When degenerate states are separated by large energy barriers, the approach to thermal equilibrium can be slow enough that physical properties are defined by the thermalization process rather than the equilibrium. The exploration of thermalization pu
shes experimental boundaries and provides refreshing insights into atomic scale correlations and processes that impact steady state dynamics and prospects for realizing solid state quantum entanglement. We present a comprehensive study of magnetic relaxation in Ho$_2$Ti$_2$O$_7$ based on frequency-dependent susceptibility measurements and neutron diffraction studies of the real-time atomic-scale response to field quenches. Covering nearly ten decades in time scales, these experiments uncover two distinct relaxation processes that dominate in different temperature regimes. At low temperatures (0.6K<T<1K) magnetic relaxation is associated with monopole motion along the applied field direction through the spin-ice vacuum. The increase of the relaxation time upon cooling indicates reduced monopole conductivity driven by decreasing monopole concentration and mobility as in a semiconductor. At higher temperatures (1K<T<2K) magnetic relaxation is associated with the reorientation of monopolar bound states as the system approaches the single-spin tunneling regime. Spin fractionalization is thus directly exposed in the relaxation dynamics.
We present the high-precision magnetization data of the valence fluctuating heavy fermion superconductor $beta$-YbAlB$_4$ in a wide temperature range from 0.02 K to 320 K spanning four orders of magnitude. We made detailed analyses of the $T/B$ scali
ng of the magnetization, and firmly confirmed the unconventional zero-field quantum criticality (QC) without tuning. We examined other possible scaling relationship such as $T/(B-B_c)^{delta}$ scaling, and confirmed that $delta = 1$ provides the best quality of the fit with an upper bound on the critical magnetic field $vert B_c vert <0.2$~mT. We further discuss the heavy Fermi-liquid component of the magnetization after subtracting the QC component estimated based on the $T/B$ scaling. The temperature dependence of the heavy Fermi-liquid component is found very similar to the magnetization of the polymorph $alpha$-YbAlB$_4$. In addition, the heavy Fermi-liquid component is suppressed in the magnetic field above $sim$ 5 T as in $alpha$-YbAlB$_4$. This was also confirmed by the magnetization measurements up to $sim 50$ T for both $alpha$- and $beta$-YbAlB$_4$. Interestingly, the detailed analyses revealed that the only a part of $f$ electrons participates in the zero-field QC and the heavy fermion behavior. We also present a temperature - magnetic field phase diagram of ybal to illustrate how the characteristic temperature and field scales evolves near the QC.
$beta$-YbAlB$_4$ is the first Yb-based heavy fermion superconductor with $T_{rm c} = 80$ mK. We measured low temperature magnetization of high-purity single crystals down to $T=$ 25 mK. The measurements have revealed a considerable amount of volume f
ractions of the superconductivity and the upper critical field $B_{c2}$ curve under field along the c axis, consistent with the previous results. In the normal state, the previously observed divergent behavior in the temperature dependence of the magnetization has been confirmed using higher quality samples and under a low field of 22 mT. In addition, the measurements have revealed a power law behavior, namely, $dM/dTpropto T^{3/2}$, which has a slightly higher exponent than the previous results.
