Unconventional Relaxation Dynamics in Co_8Zn_7Mn_5 and Co_8Zn_8Mn_4: Evidence of Inertial Effects

Magnetization relaxation dynamics serve as an essential tool for uncovering the intrinsic mechanisms governing the magnetic response and energy dissipation in magnetic systems. In this work, we examine the relaxation dynamics for Beta Mn type Co_8Zn_7Mn_5 and Co_8Zn_8Mn_4 across a frequency range of 1 kHz to 10 kHz, spanning different magnetic phases. While most magnetic systems tend to follow the Debye-like relaxation with non-zero distribution or the Cole-Cole formalism, our analysis reveal that these conventional models fail to capture frequency dependence of ac susceptibility across different magnetic phases in Co_8Zn_7Mn_5 and Co_8Zn_8Mn_4. Instead, an inertial component is needed to successfully describe the dynamics, suggesting the presence of unconventional relaxation behavior. The characteristic relaxation time is found to be of the order of 10^-5 s for both the compositions. The field dependent variation of relaxation time exhibits a non-monotonic nature, with the double peak like structure at the skyrmion phase transitions, implying slower relaxation dynamics at the phase boundaries. Furthermore, the presence of non-zero difference between isothermal and adiabatic susceptibility in the pure phases implies slower relaxation dynamics, which is consistent with the presence of finite dissipation in pure phases. The inertial term has been previously invoked to describe the dynamics in spin ice systems due to the propagation of magnetic monopoles. However, its necessity in this system, points to a wider significance in magnetization dynamics that goes beyond the conventional spin ices and skyrmions.