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Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography, we reconstruct with about 20-nanometer spatial (voxel) size the full three-dimensional spin texture of a skyrmion in an 800-nanometer-diameter and 95-nanometer-thin disk patterned into a 30× [iridium/cobalt/platinum] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number is nonuniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to nonuniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

The increasing scale of neural networks needed to support more complex applications has led to an increasing requirement for area- and energy-efficient hardware. One route to meeting the budget for these applications is to circumvent the von Neumann bottleneck by performing computation in or near memory. An inevitability of transferring neural networks onto hardware is that non-idealities such as device-to-device variations or poor device yield impact performance. Methods such as hardware-aware training, where substrate non-idealities are incorporated during network training, are one way to recover performance at the cost of solution generality. In this work, we demonstrate inference on hardware neural networks consisting of 20,000 magnetic tunnel junction arrays integrated on a complementary metal-oxide-semiconductor chips that closely resembles market-ready spin transfer-torque magnetoresistive random access memory technology. Using 36 dies, each containing a crossbar array with its own non-idealities, we show that even a small number of defects in physically mapped networks significantly degrades the performance of networks trained without defects and show that, at the cost of generality, hardware-aware training accounting for specific defects on each die can recover to comparable performance with ideal networks. We then demonstrate a robust training method that extends hardware-aware training to statistics-aware training, producing network weights that perform well on most defective dies regardless of their specific defect locations. When evaluated on the 36 physical dies, statistics-aware trained solutions can achieve a mean misclassification error on the MNIST dataset that differs from the software-baseline by only 2 %. This statistics-aware training method could be generalized to networks with many layers that are mapped to hardware suited for industry-ready applications., Comment: 17 pages, 9 figures

The increasing scale of neural networks and their growing application space have produced demand for more energy- and memory-efficient artificial-intelligence-specific hardware. Avenues to mitigate the main issue, the von Neumann bottleneck, include in-memory and near-memory architectures, as well as algorithmic approaches. Here we leverage the low-power and the inherently binary operation of magnetic tunnel junctions (MTJs) to demonstrate neural network hardware inference based on passive arrays of MTJs. In general, transferring a trained network model to hardware for inference is confronted by degradation in performance due to device-to-device variations, write errors, parasitic resistance, and nonidealities in the substrate. To quantify the effect of these hardware realities, we benchmark 300 unique weight matrix solutions of a 2-layer perceptron to classify the Wine dataset for both classification accuracy and write fidelity. Despite device imperfections, we achieve software-equivalent accuracy of up to 95.3 % with proper tuning of network parameters in 15 x 15 MTJ arrays having a range of device sizes. The success of this tuning process shows that new metrics are needed to characterize the performance and quality of networks reproduced in mixed signal hardware., Comment: 22 pages plus 8 pages supplemental material; 7 figures plus 7 supplemental figures

We report on dependence of conductance and tunnelling magnetoresistance on bias voltage at different temperatures down to 2 K in Co|Al[subscript 2]O[subscript 3](10 Å)|Si(δ)|Al[subscript 2]O[subscript 3](2 Å)|Permalloy magnetic tunnel junctions. Complementary low frequency noise measurements are used to understand the conductance results. The obtained data indicate the breakdown of the Coulomb blockade for thickness of the asymmetric silicon layer exceeding 1.2 Å. The crossover in the conductance, the dependence of the tunneling magnetoresistance with the bias voltage and the noise below 80 K correspond to one monolayer coverage. Interestingly, the zero bias magnetoresistance remains nearly unaffected by the presence of the silicon layer. The proposed model uses Larkin-Matveev approximation of tunneling through a single impurity layer generalized to three-dimensional case and takes into account the variation of the barrier shape with the bias voltage. The main difference is the localization of all the impurity levels within a single atomic layer. In the high thickness case, up to 1.8 Å, we have introduced a phenomenological parameter, which reflects the number of single levels on the total density of silicon atoms., United States. Office of Naval Research (Grant No. N00014-06-1-0235), National Science Foundation (U.S.) (Grant No. DMR-0504158), Madrid (Spain : Region) (Grant No. P2009/MAT-1726), Spain. Ministerio de Ciencia e Innovación (MICINN) (Grant No. MAT2006-07196), Spain. Ministerio de Ciencia e Innovación (MICINN) (Grant No. MAT2009- 10139), Spain. Ministerio de Ciencia e Innovación (MICINN) (Consolider Grant No. CSD2007-00010), European Science Foundation. EUROCORES Programme (Grant No. 05-FONE-FP-010-SPINTRA), European Science Foundation. Arrays of Quantum Dots adn Josephson Junctions (AQDJJ) programme, Fundação para a Ciência e a Tecnologia (FCT) (Grant PTDC/FIS/70843/2006), Poland. Ministry of Science and Higher Education

We report on dependence of conductance and tunnelling magnetoresistance on bias voltage at different temperatures down to 2 K in Co|Al[subscript 2]O[subscript 3](10 Å)|Si(δ)|Al[subscript 2]O[subscript 3](2 Å)|Permalloy magnetic tunnel junctions. Complementary low frequency noise measurements are used to understand the conductance results. The obtained data indicate the breakdown of the Coulomb blockade for thickness of the asymmetric silicon layer exceeding 1.2 Å. The crossover in the conductance, the dependence of the tunneling magnetoresistance with the bias voltage and the noise below 80 K correspond to one monolayer coverage. Interestingly, the zero bias magnetoresistance remains nearly unaffected by the presence of the silicon layer. The proposed model uses Larkin-Matveev approximation of tunneling through a single impurity layer generalized to three-dimensional case and takes into account the variation of the barrier shape with the bias voltage. The main difference is the localization of all the impurity levels within a single atomic layer. In the high thickness case, up to 1.8 Å, we have introduced a phenomenological parameter, which reflects the number of single levels on the total density of silicon atoms., United States. Office of Naval Research (Grant No. N00014-06-1-0235), National Science Foundation (U.S.) (Grant No. DMR-0504158), Madrid (Spain : Region) (Grant No. P2009/MAT-1726), Spain. Ministerio de Ciencia e Innovación (MICINN) (Grant No. MAT2006-07196), Spain. Ministerio de Ciencia e Innovación (MICINN) (Grant No. MAT2009- 10139), Spain. Ministerio de Ciencia e Innovación (MICINN) (Consolider Grant No. CSD2007-00010), European Science Foundation. EUROCORES Programme (Grant No. 05-FONE-FP-010-SPINTRA), European Science Foundation. Arrays of Quantum Dots adn Josephson Junctions (AQDJJ) programme, Fundação para a Ciência e a Tecnologia (FCT) (Grant PTDC/FIS/70843/2006), Poland. Ministry of Science and Higher Education

The carbon nanotube photoexcitation spectrum is dominated by excitonic transitions, rather than interband transitions between continuum states. There are eight distinct excitonic transitions (four singlet and four triplet), each with two-fold degeneracy. Because the triplet excitons are spin polarized with electron and hole spins both pointing in the same direction, they are optically inactive, and optical spectroscopy has revealed no evidence for their existence. Here, we show that by the interaction with a spin filter ferromagnetic semiconductor, photoexcitation of the carbon nanotube triplet exciton is possible, and its contribution to the photocurrent can be detected. The perturbation provided by the spin filter allows for inter-system mixing between the singlet and triplet excitonic states, and relaxes the spin selection rules. This supplies the first evidence for the existence of the triplet exciton, and provides an avenue for the optical excitation of spin polarized carriers in carbon nanotubes., United States Department of Energy (DE-FG02-07ER46375), National Science Foundation (NSF DMR 0504158), United States Office of Naval Research (ONR N00014-06-1-0228 and ONR N00014-06-1-0235)

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2007., Vita., Includes bibliographical references (p. 93-103)., Essential to the emergence of spin-based electronics is a source of highly polarized electron spins. Conventional ferromagnets have at best a spin polarization P-50%. Europium monoxide is a novel material capable of generating a highly spin-polarized current when used as a tunnel barrier. EuO is both a Heisenberg ferromagnet (Tc=69 K) and a semiconductor. Exchange splitting of the conduction band creates different tunnel barrier heights for spin-up and spin-down electrons, thus filtering the spins during tunneling. High-quality EuO films at the monolayer level is necessary for efficient spin-filtering. Because non-ferromagnetic, insulating Eu20 forms more readily, growth of an ultra-thin, high-quality film is quite challenging, which restricted previous studies of EuO to bulk form. EuO films were grown by reactive thermal evaporation, and various thin film characterization techniques were employed to determine the structural, optical, and magnetic properties, even on the thickness scale needed for tunneling (<3 nm). The film properties closely matched those of bulk EuO, though the Tc for ultra-thin films was found to be reduced from bulk value, in agreement with theoretical prediction., (cont.) Controlling the smoothness and chemical nature of the inter-faces between EuO and metallic electrodes was found to be of critical importance, as proven by careful interfacial chemical and magnetic analysis at the monolayer level, using x-ray absorption spectroscopy, magnetic circular dichroism, and diffuse x-ray resonance scattering techniques. EuO was successfully prepared as the barrier in Al/2.5 nm EuO/Y tunnel junctions. By fitting the current-voltage characteristics of these junctions to tunneling theory, exchange splitting in an ultra-thin layer of EuO was quantitatively determined for the first time, and complete spin filtering yielded total spin polarization, P=100%. In an alternative approach, P was directly measured using the superconducting Al electrode as a spin detector. Spin-filtering in EuO barriers was also observed in magnetic tunnel junctions (MTJs), in which a ferromagnetic electrode was the spin detector. In Cu/EuO/Gd MTJs a tunnel magnetoresistance (TMR) of 280% was measured by changing the relative alignment of magnetization of EuO and Gd, which is the largest TMR measured using a spin-filter barrier. Co/A1203/EuO/Y junctions, in which the A1203 barrier magnetically decoupled Co and EuO, also showed substantial TMR. Its matching band gap (1.1 eV) and compatibility with Si open up the novel possibility of using EuO to inject highly polarized spins into Si-based semiconductors., by Tiffany S. Santos., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2007., Vita., Includes bibliographical references (p. 93-103)., Essential to the emergence of spin-based electronics is a source of highly polarized electron spins. Conventional ferromagnets have at best a spin polarization P-50%. Europium monoxide is a novel material capable of generating a highly spin-polarized current when used as a tunnel barrier. EuO is both a Heisenberg ferromagnet (Tc=69 K) and a semiconductor. Exchange splitting of the conduction band creates different tunnel barrier heights for spin-up and spin-down electrons, thus filtering the spins during tunneling. High-quality EuO films at the monolayer level is necessary for efficient spin-filtering. Because non-ferromagnetic, insulating Eu20 forms more readily, growth of an ultra-thin, high-quality film is quite challenging, which restricted previous studies of EuO to bulk form. EuO films were grown by reactive thermal evaporation, and various thin film characterization techniques were employed to determine the structural, optical, and magnetic properties, even on the thickness scale needed for tunneling (<3 nm). The film properties closely matched those of bulk EuO, though the Tc for ultra-thin films was found to be reduced from bulk value, in agreement with theoretical prediction., (cont.) Controlling the smoothness and chemical nature of the inter-faces between EuO and metallic electrodes was found to be of critical importance, as proven by careful interfacial chemical and magnetic analysis at the monolayer level, using x-ray absorption spectroscopy, magnetic circular dichroism, and diffuse x-ray resonance scattering techniques. EuO was successfully prepared as the barrier in Al/2.5 nm EuO/Y tunnel junctions. By fitting the current-voltage characteristics of these junctions to tunneling theory, exchange splitting in an ultra-thin layer of EuO was quantitatively determined for the first time, and complete spin filtering yielded total spin polarization, P=100%. In an alternative approach, P was directly measured using the superconducting Al electrode as a spin detector. Spin-filtering in EuO barriers was also observed in magnetic tunnel junctions (MTJs), in which a ferromagnetic electrode was the spin detector. In Cu/EuO/Gd MTJs a tunnel magnetoresistance (TMR) of 280% was measured by changing the relative alignment of magnetization of EuO and Gd, which is the largest TMR measured using a spin-filter barrier. Co/A1203/EuO/Y junctions, in which the A1203 barrier magnetically decoupled Co and EuO, also showed substantial TMR. Its matching band gap (1.1 eV) and compatibility with Si open up the novel possibility of using EuO to inject highly polarized spins into Si-based semiconductors., by Tiffany S. Santos., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2007., Vita., Includes bibliographical references (p. 93-103)., Essential to the emergence of spin-based electronics is a source of highly polarized electron spins. Conventional ferromagnets have at best a spin polarization P-50%. Europium monoxide is a novel material capable of generating a highly spin-polarized current when used as a tunnel barrier. EuO is both a Heisenberg ferromagnet (Tc=69 K) and a semiconductor. Exchange splitting of the conduction band creates different tunnel barrier heights for spin-up and spin-down electrons, thus filtering the spins during tunneling. High-quality EuO films at the monolayer level is necessary for efficient spin-filtering. Because non-ferromagnetic, insulating Eu20 forms more readily, growth of an ultra-thin, high-quality film is quite challenging, which restricted previous studies of EuO to bulk form. EuO films were grown by reactive thermal evaporation, and various thin film characterization techniques were employed to determine the structural, optical, and magnetic properties, even on the thickness scale needed for tunneling (<3 nm). The film properties closely matched those of bulk EuO, though the Tc for ultra-thin films was found to be reduced from bulk value, in agreement with theoretical prediction., (cont.) Controlling the smoothness and chemical nature of the inter-faces between EuO and metallic electrodes was found to be of critical importance, as proven by careful interfacial chemical and magnetic analysis at the monolayer level, using x-ray absorption spectroscopy, magnetic circular dichroism, and diffuse x-ray resonance scattering techniques. EuO was successfully prepared as the barrier in Al/2.5 nm EuO/Y tunnel junctions. By fitting the current-voltage characteristics of these junctions to tunneling theory, exchange splitting in an ultra-thin layer of EuO was quantitatively determined for the first time, and complete spin filtering yielded total spin polarization, P=100%. In an alternative approach, P was directly measured using the superconducting Al electrode as a spin detector. Spin-filtering in EuO barriers was also observed in magnetic tunnel junctions (MTJs), in which a ferromagnetic electrode was the spin detector. In Cu/EuO/Gd MTJs a tunnel magnetoresistance (TMR) of 280% was measured by changing the relative alignment of magnetization of EuO and Gd, which is the largest TMR measured using a spin-filter barrier. Co/A1203/EuO/Y junctions, in which the A1203 barrier magnetically decoupled Co and EuO, also showed substantial TMR. Its matching band gap (1.1 eV) and compatibility with Si open up the novel possibility of using EuO to inject highly polarized spins into Si-based semiconductors., by Tiffany S. Santos., Ph.D.