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...

Using a submillimeter-sized YIG (yttrium-iron-garnet) sphere mounted in a magnetic-field-focusing cavity, we demonstrate an ultrahigh cooperativity of 10 5 between magnon and photon modes at millikelvin temperatures and microwave frequencies. The cavity is designed to act as a magnetic dipole by using a novel multiple-post approach, effectively focusing the cavity magnetic field within the YIG crystal with a filling factor of 3%. Coupling strength (normal-mode splitting) of 2 GHz (equivalent to 76 cavity linewidths or 0.3 Hz per spin) is achieved for a bright cavity mode that constitutes about 10% of the photon energy and shows that ultrastrong coupling is possible in spin systems at microwave frequencies. With straightforward optimizations we demonstrate that this system has the potential to reach cooperativities of 10 7 , corresponding to a normal-mode splitting of 5.2 GHz and a coupling per spin approaching 1 Hz. We also observe a three-mode strong-coupling regime between a dark cavity mode and a magnon-mode doublet pair, where the photon-magnon and magnon-magnon couplings (normal-mode splittings) are 143 and 12.5 MHz, respectively, with a HWHM bandwidth of about 0.5 MHz.

Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the logical True, an absence the logical False. Logical functions are calculated via interaction between roots. Two types of two-inputs-two-outputs gates are proposed: a gate x, y → xy, x + y where root apexes are guided by gravity and a gate x, y → xy, x where root apexes are guided by humidity. We propose a design of binary half-adder based on the gates.

Scattering of backward volume magnetostatic spin waves from a one-dimensional magnonic crystal, realized by a grating of shallow grooves etched into the surface of an yttrium-iron garnet film, was experimentally studied. Rejection frequency bands were clearly observed. The rejection efficiency and the frequency width of the rejection bands increase with increasing groove depth. A theoretical model based on the analogy of a spin-wave film-waveguide with a microwave transmission line was used to interpret the obtained experimental results.Comment: 4 pages, 3 figure

We have studied experimentally the excitation of propagating spin-wave modes of a microscopic Permalloy-film waveguide by a stripe antenna. We show that due to the strong quantization of the spin-wave spectrum, the excitation of particular modes has essentially different frequency dependencies leading to a nonmonotonous variation of the modulation depth of the resulting spin-wave beam as a function of the excitation frequency. In addition, we address the effect of nonreciprocity of spin-wave excitation and found that for the case of Permalloy microwaveguides this effect is much weaker pronounced than for waveguides made from dielectric magnetic films with low saturation magnetization.

Spin-wave excitations (magnons) are investigated in a one-dimensional (1D) magnonic crystal fabricated out of Ni80Fe20 nanowires. We find two different magnon band structures depending on the magnetic ordering of neighboring wires, i.e., parallel and antiparallel alignment. At a zero in-plane magnetic field H the modes of the antiparallel case are close to those obtained by zone folding of the spin-wave dispersions of the parallel case. This is no longer true for nonzero H which opens a forbidden frequency gap at the Brillouin zone boundary. The 1D stop band gap scales with the external field, which generates a periodic potential for Bragg reflection of the magnons.

Using space-, time-and phase-resolved Brillouin light scattering spectroscopy we investigate the difference in phase of the two counterpropagating spin waves excited by the same microwave microstrip transducer. These studies are performed both for backward volume magnetostatic waves and magnetostatic surface waves in an in-plane magnetized yttrium iron garnet film. The experiments show that for the backward volume magnetostatic spin waves (which are reciprocal and excited symmetrically in amplitude) there is a phase difference of π associated with the excitation process and thus the phase symmetry is distorted. On the contrary, for the magnetostatic surface spin waves (which are non-reciprocal and unsymmetrical in amplitude) the phase symmetry is preserved (there is no phase difference between the two waves associated with the excitation). Theoretical analysis confirms this effect.

We demonstrate a current-controlled, dynamic magnonic crystal. It consists of a ferrite film whose internal magnetic field exhibits a periodic, cosine-like variation. The field modulation is created by a direct current flowing through an array of parallel wires placed on top of a spin-wave waveguide. A single, pronounced rejection band in the spin-wave transmission characteristics is formed due to spinwave scattering from the inhomogeneous magnetic field. With increasing current the rejection band depth and its width increase strongly. The magnonic crystal allows a fast control of its operational characteristics via the applied direct current. Simulations confirm the experimental results.