Spin Glass Critical Dynamics just below T_g

Conventional critical dynamics are based on powers of 1/|T – T_g| in the vicinity of the glass temperature T_g. For spin glasses, the precise value of T_g is difficult to obtain, leading to a breadth of values for critical exponents. Recently, a scaling formalism was proposed¹ utilizing the coherence length, ξ(T,t_w) as the explicit variable, where t_w is the aging time at temperature T. Recent experiments of Kenning et al ² on single crystals of CuMn, performed below and close to T_g, have exhibited extraordinary results. Our goal is to combine these two studies to develop a better method of calculating T_g from experimental data and predict T_g for new materials. The characteristic relaxation time, t_w^eff drops by orders of magnitude and becomes independent of t_w as T approaches T_g from below. Our analysis of these findings uses a scaling formalism for ln[t_w^eff(H)/t_w^eff(H→0)] in a power series in H². The interplay between the H² and H⁴ terms (of opposite signs) in the expansion are shown to be responsible for the drastic drop in t_w^eff, and for t_w^eff becoming independent of t_w as T approaches T_g from below. This demonstrates that the scaling formalism is a powerful tool for examining critical dynamics below and in the vicinity of T_g spin glasses. Comparison with data for super-cooled liquids shows that it may be rather general for glassy systems.

¹ I. Paga et al J Stat. Mech. (2021) 033301.

² G.G. Kenning et al Phys. Rev. B 102, 064427 (2020).