**1. Introduction**

Metallic glasses (MGs) have been extensively studied for several decades because they exhibit unique physical, chemical and mechanical properties and have no crystal defects (i.e., dislocations, grain boundaries, and vacancies) [1–3]. Compared to other glassy materials (i.e., amorphous polymers, oxide glasses, and other non-crystalline solids), metallic glasses show high yield strength and resilience, large fracture toughness, and attractive corrosion resistance [4–8]. It is well known that the mechanical and physical properties of metallic glasses, i.e., plasticity, glass transition behavior, and di ffusion phenomena, are bound up with their mechanical relaxation modes [1,6,9–11]. Nevertheless, below the glass transition temperature, metallic glasses have insu fficient ductility due to shear band instability during plastic deformation, which dramatically reduces the use in structural applications [12]. Compared to crystalline metals, metallic glasses are basically characterized by brittleness at room temperature. One way to overcome the macroscopic brittle behavior of metallic glass is to reduce the size. Previous studies have shown that brittle behavior can be mitigated when the sample size is reduced to sub-micron levels, thereby reducing the e ffects of instability on material behavior [13,14]. Below the glass transition, metallic glasses are thermodynamically in a non-equilibrium state, as there is a large enthalpy di fference from the crystallized state [15]. However, the topological structure as well as the physical mechanism of relaxation in glassy materials remain unresolved issues [16–18].

In the supercooled liquid phase region of metallic glasses, relaxation processes drive the glass towards more stable states. The primary α relaxation and secondary β relaxation are considered the elementary relaxation processes [19–21]. Johari et al. [22] proposed that glasses and glass-forming liquids have two relaxation modes: (i) The primary (α) relaxation, which is a global, structural atomic or molecular rearrangemen<sup>t</sup> observed at relatively high temperatures and closely related to the glass transition phenomenon; (ii) The secondary (β) relaxation, a low energy process which is observed under the glass transition temperature *Tg*. While the α relaxation process shows a complex dependence on temperature, the secondary β relaxation generally submits to an Arrhenius temperature dependence rule. The β relaxation shows up as an over wing in the high-frequency tail or a side shoulder at low temperature of α relaxation [23,24]. Contrary to the main relaxation, β relaxation is associated with the motion of atoms or molecules inside a glass material without topological rearrangement. The study on the connection between the di ffusion behavior of the amorphous alloy, plastic deformation, and glass transition on the relaxation process of amorphous alloy is of grea<sup>t</sup> significance for the assessment of the potential applications of metallic glasses.

Literature results show that La-based metallic glasses display a conspicuous secondary relaxation [25]. Therefore, La-based metallic glasses are an ideal model system to investigate the relaxation process. In the present study, the dynamic mechanical properties of emblematic LaCe-based metallic glasses were investigated by mechanical spectroscopy. The physical mechanism of mechanical relaxation process was analyzed relied on the Kohlrausch–Williams–Watts (KWW) equation.
