Research articles
Thermal coupling parameters between electron, phonon, and magnon of Nickel

https://doi.org/10.1016/j.jmmm.2020.167156Get rights and content

Highlights

  • Adapting the three-temperature model in Ni/Au system.

  • Determining the coupling parameters between electron, magnon, phonon of Ni.

  • Showing the validity of the three-temperature model in the in-direct heating.

Abstract

Thermal interaction in an electron-phonon-magnon system in a ferromagnetic Ni film is investigated using a time-resolved pump-probe technique with thermoreflectance and magneto-optical Kerr effect. A nanoscale Au/Ni bilayer is used to induce thermal excitation of Ni in two ways: direct heating of Ni and indirect heating of Ni via Au. By comparing experiments and thermal modeling, we obtain the coupling parameters for electron-phonon, electron-magnon, and phonon-magnon pairs: 8.55 × 1017, 1.0–1.3 × 1017, and 0.8–1.1 × 1017 W m−3 K−1, respectively. In particular, we find that the phonon-magnon coupling parameter plays a significant role as a fast heat dissipation channel from magnon to phonon during the initial few picoseconds. In addition, both direct and indirect heating can be explained by similar coupling parameters with a variation less then 30%. Consequently, we conclude that the heat exchange between electron, phonon, and magnon is the dominant mechanism for the ultrafast demagnetization.

Introduction

Ever since Beaurepaire et al. observed ultrafast demagnetization driven by a femtosecond laser pulse [1], various kinds of physical models and mechanisms have been suggested to explain this very fast spin excitation in sub-picosecond timescale. Since Guidoni et al. verified that the magneto-optical effect is associated with a thermalized spin bath [2], there have been many efforts to depict this phenomenon with thermal models [3], [4], [5], [6], [7], [8], [9]. Specifically, three temperature model (TTM) has been used assuming that thermalization within a bath is much faster than thermalization between different baths [1], [6], [7], [8], [9].

While there was not yet a clear consensus, Battiato et al. proposed a non-thermal model based on the transport of ballistic-like electrons, so-called super-diffusive spin transport, to explain the ultrafast demagnetization [10], [11], [12]. This theory is based on the notion that the demagnetization is driven by spatial dissipation of angular momentum, which is associated with spin dependencies of both the velocity and lifetime of hot electrons [13]. Schellekens et al. observed generation of spin-transfer torque in a ferromagnet/non-magnet/ ferromagnet multilayer triggered by the ultrafast demagnetization of ferromagnet and interpreted their results with the super-diffusive transport [14]. Spin-dependent transport is important not only for hot electrons but also for thermalized electrons. With voltage gradient as a driving force, the spin-dependent transport is responsible for various magnetoresistances, such as anomalous magnetoresistance and giant magnetoresistance [15]. With laser excitation in an open circuit situation, the driving force for the net transport of electrons is the temperature gradient. In this case, the transport of thermalized electrons has been described by the spin-dependent Seebeck effect [16], [17], [18]. On the other hand, Choi et al. directly measured spin accumulation on a non-magnet followed by ultrafast demagnetization of a ferromagnet and interpreted their results in terms of electron-magnon coupling [19]. The relative contribution of electron-magnon coupling and spin-dependent transport on ultrafast demagnetization depends on the magnitude of the electron-magnon coupling parameter and the spin-dependent Seebeck coefficient [16], [17], [18], [19].

Although the thermal and non-thermal spin-dependent transport plays a certain role in ultrafast demagnetization, it was demonstrated that for a 30 nm Ni layer, a decrease of magnetization is observed at the opposite side to a pump beam, while an increase of magnetization is expected from the super-diffusive spin transport [20]. This result indicates that the local dissipation of spin via the electron-magnon scattering is dominant for the ultrafast demagnetization over the spatial transport of spin. The role of thermalized electrons would be significant in this local dissipation considering the short timescale of ~100 fs for thermalization of electrons in ferromagnet [21], but there is little reported information about the thermal exchange between three heat carriers: electron, phonon, and magnon. Even though Beaurepaire et al. estimated the thermal coupling values between those carriers for Ni in their first observation of ultrafast demagnetization [1], their model adopted heat capacity values, which are far from their well-known values. The main purpose of this paper is to suggest more realistic values for the thermal coupling parameters between different heat baths in Ni: electron-phonon coupling (ge-ph) [22], [23], electron-magnon coupling (ge-m), and phonon-magnon coupling (gph-m).

Another purpose of this work is to check the validity of TTM on ultrafast demagnetization in an indirect heating situation. We prepare two experimental configurations to induce ultrafast demagnetization: 1) direct optical heating of the Ni layer by an optical pump pulse on the Ni layer; 2) indirect heating of the Ni layer through the adjacent Au layer, which is excited by the optical pump pulse. Eschenlor et al. observed that optical excitation of Au in an Au (30 nm)/Ni (15 nm) bilayer leads to nearly the same demagnetization of Ni as does direct excitation of Ni [12]. The authors of Ref. [12] interpreted their results as direct evidence of the superdiffusive theory. In this work, we show that ultrafast demagnetization of Ni via indirect heating of Au can be explained by TTM with coupling parameters that are similar to those for direct heating. A small difference of <30% in the fitted parameters between the direct and indirect heating configurations can be attributed to the effect of the superdiffusive theory or the spin-dependent Seebeck effect.

Section snippets

Material and methods

For the experiments, we grew a nanoscale bilayer structure of Au (100 nm) and Ni (20 nm) on a sapphire substrate. Two metal layers in the sample were deposited with a magnetron sputtering system at the base pressure of <10−7 Torr. The Au thickness of 100 nm is decided to be much larger than the light penetration depth of 16 nm, so that the Ni layer is not excited directly by photons in the indirect configuration. The Ni thickness of 20 nm is chosen to have the magnetic properties of bulk Ni [24]

Theory and calculation

In this section, we explain the theoretical modeling for the heat transport in the Ni/Au bilayer. Fig. 2 schematically exhibits heat transport processes for the two experimental configurations: direct and in-direct heating. In Ni, the electronic thermal energy quickly dissipates to the phonon bath, whereas the electronic heat in Au does not easily flow to the phonon bath. This difference is due to the much larger ge-ph value of Ni than of Au [38]. With a small ge-ph and high thermal

Results and discussion

The experimental results of ΔTm of the Ni layer and ΔTph of the Au layer are well explained by the thermal modeling. Fig. 5 exhibits the overall results of experimental data of TDTR and TR-MOKE with two optical pump configurations, the direct heat to the Ni layer and the indirect heat to the Ni layer via the Au layer. TDTR and TR-MOKE data are rescaled to the equilibrium position after 200 ps where all the temperatures in all the depth of the Ni and Au layer converge and behave like a single

Conclusions

As our main purpose, three coupling parameters between electrons, phonons, and magnons in Ni are determined in two experimental configurations. Our results of ge-ph and ge-m are similar with recent results of Ni and Co [38], [54], [55], [56]. Unexpectedly, we also found that gph-m is comparable in magnitude to ge-m. Based on our results, we conclude that phonon-magnon coupling has a significant role as a heat dissipation channel from magnon bath to phonon bath during the initial few

CRediT authorship contribution statement

Kyu-Hwe Kang: Investigation, Formal analysis, Writing - original draft. Gyung-Min Choi: Conceptualization, Methodology, Supervision, Writing - review & editing. : .

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

G.M.C acknowledges the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2019R1C1C1009199) and the Creative Materials Discovery Program through the National Research Foundation of Korea (NRF) funded by Ministry of Science and ICT (2018M3D1A1058793).

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