Advanced x-ray spectroscopy

University of Sao Paulo

Graduate school – Institute of Physics

Advanced X-ray spectroscopy

Objective: in this course, we intend to provide an in depth training on advanced x-ray spectroscopy, with an emphasis on the fundamentals of synchrotron based experiments. We will start discussing the radiation matter interaction and will develop the topics related to several x-ray based experimental techniques, such as x-ray absorption spectroscopy (XAS), Angular Resolves Photoemission Spectroscopy (ARPES) and resonant inelastic scattering (RIXS). By the end of this course we expect that the student will be able to: (1) understand the outcome of several experiments based on the x-ray absorption and scattering; (2) perform data analysis of simple absorption and scattering data (qualitative and quantitative methods); (3) understand the specifics of synchrotron based experiment and write a preliminary experimental proposal.

The course: the course will run during two weeks. The first week, actually only three days, will be dedicated to the discussion of the basic processes of x-ray absorption and photonemission. We will also survey some concepts from solid state physics. Then, in the second week, this time a full 5-day week, our guest Dr. Claude Monney will take over and present us insightful lectures on angle-resolved photoemission spectroscopy (ARPES) and resonant inelastic X-ray scattering (RIXS). During all course, practical tutorials will be offered.

Schedule: 17/06, 18/06 and 19/06 - first week - Prof Fernando Garcia (IFUSP) and 24/06, 25/06, 26/06, 27/06 and 28/06 - second week - Dr. Claude Monney - University of Friburg

All lectures: 10:00 to 12:00. All tutorials: 14:00 to 16:00. Complete course: 30 hours (2 credits) -

Prerequistes: formally none. You better know: graduate level quantum mechanics (quantum mechanics I). During the first week (17 - 19) of the course, we will review relevant topics for the study of X-ray spectroscopy.

Course content: X-ray absorption spectroscopy, photoemission spectroscopy, angle-resolved photoemission spectroscopy, resonant inelastic x-ray scattering (see below for a description of each lecture).

Grading (mandatory activities, in English): (1) A paper essay/seminar (100%): a short seminar (or essay) about a paper of choice by the student (there will be a list and a guide; OR (2) A synchrotron proposal (100%): a two page document where you will propose a synchrotron based experiment applying one of the techniques discussed in the course.

Study Material

Proposals: here you may find 3 examples of beamtime proposals for XAS, RIXS and ARPES experiments. This material may guide your writing. Two models are shown (the Brazilian LNLS and the Swiss SLS), that are very similar but not the same. Please, choose ONE of the proposed models.

Review papers: here you may find 1) a review about ARPES of the Iron based superconductors; 2) a review about RIXS in solids and 3) a review about BioXAS (the application of XAS to the biological relevant matter). Take a look at the "intro" of the paper that might be of your interest.

Sample papers: some recent papers that may help you (this list is far from being exhaustive).

Hard X-rays spectroscopy... ; Anisotropic magnetic excitations...; Semiconductor-to-semiconductor...;

List of papers: TBA

The course, lecture by lecture:

First Week (17 – 19): Prof. Fernando Garcia (IFUSP)

Monday June 17:

Basics of X-ray absorption (XAS) and photoemission (PES) I: The first lecture begins with a qualitative discussion of the X-ray absorption and photoemission processes. We shall write the Hamiltonian describing the interaction of an electron with a classical magnetic vector potential A and use it to illustrate some central concepts. Afternoon, the planning of XAS and PES synchrotron based experiments will be discussed.

Tuesdar June 18:

XAS and PES processes: In this second lecture, we will give a more solid approach to the subject. The time-dependent perturbation theory is reviewed and the dipole rules for XAS and PES are deduced. Life time broadening is also discussed. We shall exemplify the theory approaching some specifics of transition metal physics. Afternoon, we shall discuss results from recent literature in the area learning how to extract useful information from these experiments.

Wednesday June 19:

Survey of solid state physics concepts: We will offer a fast paced survey of the following concepts: lattices, reciprocal lattices and electronic structure (we shall explore the square lattice, morning) and elementary excitations. This last topic will be approached with a tutorial to the application of second quantization formalism.

First Week (24 – 28): Dr. Claude Monney (University of Friburg)

In this week, each lecture (except for the last one) will be accompanied by a tutorial session, during which we will learn how to do simple analysis of data.

Monday June 24:

Basics of ARPES: The first lecture of the week is devoted to the basics of angle-resolved photoemission spectroscopy (ARPES), which is the most employed technique to access the momentum-resolved electronic structure of materials. We will learn how the photoelectric effect is used to perform photoemission spectroscopy. We will also learn how to take advantage of the conservation of momentum to perform ARPES.

Tuesday June 25:

The spectral function in ARPES: This lecture will introduce the concept of the spectral function in photoemission. We will learn under which conditions we can model photoemission with the spectral function and will derive together relevant formulas. We will then see what information about many body physics is encoded in the spectral function.

Wednesday June 26:

The spectral function in ARPES 2: This lecture is a follow-up of the previous one. We will study famous examples from the scientific literature to illustrate how ARPES can access many body effects in correlated materials and how it can be modelled through the spectral function. Typically we will discuss together the effect of electron-phonon coupling or electron-electron interactions in ARPES.

Thursday June 27:

Basics of RIXS: This lecture is devoted to the basics of resonant inelastic x-ray scattering (RIXS). RIXS is a powerful and versatile x-ray spectroscopy. We will derive together the Kramers-Heisenberg formula describing RIXS using second-order perturbation theory. We will then discuss how a RIXS experiment is planned in practice, taking advantage of the absorption edge of relevant ions in materials and of the scattering geometry.

Friday June 28:

RIXS on correlated materials: In the last 10 years, the development of the RIXS technique and its application to correlated materials followed a steady and impressive development. We will illustrate this with examples from the scientific literature and discuss them in details. We show how RIXS can measure crystal field excitations, magnetic excitations or interband electron-hole excitations. We will discuss how one can take advantage of the RIXS cross-section to discriminate between these different excitations.

Friday June 28: Special seminars (30 + 10 minutes each, 10 min interval):

14:00: Dr. Ricardo Donizeth dos Reis (SIRIUS – CNPEM). Title: TBA
14:50: Dr. Túlio Costa Rizuti da Rocha (SIRIUS – CNPEM). Title: TBA

The seminars will be about the new beamlines in SIRIUS dedicated to XAS, ARPES and RIXS.