field, S. M. A. Tabei, M. J. P. Gingras, Y.-J. Kao, P. Stasiak, and J.-Y. Fortin, PRL, 97, 237203 (2006). \newline Quantum spin-glass in anisotropic dipolar systems, M. Schechter, P.C.E. Stamp, and N. Laflorencie, J. Phys: Cond. Matt., 19, 145218 (2007). \newline Activated Scaling of Classical and Quantum Spin Glasses, B. Barbara. PRL, 99, 177201 (2007).