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Quantum Critical Matter and Phase Transitions Chapter 60 40 20 0 0 0.4 0.8 1.2 1.6 T (K) 280 305 Paramagnet Ferromagnet LiHoF4 FIG. 5 Experimental phase diagram for LiHoF4 with a ferromagnetic phase up to the Curie temperature, as a function of Tc and applied transverse field H?. The dashed line represents the mean-field theory while the solid line and data points include the correction due to the nuclear hyperfine interaction. Here, H?c is 4.93 T and the lowest measurement temperature is 0.1 K. The divergence of the ac-susceptibility (w0 and w00) in the given field determines Tc(H?). According to Bitko, D., Rosenbaum, T.F., Aeppli, G., 1996. Quantum critical behavior for a model magnet. Phys. Rev. Lett. 77 (5), 940. Fig. 5 presents the experimental phase diagram (external field H? vs T) of LiHoF4. The low temperature, high-field deviations from the mean field behavior is attributed to nuclear hyperfine interactions of the holium. Inelastic neutron scattering experiments showed that the expected mode-softening at the QPT was perturbed and discontinued by the hyperfine coupling to the nuclear spins that prevented a detailed study of the QPT (Rønnow et al., 2005, 2007). Early on, experiments of specific heat in H? were performed that spanned the H?c (Mennenga et al., 1984). However, the then unknown QCP was not reached in temperature and the results merely confirmed the reduced but smeared out in H? specific heat peak of the ferromagnetic transition with an incipient upturn at the lowest temperature. The hyperfine modification to the QPT discouraged further experiments at the QCP and attention then shifted to the diluted Li(HoxY1x)F4 and its putative quantum spin-glass (SG) phase transition according to the older work of Wu et al. (1993). How- ever, this left the quantum critical and quantum fluctuation portions of the LiHoF4 phase diagram mostly unexplored. Even before the interest in the transverse field QPT of Ising LiHoF4 became apparent, the search for a SG state in diluted Li(Y1xHox)F4 was underway via ac-susceptibility (Reich et al., 1986). The initial question posed: H⊥ (kOe)PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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