Spin current is a key concept in spintronics. In nonmagnetic metals, the spin-orbit coupling has been utilized for the spin current generation. Recently, an alternative scheme using emergent magnetic fields in moving media is demonstrated [1-5]. In this talk, we will present our recent results on spin transport in nonmagnetic metals driven by a variety of emergent magnetic fields originating from: 1. Liquid metal flow [2,3]. 2. Elastic motion [2,4]. 3. Rigid rotation [1,5]. 4. Non-uniform conductivity of gradient material [6]. 5. Surface plasmon polaritons [7,8]. Firstly, we consider the spin-current generation in moving media. In a moving media, such as elastic materials with the Rayleigh type surface acoustic wave is excited or a pipe flow of liquid metal, the vorticity field couples to conduction electron spin. As a result, the mechanical angular momentum of the moving media is converted into spin angular momentum. In particular, a spin current is generated along the vorticity gradient [2,3,4]. It should be noted that the mechanism using the spin-vorticity coupling is free from the strength of the spin-orbit coupling, and thus, weak spin-orbit coupling materials such as Cu can be utilized for the spin-current source [4]. In a rigid rotating metal, the conventional spin-orbit coupling is augmented due to the emergent magnetic field originating from mechanical rotation [1]. The mechanically induced spin-orbit coupling leads to the spin Hall effect [1]. We introduce a theory of the mechanical analog of the spin Hall effect and an experimental demonstration using magneto-optical detection of spin accumulation under the influence of mechanical rotation [5]. Next, we will discuss our recent experimentally demonstration of the nonreciprocal generation of spin current in a surface-oxidized copper film [6]. This nonreciprocity relies on the transfer of angular momentum from the velocity field of conduction electrons' collective motion. Finally, we consider a mechanism of angular momentum conversion from a transverse optical spin in surface plasmon polaritons (SPPs) to conduction electron spin. Conduction electrons in the metal follow the SPP's SPP's transversally spinning electric field, and the resulting orbital motions create inhomogeneous static magnetization in the metal. We will also present an experimental demonstration of the SPPs-induced spin current generation [8]. Such conversion from light to a spin current can be used as a coupler in next-generation spintronic computing with optical data transfer or storage.

**References:**

[1] M. Matsuo et al., Phys. Rev. Lett 106, 076601 (2011) [2] M. Matsuo et al., Phys. Rev. B 87, 180402(R)(2013); Phys. Rev. B 96,020401(R) (2017). [3] R. Takahashi et al., Nat. Phys. 12, 52 (2016); Nat. Comm. 11, 3009 (2020). [4] D. Kobayashi et al., Phys. Rev. Lett. 119, 077202 (2017). [5] A.Hirohata et al., Sci.Rept. 8, 1974 (2018). [6] G. Okano et al., Phys. Rev. Lett. 122, 217701 (2019). [7] D. Oue and M. Matsuo, Phys. Rev. B 101, 161404(R) (2020). [8] T.J. Wijaya et al., arXiv:2004.12348

**Images:**

 Spin transport driven by emergent magnetic fields

Spintronics has been expanding its fields to cover not only electronics and magnetism but also photonics, caloritronics and mechanics in recent years. Among them, photoexcitation using circularly polarised light has been commonly used to generate a spin polarised electrical current mainly in a semiconductor [1]. However, the linkage between a spin current and a propagating surface plasmon polariton (SPP) has not been well investigated theoretically until recently [2]. SPPs are generated in a PHz regime in a non-magnetic metal, which can generate a magnetisation gradient and a resulting spin current. In this study, we have experimentally measured the SPP generated spin current using an inverse spin Hall effect and confirmed it agrees with the above theoretical prediction. A high vacuum sputtering system (PlasmaQuest, HiTUS) was used to deposit 20 nm thick Ag films on a thermally oxidised Si substrate. The films were also patterned into a Hall bar with the width of 1.2 mm and the length of 11 mm. By placing a prism (ThorLab, N-BK7) on the surface of the Hall bar, the Kretschmann arrangement was achieved for SPP introduction by a semiconductor laser (Thorlabs, LDM635 with the wavelength of 635 nm and the power of 0.4 mW). As shown in Fig. 1, a linear polariser and a half-wave plate (Thorlabs, SM05 mounted zero-order 633 nm) were used to generate both s- and p-polarisations. The spot size of the incident beam was then controlled using a pair of objective and a convex lens. The measured laser spot size was 1.73 mmf. The incident angle q of the beam to the prism was controlled by a mirror. The generated spin current was detected using an inverse spin Hall effect as schematically shown in Fig. 3. The source meter (Keithley, 2400) was used to detect the spin Hall voltage by connecting electrical contacts at the diagonal corners of the continuous film and the ends of the Hall bars. The incident angle q was adjusted to show the largest Hall voltage. The measurements were carried out with 600~1,000 repetitions with 0,1 ms interval, providing an average value with a standard deviation. A source current was set to be 0.0 and 0.1 mA for the Hall voltage and resistance measurements, respectively. The continuous films were measured to demonstrate the spin current generation by SPP as shown in Fig. 1a. Ag, Pt and W films were used for the inverse spin Hall measurement with and without a prism. In order to subtract any parasitic effects, e.g., spin caloritronic and photovoltaic effects induced by the laser introduction, a spin current generated by the electro-motive force Iemf was first estimated by subtracting the current generated by the electro-motive force with and without the prism. The spin current generated by SPP ISPP was then estimated by taking the difference between those generated by s- and p-polarisations since only the p-polarised light generates SPP. By solving the wave-number matching condition between the laser and SPP, the plasma frequency of Ag is estimated to be 2.18 PHz. ISPP is estimated to be (2.128 ± 0.281) and (6.650 ± 0.169) µA for the Ag continuous film and Hall bar, respectively, confirming the SPP-induced spin currents. Such a new linkage between spintronics and photonics and lead to a new coupler to convert optical data signals into spin currents for processing and storage and vice versa.

**References:**

[1] A. Hirohata, "Optically Induced and Detected Spin Current," in Spin Current S. Maekawa, S. O. Valenzuela, E. Saitoh and T. Kimura (Eds.) (Oxford University Press, Oxford, UK, 2012) p. 49-64. [2] D. Oue and M. Matsuo, New J. Phys. 22, 033040 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3bcba07ccbb8f6e4d8383f907974c798.jpg)
Fig. 1 Schematic diagram of the spin current generation by SPP.

 Spin Current Induced by a Surface Plasmon Polariton

Einstein-de Haas (EdH) effect is the fundamental phenomenon that the microscopic spin angular momentum is converted to the angular momentum of mechanical rotation. A mechanical torque due to the EdH effect, the magnitude of which is proportional to the time derivative of the magnetization, is difficult to be detected, which keeps its practical application away. However, recent development of microfabrication technology has enabled to sensitively detect the tiny EdH torque using micro-fabricated mechanical resonators [1,2]. These findings show that the EdH effect can be utilized for the new principle of the mechanical torque generation in sub-micron scale device. Moreover, it was demonstrated that the ultrafast demagnetization due to the laser heating excited the transverse strain wave in a Fe film due to the EdH effect, where the timescale and conversion efficiency of the angular momentum transfer were quantitatively estimated [3]. Rayleigh-type surface acoustic waves (RSAWs), the displacement of which oscillates elliptically, have been widely used to excite the spin waves in a ferromagnetic thin film via the magnetoelastic interaction [4]. Recently, as the phenomena based on the angular momentum conversion from the lattice rotation to the magnetization or electron spin, the gyromagnetic spin-wave excitation [5] and the spin current generation in a nonmagnetic metal with a weak spin-orbit coupling [6] were demonstrated. In this study, we demonstrate both acceleration and deceleration of RSAW velocity in the ferromagnetic (FM) film based on the EdH effect. When the spin-wave is gyromagnetically excited by RSAW propagation through the FM film, the EdH torque is generated in the FM lattice as the back action of the spin-wave resonance (SWR) (Fig. 1(a)). As shown in Fig. 1(a), the direction of EdH torque is opposite to the time derivative of the magnetization. We theoretically expect that the transverse velocity of RSAW can be modulated by the EdH torque, resulting in the phase change of RSAW propagation. In the experiment, we successfully observed the phase change of RSAW propagation, whose magnitude and variation were consistent with our analytical prediction. Figure 1(b) shows the schematical experimental setup for measuring the phase change of RSAW. A pair of inter-digital transduces (IDTs) consisting of Ti(3)/Au(30) is fabricated on a piezoelectric LiNbO3 substrate by the electron beam evaporation. The numbers in the parentheses indicate the layer thickness in nanometers. The width and space of the electrode of IDT are 550 nm. The Ni81Fe19 (NiFe) film with a lateral size of 400×400 μm2 is sputtered between a pair of IDTs. By applying a microwave with the fundamental frequency of RSAW excitation into one of IDTs, RSAWs are excited via the piezoelectric effect. The RSAWs propagating through the NiFe film are electrically detected by the other of IDTs using a vector network analyzer (VNA) as the inverse process of the RSAW excitation. Figures 2(a) and 2(b) show the reduced RSAW energy dissipation ΔPnorm and phase difference Δθ, respectively, as a function of external magnetic field swept in the direction parallel to the RSAW wave vector at the RSAW frequency of 1.75 GHz. Steep peaks appear at 4.6 and -4.0 mT in Fig. 2(a), showing that the spin-wave is excited because the values of the resonant field and resonant frequency are matched with the spin wave dispersion of a 20-nm-thick NiFe film. A bipolar change of Δθ is observed in the vicinity of the resonance field of spin-waves. From the angle between the applied external field and RSAW wave vector, it can be seen that the spin-wave is excited via gyromagnetic effect, not the magnetoelastic coupling [5]. The increase and decrease in Δθ can be explained by our analytical model consisting of the elastic motion equation with the EdH torque term. The maximum value of phase change Δθmax is -0.035 rad at 5.0 mT. This value is as large as that in case using the magnetoelastic coupling in a single Ni film [7]. In addition, the order of Δθmax is comparative to the value analytically obtained by assuming a loss-less conversion of the angular momentum. The consistency in Δθmax suggests that the EdH effect is robust in the angular translation from the magnetization to the lattice in the gigahertz regime.

**References:**

[1] K. Harii, et. al., Nat. Commun. 10, 2616 (2019). [2] K. Mori, et. al., Phys. Rev. B 102, 054415 (2020). [3] C. Dornes, et. al., Nature 565, 209 (2019). [4] M. Weiler, et. al., Phys. Rev. Lett. 106, 117601 (2011). [5] Y. Kurimune, et. al., Phys. Rev. Lett. 124, 217205 (2020). [6] D. Kobayashi, et. al., Phys. Rev. Lett. 119, 077202 (2017). [7] R. Sasaki, et. al., Phys. Rev. B 95, 020407 (R) (2017). [8] S. Tateno, et.al., submitted.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/95a80b47499a8efb662564ebc84f2325.jpg)
Fig. 1 (a) Schematic of the stress based on EdH effect σEdHzx and the EdH torque τEdH in the Ni-Fe lattice. The direction of the EdH torque is opposite to the time derivative of the magnetization. (b) Experimental setup for measuring the phase changeΔθ of RSAW using a VNA. The external field is applied along the RSAW propagation direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/6d3a013484d0f414781f2f3ebf4436f3.jpg)
Fig. 2 The field dependence of (a) ΔPnorm and (b) Δθ at the fundamental frequency of RSAW excitation, respectively. The red solid line in (b) shows the result of the best fit using our analytical model.

 Velocity Modulation of Surface Acoustic Waves via Einstein-de Haas Effect

*Session Chair: Atsufumi Hirohata, University of York*

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CA: Spin Conversion Efficiency by Various Methods Towards Device Applications

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CE: Spin Currents

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Mamoru Matsuo

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Spin transport driven by emergent magnetic fields

Spin Current Induced by a Surface Plasmon Polariton

Velocity Modulation of Surface Acoustic Waves via Einstein-de Haas Effect

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