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Abstract
The emission with a bandwidth of 1.5 terahertz based on the spin current in the ferromagnetic heterostructure Co/Pt is demonstrated. The spin transient launched by the NIR femtosecond laser pulse in the Co/Pt is converted into the in-plane charge current due to the inverse spin Hall effect, which gives rise to the terahertz emission towards free space. The dependence of the terahertz emission on the Pt-layer thickness is investigated. To optimize the geometry structure of the new type of emitter, we developed the theoretical model by carefully analyzing the spin transport. Our model reveals the importance to take into account the interfacial spin loss. It can be used to analyze more complex heterostructures.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation provides an insight into material characteristics in the infrared and millimeter wave range. The rapid development of modern ultrafast femtosecond lasers has promoted the revolution in the broadband THz sources. The electric dipoles induced by the photo-excited carriers are one of the often-used approaches in solid THz emitter materials [1–8]. THz emission based on ultrafast photocurrents are most of the times realized in semiconductors through the diffusion current due to the photo-Dember effect [3,4] and the drift current on account of the build-in surface electric field [2–5] or the bias fields provided by photoconductive antennas [6–8]. The ultrafast laser pulses can also lead to the magnetic dipole radiation in the THz region [9]. In contrast with these conventional approaches, a conceptually new thin-film THz emitter based on the spin currents in ferromagnetic heterostructures has drawn wide interest in recent years.
The heterostructure which usually includes a ferromagnetic (FM) and a nonmagnetic (NM) layer is conventionally used in spintronic researches such as spin transfer torque [10,11], magneto-resistance [12], and spin pump effects [13]. As a new type of THz emitter, heterostructres are being considered with renewed interest by taking advantage of the spin-orbit interaction [14,15]. One of the earliest efforts in this field is the manipulation of THz spin current in Fe/Au and Fe/Ru heterostructures reported by Kampfrath et al. [14], which showed the conversion of THz electromagnetic pulses from spin current bursts due to the inverse spin Hall effect. Their work not only established a new direction for contactless excitation and detection of spin currents in the terahertz regime, but also present promising opportunities for ultra-broadband THz emitter with a bandwidth of 30 THz. This novel emitter has the potential advantages of high-power, low-cost, ultra-broad bandwidth, and flexibility.
Several subsequent schemes based on this new type of THz emitter have been reported [16–19]. Seifert et al. first developed the theoretical model by analyzing the spin current transport in the NM layers [16]. Their model showed good agreement with the experiment in large NM-layer thickness range. The spin diffusion length is treated as a variable to obtain the best fit to the experimental results. This fitting parameter can phenomenologically describe the diffusive process of the hot electrons in NM layer [20]. Torosyan et al. proposed to consider the effects of ‘dead layer’ to improve the model [19]. However, researchers have not yet perfected the theoretical model due to simplified spin transport analysis. The lack of a more detailed calculation on the spin transport limits the design of this novel THz emitter.
In this paper, we demonstrate Pt-layer-thickness dependence of the THz emission from Co/Pt heterostructures. A theoretical model is developed based on a comprehensive analysis of the spin transport. We define in our analytical model a coefficient to describe the efficiency of the spin injection from the FM to NM layer by taking into account the interfacial spin loss, which considerably impacts the optimization of the stack geometry of the heterostructure. Since we take into account the interface spin loss, our model has advantages to describe complex heterostructures which have more interfaces.
2. Experimental configuration
Figure 1(a) illustrates the principles of the THz emitter based on the spin current. Cobalt (Co) and platinum (Pt) were deposited on the 0.5-mm-thick fused silica substrates as the FM and NM layers. The metallic layers were grown by electron beam evaporation under ultrahigh vacuum condition at room temperature. The substrates were cleaned in advance using acetone and isopropyl alcohol to remove the contamination. The thickness of the FM layer is 10 nm for all samples. The thickness of the NM layer ranges from 0.5 to 20 nm. During the experiment, the samples were kept in the saturated magnetization state by an external static magnetic field M (~150 mT) along y. All samples were excited under a normal incidence scheme by laser pulses from a Ti:Sapphire amplified laser with 100-fs duration, 1-kHz repetition rate, and 800-nm central wavelength. The diameter of the laser beam was loosely focused to ~2 mm on the sample. Absorption of femtoseond laser pulses in the Co layer drives Fermi-level electrons to higher bands, generating a non-equilibrium electron distribution during a few hundred femtoseconds [20]. The excited majority- and minority-spin electrons are mainly in sp and d bands, respectively [21–24]. The nearly free electrons in sp bands have higher velocities than the more localized electrons in d bands [25]. As a consequence, a net spin-polarized current Js from the Co layer into the Pt layer will be launched immediately. According to the inverse spin Hall effect (ISHE) [26], Js is converted into an in-plane charge current Jc along x axis. The conversion is described by Jc = γJs × n, where γ is the spin Hall angle and n is the unit vector in the spin polarization direction. Jc acts as an electric dipole, causing a THz emission polarized in the x direction towards the free space. The emitted THz wave was collected and refocused by two parabolic mirrors with the reflected focal length of 2 inches. The focused THz emission is detected by electro-optic sampling using a 1-mm-thick (110)-oriented ZnTe crystal.
Fig. 1 (a) Experimental schematics of the THz emission from ferromagnetic heterostructures. The sample substrate/Co/Pt, which is magnetized in y-direction, is excited by the femtosecond laser pulses. The induced out-of-plane spin current Js is converted into an in-plane charge current Jc due to ISHE. The appearance of Jc gives rise to the THz emission into the free space. (b) The grey, red, and blue curves show the waveforms of THz emissions from the fused silica substrate, substrate/Co, and substrate/Co/Pt, respectively. The thickness of the Pt layer is 5 nm. The vertical axis shows the electric field of the THz emission that was detected by EO sampling. (c) The fluence dependence of the peak amplitude of the THz emission from substrate/Co/Pt.
3. Results and discussion
Waveforms of the THz emission from substrate/Co/Pt, substrate/Co, and substrate are shown in Fig. 1(b). The thickness of the Pt layer is 5 nm. The fluence of the NIR laser pulses is ~0.3 mJ cm−2 for all the waveforms. THz emissions from substrate/Co/Pt and substrate/Co are observed. However, no emission is observed from the bare substrate, which indicates that the substrate has no contribution to the THz emission. Compared with the emission from substrate/Co/Pt, a weak emission from substrate/Co is observed. This emission is ascribed to the sudden change of the magnetization of the Co layer under the excitation of the laser pulses [27]. In contrast, the Pt layer substantially enhances the THz emission on account of the strong spin-obit interaction [28]. The polarity of the THz emission contributed by Pt layer is opposite to that by the Co layer. Figure 1(c) demonstrates the relationship between the peak amplitude of the THz waveform and the laser fluence for substrate/Co/Pt. The amplitude of the THz waveform scales linearly with the fluence in the range we measured.
Figures 2(a) and 2(b) show the waveforms of the THz emission when the sample is pumped by the laser pulses from the Co side and the Pt side, respectively. The curves with open and closed circles correspond to the measurements with the magnetization along y and –y, respectively. The Pt-layer thickness is 5 nm. The polarity of the waveform is reversed by changing the pumping side when the samples are magnetized in the same direction, because the opposite sample orientation reverses the flow direction of the spin-current from z to –z. On the other hand, the waveforms measured under opposite magnetization directions of the samples also have inversed polarities due to the spin-polarization change of the majority-spin electrons. We draw a conclusion based on these analyses that the spin current is responsible for the THz emission from Co/Pt heterostructures. The THz emission amplitude shown in Fig. 2(b) is considerably stronger than that shown in Fig. 2(a). This behavior can be attributed to the gradient distribution of spin current density in the 10-nm thick Co layer. Given that the penetration depth of Co for 800-nm light is 13 nm [29], the spin current distribution in the sample is inhomogenous along the out-of-plane direction. Therefore, the spin current density near the boundary between two layers when it is pumped at the Pt layer side is higher than when pumped at the Co layer side. In addition, only the spin current within a certain distance from the boundary contributes to THz emission [19]. Consequently, when the sample is pumped at Pt layer side, the spin current diffuses to the Pt layer with relatively high efficiency and stronger THz emission is observed.
Fig. 2 The influences of the magnetization direction and the pumping side on the THz emission. (a) The sample is pumped by the laser pulse on the Co side. (b) The sample is pumped on the Pt side. The insets in (a) and (b) illustrate the pumped sides of the samples. The curves with open and closed circles denote the THz waveforms measured under the magnetization directions of + M and -M, respectively.
Figure 3(a) displays the waveforms of the THz emission from samples with various Pt-layer thicknesses. The waveforms are shifted for clarity. The emission amplitude is highly sensitive to the thickness of the Pt layer. The THz emission of Co layer can be completely compensated by the emission of a Pt layer with a thickness d0 less than 0.5 nm. Figure 3(b) reveals the relationship between the THz amplitude and the Pt-layer thickness dPt. The THz amplitude is evaluated using the root mean square of the THz waveforms. The THz amplitude is dramatically enhanced by increasing dPt up to 5 nm. The origin of the enhancement is qualitatively, rather than quantitatively, explained as the improved injection efficiency of the spin current flowing from Co to Pt layer [30]. Our quantitative discussion on the spin injection efficiency in the heterostructure will be given in the subsequent texts. When dPt exceeds 5 nm, the THz emission gradually decreases as the Pt-layer thickness is further increased. This decrease is on account of the increased attenuation of the THz wave in the Pt layer, which can no longer be compensated by the enhancement offered by the increased spin-current density [16].
Fig. 3 (a) The temporal waveforms of the THz emission from heterostructures with various thicknesses of Pt layers. (b) The red squares denote the experimental data for the relationship between the THz amplitudes and the Pt-layer thickness. The solid curve is a fit to the experimental results according to Eq. (4) which takes into account the interfacial spin loss. As a comparison, the dotted curve is obtained without taking into account the interfacial spin loss.
To quantitatively evaluate the relationship between the amplitude of THz emission and the thickness of the Pt layer, we develop a model that includes two parts: the calculation of the spin-current density based on the spin diffusion model and the calculation of the electromagnetic emission based on Maxwell equations. By using the quasistatic approximation of the Green’s function of the system, the derivation of the electromagnetic radiation from Maxwell equations for thin metal films leads to [16]
The Aunit is the electromagnetic radiation from a unit current source, n1 = 1 and n2 = 1.98 are the refractive index of air and fused silica, and Z0 = 377 Ω is the vacuum impedance. The integral of the conductivity σ(z) over the thickness dNM indicates the sheet conductance of the NM layer. The THz conductivity of the Pt is measured using THz time-domain spectroscopy. The value is σPt = (2.4 + 0.3i) × 106 S m−1.To reveal the feature of the spin current in the FM/NM heterostructure, we adopted the Valet-Fert spin diffusion model [30–34]. It can be expressed as, where μi, Di, and τi are the electrochemical potential, diffusion constant and spin relaxation time, respectively. In i layer (i = NM, FM), the attenuation of the spin current density is described by the finite spin diffusion length. Only the majority-spin electrons were considered in the calculation of the spin transport. Because the diameter of the excitation spot (2 mm) is much larger than the spin diffusion length (a few nanometers), we focus on the spin diffusion flowing along z by supposing that the spin current density is homogeneous in plane.
Next, we discuss the boundary conditions for the spin transport process. At z = dFM, we model the spin current launched by the laser pulse using the spin current (Fig. 4(a)). It is proportional to the pump-power absorptance AFM of the Co layer. We calculated AFM by taking into account the multi-reflections within the metal layers. The absorptance AFM sensitively depends on the total thickness of the Co and Pt layers. According to the calculation, the absorptance AFM decreases from 32% to 22% when the thickness of the Pt layer increases from 0 to 20 nm. In addition, the thickness of the Co layer (10 nm) is much bigger than the critical thickness around 1 nm [35]. It means that the easy axis of the Co layer almost perfectly lies in plane. Therefore, the impact from the ‘dead-layer’ [19] is not taken into account in our calculation. At z = dFM + dNM, the spin current finally vanishes due to the continuity of the spin current. At the interface of NM and FM layers (z = dFM), the spin loss happens both due to the interfacial spin resistance and the spin memory loss at the interfaces. The former is due to the resistance change [36], while the latter one is due to the spin scattering at the interface [37,38]. We note that the interface effect should be taken into account because the neglect of the spin loss at the interface of FM/NM heterostructure leads to an overestimation of the spin flip rate in the bulk material [39]. The interfacial spin loss (due to both mechanisms mentioned above) can be quantitatively modeled by inserting an equivalent interface layer [40], according to which the boundary condition at z = dFM can be written as
We used 0.58 fΩ m2, 0.83 fΩ m2, 3.4 nm and 0.9 for the bulk resistance rs, NM, interfacial spin resistance rs, FM/NM, intrinsic characteristic length and the spin-flip parameter δ respectively in the Co/Pt bilayer [40]. The coefficient η is a measure of the spin injection efficiency, which is also proportional to the amplitude of the THz emission. Figure 4(b) displays the Pt-layer-thickness dependence of η. The coefficient η increases dramatically in the range of the small thickness and approaches the saturated value with thicknesses of several times of the spin diffusion length.Fig. 4 (a) Model of the spin diffusion in a FM/NM heterostructure. At the interface of the FM/NM bilayer, the spin loss happens both due to the interfacial spin resistance and the spin memory loss. (b) The Pt-layer-thickness dependence of the coefficient.
The total charge current Jc, NM in NM layer is given as
where is the spin current density and γNM is the spin Hall angle of NM material [41]. In order to avoid the THz emission of the Co layer from affecting the calculation accuracy, we have only taken into account the spin current from z = dFM + d0 to z = dFM + dNM, where d0 = 0.3 nm is obtained by a linear extrapolation.Weighting the Eq. (1) with Eq. (3), we then obtain
The solid (dotted) curve in Fig. 3(b) demonstrates the fit with (without) taking into account the interfacial spin loss. Both curves are obtained with spin diffusion length λPt = 2.5 nm. The calculation with taking into account the interfacial spin loss successfully reproduced the experimental results. Compared with the published values of 3.4 nm for λPt [40], the smaller value in our calculation can be explained by the increase of the local temperature in the sample wherein hot electrons randomize their velocity over a relative shorter distance [16]. Because the interfacial spin loss sensitively depends on the metal layer thickness, the dotted curve clearly deviates from the experimental data, especially in the small Pt thickness range. To fit the dotted curve with the experimental data, a different fitting parameter of ~3.1 nm is required. The discrepancy between the fitting parameters again proves that the interfacial spin loss need to be carefully addressed for the design of efficient FM/NM heterostructure THz emitter. In more complex heterostructures such as the stacked and arrayed heterostructures [17], there are more interfaces so that the analysis on the interfacial spin loss is even more important. Our model can be conveniently extended for more complicated heterostructures via analyzing spin diffusion inside all the NM layers and the spin loss at all the interfaces in an analogous way. Furthermore, our model reveals that THz emission can be enhanced by increasing the spin injection efficiency. One possible way can be interface engineering using multilayers with a smaller spin memory loss [40].
4. Summary
In conclusion, the layer-thickness dependence of the amplitude of the THz emission from the Co/Pt heterostructure is investigated in detail. The THz emission is related to the spin current launched by femtosecond laser pulses. Our model that includes the effect of the spin current transport in the bulk material and the spin loss at the interface of the heterostructure quantitatively reproduces the experimental results. This work reveals that interfacial spin loss need to be carefully addressed for the design of efficient FM/NM heterostructure THz emitter.
Funding
Japan Society for the Promotion of Science (JSPS) (16H03886); NEDO of Ministry of Economy, Trade and Industry of Japan (METI); Ministry of Education, Culture, Sports, Science and Technology, Japan (F-17-OS-0024, S-17-OS-0024).
Acknowledgment
The fabrication of the Co/Pt heterostructures in this work was supported by “Nanotechnology Platform Project (Nanotechnology Open Facilities in Osaka University)” of Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors are very grateful to Dr. Gabayno for helping polish English.
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