Master's Thesis

Artificial Shakti ice magnets: ground state degeneracy, Coulomb phase and monopole excitations

Final Thesis 5.25 MB

Author of thesis: Ing. Marek Zálešák

Acad. year: 2022/2023

Supervisor: Nicolas Rougemaille

Reviewer: Ing. Aleš Hrabec, Ph.D.

Abstract:

Artificial spin systems have emerged as a promising platform for studying in real space and harnessing exotic states of matter. This diploma thesis investigates the unique properties of a specific artificial spin system known as the shakti ice magnet. The shakti ice magnet is a two-dimensional arrangement of interacting nano-magnets, exhibiting intriguing magnetic behaviour.

This research aimed at characterising its behaviour and its ability to be mapped onto the seminal square ice in which interesting Coulomb physics is expected. A combination of experimental measurements and numerical simulations was employed to achieve these objectives. Experiments were based on MFM measurements to determine the magnetic configuration of samples containing lithographically prepared shakti lattices.

Keywords:

artificial spin systems, artificial magnetic spin systems, shakti lattice, vertex model, magnetic force microscopy, spin dynamics, Coulomb phase.

Date of defence

20.06.2023

Result of the defence

Defended (thesis was successfully defended)

znamkaAznamka

Grading

A

Process of defence

Po otázkách oponenta bylo dále diskutováno: Závislost chování Shakti systému na velikosti magnetek. Vliv okrajů mřížky na celkovou energii sysétmu. Student na otázky odpověděl.

Language of thesis

English

Faculty

Department

Study programme

Physical Engineering and Nanotechnology (N-FIN-P)

Composition of Committee

prof. RNDr. Tomáš Šikola, CSc. (předseda)
prof. RNDr. Jiří Spousta, Ph.D. (místopředseda)
prof. Mgr. Dominik Munzar, Dr. (člen)
doc. Mgr. Adam Dubroka, Ph.D. (člen)
prof. RNDr. Petr Dub, CSc. (člen)
prof. RNDr. Bohumila Lencová, CSc. (člen)
prof. RNDr. Jiří Petráček, Dr. (člen)
prof. RNDr. Radim Chmelík, Ph.D. (člen)
doc. Ing. Radek Kalousek, Ph.D. (člen)
prof. Ing. Miroslav Kolíbal, Ph.D. (člen)
doc. Ing. Stanislav Průša, Ph.D. (člen)
RNDr. Antonín Fejfar, CSc. (člen)

Supervisor’s report
Nicolas Rougemaille

Verbal classification: Marek demonstrated professional ability in the field of artificial frustrated magnetism. He conducted a substantial amount of magnetic imaging experiments using magnetic force microscopy and run different numerical codes to extract relevant physical quantities. Marek is a serious, rigorous, hard working young scientist. We envision the publication of two articles in peer-review journals.
Evaluation criteria Grade
Splnění požadavků a cílů zadání A
Postup a rozsah řešení, adekvátnost použitých metod A
Vlastní přínos a originalita A
Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry A
Využitelnost výsledků v praxi nebo teorii A
Logické uspořádání práce a formální náležitosti A
Grafická, stylistická úprava a pravopis B
Práce s literaturou včetně citací A
Samostatnost studenta při zpracování tématu A

Grade proposed by supervisor: A

Reviewer’s report
Ing. Aleš Hrabec, Ph.D.

The master thesis of Bc. Marek Zalesak deals with the investigation of the artificial spin system based on the shakti geometry. This geometry was originally proposed by Chern et al. and further experimentally realized by Gilbert et al. Both authors showed how the Shakti spin configuration can be mapped onto a classic square spin ice, which then showed desired properties. The aim of this work was to revisit the experimental realization of this particular lattice and analyze the data in a more elaborate way, as was shown recently by Vojtech Schanilec. From the experimental point of view, the Gilbert’s results were reproduced although with a slightly less powerful demagnetization protocol. The deeper analysis of the data reveals that the underlying physics imprinted into the magnetic ordering is more complicated than previously reported by Gilbert and colleagues. The data were then analysed to identify all the vertex populations, which were then confronted with the Monte Carlo simulations. This was also confirmed by comparing the experimental and computed magnetic structure factors. The Monte Carlo model was then modified in order to reproduce the experimental data. In the final, but important, sections, it is concluded that also the mapping itself also brings some significant restrictions.
I personally find the work original and scientifically sound going beyond the groundbreaking work of Gilbert. The work is very mature containing all the key scientific ingredients: critical analysis of the literature, transparent data analysis and its critical evaluation. I am actually excited that one can reproduce the published data, which is something of great significance and which is rarely reported. It is also very transparent how the previous data were analysed and what the overlooked points were. The amount of experimental data and statistics is certainly sufficient to draw the well-supported conclusions. Mr. Zalesak also performed an extensive analysis of the Monte Carlo simulations, which were performed by the team at Neel Institute in Grenoble. The content of the manuscript is suitable and it contains all the necessary background to understand the experimental findings and the analysis. One weaker point is that sometimes it is slightly hard-to-follow some of the English expressions, which make some parts harder to understand. Nevertheless, the thesis as a whole is written at a very good level and I am looking forward to seeing this being published in a peer-reviewed journal.
I am certainly in favor to recommend this nice work to be defended in front of the examination committee.
Evaluation criteria Grade
Splnění požadavků a cílů zadání A
Postup a rozsah řešení, adekvátnost použitých metod A
Vlastní přínos a originalita A
Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry A
Využitelnost výsledků v praxi nebo teorii A
Logické uspořádání práce a formální náležitosti B
Grafická, stylistická úprava a pravopis B
Práce s literaturou včetně citací A
Topics for thesis defence:
  1. 1. The whole idea stands on the mapping of spin configurations in shakti configuration to the square spin ice. Could you please in a pedagogical way explain step-by-step the whole idea of mapping as you would explain this to your younger colleague? Figures in Chapter 2.51 would be probably the best starting point. Also, what is the meaning of the final arrows of this mapping in the rightmost figures 2.6 and 2.7? How is the orientation of the arrows orientation defined?
  2. 2. Following the first question, the whole idea of mapping relies on the fact that only Type C_I and C_II vertices are present. However, as shown in the thesis, this is not correct (This was puzzling me for the rest of the thesis and it is only discussed in the very last chapter, which is perhaps too late). Does it therefore mean that the whole analysis (here and in the work of Gilbert) does not really work?
  3. 3. The proposed solution to the discrepancy between the experimental model and the Monte Carlo is connected to an intrinsic alternating magnetic field, which was implemented in the Monte Carlo code. However, the potential physical origin of this coupling is not discussed. Do you have some suggestions about the origin of this non-intuitive effective field?
  4. 4. You discussed the difference between J_1 and J’_1 couplings. It would be straightforward to estimate the ratio by using micromagnetic simulations. Can you estimate this or justify your choice 𝐽′_1=0.9𝐽_1? I assume that there would be an interest to have these two couplings equal. Would it be achievable to adjust the coupling by, for example, reducing the width of the long magnet?
  5. 5. The numbering of the bibliography items should be fixed in the final version.

Grade proposed by reviewer: A

Responsibility: Mgr. et Mgr. Hana Odstrčilová