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This technical report details VEX Robotics team BLRSAI's development of a fully autonomous robot for VEX Robotics' Tipping Point AI Competition. We identify and develop three separate critical components. This includes a Unity simulation and reinforcement learning model training pipeline, a malleable computer vision pipeline, and a data transfer pipeline to offload large computations from the VEX V5 Brain/micro-controller to an external computer. We give the community access to all of these components in hopes they can reuse and improve upon them in the future, and that it'll spark new ideas for autonomy as well as the necessary infrastructure and programs for AI in educational robotics.

We present cmtj - a comprehensive simulation package that allows large-scale macrospin simulations for a variety of multilayer spintronics devices. Apart from conventional static simulations, such as magnetoresistance and magnetisation hysteresis loops, cmtj implements a mathematical model of dynamic experimental techniques commonly used for spintronics devices characterisation, for instance: spin diode ferromagnetic resonance, pulse-induced microwave magnetometry, or harmonic Hall voltage measurements. We demonstrate the accuracy of the macrospin simulations on a variety of examples, accompanied by some experimental results., Comment: 29 pages, 9 figures

We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$ where $\mathbb Z_p$ the group of p-adic integers. As a consequence, we obtain a dichotomy for the Reidemeister zeta function of a continuous map of a topological space with fundamental group that is non-finitely generated torsion abelian group. We also prove the rationality of the coincidence Reidemeister zeta function for tame endomorphisms pairs of finitely generated torsion-free nilpotent groups, based on a weak commutativity condition., Comment: 25 pages

We present a numerical macrospin model for harmonic voltage detection in multilayer spintronic devices. The core of the computational backend is based on the Landau-Lifshitz-Gilbert-Slonczewski equation, which combines high performance with satisfactory, for large-scale applications, agreement with the experimental results. We compare the simulations with the experimental findings in Ta/CoFeB bilayer system for angular- and magnetic field-dependent resistance measurements, electrically detected magnetisation dynamics, and harmonic Hall voltage detection. Using simulated scans of the selected system parameters such as the polar angle $\theta$, magnetisation saturation ($\mu_\textrm{0}M_\textrm{s}$) or uniaxial magnetic anisotropy ($K_\textrm{u}$) we show the resultant changes in the harmonic Hall voltage, demonstrating the dominating influence of the $\mu_\textrm{0}M_\textrm{s}$ on the first and second harmonics. In the spin-diode ferromagnetic resonance (SD-FMR) technique resonance method the ($\mu_\textrm{0}M_\textrm{s}$, $K_\textrm{u}$) parameter space may be optimised numerically to obtain a set of viable curves that fit the experimental data., Comment: 9 pages, 9 figures

The spin-orbit torque, a torque induced by a charge current flowing through the heavy-metal conducting layer with strong spin-orbit interactions, provides an efficient way to control the magnetization direction in heavy-metal/ferromagnet nanostructures, required for applications in the emergent magnetic technologies like random access memories, high-frequency nano oscillators, or bio-inspired neuromorphic computations. We study the interface properties, magnetization dynamics, magnetostatic features and spin-orbit interactions within the multilayer system Ti(2)/Co(1)/Pt(0-4)/Co(1)/MgO(2)/Ti(2) (thicknesses in nanometers) patterned by optical lithography on micrometer-sized bars. In the investigated devices, Pt is used as a source of the spin current and as a non-magnetic spacer with variable thickness, which enables the magnitude of the interlayer ferromagnetic exchange coupling to be effectively tuned. We also find the Pt thickness-dependent changes in magnetic anisotropies, magnetoresistance, effective Hall angle and, eventually, spin-orbit torque fields at interfaces. The experimental findings are supported by the relevant interface structure-related simulations, micromagnetic, macrospin, as well as the spin drift-diffusion models. Finally, the contribution of the spin-orbital Edelstein-Rashba interfacial fields is also briefly discussed in the analysis., Comment: 39 pages, 14 figures

Magnetic tunnel junctions (MTJ) have been successfully applied in various sensing application and digital information storage technologies. Currently, a number of new potential applications of MTJs are being actively studied, including high-frequency electronics, energy harvesting or random number generators. Recently, MTJs have been also proposed in designs of a new platforms for unconventional or bio-inspired computing. In the present work, it is shown that serially connected MTJs forming a multi-state memory cell can be used in a hardware implementation of a neural computing device. A behavioral model of the multi-cell is proposed based on the experimentally determined MTJ parameters. The main purpose of the mutli-cell is the formation of the quantized weights of the network, which can be programmed using the proposed electronic circuit. Mutli-cells are connected to CMOS-based summing amplifier and sigmoid function generator, forming an artificial neuron. The operation of the designed network is tested using a recognition of the hand-written digits in 20x20 pixel matrix and shows detection ratio comparable to the software algorithm, using the weight stored in a multi-cell consisting of four MTJs or more.

Modulation of a spin-torque oscillator (STO) signal based on a magnetic tunnel junction (MTJ) with perpendicularly magnetized free layer is investigated. Magnetic field inductive loop was created during MTJ fabrication process, which enables microwave field application during STO operation. The frequency modulation by the microwave magnetic field of up to 3 GHz is explored, showing a potential for application in high-data-rate communication technologies. Moreover, an inductive loop is used for self-synchronization of the STO signal, which after field-locking exhibits significant improvement of the linewidth and oscillation power., Comment: 4 pages, 5 figures

In this work, we comprehensively investigate and discuss the structural, magnetostatic, dynamic, and magnetoresistive properties of epitaxial Co/Mo superlattices. The magnetization of the Co sublayers is coupled antiferromagnetically with a strength that depends on the thickness of the nonmagnetic Mo spacer. The magnetization and magnetoresistance hysteresis loops clearly reflect interlayer exchange coupling and the occurrence of uniaxial magnetic anisotropy induced by the strained Co sublayers. Upon accounting for a deviation of the sublayer thicknesses from the nominal value, theoretical modeling, including both micromagnetic and macrospin approaches, precisely reproduces experimental magnetic hysteresis loops, magnetoresistance curves, and ferromagnetic resonance dispersion relations. The Mo spacer thickness as a function of the interlayer magnetic coupling is determined as a fitting parameter by modeling the experimental results.

In this paper we continue to study the Reidemeister zeta function. We prove P\'olya -- Carlson dichotomy between rationality and a natural boundary for analytic behavior of the Reidemeister zeta function for a large class of automorphisms of Abelian groups. We also study dynamical representation theory zeta functions counting numbers of fixed irreducible representations for iterations of an endomorphism. The rationality and functional equation for these zeta functions are proven for several classes of groups. We find a connection between these zeta functions and the Reidemeister torsions of the corresponding mapping tori. We also establish the connection between the Reidemeister zeta function and dynamical representation theory zeta functions under restriction of endomorphism to a subgroup and to a quotient group., Comment: arXiv admin note: text overlap with arXiv:chao-dyn/9603017

Serial connection of multiple memory cells using perpendicular magnetic tunnel junctions (pMTJ) is proposed as a way to increase magnetic random access memory (MRAM) storage density. Multi-bit storage element is designed using pMTJs fabricated on a single wafer stack, with a serial connections realized using top-to-bottom vias. Tunneling magnetoreistance effect above 130%, current induced magnetization switching in zero external magnetic field and stability diagram analysis of single, two-bit and three-bit cells are presented together with thermal stability. The proposed design is easy to manufacture and can lead to increase capacity of future MRAM devices.

Spin-orbit-torque (SOT) induced magnetization switching in Co/Pt/Co trilayer, with two Co layers exhibiting magnetization easy axes orthogonal to each other is investigated. Pt layer is used as a source of spin-polarized current as it is characterized by relatively high spin-orbit coupling. The spin Hall angle of Pt, $\theta = 0.08$ is quantitatively determined using spin-orbit torque ferromagnetic resonance technique. In addition, Pt serves as a spacer between two Co layers and depending on it's thickness, different interlayer exchange coupling (IEC) energy between ferromagnets is induced. Intermediate IEC energies, resulting in a top Co magnetization tilted from the perpendicular direction, allows for SOT-induced feld-free switching of the top Co layer. The switching process is discussed in more detail, showing the potential of the system for neuromorphic applications.

We report on long-range spin wave (SW) propagation in nanometer-thick yttrium iron garnet (YIG) film with an ultralow Gilbert damping. The knowledge of a wavenumber value $|\vec{k}|$ is essential for designing SW devices. Although determining the wavenumber $|\vec{k}|$ in experiments like Brillouin light scattering spectroscopy is straightforward, quantifying the wavenumber in all-electrical experiments has not been widely commented upon so far. We analyze magnetostatic spin wave (SW) propagation in YIG films in order to determine the SW wavenumber $|\vec{k}|$ excited by the coplanar waveguide. We show that it is crucial to consider the influence of magnetic anisotropy fields present in YIG thin films for precise determination of SW wavenumber. With the proposed methods we find that experimentally derived values of $|\vec{k}|$ are in perfect agreement with that obtained from electromagnetic simulation only if anisotropy fields are included., Comment: 15 pages, 7 figures

Magnetization dynamics in W/CoFeB, CoFeB/Pt and W/CoFeB/Pt multilayers was investigated using spin-orbit-torque ferromagnetic resonance (SOT-FMR) technique. An analytical model based on magnetization dynamics due to SOT was used to fit heavy metal (HM) thickness dependence of symmetric and antisymmetric components of the SOT-FMR signal. The analysis resulted in a determination of the properties of HM layers, such as spin Hall angle and spin diffusion length. The spin Hall angle of -0.36 and 0.09 has been found in the W/CoFeB and CoFeB/Pt bilayers, respectively, which add up in the case of W/CoFeB/Pt trilayer. More importantly, we have determined effective interfacial spin-orbit fields at both W/CoFeB and CoFeB/Pt interfaces, which are shown to cancel Oersted field for particular thicknesses of the heavy metal layers, leading to pure spin-current-induced dynamics and indicating the possibility for a more efficient magnetization switching., Comment: 8 pages, 4 figures, submitted to Physical Review Applied

We introduce new zeta functions related to an endomorphism $\phi$ of a discrete group $\Gamma$. They are of two types: counting numbers of fixed ($\rho\sim \rho\circ\phi^n$) irreducible representations for iterations of $\phi$ from an appropriate dual space of $\Gamma$ and counting Reidemeister numbers $R(\phi^n)$ of different compactifications. Many properties of these functions and their coefficients are obtained. In many cases it is proved that these zeta functions coincide. The Gauss congruences are proved. Useful asymptotic formulas for the zeta functions are found. Rationality is proved for some examples, which give also the first counterexamples simultaneously for TBFT ($R(\phi)$=the number of fixed irreducible unitary representations) and TBFT$_f$ ($R(\phi)$=the number of fixed irreducible unitary finite-dimensional representations) for an automorphism $\phi$ with $R(\phi)<\infty$., Comment: 15 pages

The biaxial magnetic-field setup for angular magnetic measurements of thin film and spintronic devices is designed and presented. The setup allows for application of the in-plane magnetic field using a quadrupole electromagnet, controlled by power supply units and integrated with an electromagnet biaxial magnetic field sensor. In addition, the probe station is equipped with a microwave circuitry, which enables angle-resolved spin torque oscillation measurements. The angular dependencies of magnetoresistance and spin diode effect in a giant magnetoresistance strip are shown as an operational verification of the experimental setup. We adapted an analytical macrospin model to reproduce both the resistance and spin-diode angular dependency measurements.

Perpendicular magnetic tunnel junctions (MTJ) with a bottom pinned reference layer and a composite free layer (FL) are investigated. Different thicknesses of the FL were tested to obtain an optimal balance between tunneling magnetoresistance (TMR) ratio and perpendicular magnetic anisotropy. After annealing at 400 $^\circ$C, the TMR ratio for 1.5 nm thick CoFeB sublayer reached 180 % at room temperature and 280 % at 20 K with an MgO tunnel barrier thickness corresponding to the resistance area product RA = 10 Ohm$\mathrm{\mu}$m$^2$. The voltage vs. magnetic field stability diagrams measured in pillar-shaped MTJs with 130 nm diameter indicate the competition between spin transfer torque (STT), voltage controlled magnetic anisotropy (VCMA) and temperature effects in the switching process. An extended stability phase diagram model that takes into account all three parameters and the effective damping measured independently using broadband ferromagnetic resonance technique enabled the determination of both STT and VCMA coefficients that are responsible for the FL magnetization switching., Comment: 6 pages 4 figures

We present a comprehensive theoretical and experimental study of voltage-controlled standing spin waves resonance (SSWR) in PMN-PT/NiFe multiferroic heterostructures patterned into microstrips. A spin-diode technique was used to observe ferromagnetic resonance (FMR) mode and SSWR in NiFe strip mechanically coupled with a piezoelectric substrate. Application of an electric field to a PMNPT creates a strain in permalloy and thus shifts the FMR and SSWR fields due to the magnetostriction effect. The experimental results are compared with micromagnetic simulations and a good agreement between them is found for dynamics of FMR and SSWR with and without electric field. Moreover, micromagnetic simulations enable us to discuss the amplitude and phase spatial distributions of FMR and SSWR modes, which are not directly observable by means of spin diode detection technique.

Dynamic properties of NiFe thin films on PMN-PT piezoelectric substrate are investigated using the spin-diode method. Ferromagnetic resonance (FMR) spectra of microstrips with varying width are measured as a function of magnetic field and frequency. The FMR frequency is shown to depend on the electric field applied across the substrate, which induces strain in the NiFe layer. Electric field tunability of up to 100 MHz per 1 kV/cm is achieved. An analytical model based on total energy minimization and the LLG equation, with magnetostriction effect taken into account, is developed to explain the measured dynamics. Based on this model, conditions for strong electric-field tunable spin diode FMR in patterned NiFe/PMN-PT structures are derived.

We report on the temperature and layer thickness variation of spin-orbit torques in perpendicularly magnetized W/CoFeB bilayers. Harmonic Hall voltage measurements reveal dissimilar temperature evolutions of longitudinal and transverse effective magnetic field components. The transverse effective field changes sign at 250 K for a 2 nm thick W buffer layer, indicating a much stronger contribution from interface spin-orbit interactions compared to, for example, Ta. Transmission electron microscopy measurements reveal that considerable interface mixing between W and CoFeB is primarily responsible for this effect., Comment: 4 pages, 5 figures

We present a thorough research on Ta/Ru-based buffers and their influence on features crucial from the point of view of applications of MTJs, such as critical switching current and thermal stability. We investigate devices consisting of buffer/FeCoB/MgO/FeCoB/Ta/Ru multilayers for three different buffers: Ta 5 / Ru 10 / Ta 3, Ta 5 / Ru 10 / Ta 10 and Ta 5 / Ru 20 / Ta 5 (all thicknesses in nm). In addition, we study systems with a single FeCoB layer deposited above as well as below the MgO barrier. The crystallographic texture and the roughness of the buffers are determined by means of XRD and atomic force microscopy measurements. Furthermore, we examine the magnetic domain pattern, the magnetic dead layer thickness and the perpendicular magnetic anisotropy fields for each sample. Finally, we investigate the effect of the current induced magnetization switching for nanopillar junctions with lateral dimensions ranging from 1 {\mu}m down to 140 nm. Buffer Ta 5 / Ru 10 / Ta 3, which has the thickest dead layer, exhibits a large increase in the thermal stability factor while featuring a slightly lower critical current density value when compared to the buffer with the thinnest dead layer Ta 5 / Ru 20 / Ta 5.

We report on a highly efficient spin diode effect in an exchange-biased spin-valve giant magnetoresistance (GMR) strips. In such multilayer structures, symmetry of the current distribution along the vertical direction is broken and, as a result, a non-compensated Oersted field acting on the magnetic free layer appears. This field, in turn, is a driving force of magnetization precessions. Due to the GMR effect, resistance of the strip oscillates following the magnetization dynamics. This leads to rectification of the applied radio frequency current and induces a direct current voltage $V_{DC}$. We present a theoretical description of this phenomenon and calculate the spin diode signal, $V_{DC}$, as a function of frequency, external magnetic field, and angle at which the external field is applied. A satisfactory quantitative agreement between theoretical predictions and experimental data has been achieved. Finally, we show that the spin diode signal in GMR devices is significantly stronger than in the anisotropic magnetoresistance permalloy-based devices., Comment: 10 pages, 8 figures