Inertial spin dynamics in ferromagnets

Abstract

The vast majority of digital information worldwide is stored in the form of tiny magnetic bits in thin-film materials in the hard-disk drives installed in large-scale data centres. The positions of the north and south magnetic poles with respect to the thin-film plane encodes the logical ‘ones’ and ‘zeros’, which are written using strongly localized, intense magnetic fields. The dynamics of the magnetization in the writing process is described by the Landau–Lifshitz–Gilbert (LLG) equation, which correctly models the reversal of a magnetic bit at nanosecond timescales. Until 20 years ago, it was believed that all of the relevant physics of magnetization dynamics was included in this equation and that optimization of storage devices could be based solely on it.However, the pioneering experiment of Bigot et al. in 1996 [1] revealed the occurrence of spin dynamics on subpicosecond scales that could not be described by the LLG equation, giving birth to the field of ultrafast magnetism. This field explores some of the currently most investigated and debated topics in condensed matter physics [2], with implications for both our fundamental understanding of magnetism as well as possible applications for faster and more energy-efficient data manipulation. Recently, the LLG equation was reformulated to include a term to obtain a physically correct inertial response [3], which was not present in the original formulation. This term predicts the appearance of spin nutations, similar to the ones of a spinning top, at a frequency much higher (in the terahertz range) than the spin precession described by the conventional LLG equation (typically at gigahertz frequencies), as shown schematically in Fig. 1a,b. However, the lack of intense magnetic field sources at these high frequencies has hampered the experimental observation of such nutation dynamics.In this work, we use intense narrowband terahertz magnetic field transients from a superradiant terahertz source and the femtosecond magneto-optical Kerr effect (MOKE) to detect inertial magnetization effects in ferromagnetic thin films. We find evidence for nutation dynamics with a characteristic frequency of the order of 1 THz, which is damped on timescales of the order of 10 ps. We are able to qualitatively describe the observed magnetization dynamics with a macrospin approximation of the inertial LLG equation and highlight implications for ultrafast magnetism, and magnetic data processing and storage.The basic idea is to perform a forced oscillator experiment as a function of the frequency of the terahertz magnetic field HTHz, detecting the amplitude and phase of the response with the femtosecond MOKE in an attempt to observe the signature of a resonance. The response of the magnetization is maximized when HTHz and the static magnetization (which is controlled with an external magnetic field) are orthogonal to each other. This is illustrated schematically in the top panels of Fig. 1c,d, with the corresponding experimental measurement in the bottom panels, where we show the detected polar MOKE signal.In this talk, we will present direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of the order of 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps. We anticipate that our results will allow for a better understanding of the fundamental mechanisms of ultrafast demagnetization and reversal, with implications for the realization of faster and more efficient magnetic data-processing and storage devices. **