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Bose-Einstein condensation is one of the most fascinating phenomena predicted by quantum mechanics. It involves the formation of a collective quantum state composed of identical particles with integer angular momentum (bosons), if the particle density exceeds a critical value. To achieve Bose-Einstein condensation, one can either decrease the temperature or increase the density of bosons. It has been predicted that a quasi-equilibrium system of bosons could undergo Bose-Einstein condensation even at relatively high temperatures, if the flow rate of energy pumped into the system exceeds a critical value. Here we report the observation of Bose-Einstein condensation in a gas of magnons at room temperature. Magnons are the quanta of magnetic excitations in a magnetically ordered ensemble of magnetic moments. In thermal equilibrium, they can be described by Bose-Einstein statistics with zero chemical potential and a temperature-dependent density. In the experiments presented here, we show that by using a technique of microwave pumping it is possible to excite additional magnons and to create a gas of quasi-equilibrium magnons with a non-zero chemical potential. With increasing pumping intensity, the chemical potential reaches the energy of the lowest magnon state, and a Bose condensate of magnons is formed.

Early experiments in magnonics were made using ferrite samples, largely due to the intrinsically low magnetic (spin-wave) damping in these materials. Historically, magnonic phenomena were studied on micrometre to millimetre length scales. Today, the principal challenge in applied magnonics is to create sub-micrometre devices using modern polycrystalline magnetic alloys. However, until certain technical obstacles are overcome in these materials, ferrites-in particular yttrium iron garnet (YIG)-remain a valuable source of insight. At a time when interest in magnonic systems is particularly strong, it is both useful and timely to review the main scientific results of YIG magnonics of the last two decades, and to discuss the transferability of the concepts and ideas learned in ferrite materials to modern nano-scale systems.

An attractive direction in next-generation information processing is the development of systems employing particles or quasiparticles other than electrons—ideally with low dissipation—as information carriers. One such candidate is the magnon: the quasiparticle associated with the eigen-excitations of magnetic materials known as spin waves. The realization of single-chip all-magnon information systems demands the development of circuits in which magnon currents can be manipulated by magnons themselves. Using a magnonic crystal—an artificial magnetic material—to enhance nonlinear magnon–magnon interactions, we have succeeded in the realization of magnon-by-magnon control, and the development of a magnon transistor. We present a proof of concept three-terminal device fabricated from an electrically insulating magnetic material. We demonstrate that the density of magnons flowing from the transistor’s source to its drain can be decreased three orders of magnitude by the injection of magnons into the transistor’s gate.

We demonstrate the functionality of spin-wave logic XNOR and NAND gates based on a MachZehnder type interferometer which has arms implemented as sections of ferrite film spin-wave waveguides. Logical input signals are applied to the gates by varying either the phase or the amplitude of the spin waves in the interferometer arms. This phase or amplitude variation is produced by Oersted fields of dc current pulses through conductors placed on the surface of the magnetic films.Although commonly used for data storage applications, there have been relatively few attempts to employ magnetic phenomena for performing logical operations. The suggested concepts include the control of domain wall movement [1], of magnetoresistance of individual magnetic elements [2], and of a magnetostatic field of a set of magnetic nanoelements [3]. Yet another concept is using spin-wave interferometers. It was discussed theoretically in Refs. [4,5,6], but there was only one experimental demonstration of spin wave logic gate functionality [7], where an one-input NOT gate was implemented in a interferometer-like geometry. In the present work we experimentally demonstrate the functionality of more complicated logic gates based on spin waves.The fabricated prototype of a XNOR logic gate is a direct extension of the NOT gate from Ref. [7] which was based on a Mach-Zehnder interferometer. For its implementation the reference interferometer arm of the NOT gate is replaced by an arm identical to the signal arm. Controlling phases accumulated by the spin waves in both arms allows one to perform the XNOR operation.Demonstrating the functionality of a NAND logic gate is a considerable step forward in the development of spin wave logic compared to the NOT and XNOR gates. Firstly because the NAND function belongs to a class of universal functions which means that combining NAND gates allows one to construct gates of other types. Secondly because for its implementation, we use here a new physical principle: direct control of spin wave amplitudes in the interferometer arms.Figure 1(b) shows the principle setup of an exclusive not OR (XNOR, also called logical equality) gate. It consists of two arms of a spin-wave Mach-Zehnder interferometer implemented as ferrite film structures. Spin waves are inserted in both arms using microstrip antennas connected to a common microwave pulse source, thus guaranteeing the same phase in both arms. The spin waves are phase-coherently detected using microstrip antenna detectors. The signals of both arms are brought to interference electronically. The phase accumulated by the spin waves on their paths through the two arms is controlled by applying dc currents I 1 and I 2 to the arms. Figure 1(a) shows phase inserted due to a current in an interferometer arm. One sees a linear dependence of the accumulated phase on the current. One also sees that the phase characteristics in both arms are identical.The currents I 1 and I 2 serve as logical inputs, where a logical zero is represented by I = 0 A and a logical one by the cur...