France



&lt;br/&gt;THz spintronics emitters represent today novel sources for broadband emission using nanometer-scaled materials. We present and model the THz spintronic emission based on the spin Hall effect in 3&lt;i&gt;d&lt;/i&gt; metals and on the inverse Rashba-Edelstein effect in the optimized topological insulator Bi&lt;sub&gt;1-x&lt;/sub&gt;Sb&lt;sub&gt;x&lt;/sub&gt;.&lt;br/&gt;&lt;br/&gt;1. Introduction&lt;br/&gt;&lt;br/&gt;Terahertz (THz) spintronic emitters are promising candidates for covering the so-called THz gap as they offer broadband emission going up to 30 THz [1]. Conventionally, they consist in nanometer-thin heterostructures composed by a ferromagnetic layer and a heavy metal from the 3&lt;i&gt;d&lt;/i&gt;-5&lt;i&gt;d&lt;/i&gt; family which, owing to their high spin-orbit coupling (SOC), allow spin-to-charge conversion (SCC) from a pure transient spin-current coming from the ferromagnetic layer into a transverse transient charge current. Efforts have been made recently to increase the output emission power of such devices by layer thickness engineering in order to optimize spin-to-charge interconversion and to reduce both THz absorption in metallic layers and spin current relaxation in thick ferromagnets.&lt;br/&gt;&lt;br/&gt;In this study, we evidence the processes timescales at stake in the emission properties of metallic THz spintronic emitters using Finite Domain Time Domain (FDTD) simulations. We evidence the main figure of merit which will permit to optimize the next generation of THz emitters. We then turn towards an alternative type of THz spintronic emitters based on topological insulators. We discuss the role of surface states in the conversion mechanisms and highlight promising THz emission in topological insulator Bi&lt;sub&gt;1-x&lt;/sub&gt;Sb&lt;sub&gt;x&lt;/sub&gt;.&lt;br/&gt;&lt;br/&gt;2. Optimization of THz metallic spintronic emitters based on FDTD modelling&lt;br/&gt;&lt;br/&gt;Conventional THz spintronic emitters are based on ferromagnet/heavy metal heterostructures such as Co/Pt, W/CoFeB/Pt or Fe/Pt. Shining infrared femtosecond laser pulses on the heterostructure induces a transient spin current diffusing from the ferromagnet to the heavy metal. Through spin-to-charge conversion due to the inverse spin Hall effect (ISHE), a THz wave is generated. The direction of the THz emission depends on the direction of the magnetization: the polarization can thus be easily tuned by small external magnetic field. The amplitude of the THz emission depends strongly on the amplitude of the interconversion mechanism, which is related to skew-scattering and side-jump effects in heavy metals. In first approximation, the amplitude of the emission is thus given by the spin Hall angle θ&lt;sub&gt;SHE &lt;/sub&gt;= j&lt;sub&gt;c&lt;/sub&gt;/j&lt;sub&gt;s&lt;/sub&gt;, ratio between the incoming spin current and the generated charge current given by j&lt;sub&gt;c&lt;/sub&gt; ∝ θ&lt;sub&gt;SHE&lt;/sub&gt; (j&lt;sub&gt;s&lt;/sub&gt; x σ) where σ is the spin accumulation orientation [2,3].&lt;br/&gt;&lt;br/&gt;Here, we provide a comprehensive understanding of the THz emission processes using FDTD modelling, including spin-dependent timescales such as spin-flip rates in heterostructures. We obtain a good agreement between experiments obtained by THz time-domain spectroscopy (THz-TDS) and performed simulations as shown in Fig. 1. We also evidence the crucial role of the interface quality between the heavy metal and the ferromagnet, as spin backflow or interfacial spin-flip may decrease the conversion. We thus propose a figure of merit η ∝ g&lt;sub&gt;↑↓&lt;/sub&gt;σ&lt;sub&gt;SHE&lt;/sub&gt;l&lt;sub&gt;sf&lt;/sub&gt;&lt;sup&gt;HM&lt;/sup&gt; which defines the THz emission strength in metallic heterostructures. This product includes the spin-mixing conductance g&lt;sub&gt;↑↓ &lt;/sub&gt;illustrating interface quality, spin-Hall conductivity σ&lt;sub&gt;SHE&lt;/sub&gt; linked to interconversion strength and spin diffusion length in the conversion material l&lt;sub&gt;sf&lt;/sub&gt;&lt;sup&gt;HM&lt;/sup&gt; proportional to spin-current relaxation. We believe that our results will help optimizing the next generation of THz spintronic emitters.&lt;br/&gt;&lt;br/&gt;3. Towards surface-states mediated THz emission using topological insulators&lt;br/&gt;&lt;br/&gt;Alongside ISHE-based emitters, topological insulators (TI) are studied here as an alternative source for THz emitters. They present conductive surface-states which allow interfacial interconversion via inverse Rashba-Edelstein effect (IREE). In these systems, strong spin-to-charge conversion is expected owing to&lt;i&gt; i&lt;/i&gt;) the Fermi velocity of interfacial carriers and &lt;i&gt;ii&lt;/i&gt;) the insulating behaviour of the material bulk, reducing possible THz absorption in the heterostructure. Such systems have been proven to show emission in the THz range, for example with topological insulator Bi&lt;sub&gt;2&lt;/sub&gt;Se&lt;sub&gt;3&lt;/sub&gt; [4].&lt;br/&gt;&lt;br/&gt;We report in Fig. 2 emission features from Bi&lt;sub&gt;1-x&lt;/sub&gt;Sb&lt;sub&gt;x&lt;/sub&gt;/Co interface. Experimental data are taken with standard electro optic sampling (EOS) using ZnTe(111) 500 μm thickness. Emission performance of Bi&lt;sub&gt;0.79&lt;/sub&gt;Sb&lt;sub&gt;0.21&lt;/sub&gt;(15)/Co(4) is about the same order of magnitude as Co(2)/Pt(4) single-ISHE conversion state-of-the-art emitter. As recovered on IREE-based emitter, THz emission phase is reversed as applied magnetic field direction is reversed. Topological insulators here illustrated by Bi&lt;sub&gt;1-x&lt;/sub&gt;Sb&lt;sub&gt;x&lt;/sub&gt; are thus suitable candidates for strong output THz emitters.

**References:**

[1] Seifert, T. et al., “Efficient metallic spintronic emitters of ultrabroadband terahertz radiation”, Nature Photon 10, 483–488 (2016).&lt;br/&gt;[2] Dang T. H., Rongione E. et al., “Ultrafast spin-currents and charge conversion at 3d-5d interfaces probed by time-domain terahertz spectroscopy”, Appl. Phys. Rev. 7 (2020)&lt;br/&gt;[3] Hawacker J., Rongione E. et al., “Correlation between spin-mixing-conductance, THz emission and spin-memory-loss at magnetic/heavy metal interfaces”, to be submitted&lt;br/&gt;[4] Wang, X. et al., “Ultrafast Spin-to-Charge Conversion at the Surface of Topological Insulator Thin Films”, Adv. Mater. 30, 1802356 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b0838de1ea6769af462c232ef2eef21b.jpg)
Fig. 1 – Comparison between experimental measurements (blue curve) and FDTD simulations (red curve) for Co(2)/Pt(4) metallic THz emitter considering an infrared excitation pulse duration about 100 fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/b977da06608df08ed43adbd351f5d2ed.jpg)
Fig. 2 – Bi&lt;sub&gt;0.79&lt;/sub&gt;Sb&lt;sub&gt;0.21&lt;/sub&gt;/Co emission alongside metallic ISHE-based emitters for comparison (left). Magnetic field dependence of Bi&lt;sub&gt;0.79&lt;/sub&gt;Sb&lt;sub&gt;0.21&lt;/sub&gt;/Co emission: phase reversal with field direction change proves magnetic origin of the emission (right). Thicknesses in brackets are given in nanometers.

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 Efficiency of THz spintronic emitters: from spin-Hall effect in 3d metals to surfaces states in topological insulators INVITED

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THz spintronics emitters represent today novel sources for broadband emission using nanometer-scaled materials. We present and model the THz spintronic emission based on the spin Hall effect in 3d metals and on the inverse Rashba-Edelstein effect in the optimized topological insulator Bi1-xSbx. 1. Introduction Terahertz (THz) spintronic emitters are promising candidates for covering the so-called THz gap as they offer broadband emission going up to 30 THz [1]. Conventionally, they consist in nanometer-thin heterostructures composed by a ferromagnetic layer and a heavy metal from the 3d-5d family which, owing to their high spin-orbit coupling (SOC), allow spin-to-charge conversion (SCC) from a pure transient spin-current coming from the ferromagnetic layer into a transverse transient charge current. Efforts have been made recently to increase the output emission power of such devices by layer thickness engineering in order to optimize spin-to-charge interconversion and to reduce both THz absorption in metallic layers and spin current relaxation in thick ferromagnets. In this study, we evidence the processes timescales at stake in the emission properties of metallic THz spintronic emitters using Finite Domain Time Domain (FDTD) simulations. We evidence the main figure of merit which will permit to optimize the next generation of THz emitters. We then turn towards an alternative type of THz spintronic emitters based on topological insulators. We discuss the role of surface states in the conversion mechanisms and highlight promising THz emission in topological insulator Bi1-xSbx. 2. Optimization of THz metallic spintronic emitters based on FDTD modelling Conventional THz spintronic emitters are based on ferromagnet/heavy metal heterostructures such as Co/Pt, W/CoFeB/Pt or Fe/Pt. Shining infrared femtosecond laser pulses on the heterostructure induces a transient spin current diffusing from the ferromagnet to the heavy metal. Through spin-to-charge conversion due to the inverse spin Hall effect (ISHE), a THz wave is generated. The direction of the THz emission depends on the direction of the magnetization: the polarization can thus be easily tuned by small external magnetic field. The amplitude of the THz emission depends strongly on the amplitude of the interconversion mechanism, which is related to skew-scattering and side-jump effects in heavy metals. In first approximation, the amplitude of the emission is thus given by the spin Hall angle θSHE = jc/js, ratio between the incoming spin current and the generated charge current given by jc ∝ θSHE (js x σ) where σ is the spin accumulation orientation [2,3]. Here, we provide a comprehensive understanding of the THz emission processes using FDTD modelling, including spin-dependent timescales such as spin-flip rates in heterostructures. We obtain a good agreement between experiments obtained by THz time-domain spectroscopy (THz-TDS) and performed simulations as shown in Fig. 1. We also evidence the crucial role of the interface quality between the heavy metal and the ferromagnet, as spin backflow or interfacial spin-flip may decrease the conversion. We thus propose a figure of merit η ∝ g↑↓σSHElsfHM which defines the THz emission strength in metallic heterostructures. This product includes the spin-mixing conductance g↑↓ illustrating interface quality, spin-Hall conductivity σSHE linked to interconversion strength and spin diffusion length in the conversion material lsfHM proportional to spin-current relaxation. We believe that our results will help optimizing the next generation of THz spintronic emitters. 3. Towards surface-states mediated THz emission using topological insulators Alongside ISHE-based emitters, topological insulators (TI) are studied here as an alternative source for THz emitters. They present conductive surface-states which allow interfacial interconversion via inverse Rashba-Edelstein effect (IREE). In these systems, strong spin-to-charge conversion is expected owing to i) the Fermi velocity of interfacial carriers and ii) the insulating behaviour of the material bulk, reducing possible THz absorption in the heterostructure. Such systems have been proven to show emission in the THz range, for example with topological insulator Bi2Se3 [4]. We report in Fig. 2 emission features from Bi1-xSbx/Co interface. Experimental data are taken with standard electro optic sampling (EOS) using ZnTe(111) 500 μm thickness. Emission performance of Bi0.79Sb0.21(15)/Co(4) is about the same order of magnitude as Co(2)/Pt(4) single-ISHE conversion state-of-the-art emitter. As recovered on IREE-based emitter, THz emission phase is reversed as applied magnetic field direction is reversed. Topological insulators here illustrated by Bi1-xSbx are thus suitable candidates for strong output THz emitters.

**References:**

[1] Seifert, T. et al., “Efficient metallic spintronic emitters of ultrabroadband terahertz radiation”, Nature Photon 10, 483–488 (2016). [2] Dang T. H., Rongione E. et al., “Ultrafast spin-currents and charge conversion at 3d-5d interfaces probed by time-domain terahertz spectroscopy”, Appl. Phys. Rev. 7 (2020) [3] Hawacker J., Rongione E. et al., “Correlation between spin-mixing-conductance, THz emission and spin-memory-loss at magnetic/heavy metal interfaces”, to be submitted [4] Wang, X. et al., “Ultrafast Spin-to-Charge Conversion at the Surface of Topological Insulator Thin Films”, Adv. Mater. 30, 1802356 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b0838de1ea6769af462c232ef2eef21b.jpg)
Fig. 1 – Comparison between experimental measurements (blue curve) and FDTD simulations (red curve) for Co(2)/Pt(4) metallic THz emitter considering an infrared excitation pulse duration about 100 fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/b977da06608df08ed43adbd351f5d2ed.jpg)
Fig. 2 – Bi0.79Sb0.21/Co emission alongside metallic ISHE-based emitters for comparison (left). Magnetic field dependence of Bi0.79Sb0.21/Co emission: phase reversal with field direction change proves magnetic origin of the emission (right). Thicknesses in brackets are given in nanometers.

technical paper

Metamaterial absorbers (MA) have exhibited great interest from researchers due to the near-perfect absorptive efficiency, as well as wide-angle incidence properties and an almost complete absence of polarization sensitivity [1], [2]. These materials aim to absorb the incident wave to generate a greater intensity of the electric field in the receiver. It implies that all the incident radiation is absorbed in a specific frequency range. These materials can produce resonances for the electrical and magnetic polarizations and autonomously adjust the effective parameters of the medium [1]. Although great efforts have been concentrated in the search for metamaterials with good performance in the THz range, research is still necessary to develop and improve MAs [3], [4]. The design presented in this work combines the materials used in [5] with the design suggested in [6], to produce a simpler design without noble metals. To choose the dimensions and thickness of each layer of the MA, several simulations were carried out to determine the parameters that would result in the maximum absorption of the incident waves for the frequency range under analysis. The MA is presented in Fig.1-a and Fig.1-b, and it is composed of Nickel (Ni) disks resonators arranged in a 4x4 array and a nickel ground plane separated by silicon dioxide (SiO2) substrate. The choice of materials, such as nickel rather than gold (Au), for the construction of the MA structure, aims to obtain cost-effective and easily producible metamaterials. The size and thicknesses of metals and the dielectric layers are exhibited in the top view at Fig.1-a and the side view at Fig.1-b. Boundary conditions are set as electric on the x-axis, magnetic on the y-axis, and open on the z-axis. The propagation has the direction along the positive z-axis from the open add space wave port with a separation distance to prevent near field effect between EM wave and the MA, as demonstrated in [5]. The study selected visible frequency range, but also investigated infrared and ultraviolet frequency. The dielectric parameters of nickel and silicon dioxide are complex and dependent on frequency. Nickel was chosen because it presents better absorption efficiency than other metals in the visible region and enables high-temperature applications [5]. The results are obtained using the CST Microwave Studio software. The absorption and dispersion of the incident electromagnetic waves are related to the reflected and transmitted radiation at the materials media interfaces through the Scattering Parameters [2], [7]. These parameters can be determined by the absorption capacity (A) through the relation: A = 1 - R - T. To reach the maximum absorption level, the reflection coefficient (R), as well as the transmission coefficient (T) should be minimized by using a continuous metallic plane [5]. Then, the MA response will depend only on the reflection values. Sweep simulations were performed varying the unit cell's dimensions, and the best results were presented in Fig.2-a. The proposed design has a high absorption capacity, which is above 96.14% at all frequencies in the visible light region, and the average absorption in all spectrum analyzed is 99.24%. It means that the presented MA can absorb almost all the incident radiation. Hence, the total incident energy can penetrate the structure and be converted into electrical energy. Therefore, the MA can be used in the entire frequency range of the visible light spectrum with better performance compared to the other metals proposed in the literature, such as copper, gold, and aluminium [4], [5], [6]. Furthermore, the MA's absorption behaviour is also examined at infrared and UV frequency regions and are shown in Fig.2-b. For the IR-region, the average absorption percentage is 99.79% between 800 and 1000 THz (300-375 nm). That is a good performance for an infrared detector operating in the mentioned frequency band. For the UV region, the average absorption percentage is 90.11% from 100 up to 350 THz (850-3000 nm). Additionally, the proposed MA has 99.22% of average absorption in all analyzed spectrum. The structure has an absorption value greater than 90% in the entire range of the analyzed spectrum. The reason is that the imaginary part of nickel's dielectric constant is higher than other metals in this frequency range, as shown in [5]. It should be noted that the proposed MA has an extremely wide-bandwidth absorption in a frequency range close to those reported in the current literature. Furthermore, the presented design has the thinnest thickness compared with the other structures presented in [5], [6], with a simpler design and without noble metals. The MA shown can be considered compatible with several applications, including solar energy harvesting, IR detector, cloaking, shielding for EMC, and sensing. A detailed analysis of the results will be discussed in the full paper. Acknowledgment(s): This work was supported by the Brazilian institutions CAPES, CNPq, and FAPEMIG.

**References:**

[1] H. Tao et al., Optics Express, vol. 16, no. 10, p. 7181 (2008). [2] Y. Wang et al., IEEE Transactions on Magnetics, vol. 47, no. 10, p. 2592–2595 (2011). [3] J. Y. Rhee et al., Journal of Electromagnetic Waves and Applications, vol. 34, no. 10, p. 1338–1371 (2020). [4] S. K. Patel et al., “Journal of the Optical Society of America B-Optical Physics, vol. 37, no. 7, p. 2163–2170 (2020). [5] M. Bagmanci et al., International Journal of Modern Physics B, vol. 33, no. 8, p. 1950056 (2019). [6] D. Katrodiya, C. Jani, V. Sorathiya, and S. K. Patel, Optical Materials, vol. 89, p. 34–41 (2019). [7] C. M. Watts, X. Liu, and W. J. Padilla, Advanced Materials, vol. 24, no. 23, p. OP98–OP120 (2012).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b91b0d0dda3506fd38b54de64ce4c98d.jpg)
Fig. 1. Unit cell geometry for the designed structure: (a) Top view and; (b) Side view of the MA design.

![](https://assets.underline.io/uploads/markdown_image/1/image/c9ac0aec77bcd88dbdf029bc7f962b48.jpg)
Fig. 2. Absorption (red), Transmission (blue), and Reflection (green) behaviors of the designed structure: (a) visible light region (350 to 800 THz) and; (b) all analyzed spectrum (100 to 1000 THz).

 Metamaterial Based Broadband Absorber Design

I INTRODUCTION High frequency permeability and permittivity measurement of electromagnetic material is important for radio wave absorber, noise suppressor and electromagnetic shielding materials of 5th generation or 6th generation. Usually, in order to measure the magnetic permeability and the permittivity simultaneously, the sample had to be processed into a solenoid [1]. Further, when the permittivity and the magnetic permeability are separately measured, it is necessary to process the sample into a thin shape or a needle shape, and the method using the waveguide has problems such as discontinuous frequency. In our previous work, we developed a flexible microstrip line-type probe, and presented broad bandwidth permeability measurements of magnetic thin films [2]. However application of strong DC magnetic field (about 2 T) did not completely saturate samples in calibration, so remnant ferromagnetic resonance over several 10 GHz limited the upper frequency range. In the present study, we have developed a new calibration method that estimates the state of infinite magnetic field application by changing the DC magnetic field step by step, and realized accurate evaluation at 30 GHz or higher. The probe is applied to the simultaneous evaluation of permittivity and permeability of electromagnetic materials without restriction on sample size. II EXPERIMENTAL PROCEDURE Fig. 1 shows the schematic view of the microstrip line type probe [2], which is composed of a wrap-around microstrip conductor (10 mm in length, 0.36 mm in width) on a flexible substrate (130 μm in thickness, εr =2.3), a ground plane, lead lines, and two connectors. The microstrip line sloped to meet the lead line at either end, and had slopes to maintain a characteristic impedance of around 50 Ω and to allow close contact of a large samples with the probe. An electromagnetic material was in contact with the microstrip conductor via a PET film or directly. In permeability and permittivity measurement, firstly, S21 is calibrated without sample. Secondly, the DC magnetic field was increased to 20 kOe in 2 kOe increments, S21 was measured. Then S21(sat) under an infinite magnetic field was estimated by exponential approximation. This method can separate magnetic signal from nonmagnetic signal, and can remove the effect of remnant ferromagnetic resonance under finite strong field. Thirdly, S21(sample) is measured by removing the strong dc field, and then the complex permeability is optimized by S21(sample)-S21(sat) using FEM analysis (magnetic field calculation) [2]. Then the complex permittivity also optimized by S21(sat) using FEM analysis (electric field calculation), because magnetic signal was removed in S21(sat), therefore dielectric signal mainly can be obtained. III Experimental results Fig. 2 shows the real part of permeability of Fe-Fe3O4 in polymer (10 mm x 10 mm, 0.1 mm in thickness)[3] to demonstrate permeability measurement up to 67 GHz when the DC field was changed. Ferromagnetic resonance frequency increased and the permeability decreased as DC field increased, which was reasonable frequency characteristics. The relative permittivity also shows in Fig. 2. The real part of permittivity was about 12 in lower frequency, the absolute value comes from that of the polymer. It was reasonable that the imaginary part of permittivity was negligible small.

**References:**

[1] https://www.keysight.com/jp/ja/assets/7018-03896/brochures/5991-2171.pdf [2] S. Yabukami et al., IEEE Trans. Magn. Vol. 56 (2020). [3] M. Sato et al., Autumn Meeting of the Japan Society of Powder and Powder Metallurgy, 1-49A(V) (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/78fd92842314b8de79364653cee45ff6.jpg)
Fig. 1 Schematic view of the probe.

![](https://assets.underline.io/uploads/markdown_image/1/image/6f5e8d060f681885ae08df94156d74ab.jpg)
Fig.2 The real part of permeability and permittivity of Fe-Fe3O4 in polymer.

 Simultaneous Evaluation of Permeability and Permittivity using a Flexible Microstrip Line-Type Probe up to 67 GHz

Composites filled with ferromagnetic inclusions possess a combination of promising magnetic, electrical and mechanical properties. High-frequency magnetic properties of the composites are useful in development of radar absorbers, microwave devices, etc. The effective permeability is a complicated function of frequency, the microstructure of the composite, and the properties of its constituents. Reliable techniques for determining of physical mechanisms resulting in the appearance of magnetic loss peaks at high frequencies are not found in the archived literature. A useful technique for studying microwave magnetic properties involves coaxial measurements of frequency dependence of complex permeability under external magnetic bias [1]. The calibration techniques for the coaxial line have been well established, and an accurate permeability measurement is available in the frequency range of 100 MHz to 20 GHz. The measuring coaxial cell is placed inside a coil that creates magnetic bias parallel to the coaxial axis. Making the measurement under various permanent magnetic fields gives an opportunity for comparing the magnetic characteristics of a sample in both the demagnetized and magnetized states and for determining the physical mechanisms responsible for different peaks of magnetic loss. These data may be of importance for understanding the magnetic structure and dynamic magnetic properties of tiny magnetic particles. The reported research focuses on the intrinsic permeability of magnetic powder particles under external permanent magnetic field. First, the intrinsic permeability of the particle is retrieved with a mixing rule. We selected composites whose permeability satisfies the simplest one, the Wiener mixing rule [2]. According to this mixing rule, the intrinsic permeability is equal to the effective permeability of the composite normalized to the volume fraction of inclusions. The samples under study are composites with a paraffin wax matrix filled with flake-shaped sendust particles [3]. The microwave material parameters of the samples with different fraction of inclusions are measured in a 7/3 coaxial line under external magnetic field up to 2400 Oe. The figure shows measured magnetic loss that is normalized to the volume fraction of inclusions and plotted against the external field at the fixed frequency of 5 GHz. The data for different volume fractions of inclusions are shown by different colors. When the external magnetic bias is nil, normalized loss is the same for different fractions and, therefore, the effective permeability of the composites obeys the Wiener mixing rule. However, an increase in the external field leads to a divergence of the curves. This divergence cannot be eliminated by accounting for the demagnetization on the measured sample. Therefore, the Wiener mixing rule is not valid for the permeability measured under external magnetic field. To search for the reasons of the invalidity of the mixing rule in the external field and to determine the physical mechanisms leading to the appearance of magnetic loss, the measured dependences are fitted by the Lorentzian dispersion law [2] including two Lorentzian terms. The low-frequency Lorentzian peak have a similar behavior for all volume fractions of inclusions in the composites. Namely, an increase in the external field leads to a decrease in the amplitude of the peak, with the frequency of the magnetic loss peak remaining almost unchanged. The high-frequency peak is found only in the presence of an external field. Its amplitude increases up to fields of several hundred Oersteds, then decreases. The relaxation and resonant frequencies of this peak rise with an increase in magnetic bias. It is suggested that this behavior can be attributed to the presence of a domain structure in the powder particles. An increase in the external field leads to a decrease in the amount of different domains in a particle and the amplitude of the main peak decreases with no frequency shift. The presence of a domain structure neutralized the interaction between closely spaced particles and the resonant frequencies are the same for different fraction of inclusions. The Wiener mixing rule is valid for such peaks. Under external bias, the domain structure vanishes that increases the contribution to magnetic loss from the ferromagnetic resonance (FMR), which is responsible for the second peak. In this case, the interaction occurs between the particles and the peak associated with the FMR should be described by other mixing rules. Thus, we propose a technique for determining the physical mechanisms leading to the appearance of loss peaks. The technique consists in analysis of the data on microwave permeability obtained under external magnetic field. It is shown that the mixing rule, which correctly retrieves the intrinsic permeability in the absence of the external field, is not valid under magnetic bias. Based on the measured data, the physical mechanisms leading to the appearance of loss peaks are determined, and the invalidity of mixing rules under magnetic bias is explained. It is shown that the main peak of magnetic loss is attributed to the presence of domain structure in the particles. An increase in the external field leads to an increase in the FMR contribution to magnetic loss, which may obey other mixing rules. Funding: The reported study was funded by RFBR, project number 19-32-90165.

**References:**

[1] A.O. Shiryaev, S.Y. Bobrovskii, etc., J. Magn. Magn. Mater., Vol. 477, p.329 (2019) [2] K.N. Rozanov and M.Y. Koledintseva, J. Appl. Phys., Vol. 119, p. 073901 (2016) [3] S.N. Starostenko, K.N. Rozanov, etc., J. Appl. Phys., Vol. 121, p. 245107 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c68432cc98a88856ec4b48a565eb88b0.jpg)
The measured dependence of the normalized magnetic loss on the external field at the fixed frequency of 5 GHz.

 Experimental study of microwave magnetic properties of composites under magnetic bias

To take advantage of the electron spin in future electronics, spin angular momentum needs to be transferred and detected. Heat gradients and electric fields have been shown to efficiently drive spin transport at megahertz and gigahertz frequencies. However, to probe the initial elementary steps that lead to the formation of spin currents, one needs to launch and measure transport on femtosecond time scales. To achieve this goal, we transfer spintronic concepts to the terahertz frequency range by employing both ultrashort optical and terahertz electromagnetic pulses [1]. This experimental strategy provides new insights into central transport phenomena, for instance the spin Seebeck effect [2], the anomalous Hall effect [3] and anisotropic magnetoresistance [4]. Interesting applications such as the efficient generation of ultrashort terahertz electromagnetic pulses [5] and the high-throughput characterization of spin-to-charge conversion in the bulk [6] and at interfaces [7] of spintronic structures emerge.

**References:**

[1] E.Y. Vedmedenko et al., The 2020 Magnetism Roadmap, J. Phys. D: Appl. Phys. 53, 453001 (2020) [2] T.S. Seifert et al., Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy, Nature Commun. 9, Article number: 2899 (2018) [3] T.S. Seifert et al., Frequency-independent terahertz anomalous Hall effect in DyCo5, Co32Fe68 and Gd27Fe73 thin films from DC to 40 THz, Advanced Materials (accepted) (2021) [4] L. Nadvorník et al., Terahertz anisotropic magnetoresistance reveals strong intrinsic contributions, arXiv:2010.06280 (2021) [5] J.A. Fülöp et al., Review: Laser-Driven Strong-Field Terahertz Sources and their Novel Applications, Adv. Opt. Mat. 1900681 (2019) [6] M. Meinert et al., High-throughput techniques for measuring the spin Hall effect, Phys. Rev. Applied 14, 064011 (2020) [7] O. Gueckstock et al., Terahertz spin-to-charge conversion by interfacial skew scattering in metallic bilayers, Advanced Materials (accepted) (2021)

**Images:**

 Probing and driving ultrafast spin transport with terahertz electromagnetic pulses

The vast majority of digital information worldwide is stored in the form of tiny magnetic bits in thin-film materials in the hard-disk drives installed in large-scale data centres. The positions of the north and south magnetic poles with respect to the thin-film plane encodes the logical ‘ones’ and ‘zeros’, which are written using strongly localized, intense magnetic fields. The dynamics of the magnetization in the writing process is described by the Landau–Lifshitz–Gilbert (LLG) equation, which correctly models the reversal of a magnetic bit at nanosecond timescales. Until 20 years ago, it was believed that all of the relevant physics of magnetization dynamics was included in this equation and that optimization of storage devices could be based solely on it. However, the pioneering experiment of Bigot et al. in 1996 [1] revealed the occurrence of spin dynamics on subpicosecond scales that could not be described by the LLG equation, giving birth to the field of ultrafast magnetism. This field explores some of the currently most investigated and debated topics in condensed matter physics [2], with implications for both our fundamental understanding of magnetism as well as possible applications for faster and more energy-efficient data manipulation. Recently, the LLG equation was reformulated to include a term to obtain a physically correct inertial response [3], which was not present in the original formulation. This term predicts the appearance of spin nutations, similar to the ones of a spinning top, at a frequency much higher (in the terahertz range) than the spin precession described by the conventional LLG equation (typically at gigahertz frequencies), as shown schematically in Fig. 1a,b. However, the lack of intense magnetic field sources at these high frequencies has hampered the experimental observation of such nutation dynamics. In this work, we use intense narrowband terahertz magnetic field transients from a superradiant terahertz source and the femtosecond magneto-optical Kerr effect (MOKE) to detect inertial magnetization effects in ferromagnetic thin films. We find evidence for nutation dynamics with a characteristic frequency of the order of 1 THz, which is damped on timescales of the order of 10 ps. We are able to qualitatively describe the observed magnetization dynamics with a macrospin approximation of the inertial LLG equation and highlight implications for ultrafast magnetism, and magnetic data processing and storage. The basic idea is to perform a forced oscillator experiment as a function of the frequency of the terahertz magnetic field HTHz, detecting the amplitude and phase of the response with the femtosecond MOKE in an attempt to observe the signature of a resonance. The response of the magnetization is maximized when HTHz and the static magnetization (which is controlled with an external magnetic field) are orthogonal to each other. This is illustrated schematically in the top panels of Fig. 1c,d, with the corresponding experimental measurement in the bottom panels, where we show the detected polar MOKE signal. In this talk, we will present direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of the order of 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps. We anticipate that our results will allow for a better understanding of the fundamental mechanisms of ultrafast demagnetization and reversal, with implications for the realization of faster and more efficient magnetic data-processing and storage devices.

**References:**

[1] Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y., Phys. Rev. Lett. 76, 4250–4253 (1996). [2] Kirilyuk, A., Kimel, A. V. & Rasing, T., Rev. Mod. Phys. 82, 2731–2784 (2010). [3] Ciornei, M.-C., Rubí, J. M. & Wegrowe, Phys. Rev. B 83, 020410 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6818f48089c6a1a5cd467dca5bdc36ea.jpg)
a) Top: schematic of the magnetization dynamics and relaxation around an effective magnetic field H according to the standard LLG equation. Bottom: LLG-simulated response of a ferromagnetic system to an external a.c. magnetic field of varying frequency. b) Similar to a) but considering the inertial formulation of the LLG equation described in the text. c) Top: the geometrical configuration that maximizes the torque of HTHz on the magnetization M (that is, when they are orthogonal). Bottom: measured response from the polycrystalline NiFe sample in the maximum torque configuration and with a driving field centred at around 0.6 THz. d) Similar to c) but when HTHz and M are parallel; no torque is exerted on the same sample by the same driving field.

 Inertial spin dynamics in ferromagnets

I. INTRODUCTION Femtosecond laser pumping provides a convenient way to generate transient spin or spin-polarized current from ferro-/ferri-/antiferro-magnetic materials in the picosecond regime. The subsequent conversion of the transient spin current to charge current gives rise to terahertz (THz) emission. Several spin-to-charge current conversion mechanisms have been proposed to account for the experimental observations which include but are not limited to inverse spin Hall effect (ISHE), 1,2, inverse Rashba-Edelstein effect (IREE), 3,4, and anomalous Hall effect (AHE).5,6 Since the pioneering work of Kampfrath et al.,1 many studies have been conducted to enhance the THz emission efficiency through both materials and structure engineering, which have led to the realization of broadband THz sources with magnetically controllable polarization and an efficiency comparable to that of ZnTe-based emitters. Here, we report our recent studies of THz emission based mainly on AHE from different types of structures including single ferromagnetic (FM) layers with both uniform and graded magnetization and synthetic antiferromagnet (SAF). We will also discuss THz emission from multilayers involving AFMs such as Mn3Sn. II. RESULTS AND DISCUSSION Figure 1 shows the schematics of structures investigated: (a) single FM layer with uniform magnetization, (b) and (c) single FM layer with magnetization gradient, and (d) SAF. Also shown in the figure are magnetization distributions of the four types of structures. We chose (FexMn1-x)yPt1-y as the FM layer as it exhibits much larger AHE as compared to CoFeB or NiFe. In addition, its magnetization can be tailored by varying the Pt composition via co-sputtering of Fe0.8Mn0.2 and Pt targets. By setting the Fe80Mn20 and Pt cathode power at 50 W and 15 W, respectively, we obtained (Fe0.8Mn0.2)0.67Pt0.33 (hereafter FeMnPt) films with θAHE = 0.0269. An increase of Pt power leads to a decrease of FeMnPt magnetization, and therefore, a magnetization gradient can be readily introduced in the thickness direction by varying the Pt sputtering power. Figure 2a shows the intensity of THz emission from a 9 nm single layer FeMnPt film. The polarization direction changes sign when either the pumping direction or magnetization direction is flipped, suggesting that the emission mechanism is similar to that of FM/heavy metal bilayer emitter, though there is no heavy metal involved in the present case. As illustrated in Fig.1, when the laser-excited super-diffusive electrons reach the top and bottom surfaces of FeMnPt, they will be reflected back at the two respective interfaces, one with the MgO capping layer and the other with the quartz substrate. The difference in reflectivity between the two interfaces leads to a net spin polarized current jl = jl1-jl2 flowing in the thickness direction; the subsequent conversion of jl to a transverse charge current via AHE gives rise to the THz emission. As the intensity of THz emission is proportional to θAHE m × jl with m the magnetization direction and θAHE the AHE angle, there are two possible ways to enhance the emission efficiency, one is to reduce the magnetization near one of the interfaces as much as possible, and the other is to make the magnetization near the two interfaces have opposite directions. The former can be achieved by introducing a magnetization gradient in the thickness direction and the latter can be realized in an SAF structure. The magnetization gradient introduces an additional contribution to the transverse charge current given by θSHE σs×▽(μs/2e), where θSHE is the spin Hall angle, σ the conductivity, s the net spin polarization direction of non-equilibrium electrons and μs the spin chemical potential. Therefore, the magnetization gradient may either enhance or reduce the THz emission, depending on the sign of ▽(μs) relative to jl. Figure 2b and 2c show the THz emission from 9 nm FeMnPt with the magnetization gradient profiles shown in Fig. 1b and 1c, respectively. The THz waveform in Fig. 2b exhibits the same polarity as that of the uniform film in Fig. 2a, but the peak-to-peak amplitude is increased by a factor of 5.4. This means that a positive Pt composition gradient helps to enhance the THz emission. On the other hand, the sample with a negative Pt gradient gives a much smaller THz signal with an opposite polarity. The ratio of the peak-to-peak amplitudes of the three samples is 1:5.4:-2.15. These results demonstrate that the magnetization gradient is an effective knob to tune THz emission from single layer FM. On the other hand, Fig. 2d compares the THz emission from a FeMnPt(4 nm)/Ru(0.8 nm)/FeMnPt(4 nm) SAF (solid-line: 0 Oe; dashed-line: 200 Oe) with that of a 5 nm single layer FeMnPt (dotted-line). As expected, the THz emission of SAF at zero field is almost twice of that of the single layer sample, whereas its amplitude at 200 Oe, i.e., when the two magnetizations are aligned in the same direction, is the smallest among the three peaks. Detailed field-dependent measurements of the THz polarization showed that the THz emitter is a powerful tool to probe the magnetization states of SAF subjected to an external field. In addition to FM, we have also investigated THz emission from AFM with large AHE such as Mn3Sn. Our preliminary results showed that there is negligible THz emission from Mn3Sn.

**References:**

[1] T. Kampfrath et al., Nat. Nanotech. 8, 256 (2013). [2] T. Seifert et al., Nat. Photonics. 10, 483 (2016). [3] M. B. Jungfleisch et al., Phys.l Rev. Lett. 120, 207207 (2018). [4] C. Zhou et al., Phys. Rev. Lett. 121, 086801 (2018). [5] Q. Zhang et al., Phys. Rev. Appl. 12, 054027 (2019). [6] Q. Zhang et al. Phys. Rev. Appl. 13, 054016 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/40522c909e892d79e3c2032b0ce2b34d.jpg)
FIG.1 Schematic sample structure and the corresponding magnetization profile.

![](https://assets.underline.io/uploads/markdown_image/1/image/20346797a8a29f00df800fdfdb3466f9.jpg)
FIG.2 (a)-(c) THz emission from samples corresponding to Fig. 1(a)-(c), respectively. (d) Comparison of THz emission from single layer FM and SAF.

 Terahertz Spin-Charge Conversion in Magnetic Single and Multiple Layers

In antiferromagnetic spintronics where manipulation of the antiferromagnetic spins is a central technological challenge[1], it is important to understand the dynamic properties, especially their THz spin dynamics and the magnetic damping. While both experimental and theoretical investigations of the antiferromagnetic resonance began in 1950s[2], they have been recently revisited with more advanced experimental techniques [3,4] as well as with more rigorous theoretical treatments[5] in the context of emerging antiferromagnetic spintronics. In the early stage of the investigations, the state-of-art spectroscopy with a rather inefficient and weak far-infrared source[1] was employed to investigate various antiferromagnets, such as NiO, CoO, MnO, and Cr2O3. Although their high resonant frequencies have been experimentally confirmed, the experimental technique at the time was not sufficiently sensitive to withstand detail analyses of the spin dynamics and the magnetic damping. However, thanks to the recent development of the THz technologies, frequency-domain THz spectroscopies with much better sensitivity than before has now became accessible and affordable for investigating in more detail the spin dynamics in antiferromagnets. In this work, a frequency domain continuous wave THz spectroscopy system capable of scanning up to ω = 2 THz with the frequency resolution &lt;10 MHz is employed to investigate the antiferromagnetic resonances. NiO-based materials are used to demonstrate controllability of the antiferromagnetic resonance properties, such as resonance frequency and linewidth, or Q-factor. First, we investigated temperature dependence of antiferromagnetic resonance and the damping in poly- and mono-crystalline NiO. The resonant frequency (~ 1THz at room temperature) was found to decrease with increasing temperature, which was nicely explained by the temperature dependence of the anisotropy with a power of the sublattice magnetization with the exponent n = 0.72. We also found the damping parameters to be α = 5.0 ± 0.4 x 10-4 and 7.4 ± 0.4 x 10-4 for the mono- and poly-crystalline samples, respectively. The remarkable difference in α depending on the crystallinity manifests the significance of the extrinsic damping in antiferromagnet[6]. Second, we investigated the antiferromagnetic resonance in the cation-substituted NiO of Ni1-xMxO (M = Mn, Li, or Mg). We show the wide range tunability of the resonant frequency as well as the Q-factor by the magnetic doping (Mn2+ substitute), the non-magnetic doping (Mg2+ substitute), and the hole doping (Li+ substitute). We discuss the trends of how those different doping impact the antiferromagnetic resonance properties, which will be appreciated as a design guideline for THz materials adapting to various types of applications such as THz microwave absorbers and filters where the control of resonant frequency and Q-factor is important[7]. Lastly, we investigated the spin pumping enhanced antiferromagnetic damping in the (NiO)1-xHMx (HM = Pt and Pd) granular systems (Fig. 1 (a)). The spin pumping effect due to antiferromagnetic dynamics at the THz frequency was quantitatively elucidated by characterizing the linewidth Δω of the (NiO)1-xHMx granular systems as a function of x (Fig. 1(b) and (c)). The mixing conductance of the NiO/Pt and NiO/Pd interface was found to be g↑↓= 12 nm-2 and 5 nm-2, respectively. Our experimental results resolved the missing part of the spin interaction physics in antiferromagnets at THz, i.e. the spin pumping effect. The experimental manifestation of the value of g↑↓ helps understanding various spin current transfer phenomena with antiferromagnets, and would further motivate and promote the antiferromagnetic spintronics[8]. In summary, we explored frequency-domain THz spectroscopies of antiferromagnetic NiO and showed detail quantitative analysis of the antiferromagnetic damping, observation of the THz spin pumping effect in NiO/Pt and NiO/Pd and determination of the spin mixing conductance, and control of the antiferromagnetic resonance properties by various cation substations of NiO. These results are important milestone for future THz antiferromagnetic spintronics This work was supported in part by JSPS KAKENHI Grant Numbers 17H04924, 15H05702, 17H04795, 17H05181 (“Nano Spin Conversion Science”), by the Collaborative Research Program of Institute for Chemical Research, Kyoto University (grant # 2018-61 and 2019-87), and by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-SC0012190.

**References:**

[1] V. Baltz et al., Rev. Mod. Phys. 90, 015005 (2018). [2] L .R. Maxwell et al., Rev. Mod. Phys. 25, 279 (1953). [3] T. Kampfrath et al., Nat. Photon. 5, 31 (2011). [4] T. Satoh et al., Phys. Rev. Lett. 105, 77402 (2010). [5] A. Kamra et al., Phys. Rev. B 98, 184402 (2018). [6] T. Moriyama et al., Phys. Rev. Mater. 3, 051402 (2019). [7] T. Moriyama et al., Phys. Rev. B 101, 060402 (2020). [8] T. Moriyama et al., Phys. Rev. Mater. 4, 074402 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/79126ff3a7625c31028fc6ba81a0cb8b.jpg)
Fig. 1 (a) Schematic illustration of the spin pumping effect with NiO/HM (HM = Pt, Pd) granular system (b) Transmission spectra for (NiO)1-xPtx (c) Composition dependence of Δω.

 Controlling antiferromagnetic resonances

THz radiation in the frequency range from 0.3 to 30 THz bridges the gap between electronic and optical frequencies. It has been used for probing and driving fundamental resonances in gaseous, liquid, and solid materials. However, it is still challenging to generate broadband THz radiation with sufficient power in a convenient way. Recently, a new type of THz emitter has been discovered, which is based on the inverse spin Hall effect [1, 2]. These “spintronic” THz emitters typically consist of ferromagnetic (FM)/nonmagnetic metal bilayers, which are easy to prepare. In previous studies we have shown that bilayers consisting of ferrimagnetic (FI) Tb(Gd)-Fe alloys can be utilized as well as efficient spintronic THz emitters [3,4]. We find that the THz emission amplitude closely follows the in-plane magnetization of the Fe sublattice. In a further study, we have utilized the magnetic compensation temperature of a FI layer to control the THz emission solely by temperature [5]. This is enabled by coupling two ferrimagnetic layers and depending on the relative alignment of the Fe moments in the two layers, the spintronic emitter system can be either in a high- or in a low-amplitude terahertz emitting state. This approach was extended to spin valve systems with a pinned and a free FM Fe layer, decoupled from each other by either a W or a Pt layer. In this case the THz emission amplitude can be controlled by small external magnetic fields [6] and allows for fast switching, which opens a new route for a controllable and efficient type of spintronic terahertz emitter system.

**References:**

[1] T. Kampfrath et al., Nature Nanotechnology 8, 256 (2013). [2] T. Seifert et al., Nature Photonics 10, 483 (2016). [3] R. Schneider et al., ACS Photonics 5, 3936 (2018). [4] R. Schneider et al., Appl. Phys. Lett. 115, 152401 (2019). [5] M. Fix et al., Appl. Phys. Lett. 116, 012402 (2020). [6] M. Fix et al., Appl. Phys. Lett. 117, 132407 (2020).

**Images:**

 Ferrimagnetic thin films systems for spintronic THz emitters

Understanding how fast short-range interactions build up long-range order is one of the most intriguing topics in condensed matter physics. FeRh is an example of a material for studying this problem in magnetism, where the microscopic spin-spin exchange interaction is ultimately responsible for either ferro- or antiferromagnetic macroscopic order. Femtosecond laser excitation of antiferromagnetic FeRh induces ferromagnetism and the dynamics of the emergent order on the characteristic time-scale of the exchange interaction has long been a topic of intense debates. The first-order magnetic phase transition in FeRh has attracted considerable attention in material science, magnetocalorics, magnetic recording and spintronics. Aiming to reveal femto-, pico and nanosecond kinetics of the emergent ferromagnetism in FeRh, we employed the concepts of spintronic THz emitter and THz emission spectroscopy. In particular, analyzing THz emission from a FeRh/Pt bilayer excited by a single laser pulse, we reveal the main spin-dependent sources of the laser-induced THz emission [1]. We argue that stroboscopic measurements of first-order phase transitions are hampered by thermodynamically allowed co-existence of two competing phases. In particular, the stroboscopic measurements of THz emission from FeRh may result in the absence of temperature hysteresis and domination of the measured signal not by laser-induced magnetization dynamics in the antiferromagnetic phase, but by the dynamics triggeed in co-existing ferromagnetic nuclei. To minimize the influence of the latter we employed double-pump THz emission spectroscopy. We performed a systematic analysis of the emitted radiation from FeRh/Pt bilayer and revealed the experimental conditions for ultrafast magnetometry with the best signal-to-noise ratio. We show that although femtosecond laser pulse launches ultrafast spin dynamics in the antiferromagnet, nuclei generated by femtosecond laser pulse during the first 20 ps of their lifetime do not emit THz, insusceptible to the external magnetic field and, strictly speaking, have not established ferromagnetic spin order yet [2].

**References:**

 [1] R. Medapalli et al, Appl. Phys. Lett. 117, 142406 (2020). [2] G. Li et al, https://arxiv.org/abs/2001.06799.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bc67c5c24ae7fde192aa244faea267f2.jpg)
Principle of double-pump THz emission spectroscopy and its application to FeRh

![](https://assets.underline.io/uploads/markdown_image/1/image/bbc1f2ff7f5f6e9a1aab73384c2007d6.jpg)
Double pump THz emission due to emerging ferromagnetism in antiferromagnetic FeRh/Pt. The solid lines are linear fits emphasizing a linear increase between 20 ps and 40 ps. The inset shows the magnetic field dependence of the slope of the linear fits.

 THz spintronics of antiferromagnetic FeRh/Pt

We report on ferromagnetic resonance (FMR) detected spin pumping in Fe60Al40/Pd and Py/Fe60Al40 bilayer and laterally patterned Fe60Al40 nanostructures. The magnetic properties of Fe60Al40 alloy are easily tailorable from paramagnetic to ferromagnetic state by variation of the structure through ion beam irradiation, making a promising material for the fabrication of magnetic landscapes and magnonic crystals [1,2]. Exploiting this easy tunability we show that Fe60Al40 can be used as well as spin source as spin sink in spin pumping experiments. Using the material with the identical chemical composition leads to a new pathway creating geometries for lateral spin pumping and might lead to an increase in efficiency in spin pumping as the writing of structures using ion beam irradiation allows to realize spin-based binary logic systems. Characteristic quantities to estimate the efficiency of spintronic systems are the spin mixing conductance and the spin diffusion length determined by thickness and frequency dependent FMR measurements [3]. Therefore, two sets of bilayer samples consisting of ferromagnetic (FM) and paramagnetic (PM) layers have been prepared, i.e. FM Fe60Al40 films of 5 nm thickness capped with Pd of varying thickness as well as Py of 5 nm thickness capped with PM Fe60Al40 of varying thickness. They were investigated using frequency dependent FMR measurements in a range of 2 to 35 GHz. The FMR linewidth and damping analysis reveal a spin mixing conductance of g↑↓ = (2.092 ± 0.046)×1018 m-2 and a spin diffusion length of λFeAl = 17.2 ± 0.86 nm (see Fig. 1) for paramagnetic Fe60Al40, and g↑↓ = (4.454 ± 0.0479)×1018 m-2 and λPd = 8.513 ± 1.631 nm nm for Pd. Based on a result of the determined efficiency of Fe60Al40 used as spin source and spin sink, we investigate the spin pumping in laterally patterned Fe60Al40 nanostructures (see Fig. 2) representing 500 nm wide stripes of FM Fe60Al40 separated with PM Fe60Al40 stripes of different width (100-400 nm) produced in 40 nm thick film, which demonstrate a decrease of the damping parameter with increasing width of PM Fe60Al40 areas.

**References:**

[1] D. Holzinger et al., J. Appl. Phys. 114, 013908(5) (2013). [2] B. Obry et al., Appl. Phys. Lett. 102, 202403 (2013). [3] J. M. Shaw et al., Phys. Rev. B 85, 054412 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/80f7dff979c4785dd3a19e4712cee8e7.jpg)
Fig.1: Extracted damping parameter in dependence of the paramagnetic FeAl-layer thickness. The solid red line indicates the fit for extracting the spin mixing conductance and the spin coherence length. The dashed blue line shows the intrinsic damping contribution of the Py thin film.

![](https://assets.underline.io/uploads/markdown_image/1/image/4167e5622bf8738a9ecca720f6523e0b.jpg)
Fig.2: Ion irradiation with Ne+ of the Fe60Al40 film with mask. The structural disordering occurs in the unmasked stripes, causing the transition from paramagnetic to ferromagnetic state.

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