The appearance of spontaneous coherence is a fundamental feature of a Bose–Einstein condensate (BEC) and an essential requirement for possible applications of the condensates for classical and quantum computing. Using a magnon BEC in a magnetic crystal, such computing can be performed even at room temperature. Using specially shaped bulk samples of yttrium iron garnet crystal, we developed a novel efficient method of BEC investigation by direct detection of microwave radiation emitted by parametrically driven magnon gas (Fig.1a-b). By using this method, we studied the process of coherence formation in a magnon BEC and demonstrated that no coherent BEC state could be found during the action of a strong magnetic pumping field. At the same time, after the pumping is terminated, the overpopulated magnon gas evolves toward BEC and reaches full coherence, with the width of the magnon radiation spectrum decreasing by more than two orders of magnitude (Fig. 1c). The residual bandwidth is mainly determined by the lifetime of magnons, as expected for a fully coherent BEC consisting of a single magnon state. This direct demonstration of the magnon BEC coherence [1] brings the implementation of room temperature BEC-based computing closer. Moreover, the magnon BEC coupling with dynamic stray fields outside the sample is enabled by a proper choice of the sample shape giving direct spectroscopic access to the BEC. Such an approach can function as a convenient tool for integrating magnetic quantum systems into electrical environments.

![](https://assets.underline.io/uploads/markdown_image/1/image/08092bb8bbc4772d1216c4df47190393.jpg)

(a) Experimental setup for microwave detection of magnon BEC
dynamics.
(b) Bulk BEC mode and one of the edge magnon modes in a cuboid YIG sample. The monotonic blue line schematically shows the profile of the static magnetic field H within the YIG sample. Letters denote three field values: A – deeply inside the sample, B – at the point where the bulk BEC mode becomes evanescent, C – at the sample edge.
(c) Magnon dispersion curves in the middle of the sample (at point A) and near the edge (at point B). The green, blue, and red signal intensity lines show the microwave power spectra registered during 1 µs interval before the end of pumping as well as 2 µs and 4 µs after the pump pulse is turned off.

Evolution of Room-Temperature Magnon Gas toward Coherent Bose–Einstein Condensate

Interaction between quasiparticles of a different nature, such as magnons and phonons, leads to mixing their properties and forming hybrid quasiparticles—hybrid magnetoelastic bosons, also called magnon polarons—in the areas of intersection of individual spectral branches. In garnet ferrite films, such hybridization results in several new phenomena as the resonant increase in the efficiency of the spin Seebeck effect [1,2] and the spontaneous bottleneck accumulation [3] of the magnetoelastic quasiparticles. Similar to the Bose-Einstein magnon condensation (BEC) [4], the latter phenomenon occurs at the bottom of the magnon spectrum in yttrium iron garnet films exposed to microwaves. However, unlike the BEC, which is a consequence of the equilibrium Bose statistics, the bottleneck accumulation is determined by changing interparticle interactions. Studying the transport properties of accumulated quasiparticles [5], we found that such accumulation occurs in two frequency-distant groups: quasiphonons and quasimagnons. These quasiparticles propagate in the film plane as spatially localized beams with distinctly different directions and velocities. The developed theoretical model describes the double accumulation effect. Parametrically pumped magnons scatter through a step-by-step thermalization process towards the lower energy states. At the magnon-phonon hybridization region, the efficiency of nonlinear scattering decreases, and the downward quasiparticle flux slows down. Owing to the bottleneck effect, quasimagnons form a density peak, in which intensity saturates due to their scattering to the lowest branch of the magnon spectrum. The remaining quasimagnons, scattering to phonon states below the magnon spectrum, transform into quasiphonons with vanishing scattering amplitude. These quasiphonons form the second accumulated group. By considering the 2D magnon-phonon spectrum, we determined the wavevectors and frequencies of each group and concluded about the caustic nature of the quasimagnon beams. Due to nonzero group velocity, the accumulated quasiparticles can be used for data transfer in magnon spintronics. Funded by the ERC Advanced Grant 694709 SuperMagnonics and by the DFG within TRR173 – 268565370 (project B04).

Double Accumulation and Anisotropic Transport of Magneto-Elastic Bosons in Yttrium Iron Garnet Films

A spin current - a flow of spin angular momentum - can be carried either by spin-polarized free electrons or by magnons, the quanta of spin waves. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces could transfer energy and angular momentum only along its propagation direction. In this talk, using the data of Brillouin light scattering (BLS) spectroscopy in combination with an extended theory of dipole-exchange spin-wave spectra, I show that in obliquely magnetized magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current without any corresponding transverse transport of energy [1]. It is found that in the case of oblique magnetization, the transverse profiles of in-plane-propagating dipole-exchange spin waves are formed by two co-propagating partial waves with opposite group velocities. Their superposition results in a traveling wave pattern, which carries angular momentum and can be treated as a transversal spin current. Its existence is evidenced by the behavior of thermal spectra of magnons in a yttrium iron garnet film measured in a wide range of wavenumbers using our novel wavevector-resolved BLS setup. In the case of an external excitation of the spin-wave modes carrying the transversal spin current, the angular momentum conservation law would lead to mechanical deformations or/and to the rotation of the magnetic film as a whole, which could be detected using the existing methods of spin mechatronics [2]. Furthermore, the presence of the unconventional spin current may be directly electrically detected [1, 3]. We believe that these non-trivial properties of spin-wave modes may be used in the future to control the effects of spin pumping or/and to generate spin currents in nano-scale spintronic signal processing and signal-generating devices. Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Research Unit TRR 173–268565370 “Spin+X” (projects B01 and B04), as well as financial support by the European Research Council within the AdG SuperMagnonics, is gratefully acknowledged. The work was also supported in part by the US National Science Foundation, by the US Air Force Office of Scientific Research, and by the Oakland University Foundation.

**References:**

[1] D. A. Bozhko, H. Yu. Musiienko-Shmarova, V. S. Tiberkevich, A. N. Slavin, I. I. Syvorotka, B. Hillebrands, and A.A. Serga, Unconventional spin currents in magnetic films, Phys. Rev. Research 2, 023324 (2020). [2] M. Matsuo, E. Saitoh, and S. Maekawa, Spin-mechatronics, J. Phys. Soc. Jpn. 86, 011011 (2017). [3] P. M. Gunnink, R. A. Duine, and A. Rückriegel, Electrical Detection of Unconventional Transverse Spin Currents in Obliquely Magnetized Thin Films, Phys. Rev. B 101, 220407 (2020).

**Images:**

 Unconventional spin currents in obliquely magnetized magnetic films

Nowadays a lot of effort is put into the creation of a practical quantum computer. For this ambitious aim different research fields propose and investigate new materials and technologies. One of such promising systems, a magnon Bose-Einstein condensate (BEC)in magnetic crystals, may allow the creation of magnon-BEC-based qubit at room temperature. A prerequisite for such a qubit is the appearance of spontaneous coherence in magnon BEC. Also, the presence of coherence of the magnon Bose-Einstein condensate is essential for understanding such fundamental properties of it as the possibility of a dissipative magnon supercurrent [1], excitation of Josephson oscillations [2], and propagation of Bogoliubov waves [3]. In most of the previous studies in this field, the magnon BEC is investigated by means of Brillouin light scattering (BLS) spectroscopy [4,5] delivering information about the spectral density of a magnon gas. Unfortunately, due to the limited frequency resolution of the optical Fabry-Pérot interferometers used in BLS facilities, the conventional BLS technique does not allow one to prove the coherence of a magnon BEC directly. The insufficient frequency resolution makes it impossible to separate the relaxation dynamics of condensed and thermal magnons. Moreover, the possible outflow of the condensate from a spatially localized probing light spot complicates the interpretation of the obtained experimental results (see [6] and the corresponding discussion in [7]). For all these reasons only indirect indications of the coherency, obtained on the magnon BEC in magnetic crystals, could be provided yet. Up to this day, a decisive proof of the full coherence magnon BEC remained elusive. In our work, we report a first direct experimental observation of the evolution of magnon BEC towards full coherence, whose degree is limited only by the natural processes of the magnon relaxation into the crystal lattice. To achieve this, we use a novel concept that enhances the coupling of the parametrically-driven magnon system with the probing electromagnetic field. The obtained electric signal was investigated time-resolved by a spectrum analyzer to reach the required frequency resolution necessary for the proper display of the magnon BEC state. A pulsed electromagnetic parametric pumping was used to inject magnons, increase, thus the chemical potential of the magnon gas, and trigger the BEC formation process. It is found that the radiation spectrum picked up after the terminization of a pump pulse is narrowed by two orders of magnitude, compared to the broad-band spectrum obtained during the process of parametric pumping. The resulting spectrum width is only limited by the magnon relaxation frequency. We study this spectrum evolution in many details and identify the conditions for BEC creation. We believe that this direct demonstration of the coherence of the magnon BEC brings the implementation of the room temperature BEC-based computing closer. This research was funded by the European Research Council within the Advanced Grant No. 694709 “SuperMagnonics” and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Transregional Collaborative Research Center – TRR 173 – 268565370 “Spin+X” (project B01). The authors are grateful to G. A. Melkov and H. Yu. MusiienkoShmarova for the fruitful discussions.

**References:**

[1] D. A. Bozhko, A. A. Serga, P. Clausen, V. I. Vasyuchka, F. Heussner, G. A. Melkov, A. Pomyalov, V. S. L’vov, and B. Hillebrands, Supercurrent in a room-temperature Bose-Einstein magnon condensate, Nat. Phys. 12, 1027 (2016). [2] A. J. E. Kreil, A. Pomyalov, V. S. L’vov, H. Yu. Musiienko-Shmarova, G. A. Melkov, A. A. Serga, and B. Hillebrands, Josephson oscillations in a room-temperature Bose-Einstein magnon condensate, arXiv:1911.07802. [3] D. A. Bozhko, A. J. E. Kreil, H. Yu. Musiienko-Shmarova, A. A. Serga, A. Pomyalov, V. S. L’vov, and B. Hillebrands, Bogoliubov waves and distant transport of magnon condensate at room temperature, Nat. Commun. 10, 2460 (2019). [4] S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping, Nature 443, 430–433 (2006). [5] A. A. Serga, V. S. Tiberkevich, C. W. Sandweg, V. I. Vasyuchka, D. A. Bozhko, A. V. Chumak, T. Neumann, B. Obry, G. A. Melkov, A. N. Slavin, and B. Hillebrands, Bose-Einstein condensation in an ultra-hot gas of pumped magnons, Nat. Commun. 5, 3452 (2014). [6] V. E. Demidov, O. Dzyapko, S. O. Demokritov, G. A. Melkov, and A. N. Slavin, Observation of spontaneous coherence in Bose-Einstein condensate of magnons, Phys. Rev. Lett. 100, 047205 (2008). [7] A. J. E. Kreil, H. Y. Musiienko-Shmarova, S. Eggert, A. A. Serga, B. Hillebrands, D. A. Bozhko, A. Pomyalov, and V. S. L’vov, Tunable space-time crystal in room-temperature magnetodielectrics, Phys. Rev. B 100, 020406(R) (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/72224fb139fe95447f22f54475f3939d.jpg)
Fig. 1 Sketch of the experimental setup. The sample holder section shows an open waveguide with an internally mounteddielectric resonator. A bulk YIG sample is placed in an opening of the resonator together with a large detection loop to detect the radiated signals from the whole sample volume.

![](https://assets.underline.io/uploads/markdown_image/1/image/84026c2fe3ed134957adcd953bd21b38.jpg)
Fig. 2 Radiated signal of the magnon BEC measured for different times during the free decay of the system. The signals demonstrate a lorentz shape with a FWHM bandwidth of approx. 1 MHz. In normalized view it is visible that the BEC signal demonstrates an unchanged singel-state profile for a long observation period.

 Evolution of room-temperature magnon gas toward coherent Bose-Einstein condensate

**Session chair:** Oleksii Volkov, Helmholtz-Zentrum Dresden-Rossendorf



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Evolution of Room-Temperature Magnon Gas toward Coherent Bose–Einstein Condensate

Double Accumulation and Anisotropic Transport of Magneto-Elastic Bosons in Yttrium Iron Garnet Films

Unconventional spin currents in obliquely magnetized magnetic films

Evolution of room-temperature magnon gas toward coherent Bose-Einstein condensate

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