The manuscript presented by Libor Vojacek comprises five chapters. After a short introduction clearly outlining the goal of this study focusing on magnetic anisotropy, he describes its importance for spintronics and its physical origins in chapter 1. In chapter 2, Libor describes in pedagogical manner density functional theory (DFT) that he employed to in the framework of this Master’s thesis. In chapters 3 and 4, Libor presented the main findings of his work on the behaviour of magnetic anisotropy in tunnel junctions comprising MgO and bcc magnetic transition metals. Finally, in chapter five he analyses fundamental mechanisms of magnetic anisotropy in the framework of second order perturbation theory with his excellent background revealed. The manuscript is closed by short and yet clear conclusion with a full bibliography, list of abbreviations and an appendix. Overall, in the presented Master’s thesis, which is written very well, Libor Vojacek demonstrated a depth of knowledge of the topic and deserves the highest grade in all evaluation criteria. It is not surprising that based on his accomplishments presented here Libor published his results in peer reviewed Phys. Rev. Applied.

First of all, congratulations to the student for such high-quality work. It was pleasing to read the master thesis. The thesis starts with the background of spintronics, emphasizing the necessity to shrink the device size. The following chapter gives a pedagogical explanation on magnetic anisotropy, pointing out that to achieve STT-RAM with a smaller size, it is crucial to increase the magnetic anisotropy energy against data loss due to thermal fluctuations. Chapter 2 explains ab-initio methods from the Many-body Schrodinger equation to the DFT Kohn-Sham equation, with the latter one the main method used in the study. This Chapter is also pedagogic.
The main results are elaborated on from Chapter 3 to Chapter 5. Each chapter stands an investigation itself, but the three investigations are linked on the main story-line:
1) Chapter 3 investigated the impact of the thickness of perpendicular magnetic anisotropy (PMA) for individual metal and its thickness dependent. It found that the contribution of PMA is from the interface for Fe, but the volume for Co.
2) With the conclusion of Chapter3, the Fe/Co/Fe structure is proposed for larger PMA in Chapter 4. The proof of concept is demonstrated by simulation.
3) Chapter 5 presents the extraction of PMA using the second-order perturbation theory, which indicates the orbital contribution of PMA.
I found the scientific study is original, the approaches are well justified, and the manuscript is well written. Besides, I had a few remarks, and I put them inside the question section.

A few layout problems, might due to LaTex:
1) page 22, Section Plane-wave basis and PAW method
2) page 24, Section Spin-dependent Kohn-Sham equation.

Also, on page 22, the last paragraph (In addition, there are linear scaling methods....). I found this paragraph is a bit abrupt to mention in the section which is discussing basis. Topics for thesis defence:

1. On page 33, the c/a ratio is discussed: Is the volume of the structural fixed at a constant value when vary this ratio?
2. On page 21, regarding the convergence, it is mentioned that α needs to set to 0.01 to reach convergence. If α is too small, the change of density is also small, hence the total energy. Will this setting of α lead to a false convergence?
3. On page 33, the c/a ratio is discussed: Is the volume of the structural fixed at a constant value when vary this ratio?
4. On page 41, the intermixing of Fe and Co is discussed. In reality, intermixing occurs randomly, however, due to the periodic boundary condition, the intermixing in simulation is repeated. Was a larger supercell used for a more realistic situation? If yes, how large the supercell is?
5. In section 47, for the virtual excitation, does the momentum (k-vector) preserved, namely only vertical excitation is considered? and why?