of applications.'
author:
- 'Tingsu Chen,  Anders Eklund,  Ezio Iacocca,  Saul Rodriguez,  Gunnar Malm,  Johan $\AA$kerman,  and Ana Rusu,  [^1] [^2] [^3] [^4]'
title: 'Comprehensive and Macrospin-Based Magnetic Tunnel Junction Spin Torque Oscillator Model – Part II: Verilog-A Model Implementation'
---

=1

spin torque oscillator, magnetic tunnel junction, macrospin, analytical model.

Introduction
============

is an emerging technology, utilizing both fundamental electronic charge and spin [@spintronics2001]. Spin is the intrinsic angular momentum of the electron. The spin-transfer-torque magnetoresistive random access memory (STT-MRAM), which is based on spintronic effects, has revolutionized the magnetic storage industry [@STTMRAM1]-[@STTMRAM3]. In the past few years, extensive research on modeling this device has been carried out [@MTJ_model1]-[@MTJ_model3]. The developed models of STT-MRAM enable estimation of the performance of STT-MRAMs together with its CMOS circuits, further accelerating the development of STT-MRAM technology.

Meanwhile, the spin torque oscillator (STO) [@STObook], which is another interesting spintronics-based device, has recently received a rapidly increased attention. The STO provides a widely tunable voltage oscillation at microwave frequencies, greatly extending the possible application range of spintronics. Possible applications of STOs include frequency detection [@nature2014], [@tulapurkar2005spin], magnetic field sensing [@nature2014], [@braganca2010nanoscale], microwave sources [@nature2014], [@Bonetti2009], [@Villard2010a] and microwave communications [@pufall2005frequency], [@wireless2014]. Particularly, the magnetic 