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The growth of artificial intelligence and IoT has created a significant computational load for solving non-deterministic polynomial-time (NP)-hard problems, which are difficult to solve using conventional computers. The Ising computer, based on the Ising model and annealing process, has been highly sought for finding approximate solutions to NP-hard problems by observing the convergence of dynamic spin states. However, it faces several challenges, including high power consumption due to artificial spins and randomness emulated by complex circuits, as well as low scalability caused by the rapidly growing connectivity when considering large-scale problems. Here, we present an experimental Ising annealing computer based on superparamagnetic tunnel junctions (SMTJs) with all-to-all connections, which successfully solves a 70-city travelling salesman problem (4761-node Ising problem). By taking advantage of the intrinsic randomness of SMTJs, implementing a proper global annealing scheme, and using an efficient algorithm, our SMTJ-based Ising annealer shows superior performance in terms of power consumption and energy efficiency compared to other Ising schemes. Additionally, our approach provides a promising way to solve complex problems with limited hardware resources. Moreover, we propose a crossbar array architecture for scalable integration using conventional magnetic random access memories. Our results demonstrate that the SMTJ-based Ising annealing computer with high energy efficiency, speed, and scalability is a strong candidate for future unconventional computing schemes., Comment: 5 figures

Electric generation of spin current via spin Hall effect is of great interest as it allows an efficient manipulation of magnetization in spintronic devices. Theoretically, spin current can be also created by a temperature gradient, which is known as spin Nernst effect. Here, we report spin Nernst effect-induced transverse magnetoresistance in ferromagnet (FM)/non-magnetic heavy metal (HM) bilayers. We observe that the magnitude of transverse magnetoresistance (i.e., planar Nernst signal) in FM/HM bilayers is significantly modified by HM and its thickness. This strong dependence of transverse magnetoresistance on HM evidences the spin Nernst effect in HM; the generation of thermally-induced spin current in HM and its subsequent reflection at the FM/HM interface. Our analysis of transverse magnetoresistance shows that the spin Nernst angles of W and Pt have the opposite sign to their spin Hall angles. Moreover, our estimate implies that the magnitude of the spin Nernst angle would be comparable to that of the spin Hall angle, suggesting an efficient generation of spin current by the spin Nernst effect.

The utilization of ferromagnetic (FM) materials in thermoelectric devices allows one to have a simpler structure and/or independent control of electric and thermal conductivities, which may further remove obstacles for this technology to be realized. The thermoelectricity in FM/non-magnet (NM) heterostructures using an optical heating source is studied as a function of NM materials and a number of multilayers. It is observed that the overall thermoelectric signal in those structures which is contributed by spin Seebeck effect and anomalous Nernst effect (ANE) is enhanced by a proper selection of NM materials with a spin Hall angle that matches to the sign of the ANE. Moreover, by an increase of the number of multilayer, the thermoelectric voltage is enlarged further and the device resistance is reduced, simultaneously. The experimental observation of the improvement of thermoelectric properties may pave the way for the realization of magnetic-(or spin-) based thermoelectric devices.

The relative contribution of spin pumping and spin rectification from the ferromagnetic resonance of CoFeB/non-magnetic bilayers was investigated as a function of non-magnetic electrode resistance. Samples with highly resistive electrodes of Ta or Ti exhibit a stronger spin rectification signal, which may result in over-(or under-)estimation of the spin Hall angle of the materials, while those with low resistive electrodes of Pt or Pd show the domination of the inverse spin Hall effect from spin pumping. By comparison with samples of single FM layer and an inverted structure, we provide a proper analysis method to extract spin pumping contribution., Comment: 10 pages, 4 figures