Spintronic diodes (STDs) are emerging as a technology for the realization of high-performance microwave detectors [1]. In this paper, we use their rectification properties to perform the analog multiplication between any two numbers. For this purpose, we introduce the concept of degree of rectification (DOR) and we confirm its applicability with micromagnetic and experimental data. The proposed method is suitable for highly integrated implementations and has promising perspectives for neural networks applications [2]. The multiplication can be obtained by measuring the response of a parabolic phenomenon to three well-determined inputs [3][4][5]. Therefore, we analyze the DOR of spintronic diodes, which is the output dc voltage measured for a variable input dc current in injection-locked devices. This Vdc/Idc curve can be well approximated to a parabola as shown in Fig. 1, the experimental data are taken from [6]. The voltage can be approximated by the following equation [6]: Vdc=[(RAP-RP )/4] Iac,MAX cos(φ(Idc)) √p (1) where RAP and RP are the device resistances in the antiparallel and parallel state, respectively, p is the power of the magnetoresistive signal, φ(Idc) is the intrinsic phase shift between the ac current and the magnetoresistive signal, and the cosine can be well approximated with a parable using Taylor’s second-order expansion. Moreover, Eq. 1 can be fully characterized knowing the physical parameters of the device and the values of Idc,MAX, Vdc,MAX (both represented in Fig. 1) and the second derivative of Vdc with respect to Idc evaluated in Idc=Idc,MAX. Fig. 2 shows the application of the presented method for 200 cases with random inputs, the red line shows the ideal result; the correlation coefficient found is r=99.83%. We will show how the proposed method can be used to implement the convolution for neural networks applications with excellent results for image recognition.

![](https://assets.underline.io/uploads/markdown_image/1/image/8be5d570eb2198667334d746191b22a6.jpg)

Fig. 1: Output dc voltage depending on the input dc current (data taken from [4]) for an injection-locked diode (blue circles) and parabolic fit (red line).

![](https://assets.underline.io/uploads/markdown_image/1/image/ef2d86778d75be9a7a2f863250048857.jpg)

Fig. 2: 200 multiplications obtained with the proposed method (black circles) compared with the ideal result (red line).

Analog multiplication implemented with spin-torque diodes for neural networks applications

**Session chair:** Denys Makarov, Helmholtz-Zentrum Dresden-Rossendorf


GOL - MRAM, Magnetic Logic and Related Devices II

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Analog multiplication implemented with spin-torque diodes for neural networks applications

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