## Theory of Perimeter Excitation of Magnetic Droplet Solitons

Grant Data

**Project Title**

Theory of Perimeter Excitation of Magnetic Droplet Solitons

**Principal Investigator**

Dr Zhou, Yan
(Principal investigator)

**Duration**

18

**Start Date**

2015-03-01

**Completion Date**

2016-08-31

**Amount**

35400

**Conference Title**

**Presentation Title**

**Keywords**

magnetic droplet soliton, perimeter excitation, internal mode, spin transfer torque, spin torque oscillator

**Discipline**

Physics,Nanomaterials

**Panel**

Physical Sciences

**Sponsor**

Block Grant Earmarked for Research (104)

**HKU Project Code**

201411159092

**Grant Type**

Seed Fund for Basic Research

**Funding Year**

2014/2015

**Status**

Completed

**Objectives**

1. To develop a consistent Thiele-like approach for the description of dynamics of quasi-one dimensional magnetic configurations (dynamic magnetic strings and static domain walls). 2. To develop in-house micromagnetics simulation package for studying the magnetic droplet formation and control in the nano-contact based spin torque devices. 3. To study the internal degrees of freedom of dynamic magnetic strings based on the developed theory and simulations. 4. To interpret the recent experimental results in nano-contact system by theory and simulations. 5. To guide our experimental collaborations in the manipulation of magnetic droplets in nano-contacts array, and to predict novel effects for spintronic applications. Key issues: 1) The power output of a conventional spin torque nano-oscillator is too small for applications Spin torque nano-oscillator (STNO) have attracted rapidly growing interests in the field of nanomagnetism and spintronics in the past decade [1]. STNO is a broadband microwave signal generator capable of microwave generation in the range of a few MHz up to a few tens of GHz. It is extremely compact with typical device size of a few tens to a few hundred nanometers. Its frequency can be tuned by both electrical current and applied magnetic field with a broad tuning range of tens of GHz. In addition, its frequency can be rapidly modulated from e.g., a few hundreds MHz to a few tens of GHz in a sub-nanosecond range. All these unique features of STNOs lend themselves to various applications in wireless communications, innovative types of computing architecture, and neural science etc [2]. One of the biggest roadblocks of STNO based technology for practical applications is its very low power output, typically at the level of a few nw for metallic spin valve and a few μw for magnetic tunnel junction [3]. It was recently demonstrated that an entirely new type of spin wave can be excited in STNOs with perpendicular magnetic anisotropy (PMA) in the free layers — the so-called magnetic nano-droplet [4]. The nano-droplet is a magnetic droplet soliton, confined to the region beneath the nano-contact and characterized by a very high spin wave amplitude even at low drive currents. For applications, one of the most intriguing properties of the nano-droplet is the large number of spins precessing with very large precession cone angles. While typical maximum precession angles in STNOs is of the order of 20 degrees, magnetic nano-droplets can precess at angles of 90 degrees or even higher, i.e. they can precess either exactly in-plane or even against the applied field. Since the STNO output power is generated by the variation in resistance during precession, a 90 degree precession angle will generate the maximum possible signal. As a comparison, a spin precessing at 20 degrees only generates about 12% of the power of a spin precessing at 90 degrees. This dramatic potential for higher STNO power was indeed demonstrated as their STNOs exhibited a 40x increase in output power (+16 dB) when the nano-droplet formed [4]. 2). Lack of theoretical understanding of internal modes excitations in nanodroplet recently observed in experiments Prof. Akerman’s group recently reported that the magnetic droplets can be generated by spin torque [4]. This is the first experimental evidence of spin torque driven magnetic droplet in NC-STO system [4]. Such a system (see Fig. 1) exhibits remarkable dynamics. One example is the auto-modulation of the droplet’s precession frequency (Fig. 2). Fig. 2a shows the auto-modulation at a frequency of 1.4 GHz, which can be directly observed at low frequency. Inset: Power spectral density (PSD) at 10.8 mA showing how the sideband separation agrees with the low-f signal. Fig. 2b shows theuto-modulation at 1.1 GHz leading to both first and second order sidebands (power spectral density at 4.1 mA shown in the inset). Fig. 2c shows the sidebands at fdroplet/2 and 3fdroplet/2. The signal at 3fdroplet/2 is much weaker and shown with its own scale [4]. Because all the measurements were carried out with DC drive alone, the observed modulation is unrelated to ordinary STNO modulation, where the drive current contains an intentional superimposed modulating current. The observed auto-modulation must instead be intrinsic to the droplet. However, there is not yet any theoretical explanation and understanding of these intrinsic modes of magnetic droplet solitons. A theory to elucidate the microscopic origin of the rich magnetodynamics are crucial for utilizing the magnetic droplet solitons for any practical applications. Problems to be tackled: 1) I will develop a consistent Thiele-like approach for the description of dynamics of quasi-one dimensional magnetic configurations. In this project I propose to study, experimentally, theoretically and numerically, the internal degrees of freedom of dynamic magnetic strings. I propose to investigate excitation, detection, stability, nonlinear interactions, and other properties of the excited states of dynamic magnetic strings. I aim to develop a theory to explain the characteristics of experimental observations of frequency-modulation, auto-modulation, propagation and control of nanoscale magnetic-droplet solitons in spin torque nano-contact systems. I will also develop a micromagnetic simulation package and compare the simulations with the analytical theory and the experimental results. The simulation framework will allow one to perform an in-depth study on a variety of nonlinear dynamics in nanostructured magnetic systems. 2) I will predict some properties of multiple droplet synchronization for boosting power output of STNOs Here I propose an alternative synchronization mechanism based on the spin wave interactions of multiple droplets to produce microwave signal of high power and low linewidth (or low phase noise) at zero external magnetic field. It has been shown that an effective method for increasing the output power and reducing the linewidth of STNOs is to phase-lock many STNOs through their emitted spin waves in a shared free layer [5, 6]. It is thus worth investigating the interaction of droplet pairs. Through our theory developed in the first part of this section — "Problems to be tackled" in combination with micromagnetics full simulations, I will demonstrate the synchronization mechanisms of magnetic droplet solitons in pair of STNOs with particular focus on the droplet dynamics of the STNOs. It is expected that this pioneering theoretical research will provide the most important information for design and realization of multiple droplet interaction and synchronization in experiments.