Magnonics explores precessional excitations of ordered spins in magnetic materials-so-called spin wavesand their use as information and signal carriers within networks of magnonic waveguides. Here, we demonstrate that the nonuniformity of the internal magnetic field and magnetization inherent to magnetic structures creates a medium of graded refractive index for propagating magnetostatic waves and can be used to steer their propagation. The character of the nonuniformity can be tuned and potentially programmed using the applied magnetic field, which opens exciting prospects for the field of graded-index magnonics. Over the past decade, magnonics (the study of spin waves-precessional excitations of ordered spins in magnetic materials [1]) has emerged as one of the most rapidly growing research fields in magnetism [2,3]. Moreover, recent advances in the understanding of fundamental properties of spin waves in magnetic micro-and nanostructures have highlighted magnonics as a potential rival of or complement to semiconductor technology in the field of data communication and processing [4]. The push for miniaturization renders ferromagnetic transition metals and their alloys to be materials of choice for the fabrication of spin-wave devices [5,6]. However, loss reduction, the shortening of the wavelength of studied spin waves, and the associated miniaturization of the implemented magnonic concepts and devices remain major challenges in both experimental research and technological development in magnonics [2,3].In this Rapid Communication, we explore an approach to meet these challenges that is based on the concept of gradedindex (or gradient-index) optics [7]. As applied to spin waves, this concept is based on the following basic ideas. First, the propagation of spin waves is controlled using subwavelength, often continuously varying, magnetic nonuniformities [8,9]. This should minimize scaling of the device size with the magnonic wavelength, in contrast to, e.g., magnonic crystal based approaches [3], and thereby ease the associated patterning resolution requirements. Indeed, nonuniform effective magnetic field and magnetization configurations have been shown to confine [10,11] and channel [12][13][14][15] spin waves, to continuously modify their character [16][17][18], and to enable their coupling to essentially uniform free space microwaves [19,20]. Here, we go further by exploiting in addition the anisotropic dispersion inherent to spin waves dominated by the dynamic magneto-dipole field-so-called magnetostatic spin waves [1]. The symmetry axis of the anisotropic magnetostatic dispersion coincides with the direction of the magnetization [21][22][23]. This anisotropic dispersion leads to the formation of nondiffracting caustic spin-wave beams * Corresponding author: v.v.kruglyak@exeter.ac.uk [24][25][26][27][28][29][30] and to anomalous spin-wave reflection, refraction, and diffraction [31][32][33][34][35]. Here, we explore these ideas in networks of magnonic waveguides [6,8,[12][13][14][15][16][17][18][19][20]24,...

Magnetic memory cells associated with the stress-mediated magnetoelectric effect promise extremely low bit-writing energies. Most investigations have focused on the process of writing information in memory cells, and very few on readout schemes. The usual assumption is that the readout will be achieved using magnetoresistive structures such as Giant Magneto-Resistive stacks or Magnetic Tunnel Junctions. Since the writing energy is very low in the magnetoelectric systems, the readout energy using magnetoresistive approaches becomes non negligible. Incidentally, the magneto-electric interaction itself contains the potentiality of the readout of the information encoded in the magnetic subsystem. In this letter, the principle of magnetoelectric readout of the information by an electric field in a composite multiferroic heterostructure is considered theoretically and demonstrated experimentally using [N×(TbCo2/FeCo)]/[Pb(Mg1/3Nb2/3)O3](1−x)−[PbTiO3]x stress-mediated ME heterostructures.

The features of standing spin waves (SWs) excited during ferromagnetic resonance in three different one-dimensional magnonic crystals (MC) are intensively studied. The investigated magnonic crystals were: an array of air-spaced cobalt stripes, an array of air-spaced permalloy (Py) stripes, and a bi-component MC composed of alternating Co and Py stripes. All MC structures were made by etching technique from Co and Py thin films deposited onto Si substrates. Two configurations are considered with the in-plane external magnetic field applied parallel or perpendicular to the stripes. The supporting calculations are performed by the finite element method in the frequency domain. A number of intensive SW modes occurred in periodic structures under ferromagnetic resonance conditions as a consequence of standing spin waves excitation. These modes were analyzed theoretically in order to explain the origins of SW excitations. With the support of numerical calculations, we analyze also the possible scenarios for the occurrence of standing SWs in the investigated structures. It is demonstrated that the SW propagation length is an important factor conditioning the standing SW formation in MCs.