Micromagnetic Simulations for ferromagnetic resonance using OOMMF.

Summary

In this insightful exploration of micromagnetic simulations, Suraj Joshi delves into the intricacies of ferromagnetic resonance (FMR) using the OOMMF platform. The presentation outlines the simulation process, starting from understanding micromagnetic platforms to applying the Landau-Lifshitz-Gilbert equation. Joshi explains how equilibrium configurations are determined and dynamic simulations are run with magnetic pulses. The complex interplay between experimental and simulation results is highlighted with practical examples, shedding light on phenomena like demagnetization and exchange stiffness constant effects, which influence resonance frequencies.

Highlights

• Discover how micromagnetic simulations unlock the secrets of ferromagnetic resonance! 🔍
• Learn about the OOMMF platform - a free tool for micromagnetic modeling. 🛠️
• Explore the step-by-step process of simulating FMR, from equilibrium to dynamic simulations. 🚀
• Understand how demagnetization and exchange stiffness affect magnetic resonance frequencies. 📈

Key Takeaways

• Micromagnetic simulations help understand ferromagnetic resonance (FMR) using platforms like OOMMF. 🎯
• The OOMMF framework solves the Landau-Lifshitz-Gilbert equation to model magnetic phenomena. 💡
• Simulation steps include setting equilibrium configurations and applying dynamic simulations. 🔄
• Understanding demagnetization and exchange stiffness is crucial for accurate simulations. 📊

Overview

Suraj Joshi takes us on a journey through the world of micromagnetic simulations, focusing on ferromagnetic resonance (FMR) using the powerful OOMMF platform. This presentation is packed with technical details on how these simulations are executed, starting with the solving of the Landau-Lifshitz-Gilbert equation. Joshi covers the basics of setting up the simulation using tools that are both commercially available and free, like OOMMF, developed for intricate magnetic modeling.

A meticulous breakdown of the simulation process is provided, explaining the importance of establishing equilibrium configurations and conducting dynamic simulations with precisely applied small magnetic pulses. Joshi highlights how these practices help in understanding the behavior of magnetic domains, damping, and resonance conditions. The session also elucidates the Landau-Lifshitz-Gilbert equation's critical role in these simulations, showing how it helps visualize magnetization motion under various conditions.

Joshi's analysis moves further as he evaluates how factors such as demagnetization and exchange stiffness constant impact the simulations. A comparison between theoretical models and empirically collected data from FMR experiments provides insight into the accuracy and effectiveness of these simulations. Through visuals and descriptive examples, we can see how micromagnetic simulations give experimental clarity on magnetic behaviors, essential for advancements in magnetic materials science.

Chapters

• 00:00 - 00:30: Introduction to Micromagnetic Simulations This chapter introduces the concept of micromagnetic simulations, specifically focusing on ferromagnetic resonance (FMR) in PS (likely a material or structure). The speaker outlines the use of a specific micromagnetic simulation platform to perform these simulations. The primary aim is to guide readers on how to simulate FMR in PS, setting the stage for the detailed exploration within the chapter.
• 00:30 - 02:00: Platforms and FMR Overview In this chapter, the introduction to micromagnetic simulations is discussed. The chapter covers the comparison between simulation and experimental results, detailing the outcomes of the simulations. Micromagnetic simulation platforms, both free and paid, are also explored. The chapter concludes with the results of the simulations.
• 02:00 - 04:00: OOMMF and LLG Equation The chapter discusses the applications of micromagnetic modeling software, specifically focusing on their commercial uses. It mentions certain functionalities of such software, like simulating ferromagnetic resonance (FMR), magnetic hysteresis loops (MH Loops), and domain wall motions. The study further explores the velocity of transverse domain wall motion along strips.
• 04:00 - 06:00: FMR Simulation Process The chapter discusses the FMR simulation process. It refers to a paper that describes how spin waves can be simulated in magnetic wave guides. Results from these simulations can be compared with theoretical or experimental data. The chapter also mentions that micromagnetic simulations can be used, noting that different platforms have varied capabilities for performing these simulations.
• 06:00 - 09:00: Sine Pulse Excitation The chapter 'Sine Pulse Excitation' discusses the frequency response in magnetic multilayers, as introduced in a presentation. The main focus is on 'O', an object-oriented micromagnetic framework. It is a free simulation software developed by Mike Don and Don Porter, aimed at facilitating micromagnetic simulations.
• 09:00 - 11:00: FMR Spectra and Mode Analysis The chapter discusses the resolution of the Landau-Lifshitz-Gilbert (LLG) equation using the finite difference method. It involves creating an atlas that represents the geometry of an object, which is then divided into smaller sections to solve the LLG equation. This equation is critical in describing the motion of magnetization in ferromagnetic materials. The introduction covers key concepts in ferromagnetic resonance (FMR) spectra and mode analysis.
• 11:00 - 14:00: Demagnetization Factors and Kittel Equation The chapter explains ferromagnetic resonance (FMR), which is the resonance phenomenon of the magnetization vector in response to a time-varying magnetic field or microwave frequency. It discusses the Larmor equation that contains precession torque and damping terms, introducing the concept of Gilbert damping, denoted by the parameter Alpha. The chapter suggests that the reader will learn how to solve equations using these concepts.
• 14:00 - 16:30: Effect of Exchange Stiffness Constant This chapter discusses the effects of the exchange stiffness constant on the magnetization vector, using the LG equation as a framework. The LG equation, a differential equation, is solved to understand the dynamics of the magnetization vector. The chapter describes how magnetization behaves, particularly how it damps around the axis defined by the effective magnetic field (H effective). This effective field includes contributions from both internal and external static fields.
• 16:30 - 18:00: Summary of Simulation Parameters The chapter "Summary of Simulation Parameters" discusses the damping present in the LG equation, which affects the magnetization vectors. An explanation is provided, focusing on the damping of these vectors when a static field is applied along the x-axis and an AR field along the y-axis. A visualization is suggested by plotting MX versus MZ or MY versus MZ to observe the damping behavior.

Micromagnetic Simulations for ferromagnetic resonance using OOMMF. Transcription

• 00:00 - 00:30 where I'm going to talk about the simulations of fmr in PS using is micromagnetic simulations simul simulation platform and we will tell about how to simulate fmr in P so this will be the my outline first I will tell you
• 00:30 - 01:00 uh the introduction of the micromagnetic simulations then I will introduce you to theas then I will compare the simulation and experimental results and then I will tell you about the outcomes of the simulations and finally I will conclude this by results okay so micromagnetic simulation so there are a few micromagnetic uh simulation platforms few of them are free but some of them are used for
• 01:00 - 01:30 commercial application they are paid so few of them are um anx and Etc so what can what they can do they can simulate fmr so which we'll talk about in this work uh they can also simulate the MH Loops okay and then they can also uh simulate domain wall motions we can study about the velocity of transvers domain wall motion uh along the strips
• 01:30 - 02:00 as described here by this uh paper we can see this p and yeah you can also simulates spin waves and in magnic wave guides and you can compare the results with the theoretical or experimental works and finally you can also simulate using micromagnetic simulation of course different platforms of uh have their uh own capabilities to simulate these things so finally you can also simulate
• 02:00 - 02:30 scrum and yeah and their frequency response in the magnetic multilayers as described in display so coming to the O uh I'm working on o simulations so what isph St for object oriented micromagnetic framework and it is a free free micromagnetic simulation software which is developed as a project in the list uh by Mike Don and Don Porter
• 02:30 - 03:00 and it aims to solve the LG equation the L liit Gilbert equation using finite difference method so it creates an atlas representing the geometry of an object and divides this Atlas into small sents which for which the LG equation is then soled and here you can see the LG equation as uh which describe the motion of the magnetization okay so coming to the introduction of the ferromagnetic
• 03:00 - 03:30 resonance what is aeromagnetic resonance so fmr is the resonance phenomena of the magnetization vector in response to a Time bearing magnetic field or basically the microwave wheel so the lerg equation again uh it contains a prec torque term which is given here in the green color and then also as the damping term which is as this which is parameterized by this uh parameter Alpha Gilbert temping t so using oh we will try to solve this
• 03:30 - 04:00 LG equation and we will try to get the solutions for this magnetization Vector as you can see this is a differential equation and we will try to solve it so how does the uh motion of this magnetization looks you can see in this picture so it tries to damp about the axis which is described by H effective H effective contains the all the contribution from the internal field as well as the external field external static field
• 04:00 - 04:30 okay now as we know that uh there is some damping in this LG equation so because of that there will you can see the damping of the magnetization vectors so this is let's say my component and this is MZ component where I have applied a static field along the xaxis and AR field along the let's say Y axis so then you can see the this kind of damping behavior and if you plot MX versus MZ sorry my versus MZ
• 04:30 - 05:00 then you can see this clear ding Behavior which it start from here and tries to D D D D and it will finally come at the center okay so now for small damping uh parameter Alpha uh this MZ component or basically the MX component remains constant while the other two in plane components they are essentially oscillating okay so now this uh
• 05:00 - 05:30 resonance condition is well known and it is uh described by this SK equation which this which relate this um uh resonance frequency with the applied field and the material parameter such as an isotropy and the magnetizations also you can see here a few de demagnetization factors also okay so now coming to the fmr simulation process so what it requires to simulate
• 05:30 - 06:00 the fmr uh using micromagnetic simulations so first it is required to minimize the magnetic energy to identify the equilibrium configuration for a given DC so you need to uh set the equilibrium configuration so that uh the system minimizes its energy with respect to the exchange energy as well as the Remake energy and if there is any other
• 06:00 - 06:30 an isotropy is there then with respect to that the system should go to a minimization of the energy so here you can see this uh picture uh this represent the equilibrium configuration and now what will be the second step Second Step will be the uh we need to apply a small magnetic pulse of sufficient Bend withd uh to the perpendicular to the applied DC magnetic field so here I'm applying uh the magnetic field static magnetic field along the X Direction so I will apply
• 06:30 - 07:00 the uh small magnetic pulse along the y- AIS and then I will use the equilibrium configuration which I have calculated in the first step as the starting configuration to run a dynamic simulation the dynamic simulation looks like this uh here you can see that uh the trajectory of the magnetization component and it tries to D to a the center like this okay now what I will do is I will
• 07:00 - 07:30 uh extract these magnetization vectors in a uh time step of one 10 P seconds and the total simulation time will be around 10 NS this can be Vari during different experiments and then I will try to calculate the fal transform of this time wearing magnetization to find the power spec and which I will use as a comparison for the experiment
• 07:30 - 08:00 okay now why I am choosing the syn pulse to excite the uh fmr so basically the syn pulse if you can see here this is given by this graph and it is described by the magnetic function sorry mathematical functions which is given by this s Omega T minus t / Omega C tus so here Omega C is the cut off frequency uh cut off frequency means uh up to which
• 08:00 - 08:30 frequency range it can excite this fmr and T off means the peak of this impulse where the peak is situated here in this case I have taken it as 5 NS and and yeah and this cut off frequency I have taken as 100 GH sorry it is 100 G so here you can see in the foror transform you can see here 1 and 10 power 11 so that is around 100
• 08:30 - 09:00 GHz so this syn pulse can excite frequencies up to 100 GHz okay so how it is exciting let's see in this video so this is the video when I started the time it start from zero and now see here it reaches the uh simulation time when it reaches the simulation time as five NS it excites this uh uh magnetization and they get a uh they goes to a high State and then it
• 09:00 - 09:30 lets let it damp and it will go to the equilibrium configuration okay so now how my fmr Spectra look using this simulation so here you can see there is a central Peak and there are a few other Peaks also what is the origin of these Peaks I will tell you in a minute so okay so what is the central Peak I need to uh know which Peak is my atmr signal whether this peak this
• 09:30 - 10:00 peak this peak or this peak so for that I need to do the special special transformation of the magnetization at every cell so that I can get this kind of plots where this uh where I can file the spatial modes so here you can see corresponding to this frequency I'm getting the energy or the power concentrated as the center of the field uh so this means that it is a it is the fundamental mode or the K mode or
• 10:00 - 10:30 basically the fmr mode whereas this other other Peak this current at this peak the energy is localized at the edges of the film okay uh so what does it mean this means that this peak corresponds to Edge dmed uh uh mode and similar to the other Peak here also uh the energy is localized at the edges okay so this analysis uh should be required in order to find which one of
• 10:30 - 11:00 these Peaks are my fmr mod okay now we will talk about the effect of the demagnetization factors onto the K equation so as you know that the K equation for a general ellipsoid where the X with the AIS C greater than b greater than C is given by this equation so here you can see this these are the dag factors okay so now if I choose the dimension of my sample as 5 cross 30
• 11:00 - 11:30 cross 50 so if you see that this is this is not a this do not follow a uh thin film approximation you can also see from the remagnetizing factors where n is equal to8 and in the graph also you can see it stands here this is no longer this is no not a thin F approximation so let's go for a higher value let's say this five cross 100 cross 100 so here the na
• 11:30 - 12:00 is tends to uh .9 and the other two dmac factors are tending to zero basically so in that case these uh K equations curves which are the theoretical this K equation this this tries to tends to the experimental curve so this blue curve with the dots this is the VNA frequency which which I calculated experimentally and this this
• 12:00 - 12:30 last uh Dimension this corresponds to our thin film Dimension or which we used for the experiment so here you can see that this dmac factors are approximately equal to one and the other things are uh corresponding to zero so okay so I calculated these dmac factors from these two references okay now we will study the effect of Exchange stiffness constant uh on the K
• 12:30 - 13:00 equation so I have plotted so actually I have simulated the fmr for corresponding to different a values is exchange stiffness constant so if you can see here uh this yellow curve corresponds to 8 PJ per meter which lies lower and then this uh 12 PJ per meter it is slightly above then 14 it is slightly above so what does that mean as I am increasing
• 13:00 - 13:30 the uh exchange stiffness constant the curve shifts to a higher resonance frequency so let's see at this point uh this point uh1 uh Tesla uh the resoltion frequency is somewhat here 8 or around 9 but uh if I increase this exchange stickness constant it goes above 10 and similarly for the other things so what is happening is so for a F the magnetic field there is an the this ex increase
• 13:30 - 14:00 in exchange sness constant this shift the Cal plot to a higher Revenant so why this is happening this could be because of uh The Exchange interactions which are increasing as this a is increasing which is increasing the uh effective field uh in the system uh so that the Kil equation if you can see here here uh
• 14:00 - 14:30 this HJ is the effective field basically if you uh consider this here you will see a effective field so that effective field is increasing because of that the resonance frequency are shifted to a higher value so now this practically such analysis can't be reported uh like because it is not possible to have some such a materials with different a values but all other magnetic parameters as
• 14:30 - 15:00 Same by all other par parameters I mean the damping Factor the saturation magnetization the isotropic constant and like let's say zom magnetic ratio okay so what are my simulation parameters I using simulation parameter like this Ms value I'm taking it as this value this a value I varying from 1 to 30 PJ per meter gyom magnetic ratio is 180 uh around
• 15:00 - 15:30 186 GHz per TLA and then GMA is used for the simulation okay and the dimension of my fils are around 200 to 200 and 5 nom