The explosive growth of data and its related energy consumption is pushing the need to develop energy-efficient brain-inspired schemes and materials for data processing and storage. Here, we demonstrate experimentally that Co/Pt films can be used as artificial synapses by manipulating their magnetization state using circularly-polarized ultrashort optical pulses at room temperature. We also show an efficient implementation of supervised perceptron learning on an opto-magnetic neural network, built from such magnetic synapses. Importantly, we demonstrate that the optimization of synaptic weights can be achieved using a global feedback mechanism, such that the learning does not rely on external storage or additional optimization schemes. These results suggest there is high potential for realizing artificial neural networks using optically-controlled magnetization in technologically relevant materials, that can learn not only fast but also energy-efficient.
we exploit iterative optimization of synaptic weights using a global feedback mechanism. Hence, the learning does not rely on external storage or additional optimization strategies, which simplifies the implementation.
The perceptron is an elementary model of neural computation 15 . An example of the simplest single-layer perceptron is shown in Figure 1a. It has inputs 𝑥 " , … , 𝑥 % that are connected to adaptable synaptic weights 𝑤 " , … , 𝑤 % . The output O is a nonlinear function of the weighted inputs 𝑦 ( = 𝑤 ( 𝑥 ( and the threshold 𝑏: 𝑂 = sign(∑ 𝑦 ( -𝑏), where we introduced the sign function as a simple nonlinear function. In this form, the perceptron can be interpreted as a neuron that fires when the sum of the weighted inputs is larger than a threshold. We focus on the simple perceptron as an example of a neural network that can learn (by adapting synaptic weights) a given function, also known as supervised learning. To this end, several input patterns 𝑥 " 3 , … , 𝑥 4 3 , µ=1,2,..,p with desired outputs 𝑂 6 3 are provided. The perceptron learning rule can then be defined as an iterative procedure where one cycles over the input patterns. At each pattern the actual output 𝑂 7 is evaluated and the weights are changed according to a global error E = sign(𝑂 6 3 -𝑂 3 ):
𝑤 9 = 𝑤 9 + ∆𝑤 9 Eq. ( 1) ∆𝑤 9 = η 𝑥 9 3 E Eq. ( 2) Here, η ≪ 1 is the learning rate. Learning stops when for all patterns the desired output is realized (E = 0). Note that, although a global feedback is used, weights are changed locally due to the dependence on 𝑥 9 3 in Eq. ( 2). Importantly, this iterative learning procedure does not necessitate additional external storage nor external optimization. Instead, it can exploit the nonvolatile local storage of synaptic weights in the material itself. Implementing a perceptron in a physical system therefore requires continuous adaptable and non-volatile synaptic weights as well as multiplication of the weights with given inputs. Below we describe how this is realized using a magneto-optical setup, and subsequently show how learning is achieved.
To implement the multiplication, we exploit the concept of a polarizing microscope that is illustrated in Figure 1b. The magnetic sample that features magnetization parallel or antiparallel to the optical wave vector is placed between two polarization filters. Due to the magneto-optical Faraday effect, the axis of optical polarization is rotated clockwise (anticlockwise) via the magneto-optical Faraday effect. The relative angle between the polarizers is tuned such that minimum (maximum) light passes through the analyzer when the light transmits through magnetic domains pointing parallel (antiparallel) to the light’s direction i.e. pointing up or down. From analyzing the light power P ∝ I EFG that is locally detected by the CCD camera we obtain, for small Faraday rotations as applicable here, a linear relation with the incoming illumination I 94 : I EFG = 𝐾𝑀I 94 . Eq. (3) Here K depends on the material-specific Verdet constant, the thickness 𝑑 and magnetization 𝑚 of the material, while 𝑀 = 𝑑(𝑆 " -𝑆 N )𝑚 is the net magnetic moment, where 𝑆 " (𝑆 N ) denotes the area of up (down) domains. By identifying I EFG with the weighted input 𝑦 ( , ‘𝐾𝑀’ with the synaptic weight 𝑤 ( , and I 94 with the synaptic input 𝑥 ( , we directly obtain the desired multiplication.
To realize adaptable and non-volatile synaptic weights, we optically control the magnetization M. Therefore, a magnetic material with strong out-of-plane magnetic anisotropy and a strong optomagnetic response is needed. Moreover, instead of exploiting single-shot binary switching seen in ferrimagnetic alloys and multilayers [16][17][18] , reversible gradual changes of magnetization in response to laser pulses are required. To this end, the multi-shot helicity-dependent control of magnetization in ferromagnetic Co/Pt thin films is an attractive candidate 2,13,18 . In this study, we used a sputter-grown Co/Pt multilayered thin film structure, mounted on a synthetic quartz glass substrate, with nanometer thickness composition of Glass/Ta(3)/Pt(3)/Co(0.6)/Pt(3)/MgO(2)/Ta (1). The structure has a coercive field of 20 mT.
The magneto-optical setup in which both the multiplication and optical control of synaptic weights are implemented is schematically shown in Figure 1c. Gaussian pump pulses of 800 nm central wavelength and duration of 4 ps were selected from a 1kHz repetition rate Ti:sapphire amplified laser system. The pump pulse was targeted to hit the sample at about 10° incidence angle, and focused to a spot with a Gaussian waist of 38 µm. The measured incident optical fluence was maintained at 1.3mJ/cm 2 . A rotatable quarter wave plate used to select left/right circularly polarized pump pulses to either decrease/increase the net magnetic moment of the sample and thereby adapt the synaptic weight. For ease of demonstration a continuous wave laser of 532 nm wavelength was used for probing. In Figu
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