Conductivitylike Gilbert Damping due to Intraband Scattering in Epitaxial Iron

Abstract

Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for some of the simplest ferromagnetic metals. In this Letter, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivity-like damping, 2 which cannot be accounted for by classical eddy current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the longstanding question about the role of intraband scattering inGilbert damping in pure ferromagnetic metals.Damping determines how fast the magnetization relaxes towards the effective magnetic field and plays a central role in many aspects of magnetization dynamics [1,2]. The magnitude of viscous Gilbert damping governs the threshold current for spin-torque magnetic switching and auto-oscillations [3,4], mobility of magnetic domain walls [5,6], and decay lengths of diffusive spin waves and superfluid-like spin currents [7,8]. To enable spintronic technologies with low power dissipation, there is currently much interest in minimizing Gilbert damping in thin films of magnetic materials [9][10][11][12][13], especially ferromagnetic metals [14-18] that are compatible with conventional device fabrication schemes. Despite the fundamental and technological importance of Gilbert damping, its physical mechanisms in various magnetic materialseven in the simplest ferromagnetic metals, such as pure Fehave yet to be confirmed by experiment.Gilbert damping is generally attributed to spin-orbit coupling that ultimately dissipates the energy of the magnetic system to the lattice [1,2]. Kambersky's torque correlation model [19] qualitatively captures the temperature dependence of damping in some experiments [20-23] by partitioning Gilbert damping into two mechanisms due to spin-orbit coupling, namely interband and intraband scattering mechanisms, each with a distinct dependence on the electronic momentum scattering time e. For the interband scattering mechanism where magnetization dynamics can excite electron-hole pairs across different bands, the resulting Gilbert damping is "resistivity-like" as its magnitude scales with e -1 , i.e., increased electronic scattering results in 3 higher damping [24,25]. By contrast, the intraband scattering mechanism is typically understood through the breathing Fermi surface model [26], where electron-hole pairs are excited in the same band, yielding "conductivity-like" Gilbert damping that scales with e, i.e., reduced electronic scattering results in higher damping. Conductivity-like Gilbert damping was reported experimentally more than 40 years ago in bulk crystals of pure Ni and Co at low temperatures, but surprisingly not in pure Fe [20]. The apparent absence of conductivity-like damping in Fe has been at odds with many theoretical predictions that intraband scattering should dominate at low temperatures [27][28][29][30][31][32][33], although some th...

Room-Temperature Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films

“…This damping parameter range is quantitatively in line with the value reported for epitaxial Fe (black symbol in Fig. 3(b)) 18 .…”

“…From Refs. 18,38 , we deduce that interband scattering is dominant at room temperature in Fe. According to our results (Fig.…”

“…The details of the measurement method are found in Refs. 18,34 . Figure 3(a) shows the frequency dependence of half-width-at-halfmaximum (HWHM) linewidth Δ𝐻 OOP for selected thicknesses from both sample series.…”

“…Figure 3(a) shows the frequency dependence of half-width-at-halfmaximum (HWHM) linewidth Δ𝐻 OOP for selected thicknesses from both sample series. The linewidth data of 25 nm thick epitaxial Fe film from a previous study 18 is plotted in Fig. 3 (a) as well.…”

“…In ferromagnetic metals, Gilbert damping arises predominately from "intrinsic" mechanisms [14][15][16] governed by the electronic band structure 17 . Indeed, a recent experimental study by Khodadadi et al 18 has shown that intrinsic, band-structure-based Gilbert damping dominates magnetic relaxation in high-quality crystalline thin films of Fe, epitaxially grown on lattice-matched substrates. However, it is yet unclear how intrinsic damping is impacted by the microstructure (e.g., crystallographic texture) of polycrystalline Fe films.…”