Ultrafast Electron Dynamics in Magnetic Thin Films

In past decades, ultrafast spin dynamics in magnetic systems have been associated with heat deposition from high energy laser pulses, limiting the selective access to spin order. Here we use a long wavelength terahertz pump optical probe setup to measure structural features in the ultrafast time scale. We find that complete demagnetisation is possible with<6 THz pulses. This occurs concurrently with longitudinal acoustic phonons and an electronic response, followed by the magnetic response. The required fluence for full demagnetisation is low, ruling out the necessity of a high power light source.


I. INTRODUCTION
The study of ultrafast magnetism is crucial in advancing our understanding of magnetic systems, as well as developing ultrafast memory devices. The difficulty of this subject lies in spin dynamics, and its role as a part of a larger picture of the barely understood coupled structural dynamics.
As an example, when a ferromagnetic film is excited by a femtosecond (fs) laser pulse, partial demagnetisation of the material occurs within ∼ 100f s, followed by a remagnetisation to the original state on a longer time scale. This was first observed in 1996 for optical laser pulses [1], and later also for THz laser pulses [2][3][4][5]. While this phenomenon has led to intense investigations in the field by both experimentalists and theorists, it has now become evident that this process is mediated by a complex puzzle of strongly entangled pieces [6]. To elaborate on this, it is essential to understand the physical mechanisms that can influence the spin angular momenta of the electrons responsible for magnetisation.

A. Separation of Underlying Mechanisms
In order to simplify the almost unfeasible task of tackling coupled structural dynamics, we examine the phenomena responsible and their respective timescales. This allows us to decouple mechanisms which have infinitesimal effects on each other. * hovan.lee@kcl.ac.uk † most.shalaby@gmail.com As Born and Oppenheimer pointed out, a separation of atomic nucleus dynamics and the surrounding electrons can be made. This is because electrons will adiabatically follow any comparatively slow changes of the lattice. That is, typical dynamics of the phonons is on the picosecond timescale, where as electron dynamics in metals can occur in as short a time span as the attosecond timescale.
Similarly, a separation of electron charge and spin degrees of freedom is reasonable, due to the slower time scales that are observed for the dynamics of the spins, ∼ 100f s, than that for the electron scattering, ∼ 10f s.

B. Pathways of Magnetisation Dynamics
The dynamics of magnetism in a stimulated material could be affected by any number of combinations of the mechanisms described above. In particular, there may be different channels of light-matter interactions, here we elaborate on the two extremes: direct coupling of the laser pulses to electronic spins, and intermediate charge and/or phonon excitations which induce magnetisation dynamics [1,[7][8][9][10][11][12].
In the direct scenario, the local electro-magnetic field of the stimulus directly couples with the electronic spin angular momenta [9,13], such that there is minimal heating of the electronic structure.
In the indirect channel, the laser photons do not primarily change the magnetisation, but instead photon energy is transferred to the system in the form of an increased electronic and/or atomic temperature. This process can excite electron-hole pairs, lattice phonons and magnons, which will non-selectively spin-flip scatter with the electrons responsible for magnetisation, modifying their angular momenta [14][15][16][17].
Demagnetisation effects in past reports with optical laser pulses are mediated through this indirect channel. This results in a non-equilibrium state, where the electronic temperature is raised above the phononic temperature, and an imbalance exists between chemical potentials of electrons with differing spins. This difference is the driving force for ultrafast demagnetisation [18,19]. The system then evolves through the above discussed spin-flip scatterings, leading to changes in the orientations of atomic magnetic moments. As a result of this, a temporary demagnetisation is observed, followed by remagnetisation to the original state through the balance of the chemical potentials, and the thermalisation of the electrons and phonons. Furthermore, in samples with metallic substrates there is also a contribution of a superdiffusion process [20]. In this process, the excited mobile spin carriers are transferred onto a conducting substrate.
Lastly, the total effective magnetic field exerts a Zeeman torque onto the atomic magnetic moments. This minute contribution on the magnetisation M (t) is a coherent oscillation in time, following the action of the electro-magnetic wave. However, excited electrons with the above discussed spin flip scattering alter M (t) incoherently in time, leading to fluctuations of the phase; dephasing the system. Therefore, the precessional motion is not typically observable after optical laser pulse excitations. Although the effects of Zeeman torque has been disproven to influence electronic spins to the point of demagnetisation in the Mott insulator NiO [21], this effect has not been shown in metals.

C. Unto Terahertz Laser Pulses
Although optical pulse / thin film demagnetisation have been intensively examined, it has been shown that the majority of these studies rely on indirect and indiscriminate spin excitations [22][23][24]. To increase the coherency and control of the interaction, experiments have been preformed with THz laser stimuli. The THz field cycle oscillates on a similar timescale as the natural speed of electronic spin motions, as opposed to optical pulse stimuli, which oscillate at a much faster timescale.
At low field amplitudes, THz lasers are therefore expected to directly and coherently couple with electronic spin dynamics. This interaction leads to a precessional motion of M (t) due to the Zeeman torque, allowing for selective control of the magnetic phase. Moreover, THz photon energies are three orders of magnitude smaller than optical photon energies, inducing significantly less heating at low field amplitudes, and reducing the possibility for spin flip scattering between electrons and excited particles. This direct coupling of THz and demagnetisation was reported for ferromagnetic cobalt films [25], where a coherent, phase locked demagnetisation response was observed under excitations from THz pulses.
With the recent advances of THz source technology, THz laser pulses with field amplitudes of several Teslas are now accessible. This opens new venues for exploring complete precessional reversal of M (t). From a technological perspective, obtaining such a reversal would be a milestone, as the time scales involved would be significantly shorter than the Larmor precession obtained in present-day technology. Clearing a potential pathway to increase processor speeds.
However, high field amplitudes come at the cost of a strong heating of the sample, and a loss of the coherent interaction between M (t) and the THz laser field. In this regime, incoherent electronic excitations with subsequent spin-flip scatterings induce a dephasing of M(t) without precessional motion. This is similar to the processes ob-served after optical pulses. Finally, an additional challenge at large field comes in the form of permanent modifications of film properties, and possible damage observable with scanning electron microscopy.
Here, we approach the ultrafast magnetisation dynamics from the photon energy perspective, where we compare excitation dynamics from high (optical) to low (THz) photon energies. We experimentally study the THz induced ultrafast electronic and structural dynamics in nickel thin films.
In the THz frequency range, partial demagnetisation in Ni has been previously reported, followed by permanent demagnetisation [2]. Here, we carefully design the experiment to accurately map the THz-induced demagnetisation. We report that sufficiently intense THz pulses lead to full demagnetisation on the ultrafast time scale without sample damage. The process is combined with strong electronic excitation and generation of acoustic phonons.
With the knowledge required to understand the principle mechanisms governing the effects of THz laser pulses on ferromagnetic materials, we move on to the results of our experiment.

II. RESULTS
For our experiment, a 15nm sputtered Ni thin film on a high resistivity Si substrate was chosen as the sample. This is due to the many extensive studies performed upon the ultrafast magnetism of the material, first reported by Beaurepaire et al in 1996.
The setup is a tightly focused terahertz bullet scheme where the THz is focused to the diffraction limit to reach the maximum possible intensity. The THz is generated by optical rectification of near infrared pulses (1550 nm central frequency, 100 Hz, 50 fs, 3.5 mJ, Light Conversion OPA system) and an organic crystal DAST (Swiss Terahertz GmbH), 350 um thick. The beam is expanded then focused on the sample (three off axis parabolic mirrors scheme). The probe beam is 800 nm centered, 70 fs, 100 Hz, and collinear with the THz pump. The sample was placed to allow for an incident angle of 45. Both probe and pump were linearly polarized, and the full setup is illustrated in Fig.1.a. The THz-induced magnetisation dynamics lead to birefringence on a collinear 800nm probe. The temporal and spectral contents of the THz pulse are shown in Fig.1.b-c. All measurements of the ratio between the magnetisation and its saturation value M (t)/M s , as shown in Fig.1, were performed by modulating the external magnetic field at 40mT and 25Hz. This frequency was used as a reference for our acquisition system to eliminate any non-magnetic contribution to the measured signal. This exact experimental setup was characterised in depth in [26].
The THz source contains significant spectral components up towards ∼ 18T Hz, these components were eliminated through a set of low pass filters with cut-off frequencies at 3, 6 and 9T Hz. This results in a set of pulses that are well defined in spectral content, we expect these pulses to contain several oscillation pulses in the time domain. To further characterise the pulses, we refer to a previous work on the same THz source: [27]. In the cited text, a one-to-one correspondence between the pulse fluence and the peak electric field strength was found through the Kerr effect in diamond, allowing us to infer the fluence of a filtered pulse by measuring the pulse duration and spot size (measured previously in [28]).
Through the 3T Hz filter, the maximum achievable THz fluence on the sample is 17.3mJ/cm 2 , leading to an instantaneous demagnetisation (dM/Ms) of 60% as shown in Fig.1.c. Extending the spectrum with the 6T Hz filter, presented in Fig.1.d, allows for much higher peak fluence up towards 66.8mJ/cm 2 . This offers the possibility of complete demagnetisation without sample damage at 47mJ/cm 2 , as alluded to in Fig.1.e, where magnetisation is shown to recover. Measurements of the reflected pulse show that around 90% of the pulse fluence was reflected. This suggests that roughly 10% of the incident fluence is absorbed. Therefore, this corresponds to an absorbed fluence of ∼ 4.7mj/cm 2 .
At low fluence, the extent of demagnetisation increases with the excitation fluence almost linearly, suggesting a linear THz absorption mechanism in Fig.1.f. Here, we perform a rough calculation to compare the sample temperature at various fluences with the Curie temperature of Ni. The heat equation of the system is: Q = m * c * dt, where m is the mass of the object, c is the heat capacity, and dt is the induced temperature change. Bulk nickel has a heat capacity of 0.44J/gK and a density of 8.908x10 6 g/m 3 . In our experiments, the sample thickness is 15nm and we assume that about 10% of the incident THz pulse is absorbed by the sample. Using a low pass filter of 6 THz we observe partial demagnetisation at a fluence of 16.7mJ/cm 2 , corresponding to a temperature increase of 280k. Complete demagnetisation was observed at 47.3mJ/cm 2 , corresponding to a 800k temperature increase. Taking into account that the experiment was performed at room temperature, this gives us the temperature range of 500K to 1070k, which is comparable to the Curie temperature of Ni at 627K. This identifies that the the demagnetisation observed at very large fluence is due to the existence of hot electrons at the Fermi level (whereby electrons are excited by the intense sub ps heating out of the Fermi level. These electrons are prevented from thermalising with the Fermi sea due to the non equilibrium nature of the system, and therefore dominates the subsequent dynamics [29,30]). This is similar to previously reported for optical laser sources, but has not been proven previously for THz sources.
Previous results on a similar sample [2] showed a maximum demagnetisation of 58% at 89mJ/cm 2 before the sample becomes permanently damaged. This is in contradiction to the results we present here, where higher demagnetisation was achieved at lower THz fluence without noticeable damage. We offer an explanation to this discrepancy: The MOKE probe in the previous report likely lacked the spatial resolution to pinpoint the demagnetised area exactly. Hence both the areas of demagnetisation and the areas that are unaffected contributed to the measurement, giving a lower demagnetisation percentage. In this paper we limit the spectral contents to < 6T Hz, this increases the diffraction-limited excitation spot size. This allows the area of demagnetisation to be fully resolved, and therefore achieving higher measurable demagnetisation at lower fluence.
We use this quantitative result to address the main question of the role of photons in demagnetisation. Specifically, whether demagnetisation was achieved through the direct or indirect channel discussed above. Conventionally, it was assumed that the direct mechanism was associated with excitations of low frequency electro-magnetic radiations, such as microwave radiation. In contrast, high frequency optical pulse excitations have been shown to demagnetise materials through the indirect mechanism dominantly. However, it is not impossible for both mechanisms to coexist. It is generally considered that the higher the excitation pulse frequency, the higher the excitation field amplitude is needed in order to induce changes in the magnetisation. Therefore, to achieve magnetic switching in the THz regime, it would require practically unrealistic pulse intensities (> 10 Tesla). In this limit, undesired structural changes would inevitably take place. Our experiments show that THz excitations are only capable of inducing small amplitude precessions, as is confirmed in Fig.1 where no precessions are observed in the measured signal. Therefore, our results point towards the indirect mechanism as the most likely hypothesis.
A lingering question remains: Do individual photon energies play a significant role towards the measured demagnetisation effect. Indeed, this indirect mechanism critically depends on the presence of a high integrated photon energy to raise electron temperatures above phonon temperatures. Comparing the photon en-ergies from the optical (eV energy scale) range to the THz (meV energy scale) range, we conclude that this effect is not directly possible without exponentially increasing the number of THz photons.
In contrast to this claim, the experimental results do not reveal a relationship between photon energy and demagnetisation. First, there is no high fluence threshold for demagnetisation; A nearly linear relationship between fluence and demagnetisation is observed in our experiments ( Fig.1.f). Secondly, with comparisons between our results and a previous report on a similar sample under optical excitation, the absorbed fluence needed for demagnetisation from optical and terahertz pulses are of the same order of magnitude. The difference in energy between individual optical and THz photons are three orders of magnitude apart, and thus confirms a negligible dependence of demagnetisation on individual excitation photon energy, ruling out any significant direct interaction of the THz electric field frequency on demagnetisation in our experiments. With evidence suggesting that only the net fluence absorbed influences the demagnetisation in the sample.
In light of these results, we extended our search of the mechanisms behind demagnetisation by including charge and lattice degrees of freedom. Ultrafast excitation of thin films leads to rapid heating and excitation of electrons to higher non-equilibrium states. This absorbed energy is eventually transferred to the lattice through electron-phonon interactions, leading to spatio-temporal strain pulses and coherent acoustic phonons which reverberate inside the film. This model has been used to explain ultrafast optical generation of lattice strain waves of coherent acoustic phonons, which can manipulate and coherently control the magnetisation orientation in ferromagnetic films [7,[10][11][12]. Thereby justifying our investigation into these additional dynamics.
To tackle this obstacle, we decoupled the intricately intertwined effects of charge, spin and phononic dynamics, without knowing their specific relationships with one another, by exploiting the timescale differences between them. This was achieved by modulating the THz pump excitation and repeating the experiment in Fig.1 with static magnetic fields of B + = +40mT and B − = −40mT , corresponding to biases which are parallel and antiparallel to the THz pulse magnetic field, thus maintaining a constant magnetic bias during our experiments.
The dynamics under the different biases are shown in Fig.2.a for a excitation fluence of 190mJ/cm 2 . Individually these dynamics contains all three degrees of freedom mentioned. However, by summing the effects under opposite biases we obtain the spin-averaged response, thus decoupling the charge and lattice degrees of freedom (shown in Fig.2.c) from spin dynamics. This charge-lattice combined response is characterised by a sharp transient, followed by a slow relaxation with a fast damping oscillations. Here the oscillations represent the coherent acoustic phonons and are independently ex-tracted in Fig.2.d, thereby isolating the lattice dynamics. Similarly, the spin degree of freedom is singled out by subtracting the effects under opposite biases, as shown in Fig.2

.b.
To further justify the significance of these additional dynamics, the constant bias experiments was performed again at excitation fluence of 48mJ/cm 2 and 85mJ/cm 2 as shown in Fig.3.a and Fig.3.c. Where the isolated spin and charge dynamics, corresponding to the magnetic and electronic responses are shown in Fig.3.b and Fig.3.d. It is shown that the magnetic response lags behind the electronic response for all values of fluence, and therefore substantiates the contribution of electronic and phononic dynamics in THz demagnetisation. Furthermore, it is shown that a sub picosecond magnetic response exists from a THz pulse excitation.

III. CONCLUSION
In the present paper, the physical mechanisms behind nickel thin film demagnetisation due to femtosecond laser pulses are investigated. At low field amplitudes, we observe a linear response of demagnetisation from the intensity of the pump electromagnetic field. The THz pump fluence needed to achieve full demagnetisation is similar to the optical counterpart, and therefore suggesting that the frequency of the pump pulse does not play a major role in the demagnetisation process. To support this argument, it was found that at full demagnetisation, the THz pulse induces heating within the sample that is comparable to the Curie temperature of nickel. Alluding to sample heating as the main cause of the demagnetisation process.