The term supercurrent relates to a macroscopic dissipation-free collective motion of a quantum condensate and is commonly associated with such famous low-temperature phenomena as superconductivity and superfluidity. Another type of motion of quantum condensates is second sound-a wave of the density of a condensate. Recently, we reported on an enhanced decay of a parametrically induced Bose-Einstein condensate (BEC) of magnons caused by a supercurrent outflow of the BEC phase from the locally heated area of a room temperature magnetic film. Here, we present the direct experimental observation of a long-distance spin transport in such a system. The condensed magnons being pushed out from the potential well within the heated area form a density wave, which propagates through the BEC many hundreds of micrometers in the form of a specific second sound pulse-Bogoliubov waves-and is reflected from the sample edge. The discovery of the long distance supercurrent transport in the magnon BEC further advances the frontier of the physics of quasiparticles and allows for the application of related transport phenomena for low-loss data transfer in perspective magnon spintronics devices.Supercurrent is a macroscopic quantum phenomenon when many bosons (real-or quasiparticles) being selfassembled in one quantum state with minimum energy and zero velocity-a Bose-Einstein condensate (BEC)[1-11]-move as a whole due to a phase gradient imposed on their joint wave function. This phenomenon being mostly associated with resistant-free electric currents of Cooper pairs [12] in superconductors and superfluidity of liquid Helium [13-17] is, however, much more widespread [18][19][20]. It is experimentally confirmed in the quantum condensates of diluted ultracold gases [21,22], of nuclear magnons in liquid 3 He [23-25], of polaritons in semiconductor microcavities [26] and, recently, of electron magnons in room-temperature ferrimagnetic films [27]. Supercurrents being topologically confined often manifest themselves in a form of quantum vortices [21,28,29].The quantum condensate supports another form of motion-second sound [15,30]. Second sound can be considered as elementary excitations of various types, which can propagate in continuous media with an almost linear dispersion law in the long-wavelength limit. The term second sound stems from an analogy with the ordinary sound waves or first sound-the wave oscillations of media density and mechanical momentum. The most well-known example of second sound is anti-phase oscillations of the densities ρ n and ρ s of the normal-fluid and superfluid components of superfluid 4 He, in which the total density ρ = ρ n + ρ s does not oscillate [15]. These oscillations can be associated with temperature waves, because the ratio ρ n /ρ s strongly depends on the local temperature, while ρ in 4 He is practically temperature independent. Some solid dielectrics represent another system type which supports the propagation of temperature waves at low temperatures [31][32][33][34]. In this case, the second soun...

The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mechanism of external injection of bosons by irradiation is required. Here, we present a novel and universal approach to enable BEC of quasi-particles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose-Einstein condensation.Bosons are particles of integer spin that allow for the fundamental quantum effect of Bose-Einstein Condensation (BEC), which manifests itself in the formation of a macroscopic coherent state in an otherwise incoherent, thermalized many-particle system. The phenomenon of BEC was originally predicted for an ideal gas by Albert Einstein in 1924 based on the theory developed by Satyendra Nath Bose. Nowadays, Bose-Einstein condensates are investigated experimentally in a variety of different systems which includes real particles such as ultra-cold gases (1, 2) as well as quasi-particles with the likes of exciton-polaritons (3, 4), photons (5, 6) or magnons (7-9). The phenomenon can be reached by a major decrease in the system temperature or by an increase in the particle density. In order to condensate atomic gases, extremely low temperatures on the order of mK are required since the density of such gases must be very low to prevent their cohesion. In contrast, the quasi-stationary cooling of a quasi-particle system is accompanied by a decrease in its population and prevents BEC. Thus, an artificial injection of bosons is required to reach the threshold for BEC. Since quasi-particle systems allow for high

The influence of an inhomogeneous magnetization distribution on the propagation of caustic-like spin-wave beams in unpatterned magnetic films has been investigated by utilizing micromagnetic simulations. Our study reveals a locally controllable and reconfigurable tractability of the beam directions. This feature is used to design a device combining split and switch functionalities for spin-wave signals on the micrometer scale. A coherent transmission of spin-wave signals through the device is verified. This attests the applicability in magnonic networks where the information is encoded in the phase of the spin waves.

Wave-based data processing by spin waves (SW) and their quanta, magnons, is a promising technique to overcome the challenges which CMOS-based logic networks are facing nowadays. The advantage of these quasi-particles lies in their potential for the realization of energy efficient devices on the micro-to nanometer scale due to their charge-less propagation in magnetic materials. In this paper, the frequency dependence of the propagation direction of caustic-like spin-wave beams in microstructured ferromagnets is studied by micromagnetic simulations. Based on the observed alteration of the propagation angle, an approach to spatially combine and separate spinwave signals of different frequencies is demonstrated. The presented magnetic structure constitutes a prototype design of a passive circuit enabling frequency-division multiplexing (FDM) in magnonic logic networks. It is verified that spin-wave signals of different frequencies can be transmitted through the device simultaneously without any interaction or creation of spurious signals. Due to the wave-based approach of computing in magnonic networks, the technique of FDM can be the basis for parallel data processing in single magnonic devices, enabling the multiplication of the data throughput.Multiplexing is a widely used technique of data transmission in telecommunication or computer networks. [1] The common aim of all different realizations of this concept is to transfer multiple data signals through a shared transmission line. [2][3][4][5][6] In view of the different challenges todays CMOS technology is facing, [7] the concept of multiplexing is also very interesting for new approaches of data processing like, for example, the field of magnonics. [8][9][10][11][12][13][14] In this case, spin waves (SW) are used to transport data [15][16][17] and the information can be encoded in their amplitude or phase. [18] This approach is especially interesting since wave-based logic can be realized by utilizing interference effects [19] of the SW as has been shown by, for example, the development of the spin-wave majority gate [20,21] and other interferometer-based devices. [22,23] Aiming at an efficient signal transport in magnonic circuits, spin-wave multiplexers enabling time-division multiplexing have already been experimentally demonstrated. [24,25] In this case, the information carrying spin-wave signals are getting temporally separated, successively transferred through the shared magnonic waveguide and finally allocated to different output waveguides by the spin-wave (de-) multiplexer.In contrast, frequency-division multiplexing (FDM) enables a simultaneous transport of data. [1,26] The bandwidth of the transmission medium is divided into separated frequency channels and the data signals are simultaneously transferred at different frequencies. This approach is heavily used in a broad range of applications, from radio broadcasting and fiber optics to communication satellites. [3][4][5][6] However, since the data handling is realized by transistor-based logic elemen...

Magnonic spin currents in the form of spin waves and their quanta, magnons, are a promising candidate for a new generation of wave-based logic devices beyond CMOS, where information is encoded in the phase of travelling spin-wave packets. The direct readout of this phase on a chip is of vital importance to couple magnonic circuits to conventional CMOS electronics. Here, we present the conversion of the spin-wave phase into a spin-wave intensity by local non-adiabatic parallel pumping in a microstructure. This conversion takes place within the spin-wave system itself and the resulting spin-wave intensity can be conveniently transformed into a DC voltage. We also demonstrate how the phase-to-intensity conversion can be used to extract the majority information from an all-magnonic majority gate. This conversion method promises a convenient readout of the magnon phase in future magnon-based devices.