France



In recent years, the magnon-phonon coupling in magnetostrictive materials has gained renewed interest due to emerging spintronic and magnonic applications, such as low power consumption microwave devices. Linear and parametric acoustically driven spin waves (ADSW) were studied in various hybrid magnon-phonon structures containing piezoelectric and ferro (ferri) magnetic layers [1-4]. Previously [5-7], we have demonstrated the piezoelectric excitation of linear and parametric ADSW in the gigahertz frequency range and their detection by the combination of spin pumping and inverse spin Hall effect (ISHE) in the spintronic hybrid High overtone Bulk Acoustic wave Resonator (HBAR) with the structure ZnO – YIG– GGG–YIG – Pt (Fig.1a).&lt;br/&gt;Here, the features of phonon-magnon interconversion in the phononic cavity mentioned above are studied in detail. The pump frequency &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt; , power &lt;i&gt;P&lt;/i&gt;, and magnetic field &lt;i&gt;H&lt;/i&gt; dependences of the ISHE voltage &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE &lt;/sub&gt;as well as resonance frequencies &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; are experimentally and theoretically studied. As a result of magnetoelastic interaction, bulk acoustic waves (BAW) cavity modes excite magnons in the YIG films either at frequencies&lt;i&gt; f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; or at half resonance frequencies (when the threshold power is exceeded). When specifying a certain frequency range, depending on the value of the applied magnetic field, either direct excitation of linear ADSWs or parametric excitation (in low magnetic fields) is observed.&lt;br/&gt;In the first case the important features of ADSW and acoustic spin pumping are determined by double resonance: the magnetoelastic (MER) in YIG films and BAW resonance of the entire resonator structure. Electrical detection of ADSWs occurs while simultaneously measuring the electrical response of the ZnO transducer and the dc voltage signal on the Pt stripe. The dependences of the resonance frequencies &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt; on the field &lt;i&gt;H&lt;/i&gt; and the frequency &lt;i&gt;f&lt;/i&gt; are correlated with each other (Fig. 1b). The fitting of the theoretical and experimental dependences allows us to determine a number of magnetic and magnetoelastic parameters of YIG and field dependencies of the resonance frequencies: magnetoelastic &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;MER&lt;/sub&gt; (&lt;i&gt;H&lt;/i&gt;) and ferromagnetic &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;). For the frequency range around 2.4 GHz, the magnetic field corresponding to the ferromagnetic resonance is &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt; &lt;i&gt;≈&lt;/i&gt; 534Oe.&lt;br/&gt;In the second case when the field decreases below &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;, the HBAR spectrum &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; is practically independent of the magnetic field, but the clearly detectable voltage &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt; (&lt;i&gt;f, H&lt;/i&gt;) is significantly field dependent. The signal from the parametric ADSW was observed when: (i) the pump frequency coincided with one of the HBAR resonant frequencies, (ii) half of the pump frequency coincided with one of the spin wave frequencies for a given magnetic field (see Fig.2a), and (iii) the pump power exceeded a threshold, depending on the field (see Fig 2b). It can be seen from Fig. 2 the field of the maximum voltage is close to the critical field &lt;i&gt;H&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt; = 184 Oe, at which &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;c&lt;/i&gt;&lt;/sub&gt;) = &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;/2. It indicates that &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;&lt;i&gt;&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;) originates from the detection of parametric ADSW with wave number &lt;i&gt;q&lt;/i&gt; = 0. The voltage signal is observed in the field range below 432 Oe. This field correlates with the value &lt;i&gt;H&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; = &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt; /(2γ) in Fig. 2a. Above this field, the excitation of any parametric spin wave is impossible; therefore, the voltage signal is suppressed. But at the higher fields, the linear excitation of ADSW takes place at the &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;, at which &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;) = &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;. In Fig. 2, the field &lt;i&gt;H&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;= &lt;i&gt;H&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;/2=&lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;/(4γ) corresponds to the upper limit on &lt;i&gt;H&lt;/i&gt; for the possible decays of parametric magnons with the frequency &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;/ 2 into two secondary parametric ones at a frequency &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt;/4. Measurements with a smaller field step show that, in some field ranges, the &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt; (&lt;i&gt;H&lt;/i&gt;) dependence has additional features, which can be explained by parametric excitation of various groups of magnons. For example, in a field near &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;c3&lt;/sub&gt; = 100 Oe, the nonmonotonic behavior of the &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt; (&lt;i&gt;H&lt;/i&gt;) dependence is apparently due to the magnon confluence process, for which the condition &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt; (&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;c3&lt;/sub&gt;) = &lt;i&gt;f&lt;/i&gt;p /3 is satisfied [8].&lt;br/&gt;For certain ranges of fields and powers, the data of Fig. 2b can be fitted as &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt; (&lt;i&gt;P&lt;/i&gt;, &lt;i&gt;H&lt;/i&gt;) ~ (&lt;i&gt;P&lt;/i&gt;-&lt;i&gt;P&lt;/i&gt;&lt;sub&gt;th &lt;/sub&gt;(H))&lt;sup&gt;1/2&lt;/sup&gt;, where the fitting parameter &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;th&lt;/sub&gt; (&lt;i&gt;H&lt;/i&gt;) ≈ 0.4 mW can be interpreted as a threshold power. We explain the low threshold obtained by the high efficiency of electric power transmission into the acoustic pump confined in the phononic cavity - high-Q hybrid HBAR.&lt;br/&gt;This work was carried out in the framework of the State task 0030-2019-0013 &quot;Spintronics&quot; and with partial support of the RFBR (Project No. 20-07-01075).

**References:**

1. M. Weiler, H. Huebl and F. S. Goerg, Phys. Rev. Lett., Vol.108, p.176601 (2012).&lt;br/&gt;2. P. Chowdhury, A. Jander and P. Dhagat, IEEE Magn. Lett., Vol. 8, p.1 (2017).&lt;br/&gt;3. H. Keshtgar, M. Zareyan and G. E. Bauer, Solid State Commun., Vol.198, p.30 (2014).&lt;br/&gt;4. I. Lisenkov, A. Jander and P. Dhagat, Phys. Rev. B., Vol.99, p.184433 (2019).&lt;br/&gt;5. N. I. Polzikova, S. G. Alekseev, I. I. Pyataikin., AIP Adv., Vol.8, p.056128 (2018).&lt;br/&gt;6. N. Polzikova, S. Alekseev, V. Luzanov, J. Magn. Magn. Mater., Vol. 479, p.38 (2019).&lt;br/&gt;7. S. G. Alekseev, S. E. Dizhur and N. I. Polzikova, Appl. Phys. Lett., Vol.117. p.072408 (2020).&lt;br/&gt;8. T. B. Noack, V. I. Vasyuchka and D. A. Bozhko, Phys. Stat. Sol. b, Vol.256. p.1900121(2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d9e5c5203a96b021bee099c786fa45d6.jpg)
Fig.1 (a) Schematic of hybrid HBAR for ADSW excitation and acoustic spin pumping. The rf voltage &lt;i&gt;V&lt;/i&gt; is applied across the piezoelectric transducer sandwiched between thin-film Al electrodes. The transducer launches and detects a bulk shear acoustic waves, which propagate vertically. (b) Left panel – the fragment of HBAR spectrum, containing two resonant frequencies &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt; &lt;/i&gt;and &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;&lt;i&gt;n&lt;/i&gt;-1&lt;/sub&gt; at zero magnetic field. Right panel –3D colour plot &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt;(&lt;i&gt;f,H&lt;/i&gt;) . The red points correspond to positions of HBAR resonant frequency &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt; &lt;/i&gt;positions. The calculated frequencies &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;MER&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;) and &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;) are shown by black lines.

![](https://assets.underline.io/uploads/markdown_image/1/image/c6be37479dfd46f03c0afe4c66f67145.jpg)
Fig. 2. (a) Dependences of spin wave frequencies at q = 0 on the magnetic field: f = &lt;i&gt;f&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt;(0) at θ=0;&lt;i&gt; f&lt;/i&gt; = &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;FMR&lt;/sub&gt; at θ=90&lt;sup&gt; &lt;/sup&gt;deg (θ is the angle between wave vector and magnetic field), &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;D&lt;/sub&gt; =&lt;i&gt;f&lt;sub&gt;H&lt;/sub&gt;&lt;/i&gt;(0)+&lt;i&gt;f&lt;sub&gt;M&lt;/sub&gt;&lt;/i&gt; /2- upper boundary of dipole (non-exchange) surface magnetostatic waves, &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p&lt;/sub&gt; = &lt;i&gt;f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; =2.412 GHz. (b) 3D plot represents &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt;(&lt;i&gt;H, P&lt;/i&gt;) measured at &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;p &lt;/sub&gt;=&lt;i&gt; f&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; = 2.412 GHz. Red lines – power dependences  &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt;(&lt;i&gt;H&lt;sub&gt;c&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;P&lt;/i&gt;) and &lt;i&gt;U&lt;/i&gt;&lt;sub&gt;ISHE&lt;/sub&gt;(&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;c&lt;/i&gt;2&lt;/sub&gt;, &lt;i&gt;P&lt;/i&gt;).

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 Spin Waves and Spin Pumping Driven by Cavity Confined Bulk Hypersonic Waves

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In recent years, the magnon-phonon coupling in magnetostrictive materials has gained renewed interest due to emerging spintronic and magnonic applications, such as low power consumption microwave devices. Linear and parametric acoustically driven spin waves (ADSW) were studied in various hybrid magnon-phonon structures containing piezoelectric and ferro (ferri) magnetic layers [1-4]. Previously [5-7], we have demonstrated the piezoelectric excitation of linear and parametric ADSW in the gigahertz frequency range and their detection by the combination of spin pumping and inverse spin Hall effect (ISHE) in the spintronic hybrid High overtone Bulk Acoustic wave Resonator (HBAR) with the structure ZnO – YIG– GGG–YIG – Pt (Fig.1a). Here, the features of phonon-magnon interconversion in the phononic cavity mentioned above are studied in detail. The pump frequency fp , power P, and magnetic field H dependences of the ISHE voltage UISHE as well as resonance frequencies fn are experimentally and theoretically studied. As a result of magnetoelastic interaction, bulk acoustic waves (BAW) cavity modes excite magnons in the YIG films either at frequencies fn or at half resonance frequencies (when the threshold power is exceeded). When specifying a certain frequency range, depending on the value of the applied magnetic field, either direct excitation of linear ADSWs or parametric excitation (in low magnetic fields) is observed. In the first case the important features of ADSW and acoustic spin pumping are determined by double resonance: the magnetoelastic (MER) in YIG films and BAW resonance of the entire resonator structure. Electrical detection of ADSWs occurs while simultaneously measuring the electrical response of the ZnO transducer and the dc voltage signal on the Pt stripe. The dependences of the resonance frequencies fn and UISHE on the field H and the frequency f are correlated with each other (Fig. 1b). The fitting of the theoretical and experimental dependences allows us to determine a number of magnetic and magnetoelastic parameters of YIG and field dependencies of the resonance frequencies: magnetoelastic fMER (H) and ferromagnetic fFMR(H). For the frequency range around 2.4 GHz, the magnetic field corresponding to the ferromagnetic resonance is HFMR ≈ 534Oe. In the second case when the field decreases below HFMR, the HBAR spectrum fn is practically independent of the magnetic field, but the clearly detectable voltage UISHE (f, H) is significantly field dependent. The signal from the parametric ADSW was observed when: (i) the pump frequency coincided with one of the HBAR resonant frequencies, (ii) half of the pump frequency coincided with one of the spin wave frequencies for a given magnetic field (see Fig.2a), and (iii) the pump power exceeded a threshold, depending on the field (see Fig 2b). It can be seen from Fig. 2 the field of the maximum voltage is close to the critical field Hc = 184 Oe, at which fFMR(Hc) = fp/2. It indicates that UISHE(Hc) originates from the detection of parametric ADSW with wave number q = 0. The voltage signal is observed in the field range below 432 Oe. This field correlates with the value Hc1 = fp /(2γ) in Fig. 2a. Above this field, the excitation of any parametric spin wave is impossible; therefore, the voltage signal is suppressed. But at the higher fields, the linear excitation of ADSW takes place at the HFMR, at which fFMR(HFMR) = fp. In Fig. 2, the field Hc2= Hc1/2=fp/(4γ) corresponds to the upper limit on H for the possible decays of parametric magnons with the frequency fp/ 2 into two secondary parametric ones at a frequency fp/4. Measurements with a smaller field step show that, in some field ranges, the UISHE (H) dependence has additional features, which can be explained by parametric excitation of various groups of magnons. For example, in a field near Hc3 = 100 Oe, the nonmonotonic behavior of the UISHE (H) dependence is apparently due to the magnon confluence process, for which the condition fFMR (Hc3) = fp /3 is satisfied [8]. For certain ranges of fields and powers, the data of Fig. 2b can be fitted as UISHE (P, H) ~ (P-Pth (H))1/2, where the fitting parameter Pth (H) ≈ 0.4 mW can be interpreted as a threshold power. We explain the low threshold obtained by the high efficiency of electric power transmission into the acoustic pump confined in the phononic cavity - high-Q hybrid HBAR. This work was carried out in the framework of the State task 0030-2019-0013 "Spintronics" and with partial support of the RFBR (Project No. 20-07-01075).

**References:**

1. M. Weiler, H. Huebl and F. S. Goerg, Phys. Rev. Lett., Vol.108, p.176601 (2012). 2. P. Chowdhury, A. Jander and P. Dhagat, IEEE Magn. Lett., Vol. 8, p.1 (2017). 3. H. Keshtgar, M. Zareyan and G. E. Bauer, Solid State Commun., Vol.198, p.30 (2014). 4. I. Lisenkov, A. Jander and P. Dhagat, Phys. Rev. B., Vol.99, p.184433 (2019). 5. N. I. Polzikova, S. G. Alekseev, I. I. Pyataikin., AIP Adv., Vol.8, p.056128 (2018). 6. N. Polzikova, S. Alekseev, V. Luzanov, J. Magn. Magn. Mater., Vol. 479, p.38 (2019). 7. S. G. Alekseev, S. E. Dizhur and N. I. Polzikova, Appl. Phys. Lett., Vol.117. p.072408 (2020). 8. T. B. Noack, V. I. Vasyuchka and D. A. Bozhko, Phys. Stat. Sol. b, Vol.256. p.1900121(2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d9e5c5203a96b021bee099c786fa45d6.jpg)
Fig.1 (a) Schematic of hybrid HBAR for ADSW excitation and acoustic spin pumping. The rf voltage V is applied across the piezoelectric transducer sandwiched between thin-film Al electrodes. The transducer launches and detects a bulk shear acoustic waves, which propagate vertically. (b) Left panel – the fragment of HBAR spectrum, containing two resonant frequencies fn and fn-1 at zero magnetic field. Right panel –3D colour plot UISHE(f,H) . The red points correspond to positions of HBAR resonant frequency fn positions. The calculated frequencies fMER(H) and fFMR(H) are shown by black lines.

![](https://assets.underline.io/uploads/markdown_image/1/image/c6be37479dfd46f03c0afe4c66f67145.jpg)
Fig. 2. (a) Dependences of spin wave frequencies at q = 0 on the magnetic field: f = fH(0) at θ=0; f = fFMR at θ=90 deg (θ is the angle between wave vector and magnetic field), fD =fH(0)+fM /2- upper boundary of dipole (non-exchange) surface magnetostatic waves, fp = fn =2.412 GHz. (b) 3D plot represents UISHE(H, P) measured at fp = fn = 2.412 GHz. Red lines – power dependences UISHE(Hc, P) and UISHE(Hc2, P).

technical paper

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

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

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.

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

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.

 Spin pumping in embedded lateral nanostructures in Fe60Al40

The use of a nonmagnetic (NM) capping layer on top of a ferromagnetic (FM) layer can efficiently increase the Gilbert damping parameter when the choice of the NM layer is a heavy metal (HM)[1][2]. Spin pumping is an efficient method for the generation of spin currents in FM/NM bilayer films where magnetization precession driven by ferromagnetic resonance (FMR) pumps spin current into NM layer via spin angular momentum transfer[3][4]. The saturation magnetization, Gilbert damping and spin mixing conductance are the critical parameters for efficient spin pumping mechanism. An anti-damping torque can be generated by the application of external DC to the NM layer due to the involvement of Rashba spin-orbit interaction [5][6]. Nevertheless, this procedure reduces the efficiency of the device operation [7]. On the other hand, lower damping value can be achieved for the smaller or comparable thickness of heavy metal NM layer to its spin diffusion length in absence of external DC[8]. In this scenario, a non-equilibrium spin accumulation occurs at the interface due to Rashba spin orbit interaction, which does not allow dissipation of spin angular momentum at the interface. As a result, an anti-damping effect can be observed in FM/HM bilayer system. Heavy metals such as Pt, Ta, etc. show high spin-orbit coupling (SOC) and possess short spin diffusion length up to few nm[9] Bilayers such as Permalloy(Py)/Tantalum(Ta) and CoFeB/Ta has been extensively studied in this context[2], [10]. CoFe alloys as a choice of FM layer provides high saturation magnetization and the composition of the CoFe alloy plays a vital role as the concentration of Co and Fe tune the saturation magnetization and coercivity[11], [12]. Therefore, a systematic variation of NM layer thickness and its effect on magnetization dynamics of CoFe alloy offers the possibility of optimization of Gilbert damping parameter and exploration of interfacial phenomena. In this work, we report a comprehensive study of static and dynamic magnetic properties of a series of sample considering Co50Fe50 and Ta as FM and NM layer respectively. A series of Co50Fe50 (20 nm)/Ta (t nm), henceforth CoFe (20)/Ta (t), samples were deposited on Si substrates at a base pressure of 2×10-7 Torr using UHV magnetron sputtering system. The thickness of the Ta layer was varied as 0, 2, 5, 10, 20, and 30nm. In-plane magnetic hysteresis measurements were carried out using magneto-optical Kerr effect (MOKE) technique with a field variation from -50 mT to 50 mT. A lock-in based FMR technique was used to study the magnetization dynamics where samples were placed on a coplanar waveguide (CPW) in flip-chip configuration. FMR responses were recorded by varying the magnetic field from -300mT to +300mT at a fixed excitation frequency in field sweep mode. The frequency was varied from 2-18 GHz with a step of 1 GHz. MOKE measurements revealed that there were almost negligible variations in coercive fields (HC) for all samples except for CoFe (20)/Ta (2). Fig.1 shows the variation of HC as a function of Ta thickness. The HC for bare CoFe and CoFe (20)/Ta (2) sample was 24 mT and 19 mT respectively. The drop in HC for CoFe (20)/Ta (2) sample may occur due to various reason such as interface strain, variation of microstructure or oxidation at the surface. FMR measurements were performed to investigate the magnetization dynamics of our samples. The linewidth (ΔH), resonance field (Hres), magnetic anisotropy field (HK), saturation magnetization (4πMs), effective Gilbert damping (αeff) and spin mixing conductance (g↑↓) were extracted by fitting the experimental spectra to the appropriate fitting equation. Hres for our samples were found invariant irrespective of Ta layer thickness, which was clear evidence of negligible extrinsic two magnon scattering contribution to the overall damping [13]–[15]. The minimum and maximum 4πMs values were obtained as 1756 mT and 1878 mT for CoFe (20)/Ta (2) and CoFe (20)/Ta (30) sample respectively. 1872 mT was obtained for bare CoFe (20) sample. HK was almost unchanged for all the samples except for CoFe (20)/Ta (2) sample where it was reduced slightly to -105 mT. In-homogenous linewidth broadening (ΔH0) for our samples was varying in between (70 ~ 90 mT). Fig.2 represents the variation of (αeff) as a function of Ta thickness. FMR measurement revealed that there was a significant reduction in αeff for CoFe (20)/Ta (2) sample i.e. 0.041 as compared to bare CoFe (20) sample i.e. 0.068. The sudden decrease in αeff can be attributed to Rashba spin-orbit interaction at the interface. The capping layer thickness of Ta in this sample is lower than the spin diffusion length of Ta which is 2.7 nm [9]. Hence, the non-equilibrium spin accumulation at the interface doesn’t dissipate their spin angular momentum in the regime of spin diffusion length, which leads to the anti-damping phenomena and ultimately reduces the damping. αeff was further increased to 0.055 for CoFe (20)/Ta (5) sample and saturated to 0.049 for the higher thickness of Ta capping layer. An anomalous trend in αeff was observed due to the absence of DC current in the NM layer and this behaviour is consistent with the earlier report on Py/Ta bilayer [8]. The maximum g↑↓ was obtained as 38.7 x 1018 m-2 for CoFe (20)/Ta (2) sample. It is expected due to the enhancement of Δα with the involvement of Rashba spin orbit interaction and higher thickness of FM layer.

**References:**

[1] S. Azzawi et al., “Evolution of damping in ferromagnetic/nonmagnetic thin film bilayers as a function of nonmagnetic layer thickness,” Phys. Rev. B, vol. 93, no. 5, pp. 1–6, Feb. (2016). [2] E. Montoya et al., “Spin transport in tantalum studied using magnetic single and double layers,” Phys. Rev. B, vol. 94, no. 5, p. 054416, Aug. (2016). [3] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, “Spin pumping and magnetization dynamics in metallic multilayers,” Phys. Rev. B, vol. 66, no. 22, p. 224403, Dec. (2002). [4] M. Jamali, A. Klemm, and J.-P. Wang, “Precessional magnetization induced spin current from CoFeB into Ta,” Appl. Phys. Lett., vol. 103, no. 25, pp. 1–5, Dec. (2013). [5] A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, “New perspectives for Rashba spin–orbit coupling,” Nat. Mater., vol. 14, no. 9, pp. 871–882, Sep. (2015). [6] G. Allen, S. Manipatruni, D. E. Nikonov, M. Doczy, and I. A. Young, “Experimental demonstration of the coexistence of spin Hall and Rashba effects in β-tantalum/ferromagnet bilayers,” Phys. Rev. B, vol. 91, no. 14, pp. 1–9, Apr. (2015). [7] S. E. Barnes, J. Ieda, and S. Maekawa, “Rashba Spin-Orbit Anisotropy and the Electric Field Control of Magnetism,” Sci. Rep., vol. 4, no. 1, pp. 1–5, May (2015). [8] N. Behera, S. Chaudhary, and D. K. Pandya, “Anomalous anti-damping in sputtered β-Ta/Py bilayer system,” Sci. Rep., vol. 6, pp. 1–9, May (2016). [9] M. Morota et al., “Indication of intrinsic spin Hall effect in 4d and 5d transition metals,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 83, pp. 1–5, (2011). [10] V. Lauer, P. Pirro, B. Heinz, M. Geilen, and A. V Chumak, “The role of the non-magnetic material in spin pumping and magnetization dynamics in NiFe and CoFeB multilayer systems,” vol. 163901, pp. 1–9, (2015). [11] A. Melloul and A. Kharmouche, “Synthesis, structure and magnetic properties of CoxFe100–x thin films thermally evaporated onto Si (111) substrate,” J. Mater. Sci. Mater. Electron., vol. 30, no. 14, pp. 1–7, Jul. (2019). [12] S.-M. Ahn and G. S. D. Beach, “Crossover between in-plane and perpendicular anisotropy in Ta/Co x Fe 100- x /MgO films as a function of Co composition,” J. Appl. Phys., vol. 113, no. 17, pp. 1–3, May (2013). [13] J. Lindner et al., “Non-Gilbert-type damping of the magnetic relaxation in ultrathin ferromagnets: Importance of magnon-magnon scattering,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 68, no. 6, pp. 1–4, (2003). [14] K. Lenz, H. Wende, W. Kuch, K. Baberschke, K. Nagy, and A. Jánossy, “Two-magnon scattering and viscous Gilbert damping in ultrathin ferromagnets,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 73, no. 14, pp. 1–6, (2006). [15] N. Behera, A. Kumar, S. Chaudhary, and D. K. Pandya, “Two magnon scattering and anti-damping behavior in a two-dimensional epitaxial TiN/Py(t Py )/β-Ta(t Ta ) system,” RSC Adv., vol. 7, no. 14, pp. 8106–8117, (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5cc7f9fc85cd12c6667f92610bc761ad.jpg)
Variation of Hc values for different thicknesses of Ta.

![](https://assets.underline.io/uploads/markdown_image/1/image/c14ac435fa75d8bacc4fd5c1de9bff0a.jpg)
Effective Gilbert damping (αeff) as a function of Ta thickness.

Spin Waves and Spin Pumping Driven by Cavity Confined Bulk Hypersonic Waves

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