Inertial spin dynamics in ferromagnets

Abstract

The understanding of how spins move and can be manipulated at pico-and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data processing and storage applications. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Nutation in antiferromagnetic resonance

“…The FiM is observed to interpolate between the FM and AFM limits. The reduced effective damping gives rise to particularly sharp and high-intensity nutation resonance peaks in AFMs, with frequencies comparable to the values already observed in FMs [23,25]. These findings are expected to motivate the search for the signs of intrinsically inertial spin dynamics on ultrafast timescales using AFMR techniques.…”

“…[20,23,24] and the values of around 300 fs in Ref. [25]. It can be observed that the inertial dynamics reduces the precession resonance frequency.…”

“…Note that an alternative notation for the inertial term with η i = α i τ i is also used in the literature [15,23,25]; where comparison with earlier works is mentioned in the following, the relaxation time is converted to the formulation of Eq. (1).…”

“…The characteristic inertial relaxation time, using its definition in Eq. (1) below, is expected to range from 1 fs [15,20,23,24] to a few hundred fs [25].…”

“…An indirect evidence of the inertial dynamics was found in NiFe and Co samples [23] by following the field dependence of the ferromagnetic precession resonance (FMR) peaks. The experimental observation of the nutation resonance has only been achieved very recently in NiFe and CoFeB using intense terahertz magnetic field transients [25].…”