Spin-orbit torque rectifier for energy harvesting from weak radio-frequency

Abstract

Harvesting of the ambient radio-frequency (RF) energy is of great interest to address the increasing energy demand for emerging applications, e.g., the internet of things, wearable devices, various sensors and implants, and 3D integrated circuits. To use the weak ambient RF power density for such applications, we need rectifiers capable of operating much below 1 μW RF power with high efficiencies. However, the development of such technologies is severely limited by the conventional semiconductor rectifiers [1], which fail to operate in the weak RF limit. We propose a new rectifier concept [2], simultaneously utilizing the spin-orbit torque (SOT) and the Hall effect, that can provide ~200 μV DC voltage from a 500 nW of radio-frequency (RF) power using existing materials, with a power conversion efficiency as high as 71%. The DC voltage strength can be efficiently enhanced to ~300 mV from the same RF power with a series array of such devices while matching the low impedance of the receiver antenna. We estimate a very high curvature coefficient of the proposed rectifier, in the order of 104 V-1, where the theoretical limit of conventional Schottky diodes is determined by the inverse of the thermal voltage q/kBT ~ 40 V-1 [3].Various SOT materials are being extensively studied for efficient current-induced switching of scaled ferromagnets for memory applications (see, e.g., Ref. [4] and references therein). Here, we propose a new application of SOT in the rectification of weak RF by coupling it to conventional Hall devices. The basic idea can be explained using a Hall bar and a solenoid connected in parallel, see figure. A current-carrying conductor placed in a magnetic field (B) exhibits a voltage drop in the direction orthogonal to both the current and the B-field, known as the Hall effect. If a fraction of the current flows through a solenoid underneath the Hall bar to generate the B-field, the Hall voltage will be unidirectional irrespective of the current direction, leading to a rectification. We propose a structure where such a solenoid is replaced with a bilayer consisting of a material exhibiting SOT and a ferromagnet (FM) with a low anisotropy energy barrier. We design the device such that the current equally divide between the Hall and the SOT layers. The FM magnetization, on average, follows the fraction of the current flowing in the SOT layer, provided that the current can produce sufficiently strong SOT. The FM applies an effective B-field to the Hall layer and thus leads to a similar rectification case as described in the solenoid case. The Hall effect and spin-orbit-torque are both proportional to current density, which improves inversely with device cross-sectional area, providing the largest signals at the nanoscale.To make the proposed rectifier sensitive to weak RF current, we need a material with a high SOT factor, an FM with low anisotropy energy, and a low Gilbert damping constant. An FM with low anisotropy energy is typically achieved by lowering the total magnetic moment or by tuning the FM thickness to optimize near the transition point between in-plane and perpendicular anisotropies or by using isotropic geometries. We consider a soft ferrite with a very low anisotropy field and a low total magnetic moment, that is expected to easily follow a SOT induced by a weak RF current. Such a low anisotropy energy magnets can achieve a wide frequency bandwidth of operation, depending on the total magnetic moment in the FM and the angular momentum conservation [5]. We simulate the magnetization dynamics using the stochastic-Landau Lifshitz Gilbert equation, which considers the stochastic nature of such low anisotropy energy magnets due to the presence of thermal noise. We can further optimize the device structure and use emerging materials to enhance the figure-of-merits at even lower RF power. The proposed device can lead to important new technologies addressing the alarming energy issues in the era of the internet of things, wearable devices, and densely integrated 3D circuits.This work is supported by the Center for Energy Efficient Electronics Science (E3S), NSF Award 0939514. **