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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., &lt;i&gt;The 2020 Magnetism Roadmap&lt;/i&gt;, J. Phys. D: Appl. Phys. 53, 453001 (2020)&lt;br/&gt;[2] T.S. Seifert &lt;i&gt;et al&lt;/i&gt;., &lt;i&gt;Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy&lt;/i&gt;, Nature Commun. 9, Article number: 2899 (2018)&lt;br/&gt;[3] T.S. Seifert &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Frequency-independent terahertz anomalous Hall effect in DyCo&lt;sub&gt;5&lt;/sub&gt;, Co&lt;sub&gt;32&lt;/sub&gt;Fe&lt;sub&gt;68&lt;/sub&gt; and Gd&lt;sub&gt;27&lt;/sub&gt;Fe&lt;sub&gt;73&lt;/sub&gt; thin films from DC to 40 THz&lt;/i&gt;, Advanced Materials (accepted) (2021)&lt;br/&gt;[4] L. Nadvorník et al., &lt;i&gt;Terahertz anisotropic magnetoresistance reveals strong intrinsic contributions&lt;/i&gt;, arXiv:2010.06280 (2021)&lt;br/&gt;[5] J.A. Fülöp &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Review: Laser-Driven Strong-Field Terahertz Sources and their Novel Applications&lt;/i&gt;, Adv. Opt. Mat. 1900681 (2019)&lt;br/&gt;[6] M. Meinert &lt;i&gt;et al&lt;/i&gt;., &lt;i&gt;High-throughput techniques for measuring the spin Hall e&lt;/i&gt;&lt;i&gt;ff&lt;/i&gt;&lt;i&gt;ect&lt;/i&gt;, Phys. Rev. Applied 14, 064011 (2020)&lt;br/&gt;[7] O. Gueckstock &lt;i&gt;et al.&lt;/i&gt;, &lt;i&gt;Terahertz spin-to-charge conversion by interfacial skew scattering in metallic bilayers&lt;/i&gt;, Advanced Materials (accepted) (2021)

**Images:**





INTERMAG 2021

 Probing and driving ultrafast spin transport with terahertz electromagnetic pulses

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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:**

technical paper

In the last two decades, the rapid development of broadband communication systems is the cause of the creation of the ultrashort pulse (USP) sources. In optics, there are various methods for USP generation, one of which was given the Nobel Prize in Physics [1]. Nowadays, some optical methods for USP generation start to be used in the microwave range to generate both the USPs of "giant" amplitude [2] and the multisoliton complexes consisting of bright and dark spin-wave envelope solitons [3]. Recently, a new method for the ultrashort dark pulse generation was proposed [4]. It is based on the use of three-wave nonlinear spin-wave interactions and a nonlinear amplification. Using this method, the generation of microwave dark multisoliton complexes was obtained. Each multisoliton complex consists of some dark parametric pulses of submicrosecond duration that contains the trains of dark incoherent spin-wave envelope solitons possessing a subnanosecond duration. The characteristics of such patterns are controlled by a variable attenuator that is managed by the nonlinear loss of a magnetostatic spin wave (MSW), propagating in an irregular magnonic waveguide. Dynamic control of the MSW loss can be realized with the help of direct current (DC) [6,7]. If DC flows in a wire conductor located on the ferromagnet surface, then the internal magnetic field is locally changed in the ferromagnet. This causes a change not only in the MSW dispersion, but also in its linear loss. Dynamic control of the MSW loss by means of DC underlies the operation of a dynamic magnonic crystal (MC) [7]. The dynamic MC is a ferromagnetic medium, the internal magnetic field of which is periodically changed in space by DC. By analogy with photonic crystals, a periodic change in the parameters of the medium is the reason for the forbidden zones (FZs) formation. At FZs frequencies, the MSW linear loss undergo a significant change. Dynamic control of the MSW loss can also be realized for a static MC, if a DC-controlled local inhomogeneity is created on the surface of a periodic structure. This will make it possible to control not only the MSW loss at the frequencies of the FZs, but also the FZ location in the MSW spectrum. In this work, it is demonstrated the dynamic control of the loss and FZs of the static MC due to a local change in the MC internal magnetic field. In addition, the static MC with dynamic control of the loss and FZs is used in a feedback loop of an active ring resonator to manage a duty cycle of the chaotic dark parametric envelope solitons.The parametric wave model with nonlinear amplification is used to explain the experimental results. As shown in Fig.1a, the MC, contained in the feedback loop of the active ring resonator, is a periodic structure of crests and grooves that are formed on the surface of an yttrium-iron garnet film with a thickness of 10 μm. The crests and grooves have the same width of 100 μm. An external bias field H0=356 Oe is applied tangentially to the surface of the MC and directed along to the input and output microstrip lines. Such field configuration supports a magnetostatic surface spin wave (MSSW) propagation. The strength of the bias field is chosen so that three-wave nonlinear spin-wave interactions are allowed for the MC. A wire conductor connected to a DC source is placed along the longitudinal symmetry axis of the MC. Depending on the polarity of the DC, the MC internal magnetic field can either increase or decrease. As shown in Fig.1b, such changes of the internal magnetic field lead to the management of both the linear and nonlinear MSSW loss. In addition to the MC, the generator contains an amplifier stage, consisting of a klystron amplifier and two transistor amplifiers, that are necessary to compensate the loss. The output transistor amplifier of the stage operates in the output power saturation mode, and the other two amplifiers operate in the linear amplification mode. In addition, a resonant frequency of the klystron amplifier is tuned to a frequency located near the center frequency of the MC first FZ. This is necessary in order to realize the amplitude and phase conditions for signal generation. A generated microwave signal is fed through the directional couplers to the inputs of a spectrum analyzer and a real-time oscilloscope for analysis and processing. In Fig.2, the dark parametric soliton modes obtained both experimentally and calculated on the basis of the parametric wave model with nonlinear amplification are presented. The presented in Fig2a experimental results show that a change in the DC polarity leads to a change in the duty cycle of the generated chaotic dark parametric solitons. A similar effect is observed in a numerical experiment (see Fig2b), if the frequency of the parametrically excited spin waves is detuned from the half value of the MSSW frequency. This work was supported by the Russian Science Foundation (Project No.19-79-20121).

**References:**

1. D. Strickland and G. Mourou, Opt. Commun., Vol.55, p.447 (1985). 2. N.S. Ginzburg, G.G. Denisov, M.N. Vilkov, and et al., Phys. Plasmas, Vol.24, p.023103 (2017). 3. S.V. Grishin, B.S. Dmitriev, O.I. Moskalenko, and et al., Phys. Rev. E, Vol.98, p.022209 (2018). 4. A.S. Bir, S.V. Grishin, O.I. Moskalenko, and et al., Phys. Rev. Lett., Vol.125, p.083903 (2020). 5. M. Tsoi, A.G.M. Jansen, J. Bass, and et al., Phys. Rev. Lett., Vol.80, p.4281 (1998). 6. S.O. Demokritov, A.A. Serga, A. Andre, and et al., Phys. Rev. Lett., Vol.93, p.047201 (2004). 7. A.V. Chumak, T. Neumann, A.A. Serga, and et al., J. Phys. D: Appl. Phys., Vol.42, p.205005 (2009).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/191173d877ed2fc4ea8c44926e431f0f.jpg)
Fig.1 (a) Block diagram of the dark parametric soliton active ring resonator based on direct current-controlled magnonic crystal. (b) Dependences of the MSSW loss on the input power, measured at the MC FZ frequency at various values and polarity of DC.

![](https://assets.underline.io/uploads/markdown_image/1/image/2807bd8f2d795d58d447a183b7d44cb9.jpg)
Fig.2 Sequences of the dark parametric envelope solitons obtained (a) experimentally and (b) calculated by the model. In (a), the pulses are obtained for two DC polarities: +320 mA (top panel) and -200 mA (bottom panel). In (b), the pulses are obtained for two values of the SW frequency detuning: 10-25 Hz (top panel) and 10-315 Hz (bottom panel).

 Direct Current Control of the Chaotic Dark Parametric Solitons in a Magnonic Crystal Active Ring Resonator

Sheet- and film-type soft magnetic materials have been widely used to suppress unexpected noise in mobile and wearable devices using ferromagnetic resonance (FMR) losses [1][2]. The designs of these magnetic noise suppressors are mainly based on large-scale electromagnetic field simulations and "trial and error" experiences. In previous studies, the effect of the complex permeability of the magnetic sheet and film on circuit parameters of transmission lines was investigated by a simple magnetic circuit analysis using only the cross-sectional size and material parameters [3]. However, the effect on the reflection and the transmission coefficients have not been estimated quantitatively and the design guideline of the noise suppressor has not been clarified. In this paper, the estimation method of the reflection and the transmission coefficients of a transmission line with a noise suppressor is investigated including the effect of the complex permeability. A 95 μm-width microstrip line (MSL) with a Co-Zr-Nb film is discussed as a test bench. The electrical equivalent circuit parameters of the MSL with Co-Zr-Nb film were calculated by the magnetic circuit analysis and the characteristic impedance was estimated. The thickness of the Co-Zr-Nb film was determined considering impedance matching below 1 GHz range, where it was assumed that a signal frequency range, and the conductive noise suppression by the Co-Zr-Nb film at 3 GHz was estimated. Figure 1 illustrates the magnetic circuit in the cross-sectional view of the MSL with the Co-Zr-Nb film. The MSL was fabricated on low-temperature co-fired ceramic (LTCC) substrate with the thickness h=100 µm and the relative permittivity of 9.8. The width, thickness and length of the signal line are ws=95 μm, ts=3 μm, and 10 mm, respectively. The Co-Zr-Nb film was fabricated using radio frequency (RF) sputtering and deposited on a SiO2 substrate. The film thickness t was obtained by the magnetic circuit analysis and the electromagnetic simulation so that the characteristic impedance of the MSL with and without the film have a same value. The electrical equivalent circuit of the MSL with the Co-Zr-Nb film was obtained to calculate the characteristic impedance. The circuit consists of series impedance Z = R + jωL = (Rm+Re+Rs) + jωLm and parallel conductance Y = jωC, where Rm and Lm were calculated by the magnetic circuit analysis considering the effect of the complex permeability of the Co-Zr-Nb film. Rs and Re were the resistance of the signal line including the skin effect and the increase of resistance due to the eddy current loss generated in the film [3], respectively. C = 2 pF calculated by experimental value at 0.1 GHz [4]. Figure 2(a) shows the estimated characteristic impedance Z0 = (Z/Y)0.5 with t = 0.1-1 μm. Below 1 GHz, the impedance is roughly constant and the estimated impedance of the MSL with 1-μm-thick film is almost the same as the measured value of MSL without the film. Therefore, t = 1 μm was used to calculate the reflection and the transmission coefficient. Figure 2(b) and (c) shows the reflection coefficient |S11|, transmission coefficient |S21|, and the noise suppression Ploss/Pin = 1-(|s21|2 +|s11|2) of the MSL with 1-μm-thick film obtained by the electrical equivalent circuit analysis. In the case with the film, |S11| and |S21| were almost the same as the measured value within about 8 dB and 0.1 dB below 5 GHz, respectively. |S11| increased up to 8 dB below 1 GHz but the value kept less than -25 dB. On the other hand, |S21| decreased as the frequency increased because of the combination of FMR and Joule losses in each film at 3 GHz. Ploss/Pin is maximized at 3 GHz. In summary, the reflection and the transmission coefficients of a transmission line with a noise suppressor were quantitatively estimated including the effect of the complex permeability using the magnetic circuit analysis using the cross-sectional size and material parameters. The thickness of the Co-Zr-Nb film was determined considering characteristic impedance matching. As a result, the reflection coefficient was lower than -25 dB below 1 GHz, and the conductive noise suppression was obtained at 3 GHz. Those results give a way to clarify the design guideline of the noise suppressors. This work was supported in part by JSPS KAKENHI Grant Number 20K04497. Part of this work was carried out under the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University.

**References:**

[1] S. Yoshida et al., IEEE Trans. Magn., Vol.37, No.4, pp.2401-2403 (2001). [2] K. Kondo et al., IEEE Trans. Magn., Vol.45, No.10, pp.4250-4252 (2009). [3] S. Muroga et al., J. Elec. Materi., Vol.48, No.3, pp.1342-1346 (2019). [4] T. Mikami et al., The 44th Annual Conf. Magn. Jpn, 14aD-11 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f49f11a1a0eaeda3f369b57ea16aa68b.jpg)
Fig.1 cross-sectional dimensions and magnetic circuit of a one kine MSL with Co-Zr-Nb film

![](https://assets.underline.io/uploads/markdown_image/1/image/c0f049207352d2aa4d74175eaaee669e.jpg)
(a) Charateristic impedance (b) S parameter (c) Input loss ratio 
Fig.2 Transmission characteristics

 Estimation of Noise Suppression in MSL with Co-Zr-Nb films Considering Impedance Matching

Nowadays, the Wireless Power Transfer (WPT) presents itself as a new option to charge batteries, in order to eliminate the respective cables and gain mobility, convenience and ease for the user. One of the WPT techniques uses the Coupled Magnetic Resonance (CMR). This technology is capable of transmitting electromagnetic energy from a power source (transmitter coil) to an electric load (in the receiver coil) through a gap in the air and the variation and oscillation of magnetic fields [1]. Metamaterials (MM’s) are typically conductive elements such as copper, gold and silver [2]. They present unnatural magnetic properties, obtained from their internal arrangement, which allow them to obtain a negative refractive index, making them perfect lens. Thus, they are used between the coils to increase the efficiency of WPT. Veselago called the MM's as left-handed materials (LH materials) because the propagation of electromagnetic waves with the electric and magnetic fields and propagation vector forms a left-handed triad when compared to conventional materials. He predicted several behavioral phenomena that occur in LH media such as the reversal of the Doppler effect and the Snell's law and negative refraction [3]. In this work, since the technique chosen was that of strong resonant magnetic coupling, where the magnetic characteristic of the evanescent field prevails, we opted to use a structure with MNG characteristics (Mi-negative Medium, ε &gt; 0, μ &lt;0), which can be obtained from the Split Ring Resonators (SRR's). If the magnetic field H is perpendicular to the plane of the rings, in order to induce resonant currents in the loop and generate equivalent magnetic dipole moments, this MM exhibits plasmatic permeability as a function of frequency [4]. The main goal is to propose a metamaterial topology that allows a horizontal misalignment between transmitter and receiver coils, resulting in a more efficient system. The system was simulated on CST® Studio software. The transmitter and receiver coils are flat and have 7 loops, width of 2.49 mm, spacing of 1.0 mm, inner radius of 22 mm and outer radius of 47 mm. These coils are in a FR4 substrate with dimensions of 100 x 100 x 1.5 mm. The distance between the coils ranged from 4 cm to 10 cm without misalignment. The transmitter coil has an alternating voltage source (Vmax of 100 V) and the receiver has a resistor of 100 Ω as load. This same system was simulated with a metamaterial slab placed at half way between the coils. The metamaterial slab has the dimensions of 100 x 150 x 1.5 mm, and 12 unit cells arranged in a 4x3 array with two copper Split-ring resonators (SRR’s) with height of 0.02 mm, width of 1.63 mm, and spacing of 1.47 mm, and 2 capacitors of 47 nF. The system was designed and computed for a resonance frequency of 1 MHz. The best results were at 4 cm with the MM slab, where there was an increase of 77.32% in the efficiency (12.23% to 23.46%), 24% in the maximum voltage (67.19 V to 83.42 V) and current (671.89 mA to 834.20 mA), 54% in the power (45.14 W to 69.59 W). Figure 2 shows the efficiency of the system, at 4 cm, simulated with a horizontal misalignment between the coils, with and without metamaterial. Although the system is very sensitive to the misalignment, it still presents a better efficiency compared to no MM setup. After introducing the MM slab, there was an increase in the efficiency of 55.63% (13.14% to 20.45%) in 1 cm, 52.72% (10.81% to 16.51%) in 2 cm and 49.41% (7.67% to 11.46%) in 3 cm of misalignment. Even with 2 cm of misalignment, the system with MM is more efficient than the one without it (16.51 to 13.23%). Thus, the MM was able to increase efficiency in wireless power transfer even with horizontal misalignment between coils.

**References:**

[1] D. C. Corrêa, U. C. Resende and F. S. Bicalho, "Experiments With a Compact Wireless Power Transfer System Using Strongly Coupled Magnetic Resonance and Metamaterials," in IEEE Transactions on Magnetics, vol. 55, no. 8, pp. 1-4, Aug. 2019. [2] X. Wang, Y. Wang, Y. Hu, Y. He and Z. Yan, "Analysis of Wireless Power Transfer Using Superconducting Metamaterials," in IEEE Transactions on Applied Superconductivity, vol. 29, no. 2, pp. 1-5, March 2019. [3] D. Smith, J. B. Pendry; Reversing light negative refraction. Physics Today, 57, pp. 37-45, 2009. [4] C. Caloz.; T. Itoh; T. Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. The Engineering Approach. [s.l.] Wiley, 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2fbd97c45539a51f7b042db4481bbc6.jpg)
Fig. 1 – Efficiency comparison without misalignment

![](https://assets.underline.io/uploads/markdown_image/1/image/3c7c8a96fe9a7c72453d1acd4bf36f6b.jpg)
Fig. 2 - Efficiency comparison with misalignment between coils

 High Efficient Wireless Power Transfer Through Metamaterial Coupled Magnetic Resonance

In modern radar and communication systems it is important to determine the frequency composition of complex external signals on the µs time scale and faster [1]. Common swept-tuned spectrum analyzers (SA) are limited to sweep times of 10-100 ms determined by the characteristic times of macroscopic VCOs and YIG-tuned reference oscillators. In contrast, recent progress in spintronics has led to the development of spin-torque nano-oscillators (STNO) generating in the GHz frequency range, and naturally having time constants of the order of several nanoseconds determined by the intrinsic properties of magnetization dynamics at nano-scale [2]. In [3] it was proposed theoretically and in [4] demonstrated experimentally for a vortex-state configuration that STNOs can be used as a central element of an ultra-fast spectrum analyzer. A fastest sweep rate of 0.67us was achieved for spectral analysis in the range of 25MHz around center frequency of 300MHz. Here we focus on increasing the bandwidth and operational frequency of the STNO SA concept. For this purpose a special uniform-state STNO was nanofabricated. We show that our uniform-state STNO has a very wide frequency-current tuning range and high operational frequency. With such an STNO we pushed the STNO-based SA concept to a central frequency of 9 GHz. The corresponding SA performances sufficiently exceed the results obtained with a vortex-state STNO with a reduced sweep time of T = 20 ns, and a record sweep range of 1GHz (limited mostly by STNO power and not by the tuning range capabilities) keeping the RBW (resolution bandwidth) close to the theoretical limit (50 MHz). This GHz-frequency technique of spectrum analysis was implemented as shown in Fig.1. The STNO was used as a local oscillator whose frequency was sweep-tuned via an additional saw-tooth sweep signal. The STNO output is, then, mixed with the input signal, digitized, and processed with a matched filter, resulting in a narrow output peak whose temporal position corresponds to the input frequency while the width determines the RBW. In the top panel of the inset of Fig.1 we show a series of peaks obtained with an input signal whose frequency was changing in time in a saw-tooth manner with a period of 500ns. The sweeping rate of the STNO SA was chosen 10 times faster so that the changes of the input signal frequency could be correctly tracked. As can be seen from the spectrogram in the bottom panel of the inset, the shape of the instantaneous input frequency was successfully tracked with sufficient RBW of 34.6MHz. Financial support is acknowledged from the EC program ERC MAGICAL 669204, from the NSF of the USA (Grants # EFMA-1641989 and “ECCS-1708982), and by the US AFOSR (MURI grant # FA9550-19-1-0307).

**References:**

[1] V.C., Chen and W.J., Miceli, “Time-varying spectral analysis for radar imaging of manoeuvring targets”, IEEE Proceedings - Radar, Sonar and Navigation 145, 262-268 (1998). [2] T. Chen, et al., “Spin-Torque and Spin-Hall Nano-Oscillators”, IEEE Proceedings, 104, 1919-1945 (2016). [3] S. Louis, et al., “Ultra-fast wide band spectrum analyzer based on a rapidly tuned spin-torque nano-oscillator”, Applied Physics Letters 113, 112401 (2018). [4] A. Litvinenko, et al., “Ultrafast sweep-tuned spectrum analyzer with temporal resolution based on a spin-torque nano-oscillator,” Nano Letters 20; 6104-6111 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae175606696079038bdd43c4e48d7b6b.jpg)
Fig.1. Ultra-fast GHz STNO-based spectrum analyzer. In the inset, top panel, left axis: Vspec vs time for 10 consecutive sweeps. Right axis: The time variation of the input signal frequency fin. 
Bottom panel: fspec vs time in the form of waterfall spectrogram.

 Ultra-fast spectrum analysis at GHz frequencies using spin-torque nano-oscillators

Two-dimensional Airy beam can be widely used in long distance high-efficiency wireless power transfer and security communication in microwave band. How to excite Airy beams effectively has drawn a lot of attentions in recent years. Wen-Long Guo et al. proposed a metasurface-based one-dimensional Airy beam excitation method [1], which successfully generated the one-dimensional Airy beam. Yongjun Huang et al. successfully generated the two-dimensional Airy beam in the microwave band by using a metasurface composed of a-single-layer C-shaped complementary split ring resonators (C-SRR) [2] operating in microwave band. While the manipulation of the deflection of the main lobe has not been achieved in the previous works, and the size of the proposed metasurface is too large to integrate with other devices. In this paper, a novel method to generate and control two-dimensional Airy beam is proposed. By changing the parameters and rotation angles of the unit cell structures, as shown in Fig. 1(a), the amplitude and phase of the transmission coefficient can be adjusted, then the desired two-dimensional Airy beam can be excited by arranging the unit cells to construct the metasurface. In addition, the deflection conditions of the main lobe can be manipulated by changing the attenuation coefficient of the two-dimensional Airy function. The envelope of the two-dimensional Airy beam can be described by equation (1): U(x,y)=fai (x)fai (y)exp(ax)exp(ay) (1) fai(x)=(∫cos(t3÷3+xt)dt)÷π (2) Here, a is the attenuation coefficient in the two-dimensional Airy function. In this paper, simplified amplitude modulation method is used, as shown in Fig.1 (b), the main amplitude region of the two-dimensional Airy function is selected to design the desired envelope. As shown in Fig.1 (c), the number of horizontal and vertical elements of the proposed metasurface is 22, which greatly reduces the size of the device that exciting the two-dimensional Airy beam. Fig.1 (d) to (f) show the normalized energy distribution of the two-dimensional Airy beam at different distances along the propagating direction when a equals 0.1. It can be seen that the main lobe moves along the diagonal direction, which shows the self-acceleration phenomenon of the two-dimensional Airy beam. The self-acceleration direction of the two-dimensional Airy beam is the diagonal direction, and the deflection of the main lobe is related to the amplitude distribution in the self-bending direction [3]. By changing the attenuation coefficient, different amplitude distribution of the unit cells on the diagonal of proposed metasurface can be achieved to control the deflection of the main lobe. Fig.2 (a) to (c) show the calculated and simulated results of electric field distribution of the vertical diagonal plane with different attenuation coefficients. The simulated results agree well with the calculated results in the deflection trajectory, which verifies that the deflection conditions of the main lobe can be manipulated effectively.

**References:**

[1] Wen-Long Guo, Ke Chen, Guang-Ming Wang, Adv. Optical Mater., Vol. 8 (2020) [2] Huang Y , Li J , Xu H X, IEEE Transactions on Antennas and Propagation., pp(99):1-1 (2020) [3] Zhi Li, Hua Cheng, Zhaocheng Liu, Advanced Optical Materials., Vol. 4, pp.1230-1235 (2016) [4] Qingbin Fan, Wenqi Zhu, Yuzhang Liang, Nano Letters., Vol. 19, pp.1158−1165 (2018) [5] X. Ding, F. Monticone, K. Zhang, Advanced materials., Vol. 27, pp.1195 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e9ce3e87601acf49f05b53c62e447125.jpg)
Fig.1. a) Schematic diagram of a unit cell of the proposed single layer metasurface b) Normalized amplitude distribution of two-dimensional Airy function c) Schematic diagram of the entire surface array. The normalized horizontal plane energy distribution when the propagation distance is d) 90mm, e) 180mm, f) 240mm.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc1a45c622148af375a80cd5c8053a81.jpg)
Fig.2. The energy distribution at the vertical diagonal plane when the attenuation coefficient is a) 0.3, b) 0.1, c) 0.0005.

 Two-dimensional Airy beam generation and manipulation utilizing metasurface

Soft magnetic thin films and multilayered structures deposited onto flexible substrates are attracting more attention for variety of technological applications [1,2]. Flexible electronics and magnetic field sensors require fabrication of complex elements which can operate using different magnetic effects: magnetoelastic effect, magnetoresistance and magnetoimpedance (MI) among others [3,4]. Low weight, high adaptability in multipurpose devices combining more than one functional component may compensate the lower magnetic characteristics of thin films deposited onto flexible in comparison with traditional rigid substrates. One of rapidly developing areas of flexible MI specialized detectors is MI biosensing [5]. It was shown earlier that high sensitivities with respect to applied magnetic field can be achieved for Fe19Ni81/Ti-based sensitive elements fabricated onto cyclo olefin copolymer (COC) flexible transparent substrates widely used in microfluidic systems [3,5]. Transparency is an additional request for microfluidic systems. For successful biosensing weak fields should be detected at the level at least micro Oersteds. This requires special environments without electronic interferences and random magnetic fields. We therefore propose to use COC substrates and the same magnetic material Fe19Ni81 both as functional magnetic layers of sensitive element of MI biosensor and shielding material preventing undesirable electronic interferences. In this work the structure, transparency, static magnetic properties and microwave absorption of Fe19Ni81 thin films deposited onto COC substrates were studied as a function of the permalloy layer thickness. Thin films of the thicknesses of 12, 20, 25 and 80 nm were deposited by magnetron sputtering technique onto COC substrates (Zeonor ZF14 100 μm thick commercial film) at room temperature using alloyed FeNi target for deposition. Background pressure was 3×10-7 mbar and the argon gas pressure during sputtering was 3.8×10-3 mbar. The deposition rate of 28 nm/min for was defined by special calibration of the system. The thicknesses of the films were determined by the deposition time and calculated using the deposition rate. The microstructure was analyzed by XRD technique with a PHILIPSX’PERT PRO diffractometer (working parameters are 40 kV and 40 mA) employing Cu-Kα radiation (λ = 1.5418 Å). The magnetic hysteresis loops were measured by a vibrating sample magnetometer (VSM). Microwave properties were studied at a fixed frequency. Gunn diode microwave transmitter was employed as a microwave radiation source. It consists of the gun diode in 10.525 GHz cavity, a microwave horn to direct the output and 18 cm stand to reduce reflections. Transmitter provides coherent linearly polarized along the axis of the diode microwave output at a wavelength of 2.85 cm. In order to characterize the properties of FeNi films, the transmission and reflection properties were studied. XRD spectra for FeNi films showed the presence of intensive maximum at 2θ » 44° being (111) reflection. Figure 1 shows the results of the VSM measurements in-plane magnetic hysteresis loops of FeNi thin films with different thickness (t). As to expect the total magnetic moment (m) is increased with the increase of the film thickness. The lowest coercivity close to 6 Oe was observed for the most thick film of 80 nm. This value is consistent with the coercivities of permalloy films obtained for flexible substrates in previous studies. In the other cases, the coercivities were increased (being below 19 Oe) most probably due to special contribution of the surface roughness, which is higher for COC substrate in comparison with standard rigid substrates. As the first step of the microwave studies, the output voltage signal of the receiver was measured for head-to-head aligned configuration of the microwave transmitter and receiver in as a function of the distance (r) between them in two cases. In the first one no intermediate substances between the transmitter and receiver was allowed. In the second case COC 100 μm thick top was covering the horn open plane being parallel to the axis of the diode. It was confirmed that for the frequency of 10.525 GHz COC substrates contributions to the microwave absorption can be neglected: both output voltages V(1/r) were linear and showing the same slope and regression. As the next step, the power absorption was measured in the same configuration for all thin films deposited onto COC substrates (Figure 2). One can clearly see that 80 nm thin FeNi film, which still has transparency of about 10% insures a complete protection with respect to the component of microwave signal polarized along the diode axis. It worse mentioning that even 12 nm permalloy film is almost as effective as 80 nm film but having much higher transparency. Obtained results indicate that Fe19Ni81 films deposited onto COC substrates can be used as effective shielding materials in complex multipurpose devises. This work was supported by the RSF grant 18-19-00090. Selected measurements were performed at SGIker services UPV-EHU.

**References:**

[1] C.A. Grimes, IEEE Trans. Magn. 31(6) (1995) 4109. [2] M. Melzer, D. Makarov, A. Calvimontes, D. Karnaushenko, S. Baunack, R. Kaltofen, Y.F. Mei, O.G. Schmid, Nano Lett.11(2011) 2522. [3] E. Fernández, A.V. Svalov, A. García-Arribas, J. Feuchtwanger, J. M. Barandiaran, G.V. Kurlyandskaya, J. Nanosci. Nanotech. 12 (2012) 7496. [4] K. Agra, F. Bohn, T.J.A. Mori, G.L. Callegari, L.S. Dorneles, M.A. Correa, J. Magn. Magn. Mater. 420 (2016) 81. [5] A. García-Arribas, F. Martínez, E. Fernández, I. Ozaeta, G.V. Kurlyandskaya, A.V. Svalov, J. Berganzo, J.M. Barandiaran, Sens. Act. A 172 (2011) 103.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2f0b8852d5521174ee44fa085aa69ebf.jpg)
VSM hysteresis loops of FeNi films with different thicknesses t deposited onto flexible COC substrates: m is a total magnetic moment of the sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/81c560ca697d66ba21704e790bb22bd4.jpg)
Output voltage dependence of the microwave receiver on the thickness of FeNi film deposited onto flexible COC substrates with an exponential decay fit. Inset shows the same output voltages in a logarithmic scale.

 Magnetic and microwave properties of FeNi thin films of different thicknesses deposited onto cyclo olefin copolymer flexible substrates

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

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.

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