The concept of spin current, introduced analogously to the charge current, has gained a great significance in spintronic and magnonic systems. Two distinct types of spin transport mechanisms can be identified. The first one is associated with diffusion of spin-polarized conduction electrons from one part of the system to another, followed by their spin relaxation mainly due to the exchange interaction with the localized electrons. The second mechanism is mediated by the transfer of spin between localized magnetic moments due to their mutual interaction. The latter can be also described as spin transport by propagating spin waves. Interplay between these two phenomena enables generation of propagating spin waves by spin currents carried by conduction electrons. Reciprocally, spin waves can produce spin currents carried by spin-polarized electrons, which is known as spin pumping. In my talk I will discuss several phenomena involving interplay between spin waves and electron spin currents, including the excitation of propagating spin waves by spin polarized electric current [1] and the spin-Hall effect (SHE) [2]. In the first case a simplified model considering only the exchange interaction provides an adequate description of the observed phenomena, based on the conservation of angular momentum in the spin subsystem. However, the physical origin of SHE is the relativistic spin-orbit coupling, which mixes the angular momentum of spin subsystem with that of the lattice. Surprisingly, the same is valid for the magnetic dipole interaction. I will illustrate the importance of mixing between spin and orbital degrees of freedom with the examples of spin-wave pumping experiments [3] and the dynamics of Bose-Einstein condensate of magnons [4].

**References:**

 [1] S. Urazhdin et al. Nature Nanotech. 9 509 (2014) [2] B. Divinskiy et al. Adv. Mater. 1802837 (2018) [3] H. Kurebayashi et al., Nature Mat. 10, 660 (2011). [4] I.V. Borisenko et al., Nature Comm. 11, 1691443 (2020).

**Images:**

 Spin waves and spin currents

Spin wave (SW) based computing i.e. magnonics relies on propagating SW as information carriers. Being quasiparticles, magnons (the SW quanta) have a fine lifetime characterizing the exponential decay of the magnons population. Consequently, up to now, all magnonic devices operate within a short time-window and on short propagation distances. Finding a SW amplification paradigm is hence a prerequisite for the development of magnonics as a credible CMOS alternative. Two schemes are currently envisioned for SW amplification: Parametric pumping1 and spin-orbit-torque amplification (SOT)2. Here we will discuss SOT amplification in BiYIG/Pt bilayer3 (Fig.1). Using micro Brillouin light scattering spectroscopy (µ-BLS) on a 500 nm wide Pt/BiYIG waveguides, we take advantage of the strong BLS signal of BiYIG (nearly two orders of magnitude the one of YIG3) to extensively study the influence of SOT on coherent propagating magnon modes. By passing current in the Pt layer, the spin accumulation resulting from the spin-Hall effect induces a positive torque that compensates the Gilbert damping of BiYIG when the magnetic field orientation is perpendicular to the waveguide axis. At subcritical values, the current has a linear effect that lowers the effective damping, thus significantly increasing the decay length of the propagating magnons, similar to what was observed previously in a YIG/Pt waveguide4. However, by increasing the excitation frequency of these propagating magnons for a constant external field, we observe a gradual but strong decrease of the modulation efficiency of their lifetime in our BiYIG/Pt waveguide. Once the current in the Pt layer reaches a threshold value, the vanishing effective damping allows for the onset of the auto-oscillation regime5 where the thermal magnons get incoherently amplified and the magnetization auto-oscillates in the main uniform mode. However, coherent propagating magnons strongly interact with the auto-oscillations6, preventing the observation of their propagation at continuous supercritical current. To circumvent these non-linear interactions, we study the auto-oscillation transient regime for the first time by performing time-resolved µ-BLS measurements. When the SOT is switched on, the uniform auto-oscillation grows exponentially, in agreement with the Slavin & Tiberkevitch non-linear auto-oscillator model7 in the linear regime limit. The onset of non-linearities only occurs when the auto-oscillation reaches its stable orbital, after few hundreds of nanoseconds typically. Using a rf and DC pulse scheme, we propagate rf-excited magnons before the onset of non-linearities at supercritical currents and observe the amplification of propagating magnons (Fig. 2-a). Similarly to what was observed in the continuous regime at subcritical currents, the modulation efficiency of the propagating magnons lifetime strongly decreases with frequency (Fig. 2-b). This experiment sheds new light on the influence of SOT on propagating magnons and pave the way toward a magnonic spin-wave amplifier using DC current.

**References:**

1 T. Brächer, P. Pirro, and B. Hillebrands, Phys. Rep. 699, 1 (2017). 2 V.E. Demidov, S. Urazhdin, A. Anane, V. Cros, and S.O. Demokritov, J. Appl. Phys. 127, 170901 (2020). 3 L. Soumah, N. Beaulieu, J. Ben Youssef, and A. Anane, Nat. Commun. 9, 3355 (2018). 4 M. Evelt, V.E. Demidov, and A. Anane, Appl. Phys. Lett. 108, 172406 (2016). 5 M. Collet, V. Cros, A. Anane, G. de Loubens, and O. Klein, Nat. Commun. 7, 10377 (2016). 6 B. Divinskiy, S. Urazhdin, S.O. Demokritov, and V.E. Demidov, Nat. Commun. 10, 5211 (2019). 7 A. Slavin and V. Tiberkevich, IEEE Trans. Magn. 45, 1875 (2009).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c591b0f58bbf93bc6d6866a53fdf516.jpg)
Fig. 1 : Schematic representation of the 0.5µm-wide BiYIG/Pt waveguide. The DC current is applied in the Pt along the waveguide axis and a 300nm-wide strip rf-antenna is used to excite propagating magnons. The µ-BLS laser spot is focused from the back of the sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/b8aea6e40370d823a1c720f70ddf0448.jpg)
Fig. 2 : Spin-wave intensity as a function of the distance to the antenna. The experimental curves (solid lines) are linearly fitted (dotted lines) in log scale for 4 frequencies (only 2 shown here) 4.925 GHz (a), 4.95 GHz, 4.975 GHz and 5.0 GHz (b) and 4 DC voltages corresponding to one subcritical current (1.7V) and three supercritical currents (2.2, 2.3 and 2.4V). The FMR is constant during the pulse with value 4.885 ± 0.01 GHz. 
The positive slope at supercritical currents at 4.925 GHz indicates an amplification of the propagating spin-waves (negative effective damping) due to SOT. The damping compensation efficiency gradually decreases as the frequency is increased, and the spin-waves are no longer amplified at 5.0 GHz for the applied voltages.

 Insight on the effect of SOT on propagating magnons: Spin-wave amplification and frequency dependent efficiency

It is now well established that the propagation of spin waves can be controlled by using approaches similar to those used in optics. In recent years particular attention was given to the possibility to controllably focus propagating spin waves. Such focusing can be achieved relatively easily in confined geometries. In the case of extended magnetic films, the implementation of spin-wave focusing appears to be less straightforward. Several approaches have been suggested. However, all of them are rather complex in terms of practical implementation, particularly on the nanoscale. Here, we experimentally demonstrate tight focusing of a spin-wave beam excited in extended nanometer-thick films of YIG by a simple microscopic antenna functioning as a single-slit near-field lens. We show that the focal distance and the minimum transverse width of the focal spot can be controlled in a broad range by varying the frequency/wavelength of spin waves and the antenna geometry. The experimental data are in good agreement with the results of numerical simulations. Our findings provide a simple solution for the implementation of magnonic nanodevices requiring a local concentration of the spin-wave energy.

**References:**

B. Divinskiy, N. Thiery, L. Vila, O. Klein, N. Beaulieu, J. Ben Youssef, S. O. Demokritov, and V. E. Demidov, Appl. Phys. Lett. 116, 062401 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/678744363a23cd07e63934a39dba2cab.jpg)
Fig.1 Schematic of the experiment.

![](https://assets.underline.io/uploads/markdown_image/1/image/224225623364fe1dd737aeb316342533.jpg)
Fig. 2 Measured intensity map of spin waves radiated by the antenna.

 Sub-Micrometer Near-Field Focusing of Spin Waves in Ultrathin YIG Films

*Session Co-Chair: Timo Kuschel, Bielefeld University*

*Session Co-Chair: Matthias Althammer, Walther-Meißner-Institut*

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EA: Spin Angular Momentum Transport: Spin Waves Pushing New Frontiers

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ED: Magnon Spintronics

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Boris Divinskiy

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Presentations

Spin waves and spin currents

Insight on the effect of SOT on propagating magnons: Spin-wave amplification and frequency dependent efficiency

Sub-Micrometer Near-Field Focusing of Spin Waves in Ultrathin YIG Films

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