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This work introduces an approach to compute periodic phase diagram of micromagnetic systems by solving a periodic linearized Landau-Lifshitz-Gilbert (LLG) equation using an eigenvalue solver with the Finite Element Method formalism. The linear operator in the eigenvalue problem is defined as a function of the periodic phase shift wave vector. The dispersion diagrams are obtained by solving the eigenvalue problem for complex eigen frequencies and corresponding eigen states for a range of prescribed wave vectors. The presented approach incorporates a calculation of the periodic effective field, including the exchange and magnetostatic field components. The approach is general in that it allows handling 3D problems with any 1D, 2D, and 3D periodicities. The ability to calculated periodic diagrams provides insights into the spin wave propagation and localized resonances in complex micromagnetic structures.

Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based on a non-periodic FEM-based micromagnetic solver and extends it in several aspects to account for periodicities, including the computation of exchange and magnetostatic fields. For the exchange field, PM-FEM modifies the sparse matrix construction for computing the Laplace operator to include additional elements arising due to the periodicities. For the magnetostatic field, the periodic extensions include modifications in the local operators, such as gradient, divergence, and surface magnetic charges as well as the long-range superposition operator for computing the periodic scalar potential. The local operators are extended to account for the periodicities similar to handling the Laplace operator. For the long-range superposition operator, PM-FEM utilizes a periodic Green's function (PGF) and fast spatial convolutions. The PGF is computed rapidly via exponentially rapidly convergent sums. The spatial convolutions are accomplished via a modified fast Fourier transform based adaptive integral method that allows calculating spatial convolutions with non-uniform meshes in $O(N\log N)$ numerical operations. PM-FEM is implemented on CPU and GPU based computer architectures. PM-FEM allows efficiently handling cases of structures contained withing the periodic unit cell touching or not touching its boundaries as well as structures that protrude beyond the unit cell boundaries. PM-FEM is demonstrated to have about the same or even higher performance than its parent non-periodic code. The demonstrated numerical examples show the efficiency of PM-FEM for highly complex structures with 1D, 2D, and 3D periodicities.

Synchronization of coupled oscillators is a fundamental phenomenon that has been observed in many natural and engineered systems, ranging from biological cells to electronic circuits. In recent years, spin torque nano-oscillators (STNOs) have emerged as a promising platform for a variety of applications in nanoscale systems such as neuromorphic computing, due to their compact size, low power consumption, and tunable properties. However, achieving synchronization in a large array of STNOs remains a challenge, for the complexity of the interactions between the oscillators. To address this challenge, we report on the achievement of synchronization across a 2D array of STNOs. We designed a honeycomb model that created a network of interactions among the oscillators that only involved nearest neighbors. Using micromagnetic simulations, we demonstrated the effectiveness of our design and observed that global synchronization across the whole array. Such global synchronization can also be tuned by enable/disenable next-nearest neighbor interactions. We also found that our design enables synchronization at room temperature, which is crucial for practical applications. Our work contributes to the growing body of research on the synchronization of coupled oscillators in spintronics and could pave the way for the development of new types of spintronic devices and potential applications.

Coherent X-ray Diffraction Imaging (CXDI) technique offers unique insights into the nanoscale world, enabling the reconstruction of 3D structures with a nanoscale resolution achieved through computational phase reconstruction from measured scattered intensity maps. Computational demands of 3D CXDI, however, limit its real-time application in experimental settings. This work presents a carousel phase retrieval algorithm (CPRA) that enables the real-time, high-resolution reconstruction of computationally complex 3D objects. CPRA is based on representing the 3D reconstruction problem as a set of 2D reconstructions of projected images corresponding to different experimentally collected angles via the Fourier slice theorem. Consistency between the 2D reconstructed images is based on an iterative procedure, in which each 2D reconstruction accounts for the adjacent 2D reconstructed images in a periodic (carousel) manner. Demonstrations on complex systems, including a lithium-rich layered oxide particle and a Staphylococcus aureus biological cell, demonstrate that CPRA significantly enhances the reconstruction quality and enables the reconstruction process to be completed in real time during experiment.

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic and static problems, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of $O(N \log N)$ for $N$ spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations in computational electromagnetic and acoustic, micromagnetic solvers, and density functional theory solvers.

Fatigue failure of crystalline materials is a difficult problem in science and engineering, and recent results have shown that fatigue crack growth can occur in intermittent jumps which have fat-tailed distributions. As fatigue crack propagation is known to leave markings -- called striations -- on the fracture surface, the distances between these should also have fat-tailed distributions, if the crack propagation is intermittent. Here, we combine macroscale crack tip tracking in fatigue crack growth measurements of aluminum 5005 samples with \emph{post-mortem} scanning electron microscopy imaging of the striation lines. We introduce two different methods for extracting the striation line spacing from the images. What we find is a similar distribution of striation spacings as jump sizes using one of our methods, but the average striation spacing does not correlate with the crack growth rate. We conclude that we observe avalanche-like crack propagation, reflected in both the macroscale crack tip tracking as well as the analysis of the fracture surfaces. Our results show that the fracture surfaces can be used to study the intermittency of fatigue crack propagation and in development of crack-resistant materials. The advantages and disadvantages of the two methods introduced are discussed.

This study conducts a comprehensive investigation into the reversal mechanism of magnetic vortex cores in a nanopillar system composed of two coupled ferromagnetic dots under zero magnetic field conditions. The research employs a combination of experimental and simulation methods to gain a deeper understanding of the dynamics of magnetic vortex cores. The findings reveal that by applying a constant direct current, the orientation of the vortex cores can be manipulated, resulting in a switch in one of the dots at a specific current value. The micromagnetic simulations provide evidence that this switch is a consequence of a deformation in the vortex profile caused by the increasing velocity of the vortex cores resulting from the constant amplitude of the trajectory as frequency increases. These findings offer valuable new insights into the coupled dynamics of magnetic vortex cores and demonstrate the feasibility of manipulating their orientation using direct currents under zero magnetic field conditions. The results of this study have potential implications for the development of vortex-based non-volatile memory technologies. \end{abstract}

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

Current-induced self-sustained magnetization oscillations in spin-torque nano-oscillators (STNOs) are promising candidates for ultra-agile microwave sources or detectors. While usually STNOs behave as a monochrome source, we report here clear bimodal simultaneous emission of incommensurate microwave oscillations, where the two tones correspond to two parametrically coupled eigenmodes with tunable splitting. The emission range is crucially sensitive to the change in hybridization of the eigenmodes of free and fixed layers, for instance, through a slight tilt of the applied magnetic field from the normal of the nano-pillar. Our experimental findings are supported both analytically and by micromagnetic simulations, which ascribe the process to four-magnon scattering between a pair of radially symmetric magnon modes and a pair of magnon modes with opposite azimuthal index. Our findings open up new possibilities for cognitive telecommunications and neuromorphic systems that use frequency multiplexing to improve communication performance.