Journal of Nanotechnology

Volume 2016, Article ID 8347280, 11 pages

http://dx.doi.org/10.1155/2016/8347280

## Performance Optimization of Spin-Torque Microwave Detectors with Material and Operational Parameters

^{1}Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong^{2}Department of Physics, The University of Hong Kong, Hong Kong^{3}School of Electronics Science and Engineering, Nanjing University, Nanjing 210093, China

Received 1 February 2016; Accepted 30 May 2016

Academic Editor: Oded Millo

Copyright © 2016 X. Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Sensitivity, bandwidth, and noise equivalent power (NEP) are important indicators of the performance of microwave detectors. The previous reports on spin-torque microwave detectors (STMDs) have proposed various approaches to increase the sensitivity. However, the effects of these methods on the other two indicators remain unclear. In this work, macrospin simulation is developed to evaluate how the performance can be optimized through changing the material (tilt angle of reference-layer magnetization) and operational parameters (the direction of magnetic field and working temperature). The study on the effect of magnetic field reveals that the driving force behind the performance tuning is the effective field and the equilibrium angle between the magnetization of the free layer and that of the reference layer. The material that offers the optimal tilt angle in reference-layer magnetization is determined. The sensitivity can be further increased by changing the direction of the applied magnetic field and the operation temperature. Although the optimized sensitivity is accompanied by a reduction in bandwidth or an increase in NEP, a balance among these performance indicators can be reached through optimal tuning of the corresponding influencing parameters.

#### 1. Introduction

Spintronics is an emerging field of research on the interaction between the spin of electrons and the magnetization of magnetic materials. The discovery of giant magnetoresistance (GMR) effect, for which Fert [1] and Grünberg [2] were awarded the 2007 Nobel Prize, has proved that the spin of electrons can be polarized by the magnetization of magnetic materials. Meanwhile, the spin current is also capable of altering the magnetization of the ferromagnetic material [3, 4] through the spin-transfer torque (STT) effect [5, 6]. This observation has led to the development of spin-torque oscillators [7, 8], which can change direct current into frequency-tunable microwave signal. It was later shown that when microwave current flows through a magnetic tunnel junction (MTJ) nanopillar, a rectified DC voltage is generated, revealing its potential application as spin-torque microwave detectors (STMDs) [9].

Sensitivity, bandwidth, and noise equivalent power (NEP) are three important performance indicators for STMDs. Through adjusting the magnitude of the magnetic field , the working frequency of STMDs can be tuned to match that of the incident microwave to achieve the largest DC output. The sensitivity is defined as the ratio of the peak DC voltage to the incident microwave power. The bandwidth is an evaluation of the range of achievable within a certain range of . NEP, on the other hand, is a parameter reflecting the minimum detection power, defined by noise power spectrum density over sensitivity. Although the three indicators are all important for a microwave detector, most of the scientific efforts are devoted to the optimization of sensitivity since competitive sensitivity is the prerequisite for industrial application [10]. The previous publications reported increased sensitivity through applying DC bias [11], optimizing the orientation of in-plane (IP) and out-of-plane (OOP) magnetic field [10, 12, 13], and adjusting the IP shift angle of reference-layer magnetization [14]. All these optimizations have resulted in the record high sensitivity of over 14,000 mV/mW under tilted magnetic field [15] and 75,400 mV/mW under zero magnetic field [16]. Although these reported sensitivities far exceed that of the existing Schottky diode detector, the effects of these approaches on bandwidth and NEP are seldom mentioned. On the other hand, the number of reports aiming at extending the bandwidth or reducing the NEP is small. It has been shown that the bandwidth can be extended through the introduction of reference layer with tilted magnetization [17]. It has also been shown that the minimum detection power of an STMD can be reduced through working at cryogenic temperatures [18]. A comprehensive investigation on how these three performance indicators are influenced by the material or operational parameters is required to extend the understanding in the behavior of STMDs. The outcome of this work is beneficial for optimizing the performance of STMDs.

#### 2. Modeling and Computational Details

The device under investigation is a 200 × 100 nm^{2} elliptical MTJ nanopillar with reference-layer magnetization () tilted out of plane by (Figure 1(a)). is applied at 3D direction defined by the polar () and azimuthal () angles. In a coordinate system where the *-axis* is perpendicular to the thin-film plane and the *-axis* is parallel to the magnetic easy axis, the unit vector of and free-layer magnetization () can be written asMicrowave current with = 10 *μ*A and = 0.1–10 GHz is injected into the MTJ and a steady-state oscillation in is excited by the STT of spin current. Time evolution of can be obtained by numerically solving the Landau-Lifshitz-Gilbert equation:where = 176 GHz/T represents the gyromagnetic ratio, = 0.01 the Gilbert damping parameter, the volume of free layer, the charge of an electron, and the vacuum magnetic permeability. is the effective field comprised of external field, IP anisotropy field (), and demagnetization field (), defined, respectively, bywhere = 0.016 is the demagnetization factor in the *-axis*. is the time-dependent angle between and :The contribution of field-like STT is considered, and = 0.1 is its ratio to the IP torque [19]. The thermal fluctuation term is introduced as in [20]:where is a random vector whose components are normally distributed random numbers with mean of 0 and variance of 1. The temperature dependence of polarization ratio (), parallel resistance (), antiparallel resistance (), and saturation magnetization () are expressed, respectively, aswhere = 0.385, = 1.7 × 10^{−5} K^{−3/2}, = 800 Ω, = 7.65 × 10^{−4} K^{−1}, = 1.3 × 10^{6} A/m, = 0.4, and = 1300 K.