During the first week, we had a lot of tours, lectures and barbeques. On and Tuesday and Wednesday we sat through the project presentations from the AMO group, the condensed matter group, as wellas the high energy physics professors. We made our project choices, and I got to work on vortices with Dr. Wysin. On Thursday I met with Dr. Wysin briefly to go over some of the details of the project, and I was introduced to vortices. Then on Friday, I was assigned some readings to do by my mentor. At this stage I had acquainted myself with the project ideas and the path we’ll be going. I was still curious as to the kind of programming I’ll be doing and was yet to learn Monte Carlo Simulation.
On Monday, I met with my advisor, and we talked at length about the project, and also reviewed some publications on vortices. There were some sections of the readings I was assigned that I did not fully comprehend, and I asked Dr. Wysin for help regarding those sections. We went over some of the programming I will be doing in C, and my mentor asked me to search for some books on Monte Carlo Simulation and the reasoning behind it. Later this week, Dr. Wysin loaned some books on random processes, computer simulation and statistical mechanics. He specifically referred me to the chapters on the canonical and microcanonical ensemble to read. On Friday, my mentor gave me an assignment to revise some sections of a program for the purposes of this summer project.
During this week, I worked with my mentor to change sections of the program to suit the project we were pursuing this summer. Specifically we had designed the model nanomagnet to have two holes, where spin interactions are minimized and also decided to apply a constant magnetic field, which will be applied after a certain number of Monte Carlo steps.
At this point I was ready to run some simulations of the project. The first simulations I ran were without any applied magnetic field, and we’ll start with the vortex located at the center of the nanodot, or any other location to see if it gets pinned on either hole. Some of the simulations I ran include the following
· Simulation1-> Vortex located at centre, holes 10 lattice units from the center on either side, hole radius of 2 lattice units, and system size of 20 lattice units, coupling constant of 0.08, no magnetic field.
· Simulation2-> Vortex offset from center, (location 0,-7) with holes 10 lattice units from the center on either side, hole radius of 2 lattice units, and system size of 20 lattice units, coupling constant of 0.08, no magnetic field.
· Simulation3-> Vortex offset from center, (location 4, 20) with holes 15 lattice units from the center on either side, hole radius of 2 lattice units, and system size of 30 lattice units (approx = 200nm), coupling constant of 0.08, no magnetic field.
On Friday, I gave a report about the progress I’m making on my project to the group
During this week, I ran a lot of simulations, changing several parameters like the hole positions, the initial vortex location, the size of the dipole coupling constant, and the size of the system lattice to study the movement of the vortex.
I had to organize the files in my linux account to keep track of the simulations I ran. Dr. Wysin also proposed that I work on a section of the program that will generate a graph of the vortex location along the x- axis and the internal energy with each Monte Carlo step. The logic behind this was that should the vortex get pinned on either hole, the total internal energy will drop be lower and this should indeed confirm that the hole locations are stable positions for the vortex. I also fixed a section of the program which is the seeding option and it took a random number from 0 - 216 to control the configuration of the Monte Carlo simulation. At this stage it was significantly difficult to see the vortex getting pinned to either hole in my simulations
The graphs showing the energy vs position of the vortex were not telling us much. In a couple of the simulations the vortex did not move significantly far from its initial location along the x-axis. This was not good for the purposes of my project. Eventually we had to scrap this idea and seek an alternative approach. I continued with some more simulations, using different parameters for the system size, hole radius, as well as the hole and the vortex positions
During this week, Dr. Wysin noticed an error in some of the simulations with the seeding option, this was duly fixed. It was reflected in the more random MC configurations that we were generating. There was a minor bug as well that I had to fix, and by Friday I had set some simulations running, in the hope of getting some results in these tests next week.
Some major landmarks were achieved during work this week. First I was able to ran some simulations to show how the vortex which is initially pinned on one hole moves to the second hole with a directed magnetic field against the spins.
Later during the week, I was able to see through one of my simulations that without applying a magnetic field, and having the vortex initially located at the center, the vortex eventually moves to one of the holes and get pinned on it.
These were very significant results.
During this week, my mentor and I spent a lot of time thinking of appropriate values to use for the Monte Carlo Simulation. We to choose a cell size that will be a more accurate modeling of the number of spins in a nanodot. However, increasing the thickness of our nanodots meant that our Monte Carlo Simulations will run for way too long. My mentor worked out values for the cell size as 200nm, and a thickness of 15nm.
For this week, I spent a lot of time running simulations, using these new values. This proved to be a daunting task, as the MC simulations took a long time to run. Aside the vortex seemed to be trapped a lot in it initial position. Incidentally, this was because of the high dipole to exchange coupling ratio. Ultimately this was resolved by choosing a smaller thickness for our model nanodots. Our new dipole to exchange coupling ratio worked out to be 0.0427 compared to our previous value of 0.128. Also, I was interested in finding out the critical magnetic field value that will cause the vortex to move from a hole.
The final week of the program was spent running and taking results of our Monte Carlo simulations.
Aside that a fair amount of time was spend preparing my final PowerPoint presentation and a formal lab report