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The nickel (Ni) films of three different thicknesses, 65 nm, 135 nm and 1018 nm, were deposited by the RF magnetron sputtering technique. These films were subjected to femtosecond laser pulses of ~140 fs duration at 80 MHz repetition rate for generation of terahertz (THz) radiation. The obtained electromagnetic radiation was detected using photoconductive antennas by a sampling technique. The THz generation mechanism of Ni films is attributed to the ultrafast demagnetization process and its time depends on the Gilbert damping factor. The ascertained values of the Gilbert damping parameter of Ni films using ferromagnetic resonance (FMR) measurements lies between 0.011 and 0.0069. We have observed that the amplitude of emitted THz radiation from Ni films is proportional to Gilbert damping factor of films. The amplitude of emitted THz radiation from 65 nm Ni film is 1.19 and 1.66 times higher than 135 and 1018 nm films.
© 2016 Optical Society of America
1. Introduction
Present material science research based on thin film technology has identified the large number of magnetic materials possessing useful characteristic information in the low frequency phonons (≤ 5THz) range. These materials belong to semimetals, metals or transition metallic class. The single and multilayer ultrathin films of these materials are grown on different substrates with Au capping for protection in ambient conditions. The instrumental techniques such as XRD, SEM, EDX and AFM etc., provide significant information about these materials. However, effect of low energy phonon modes on THz generation can only be realised, when these films are subjected to ultrafast laser pulses. The THz range (0.1-3THz) has potential application in the field of defense, medical and material science [1–6]. Photoconductive (PC) antennas, periodic poled LiNbO3, four wave mixing of harmonics in air, Coherent lattice vibrations, Cooper pair breaking in superconducting material and Josephson Junction etc., are some of the widely used techniques for THz generation [6–12]. Though, these techniques are well established and very efficient in THz generation but require additional infrastructure facilities like special type lithographic lab for material and PC antenna fabrication, crystal growth facilities and other high sophisticated semiconductor etching techniques, which is high cost effective. Hence, emphasis is given to develop low cost, robust/smart THz source materials, which need minimum efforts for growing. The development of metallic and non-metallic films possessing ferromagnetic resonance properties is one of the simple approaches for THz generation. Moreover, understanding of THz generation mechanism of these materials is one of the core areas of research for developing ultrafast read write magnetic memory devices [13–16].
Kadlec et al. generated the THz radiation from gold and silver metallic surfaces for the first time using 100 fs laser pulses in 2004 [17]. After his finding, a number of studies were reported on THz generation using metallic nanoparticles, semi-continuous and nanostructured metallic films etc [18–23]. Optical rectification and multi photon photoelectron emission (MPE) mechanisms are responsible for THz emission from metallic films. Apart from non-magnetic films, magnetic metallic films are also used for generation of THz radiation [13, 24–26]. Beaurepaire et al. reported THz emission from ferromagnetic (Nickel) films for the first time by illuminating with 100 fs laser pulses in 2004. The ultrafast demagnetization of ferromagnetic order (i.e. due to intrinsic spin dynamics) using ultrafast lasers is identified as an evident mechanism for THz generation from ferromagnetic film [13]. The focused ultrafast laser pulses on film surface, produces sudden change in spin temperature, which decreases the magnetization as it approaches to Curie temperature. The rapid decrease in magnetization (in ultrafast time domain) emits an electromagnetic wave, which falls in gigahertz or terahertz frequency domain. The demagnetization process in films with respect to time is related to Gilbert-damping coefficient that reveals the process of rapid relaxation of magnetization vector towards its equilibrium [27]. Hence, Gilbert-damping factor plays vital role for understanding the characteristics of emitted THz signal. R. Urban et al., investigated the Gilbert damping by ferromagnetic resonance (FMR) in a magnetic multilayer’s [28]. In addition, it is associated with FMR signal broadening, which also influences the electron angular momentum transfer between the magnetic layers and leads to generate additional relaxation torques. However, there are only few reports are available to understand the implication of the Gilbert damping effect on THz generation [29, 30]. J. Shen et al. reported the effect of damping factor on THz generation from FeNi films by changing the non-magnetic layer associated with it. The damping factor of magnetic films is also governed by changing the thickness of film and non-magnetic layer associated with it [31–34]. In this report, we have studied the effect of Gilbert damping factor on THz generation by changing the thickness of Ni thin films.
2. Experimental details
2.1 Deposition of films
The ferromagnetic Nickel (Ni) films were deposited on silicon substrate by RF magnetron sputtering technique at room temperature (RT). The various deposition conditions are summarized in Table 1. The films were deposited at three working pressures of Ar ranging 10 m torr, 15 m torr and 20 m torr. The deposition was carried out for two different times duration (i.e. 15 min and 2 hr) to get different thickness films. The thickness of films is measured by FESEM technique and the obtained values are 65 nm, 135 nm and 1018 nm respectively.
Table 1. This table summarizes the deposition conditions and naming of Ni Films deposited at various working pressures of Ar.
2.2 Schematic of THz radiation generation and detection
The experimental schematic for THz generation and detection is depicted in Fig. 1. The employed laser source is supplied by coherent chameleon ultra-II which delivers transformed limited pulses of duration ~140 fs at a repetition rate of 80 MHz. The maximum average power of the laser is 3.8 W at 800 nm central wavelength. The Ni films, Baptop SI-GaAs PC antennas are used as THz sources and detector, respectively. The gap, length of employed PC antenna is ~5 µm and ~20 µm, respectively. The variable attenuator is used for attenuation of incident laser pulses and selected average power from it is allowed to incident on the Ni films . The laser beam is allowed to incident on 90:10 beam splitter (BS) and reflected part of it (pump) is focused (plano-convex lens f ~10 cm) on to the sources at an angle of 45° with respect to source surface normal. Laser illuminated Ni films emit THz radiation due to ultrafast demagnetization process. The reflected residual pump beam and generated THz radiation from source are allowed to fall on the combination of teflon (thickness (t) ~2 mm, diameter (D) ~10 mm) and black polyethylene filter (0.2 μm thickness). These filters are used to stop/prevent the residual pump beam to propagate along with THz radiation. The diverging THz pulses obtained from a source in quasi reflection mode is collected, collimated and focused onto the THz detector i.e., PC antenna by parabolic mirrors (PM1 and PM2). The parabolic mirrors are of diameter (D) ~50 mm and a effective focal length (fe) ~150 mm are employed in experiment. The transmitted part (probe beam) of laser beam from BS is focused on to the THz detector by another plano convex lens of focal length 50 cm and detected using PC sampling technique. The output of PC antenna is connected to low noise current preamplifier, which is fed to voltage input of Lock in amplifier (SR 830) for measurement of THz induced voltage. The mechanical Chopper is used for synchronizing Lock in amplifier with THz pulses at 1.569 kHz frequency which enabled us to enhance the signal to noise ratio. The temporal profile of THz radiation is measured by varying the delay of probe beam with respect to THz pulse.
Fig. 1 Experimental layout of THz generation using semiconductors and detection by PC antennas (VA-Variable attenuator, C - mechanical chopper, L1 & L2 - Plano Convex Lens, S- THz sources, PM1 & PM2 –parabolic mirrors, SL- Hyper hemispherical silicon lens).
3. Results and discussion
3.1 Structural and micro structural studies
Figure 2 shows the growth of (200) oriented Ni films formation of Face Centred Cubic (FCC) crystal structure in the all above cases of deposition (10 m torr, 15 m torr and 20 m torr.). There is a presence of compressive strain in all films as compared to bulk Ni. Since the films are grown in (100) direction the anisotropy of the system depends on the direction of applied field. When the deposition duration increased for the films at 10 m torr working pressure, the XRD shows the right shift of (200) peak which clearly supports the relaxation of tensile strain with further increase in the thickness of film. However, in case of bulk Ni the order of direction of magnetization varies as (111), (110) and then (100). Since the films are two-dimensional, therefore, we have ruled out the (111) stacking direction which is the lowest energy direction. Thus, the films are left with a (110) easy direction of magnetization. The incident laser pulses excite the electrons by spin-orbit coupling and spin excitation process of these materials. As the films show the presence of strain in it, the magneto crystalline anisotropy energy (MAE) can be changed by means of strain
Fig. 2 XRD patterns of above deposited nickel films and inset shows AFM images of corresponding films.
In addition, Si substrate peaks are also observed in the XRD pattern along with the Ni peaks in Fig. 2. From AFM images (inset), it is clear that RKNi-09 has smooth morphology compared to other two films. The higher clustering of grains is more visible in thicker film (RKNi-05) which is an agreement with film growth mechanism. In case of low thickness film (RKNi-12), the grain growth is started and as thickness increased further (RKNi-09) to 165nm a smooth morphology films are obtained. After this the breaking of smooth morphology is occurred and we got highly clustered (RKNi-05) thick film (1018 nm).
3.2 Discussions on THz generation process
Figure 3 depicts the temporal profiles and spectral amplitude of generated THz radiation from Ni films of different thickness. The average laser power employed for THz generation is ~1.2 W and the radiation detection is carried out using antennas. The obtained THz peak-peak amplitude values of RKNi- 12, RKNi-09 and RKNi-05 are 4.15 a.u., 3.47 a.u., 2.49 a.u., respectively as shown in Fig. 3(a). Therefore, the RKNi-12 film has high peak-peak amplitude as compared to other films. Since the film thickness plays major role in changing the signal shape, which is attributed to different phenomena’s like magnetic anisotropy in the film or interface of film and substrate and corresponding Gilbert damping factor which influence the demagnetization and relaxation time of the film. In addition, it is also attributed to non uniform spins arrangement in thin films. Hence RKNi-12 has bipolar THz temporal profile.
The spectral peak amplitudes of generated THz pulses are 4.96 a.u., 4.83 a.u. and 2.81a.u. for RKNi-12, RKNi-09, RKNi-05 films, respectively and spectral range is extended up to 0.8 THz. The generated THz peak-peak amplitude and spectral peak amplitude is decreasing with increase in film thickness. RKNi-12 film generated THz peak amplitude is 1.19 and 1.67 times intense compared to RKNi-09 and RKNi-05 films, respectively. It can be explained on the basis of Gilbert damping effect on ultrafast demagnetization process, which governs THz generation in Ni films.
3.3 Ultrafast demagnetization and Gilbert damping effects on THz radiation
The precessional dynamics of magnetization is explained by Landau Lifishitz Gilbert (LLE) equation. The expression for LLE is given by [27]
Where represents magnetization vector, is effective field, γ is gyromagnetic ratio and α is damping coefficient. The first term in equation stands for precession of torque while second term represents the energy dissipation (α). From equation, the rate of change of magnetization with time is proportional to Gilbert damping coefficient (α). Therefore, the damping term is very crucial in explaining the generated electromagnetic radiation. As the THz generation in Ni films is related to ultrafast demagnetization process and hence it is important to understand this mechanism and verify the relation between demagnetization parameters and THz signal parameters. Previously, the experimental results shown that the ferromagnetic magnetic order quenching time of thin films lies in sub ps time scales [35]. Consequently, the illumination of material with ultra-short laser pulse creates a strong non equilibrium situation among the excited electronic, non-excited spin and lattice degrees of freedom. Thus, in these kinds of systems there are three reservoirs for the energy and momentum transfer. The effective energy and momentum transfer between the reservoirs depends on the strength of coupling [35, 36]. The ultrafast dynamics were well explained by considering the phenomenological three temperature model [37].
For a single quantum particle (e.g., electron), the orbital (L) and spin (S) magnetic moments can change such that the total angular momentum will be conserved. The Quenching of S and L or spin flipping is lead to the various other mechanisms like, Stoner-excitations, Electron- Magnon scattering, Phonon - Mediated spin-flip etc [38, 39]. These demagnetization processes involved intrinsic spin dynamics that responsible for the electromagnetic radiation generation with frequency in the THz range. The generated electric field is given by following equation [29, 30].
Where ‘r’ is the distance to the magnetic dipole and ‘t’ is time. The ‘x’ and ‘y’ represents the direction of elementary magnetic dipole and emitted THz radiation, respectively. The time dependence of magnetization is given in Eq. (3) [29,30].
Where ‘Θ (t)’is Heaviside step function, c1 and c2 are constants. Here τm and τR are called as demagnetization time and recovery time respectively. B. Koopmans et al. tried to unify and explain the ultrafast demagnetization at all time scales by considering the Landau-Lifshitz-Gilbert equation [27]. As per their analysis demagnetization time is inversely related to the Gilbert damping factor (α). Thus the relationship between ultrafast demagnetization time constant and Gilbert damping factor is defined as [27].
Where ‘ћ’ is Planck constant, ‘kB’ is Boltzmann constant, Tc is Curie temperature, prefactor C0 value is 0.25 and ‘α’ is dimensionless Gilbert damping constant. Therefore, the emitted THz radiation from ferromagnetic films can be controlled by changing the demagnetization time, which depends on Gilbert damping factor of films. The Gilbert damping factor depends upon various factors such as thickness of film, thickness and material of non-magnetic layer associated with magnetic film [29–34]. The decrease in damping constant with increase in film thickness was elucidated on Ni-based bi-layers [34]. Fognini et al. also reported the increment in demagnetization time (i.e. decrement in damping constant) as a function of Ni film thickness [40]. On other hand, Barati et al. reported the magnetic damping constant was increasing with thickness of FCC Ni films and its value was strongly varied up to 304 microns due to quantum well states in Ni films [32]. The thickness of our FCC Ni films employed for THz generation was less than 304 microns. Hence, we could not decide the trend of magnetic damping constant with film thickness (< 304 μm). Hence, we measured the Gilbert damping constants for our Ni films using ferromagnetic resonance experiments [41].
The Eq. (5), is used to calculate the Gilbert damping parameter (α) [41]
where, the quantity ΔHPP is called FMR peak-to-peak line width, which is the measured from ferromagnetic resonance experimental set-up. Where γ1 = ω/H and f shows the resonance frequency. The ΔHPP values for above three films at 9.54 GHz are 249, 208 and 150 Oe respectively. The measured values of the Gilbert damping factor using ΔHPP and corresponding correlation with THz peak-peak amplitude are shown in Fig. 4. The obtained Gilbert damping values of RKNi-12, RKNi-09, and RKNi-05 films are 10.6 x 10-3, 8.8 x 10-3, and 6.9 x 10-3, respectively. Gilbert damping values are decreasing with increase in film thickness which indicates the rise in ultrafast demagnetization time from Eq. (4). The demagnetization time affects the generated THz signal from Eq. (3),(2). The figure shows that the THz peak-peak amplitude is increased with Gilbert damping factor (α). Therefore, intense THz radiation can be generated by increasing the Gilbert-damping constant of films having different thicknesses. Furthermore we could conclude that enhanced THz radiation in RKNi-12 might be due to decrease in demagnetization time and increase in damping constant of films.
Fig. 4 Dependence of Gilbert damping coefficient (α) and THz peak-peak amplitude with Nickel film thickness
4. Conclusions
The Ni films of <200> orientation having thickness ~65, ~135 and ~1056 nm are successfully deposited on Si (100) substrates using RF magnetron sputtering technique. The Gilbert damping parameter is obtained from FMR measurements and it is decreased with increase in film thickness. THz pulses are generated from these films and detected using PC antennas. The generated THz intensity from RKNi-12 film is 1.19 and 1.67 times higher than the RKNi-09 and RKNi-05 films, respectively. Therefore, the generated THz peak–peak amplitude is high for film with thickness 65 nm and correlated on the basis of Gilbert damping factor. The experimental findings show that the generated THz peak-peak amplitude for Ni-films is increasing with Gilbert damping parameter (α).
Acknowledgments
The authors acknowledge the financial support received from DRDO, Ministry of Defense, Govt. of India, India. We also acknowledge the UGC, MHRD, India for providing the facility for macro structural based characterization.
References and links
1. C. W. Lawn, D. Jason, and M. M. Daniel, “Imaging with Terahertz radiation,” Rep. Prog. Phys. 70(8), 1325 (2007).
2. R. Miles, X.-C. Zhang, H. Eisele, and A. Krotkus, Terahertz Frequency Detection and Identification of Materials and Objects (Springer Science & Business Media, 2007).
3. A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008). [CrossRef]
4. A. Davies, E. Linfield, and M. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47(21), 3679 (2002).
5. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory 52(10), 2438–2447 (2004).
6. T. Masahiko, H. Michael, and S. Kiyomi, “Generation and detection of terahertz pulsed radiation with photoconductive antennas and its application to imaging,” Meas. Sci. Technol. 13(11), 1739–1745 (2002). [CrossRef]
7. M. Venkatesh, K. S. Rao, T. S. Abhilash, S. P. Tewari, and A. K. Chaudhary, “Optical characterization of GaAs photoconductive antennas for efficient generation and detection of Terahertz radiation,” Opt. Mater. 36(3), 596–601 (2014). [CrossRef]
8. C. Zhang, Y. Avetisyan, A. Glosser, I. Kawayama, H. Murakami, and M. Tonouchi, “Bandwidth tunable THz wave generation in large-area periodically poled lithium niobate,” Opt. Express 20(8), 8784–8790 (2012). [CrossRef] [PubMed]
9. X. Xie, J. Dai, and X. C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. 96(7), 075005 (2006). [CrossRef] [PubMed]
10. T. Dekorsy, H. Auer, H. J. Bakker, H. G. Roskos, and H. Kurz, “THz electromagnetic emission by coherent infrared-active phonons,” Phys. Rev. B Condens. Matter 53(7), 4005–4014 (1996). [CrossRef] [PubMed]
11. T. Kondo, M. Tonouchi, and M. Hangyo, “THz beam generation from YBCO thin films using a 1.55 m femtosecond laser,” IEEE Trans. Appl. Supercond. 11(1), 3166–3169 (2001). [CrossRef]
12. T. M. Benseman, A. E. Koshelev, W.-K. Kwok, U. Welp, V. K. Vlasko-Vlasov, K. Kadowaki, H. Minami, and C. Watanabe, “Direct imaging of hot spots in Bi2Sr2CaCu2O8+δ mesa terahertz sources,” J. Appl. Phys. 113(13), 133902 (2013). [CrossRef]
13. E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465–3467 (2004). [CrossRef]
14. V. V. Kruglyak, M. E. Portnoi, and R. J. Hicken, “Use of the Faraday optical transformer for ultrafast magnetization reversal of nanomagnets,” J. Nanophotonics 1(1), 013502–013502–013508 (2007). [CrossRef]
15. R. Rungsawang, F. Perez, D. Oustinov, J. Gómez, V. Kolkovsky, G. Karczewski, T. Wojtowicz, J. Madéo, N. Jukam, S. Dhillon, and J. Tignon, “Terahertz radiation from magnetic excitations in diluted magnetic semiconductors,” Phys. Rev. Lett. 110(17), 177203 (2013). [CrossRef] [PubMed]
16. R. V. Mikhaylovskiy, E. Hendry, V. V. Kruglyak, R. V. Pisarev, T. Rasing, and A. V. Kimel, “Terahertz emission spectroscopy of laser-induced spin dynamics in TmFeO3 and ErFeO3 orthoferrites,” Phys. Rev. B 90(18), 184405 (2014). [CrossRef]
17. F. Kadlec, P. Kužel, and J.-L. Coutaz, “Optical rectification at metal surfaces,” Opt. Lett. 29(22), 2674–2676 (2004). [CrossRef] [PubMed]
18. G. H. Welsh, N. T. Hunt, and K. Wynne, “Terahertz-pulse emission through laser excitation of surface plasmons in a metal grating,” Phys. Rev. Lett. 98(2), 026803 (2007). [CrossRef] [PubMed]
19. G. H. Welsh and K. Wynne, “Generation of ultrafast terahertz radiation pulses on metallic nanostructured surfaces,” Opt. Express 17(4), 2470–2480 (2009). [CrossRef] [PubMed]
20. D. K. Polyushkin, I. Márton, P. Rácz, P. Dombi, E. Hendry, and W. L. Barnes, “Mechanisms of THz generation from silver nanoparticle and nanohole arrays illuminated by 100 fs pulses of infrared light,” Phys. Rev. B 89(12), 125426 (2014). [CrossRef]
21. D. K. Polyushkin, E. Hendry, E. K. Stone, and W. L. Barnes, “THz generation from plasmonic nanoparticle arrays,” Nano Lett. 11(11), 4718–4724 (2011). [CrossRef] [PubMed]
22. G. Ramakrishnan and P. C. Planken, “Percolation-enhanced generation of terahertz pulses by optical rectification on ultrathin gold films,” Opt. Lett. 36(13), 2572–2574 (2011). [CrossRef] [PubMed]
23. X. Wu, B. Quan, X. Xu, F. Hu, X. Lu, C. Gu, and L. Wang, “Effect of inhomogeneity and plasmons on terahertz radiation from GaAs (1 0 0) surface coated with rough Au film,” Appl. Surf. Sci. 285, Part B853–857 (2013). [CrossRef]
24. D. J. Hilton, R. D. Averitt, C. A. Meserole, G. L. Fisher, D. J. Funk, J. D. Thompson, and A. J. Taylor, “Terahertz emission via ultrashort-pulse excitation of magnetic metal films,” Opt. Lett. 29(15), 1805–1807 (2004). [CrossRef] [PubMed]
25. J. Nishitani, K. Kozuki, T. Nagashima, and M. Hangyo, “Terahertz radiation from coherent antiferromagnetic magnons excited by femtosecond laser pulses,” Appl. Phys. Lett. 96(22), 221906 (2010). [CrossRef]
26. C. A. Meserole, G. L. Fisher, D. J. Hilton, R. D. Averitt, D. J. Funk, and A. J. Taylor, “Growth of thin Fe(0 0 1) films for terahertz emission experiments,” Appl. Surf. Sci. 253(17), 6992–7003 (2007). [CrossRef]
27. B. Koopmans, J. J. M. Ruigrok, F. D. Longa, and W. J. M. de Jonge, “Unifying Ultrafast Magnetization Dynamics,” Phys. Rev. Lett. 95(26), 267207 (2005). [CrossRef] [PubMed]
28. R. Urban, G. Woltersdorf, and B. Heinrich, “Gilbert Damping in single and Multilayer Ultrathin Films: Role of Interfaces In Nonlocal Spin Dynamics,” Phys. Rev. Lett. 87(21), 217204 (2001). [CrossRef] [PubMed]
29. J. Shen, X. Fan, Z. Chen, M. F. DeCamp, H. Zhang, and J. Q. Xiao, “Damping modulated terahertz emission of ferromagnetic films excited by ultrafast laser pulses,” Appl. Phys. Lett. 101(7), 072401 (2012). [CrossRef]
30. S. Jian, Z. Huai-Wu, and L. Yuan-Xun, “Terahertz Emission of Ferromagnetic Ni-Fe Thin Films Excited by Ultrafast Laser Pulses,” Chin. Phys. Lett. 29(6), 067502 (2012). [CrossRef]
31. S. Mizukami, Y. Ando, and T. Miyazaki, “Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films,” Phys. Rev. B 66(10), 104413 (2002). [CrossRef]
32. E. Barati, M. Cinal, D. M. Edwards, and A. Umerski, “Gilbert damping in magnetic layered systems,” Phys. Rev. B 90(1), 014420 (2014). [CrossRef]
33. S. Serrano-Guisan, H.-C. Wu, C. Boothman, M. Abid, B. S. Chun, I. V. Shvets, and H. W. Schumacher, “Thickness dependence of the effective damping in epitaxial Fe3O4/MgO thin films,” J. Appl. Phys. 109(1), 013907 (2011). [CrossRef]
34. J. Walowski, M. D. Kaufmann, B. Lenk, C. Hamann, J. McCord, and M. Münzenberg, “Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti: sapphire laser fs spectroscopy,” J. Phys. D Appl. Phys. 41(16), 164016 (2008). [CrossRef]
35. A. Eschenlohr, M. Sultan, A. Melnikov, N. Bergeard, J. Wieczorek, T. Kachel, C. Stamm, and U. Bovensiepen, “Role of spin-lattice coupling in the ultrafast demagnetization of Gd 1−x Tb x alloys,” Phys. Rev. B 89(21), 214423 (2014). [CrossRef]
36. M. Johnson and R. H. Silsbee, “Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals,” Phys. Rev. Lett. 55(17), 1790–1793 (1985). [CrossRef] [PubMed]
37. E. Beaurepaire, J. Merle, A. Daunois, and J. Bigot, “Ultrafast spin dynamics in ferromagnetic nickel,” Phys. Rev. Lett. 76(22), 4250–4253 (1996). [CrossRef] [PubMed]
38. H. S. Rhie, H. A. Dürr, and W. Eberhardt, “Femtosecond Electron and Spin Dynamics in Ni/W(110) films,” Phys. Rev. Lett. 90(24), 247201 (2003). [CrossRef] [PubMed]
39. M. G. Münzenberg, “Magnetization dynamics: Ferromagnets stirred up,” Nat. Mater. 9(3), 184–185 (2010). [CrossRef] [PubMed]
40. A. W. Fognini, Ultrafast demagnetization: an electronic point of view (Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 21775, 2014).
41. S. S. Kalarickal, P. Krivosik, M. Wu, C. E. Patton, M. L. Schneider, P. Kabos, T. J. Silva, and J. P. Nibarger, “Ferromagnetic resonance linewidth in metallic thin films: Comparison of measurement methods,” J. Appl. Phys. 99(9), 093909 (2006). [CrossRef]
