Angle- and spin-resolved photoemission on La 2/3 Sr 1/3 MnO 3

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Universit´e de Cergy-Pontoise

D´epartement de Physique

TH` ESE

pour obtenir le titre de

Docteur de l’Université de Cergy-Pontoise (Spécialité : Physique)

pr´esent´ee par

Juraj K REMPASK´ Y

Angle- and spin-resolved photoemission on La _2/3 Sr _1/3 MnO ₃

Thèse soutenue le 4 juillet 2008 devant le jury composé de : Jean-Michel MÂRIOT Président

Nick B^ROOKES Rapporteur Jürg O^STERWALDER Rapporteur Agnès BÂRTH´ÊL´ÊMY Examinateur Dominique C^HANDESRIS Examinateur Karol H^RICOVINI Directeur de thèse Luc PÂTTHEY Co-directeur de thèse

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To Renata, Nat´alia and Krist´ına

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near the Fermi level.

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Part I

Background, experimental and theoretical aspects

1

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Chapter 1 Introduction

1.1 Why are manganites interesting?

This work is devoted to manganese oxides with perovskite structure (from here on, manganites). The manganites are a family of compounds that have provided harmless pleasure to generations of solid-state physicists and chemists since their discovery at the Philips Research Laboratories in the Netherlands more than 50 years ago. Jonker and van Santem [34] first reported the correlation between ferromagnetism and metallic resistivity in the hole-doped manganese oxide perovskites. This correlation was explained by Zener [88] who proposed that ferromagnetism arises from an indirect coupling among the manganese ion spins via the carriers, the so-called double-exchange model. In this model, Hund’s coupling is considered very large. Hund’s coupling forces the spin of the carriers to be parallel to the ion spins. The minimization of the kinetic energy leads to ferromagnetic alignment of the core spins, which for manganites was believed to be at the heart of the correlation between ferromagnetism and metallic resistivity.

The family of manganites is very rich; this work focus on the experimental and theoretical description of one member of family: La_1−xSr_xMnO₃ (LSMO). It is one of the manganese oxide compounds that has received the most attention. The hole-doping in this compound give rise to a very rich phase diagram where the charge, lattice, orbital, and spin degrees of freedom determine the ground state of the system depending on temperature, external magnetic field, and pressure.

The parent compound LaMnO₃ is an antiferromagnetic insulator that be- comes, upon Sr doping x, La_1−xSr_xMnO₃, a ferromagnetic metal. The growing interest in the manganite research is, in author’s view, due to the following main reasons:

3

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Figure 1.1: Electronic phase diagram of La1−xSrxMnO3 (LSMO).

Open circles and filled triangles are the N´eel and Curie temperatures, respectively (PI: paramagnetic insulator; PM: paramagnetic metal; CNI:

spin-canted insulator; FI: ferromagnetic insulator; FM: ferromagnetic metal). The red arrow indicates optimally doped LSMO system (x = 0.3) considered in this work (figure adapted from Ref. [83]).

1. The magnetoresistance effect.

2. The very rich phase diagram (see Fig. 1.1), exhibiting a variety of phases, with unusual spin, charge, lattice, and orbital degrees of freedom. The competing interactions between them make the system change from insulator to “bad” metal even without an external magnetic field.

3. The connection with important physics also unveiled in the cupra- tes. Even in the best-quality crystals available, there is an inho- mogeneity which seems to be intrinsic to the system: the states formed in these compounds are dominated by competing phases, for the LSMO this is typically a ferromagnetic and antiferromagnetic competition.

1.2 The colossal magnetoresistance effect

From the carrier transport point of view, magnetoresistance is a property of magnetic materials which is being crucial for a rapid development of new technologies such as magnetic sensors. It is defined as the change in the electrical resistance produced by the application of an external magnetic field. It is usually given as a percentage M R:

M R = 100 ×ρ(H) − ρ(H = 0)

ρ(H = 0) , (1.1)

where ρ is the resistivity measured with and without magnetic field (H = 0). In 1994, a very large magnetoresistance, also termed as colossal magnetoresistance (CMR), was reported in hole-doped manganese oxide perovskites [33]. The external magnetic field H greatly reduces the resistivity near the Curie temperature (T_C) which is the effect known as CMR.

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1.2. THE COLOSSAL MAGNETORESISTANCE EFFECT 5

Figure 1.2: (left) A generic correlation between ferromagnetic state and metallicity, compared to a thin LSMO film (right) prepared by pulsed laser deposition (sample F#C, see Sec. 7.1).

For higher magnetic fields the peak maximum is shifting to higher TC, whereby the maximum resistivity is strongly suppressed due to CMR. The trend in the shifts on both curves in higher magnetic fields are indicated by arrows: the magnetization minimum follows the TC.

The La_1−xSr_xMnO₃ samples used in this work were prepared by pulsed laser deposition. A typical dependence of the sample resistivity is seen in Fig. 1.2 (right). The CMR effect was not estimated by measuring the resistivity ρ in a magnetic field. Instead, ρ is plotted against temperature, which is an equivalent way to demonstrate the CMR. At first glance the resistivity change does not appear to be “colossal”. According to Eq. 1.1, where we substitute ρ(H = 0) by ρ(T_C) and ρ(H) by ρ(100 K), we get a negative MR of 96%.^∗ Below the ferro- paramagnetic transition T_C, the system is spontaneously magnetized, as indicated by the phase diagram in Fig. 1.1. This is the so-called intrinsic magnetoresistance property. Intrinsic magnetoresistance is maximum close to T_Cand appears due to the intrinsic interactions in the material. A general form of the magnetization and the resistivity temperature dependence of CMR materials is sketched in Fig. 1.2 (left). As shown there, the magnetic transition is accompanied by a change in the behavior of the resistivity with temperature: the system is metallic below T_C (namely, dρ/dT > 0) and insulator activated in the paramagnetic region (dρ/dT < 0). As indicated in Fig. 1.1, optimally doped LSMO may have T_C close to 400 K.

Approaching T_C from below, the resistivity increases dramatically. When external magnetic field is applied, the height of the resistivity peak greatly dimin- ishes with a concomitant T_C shift towards higher temperatures [Fig. 1.1 (left)].

Urushibara et al. [83] introduced a scaling relation between magnetoresistance and magnetization which holds close to T_C where the magnetization is small:

− δρ ρ(0) = C

M

Msat

2

, (1.2)

where Msatis the saturation magnetization. They demonstrated, that C is characteristic to doping x in La_1−xSr_xMnO₃, which clearly shows that hole-doping

∗Some authors normalize M R with ρ(H) and find values of thousands.

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EF

(a) (b) Figure 1.3: Schematic of a spin valve.

The outside layers are ferromagnets while the thin layer in between is an non- magnetic metal or insulator. Supposing the spin scattering is not happening at the interfaces, resistivity is low in the antiparallel configuration (a) because there are available up states in the layer on the right side to be occupied by the spin-up states on the left. The situation in (b) is opposite: the resistivity is high.

drives the system towards a weak coupling regime. For some systems the relation between carrier density n and C could be determined, but not for manganites.

This negative conclusion for manganites is further evidence of non-magnetic interactions, which are driving the metal-insulator transition in these materials.

And it is not surprising, that also the double-exchange model alone cannot account for the metallic transition in the ferromagnetic regime. Namely the physics of manganites, and many other strongly correlated electron systems, is driven also by electron-phonon coupling.

1.3 Spintronic devices: the future in microelectronics

A technology called spintronics has emerged, where it is not the electron charge but the electron spin that carries information. This offers opportunities for a new generation of devices combining standard microelectronics with spin-dependent effects that arise from the interaction between spin of the carrier and the magnetic properties of the material [68]. Figure 1.3 is a sketch of a spin valve based on the tunnel junction concept. The all-metal transistor has the same design philosophy as do magnetoresistance devices: The current flowing through the structure is modified by the relative orientation of the magnetic layers, which in turn can be controlled by an applied magnetic field. Neither current nor voltage is amplified, but the device acts as a switch or spin valve to sense changes in an external magnetic field. The main property that makes manganites so interesting for such applications is the fact that majority and minority spins are well separated in energy (≈ 2.5 eV, see Fig. 1.4).

It should be emphasized, that term “colossal” magnetoresistance was coined to make a distinction with the already giant magnetoresistance (GMR) found earlier in magnetic/non-magnetic metallic superlattices [2]. The effect is at the heart of modern devices that record data, music or snippets of video as a dense magnetic patchwork of zeros and ones, which is then scanned by a small head and converted to electrical signals. The MP3 and iPod industry would not have existed without this discovery by A. Fert and P. Gr¨unberg, rewarded by the Nobel

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1.4. HALF-METALLIC FERROMAGNETS 7

Figure 1.4: Schematic representation of the DOS for an itinerant ferromagnetic metal (Ni) and a half-metallic material (La_2/3Sr_1/3MnO3), after Hwang et al. [31].

The main property that makes manganites so interesting for applications is the fact that majority and minority spins are well separated in energy. Therefore, only one spin channel conducts; hence manganites are half metallic. Despite the fact that such system has no spin down states at the Fermi level (N↓= 0), in the literature the system is often presented as nearly half-metallic, i.e., N↓6= 0.

prize in physics in 2007. The Nobel citation also heralded the advent of a new, even smaller and denser, type of memory storage called spintronics, in which information is stored and processed by manipulating the spins of electrons. This spin manipulation is based on extrinsic magnetoresistance properties, where the notion of half-metallic ferromagnets is often invoked. However, as mentioned by A. Fert at the 2008 Swiss Physical Society meeting, spintronic devices based on half-metallic LSMO ferromagnets are presently not at the forefront of the spintronics industry because of their low T_C (≈ 350 K).

1.4 Half-metallic ferromagnets

Half-metallic ferromagnets are systems where spins with a particular direction (for example spin up) have a partially occupied band, while the opposite spin down direction has filled bands separated from the unoccupied ones by a gap, termed also as half-gap. Following the classification of the half-metallic ferromagnets by Coey and Venkatesan [8], there are 10 types of half-metals, subdivided into 5 groups according to:

1. density of states (metal, half-metal, semimetal and semiconduc- tor);

2. conductivity (metallic, nonmetallic, semiconducting);

3. type of the spin-up (down) electrons at the Fermi level (itinerant or localized).

A simple sketch of the LSMO-type density of states (DOS) compared to the Ni DOS is seen in Fig. 1.4. It must be emphasized that Ni is a typical itinerant ferromagnet with a very wide conduction band (≈ 4.5 eV for d electrons), which is split into minority and majority carrier bands offset by a small exchange energy (≈ 0.6 eV), leading to a partial polarization (≈ 11%) of the electrons [31]. On

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E_F

sf

EF sf E_F

heavy electrons

(a) (b) (c)

IA IB IIIA

Figure 1.5: (a) Schematic DOS for type IA half-metal with only ↑ electrons at E^F. (b) Type IB half-metal with only ↓ electrons at E^F. In narrow Mn d bands, the states at EF

may be localized, which is a nonmetallic type II half-metallic ferromagnet (not shown). (c) Schematic DOS for optimally doped LSMO (La2/3Sr1/3MnO3), which is a type IIIA half-metallic ferromagnet where ↑ electrons are itinerant and the others are localized (heavy electrons). ∆↓is the energy separation between minority-spin unoccupied and occupied states, ∆sfis the energy needed for a spin-flip excitation (figure adapted from Ref. [8]).

the other hand in LSMO a relatively narrow majority carrier e_g conduction band (≈ 1.5 eV) is completely separated from the minority band by a large Hund’s energy, as well as an exchange energy (≈ 2.5 eV), leading to a “nearly” complete polarization of the electrons [31]. This seems at odds with Fig. 1.4, because for LSMO no DOS is expected for the spin-down (↓) electrons at the Fermi level [(FL) ≡ EF]. Unfortunately, also the pioneering work of Park et al. based on photoemission [56, 55], did not provide a satisfactory evidence for the LSMO system to be a genuine (100%) half-metal. Coey and Venkatesan in Ref. [8] are more explicit: they say LSMO is a half-metal of type IIIA, also known as the transport half-metal. They have localized spin-up (↑) carriers and delocalized spin-down (↓) carriers or vice versa. A DOS exists for both sub-bands at E^F, but the carriers in one band have a much larger effective mass than those in the other.

As far as electronic transport properties are concerned, only one sort of carriers contributes significantly to the conduction. A schematic DOS of such half-metal is seen in Fig. 1.5(c). The heavy ↓ carriers give an activated conduction but they are short-circuited by the light ↑ carriers which are metallic with mobile (delocalized or itinerant) Mn d(e_g) electrons and immobile (localized) Mn d(t_2g) electrons at E_F. In contrast to this “transport half-metal”, Fig. 1.5(a,b) diagrammatically shows ↑ and ↓ DOS for a class IA (a) and a class IB (b) half-metal, where ∆↑(∆_↓) clearly indicates a gap in spin-up (spin-down) DOS. In this thesis, detailed spin- and angle-resolved photoemission studies indicate that LSMO does not fit to the type IIIA class of half-metallic ferromagnets. It seems to be a IA half-metallic ferromagnet that suffers from surface effects, the strength of which presumably depends on LSMO doping.

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1.4. HALF-METALLIC FERROMAGNETS 9

Photoemission hn

I

H

I

H

I

H Magnetic Tunnel

Junction

Point Contact Tedrow- Mersewey

Andreev Reflection Sc

I Sc

Figure 1.6: Diagrammatic comparison of five methods of measuring the spin polarization: photoemission, tunnel junction, point contact, Tedrow–Meservey experiment, Andreev reflection (from Ref. [8]).

While the photoemission method directly probes the majority (↑) and minority (↓) spin states, the other methods are based on a carrier transport. In the last two methods the transport is in a superconducting state.

1.4.1 Ambiguity in spin polarization definition

From the experimental point of view, half metallicity does not show any clear electrical signature and therefore is not easy to determine. Moreover, the measured value of the spin polarization depends on the experimental technique, as summarized in Fig. 1.6. In the literature there is a large inconsistency in the experimental determination of the spin polarization. Below I explain that this is probably due to a certain ambiguity in the spin polarization definition employed by different experimental techniques.

The tunnel junction method is based on trilayer structure consisting of a non- magnetic metallic layer sandwiched between two ferromagnets (electrodes). Such structure is capable to produce magnetoresistance effects, as briefly introduced in Sec. 1.2. However, contrary to CMR, they are caused by extrinsic properties and the clue is in the spin-dependent transport across a surface boundary. When the electrodes are ferromagnetic, the tunneling of electrons across the insulating barrier is spin-polarized, and this polarization reflects the DOS at the FL of the electrodes. This spin polarization is the origin of the tunneling magnetoresistance across the insulation barrier. Paradoxically, even though applications have already begun to be developed, there are still gaps in the understanding of spin- polarized tunneling. For example, the physics governing the spin polarization of tunneling electrons is not clearly understood. Previously, the spin polarization P of electrons tunneling from a given ferromagnetic electrode was generally thought to reflect a characteristic intrinsic spin polarization of the DOS in the ferromagnet:

P = N^↑(E_F) − N^↓(E_F)

N^↑(E^F) + N^↓(E_F) . (1.3) The experimental results from magnetoresistance junctions [5] based on LSMO underline the half-metallic nature of these mixed-valence manganites. A spin polarization of 95% is reported for LSMO tunnel junctions at 4 K. Similar results were obtained with transport spin polarization measurements based on point- contact Andreev reflection technique that give a polarization ranging from 58%

to 92% in thin films and bulk LSMO. Because no 100% spin polarization is

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reached, the measurements suggest minority spin contribution to the conductivity. Therefore LSMO was classified as a transport half-metallic ferromagnet, as mentioned in Sec. 1.4.

Recently Mazin [44] showed that in the case of transport techniques, such as the magnetic tunnel junction or point contact Andreev reflection, one must take into account the mobility of both majority and minority carriers. The spin polarizations are always related somehow to an experimental asymmetry detection. Mazin proposed that in a ferromagnet classical Bloch–Boltzmann transport theory allows to separate the currents of the spin-up and spin-down electrons and to define the spin polarization via the current densities J^↑(↓) as (J^↑− J↓)/(J^↑+ J^↓) ∝ hNv²i^↑(↓)τ^↑(↓). Assuming the same relaxation time τ for both spins, this definition leads to a definition of spin polarization weighted by the

↑ (↓) mobilities in the Nv² terms instead of just considering the ↑ (↓) DOS given by Eq. 1.3. Hence, following the definition of the “degree of spin polarization”

in [44], the spin polarization is defined as:

P_n= hN^↑(E_F)v_F↑ⁿ i − hN^↓(E_F)v_F↓ⁿ i

hN^↑(E_F)v_Fⁿ_↑i + hN^↓(E_F)v_Fⁿ_↓i , (1.4) where N^↑(E_F) [N^↓(E_F)], v_F↑[v_F↓] are the majority (and minority) spin DOS and the Fermi velocities, respectively. The parameter n stands for different limits for which the spin polarization is measured. One can immediately see, that depending on n, the N^↑(E_F) and N^↓(E_F) DOS are weighted differently. In the so-called ballistic limit, in which the mean free path of the electrons is larger that the contact size, the DOS is weighted linearly with v_F and P₁ is measured.

In the so-called diffusive regime (as in the classical Bloch–Boltzmann theory of transport in metals), the weighting is quadratic in v_F (n = 2) and P₂ is measured (assuming the transport relaxation time τ is constant). Tunneling experiments probe yet another spin polarization, PT, which may still be formally defined using Eq. 1.4 for n = 2 by replacing the velocities with spin-dependent tunneling matrix elements.

The additional complexity with the tunneling experiments is that they measure the spin polarization through suitable barriers. The metal-oxide interface of these barriers may change the polarization of the injected electrons across the tunneling magnetoresistance junction [15]. For the other methods, which use a ferromagnet-superconductor contact, the validity of Eq. 1.4 relies on the assumption that the J^↑ and J^↓ currents can be measured separately. This problem is suppressed in the point-contact Andreev reflection method, but it is still ques- tionable whether the limit n is 1 or 2. Equation 1.4 suggests that depending on the parameter n, the spin polarization can be dramatically different. This is probably one of the reasons which give rise to a large scatter in transport spin polarization measurements [5, 74].

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1.5. THESIS GOALS 11

1.4.2 The LSMO case: comparison with the P0 limit

In the simplest case the limit of n = 0 in Eq. 1.4 simplifies the determination of the spin polarization P₀ = P to Eq. 1.3. In this case the additional complexity related to the Fermi velocities v_F↑ (v_F↓) drops out. This is the case in photoemission experiments which provide direct information from the occupied DOS. In a spin-resolved photoemission experiment, N^↑(E_F) and N^↓(E_F) are “two currents”

that are directly measurable quantities (Fig. 5.3) which, inserted into Eq. 1.3, can provide absolute spin polarization not only at E_F. This is the most interesting quantity for comparison with transport measurements. The price is that the complexity associated with spin-resolved photoemission experiments is much higher compared to transport spin polarization measurements. This is likely the reason for which, to date, the only spin-resolved measurements reported on LSMO were made by Park et al. [56, 55], where P₀ = 100 ± 5% was reported.

In the literature this pioneering result was subject to discussions, mainly con- cerning the sample preparation. The sample preparation was referred to the work of Kwon et al. [39] which suggests that the sample was prepared by pulsed laser deposition. In particular, the discrepancy between P₀= 100 ± 5% [56] and the transport spin polarization measurements is not clear. To author’s knowl- edge the highest spin polarization with a LSMO/SrTiO₃/LSMO structure was reported by Bowen et al. [5], where 95% spin polarization was reached at 4 K.

This was probably the reason why Dagotto, in his book on manganites [10], reduced the achieved spin polarization measured by Park et al. to 95%. Conse- quently, according to the diagrammatic DOS layout in Fig. 1.5, La_2/3Sr_1/3MnO₃ seems to better fit with class IIIA half-metallic ferromagnets rather than with IA half-metallic ferromagnets.

As mentioned by Nadgorny [47, 48], a possible explanation for these con- troversial results between photoemission and transport measurements is (i) surface sensitivity in photoemission experiments; (ii) Park’s sample had undergone a complex cleaning procedure after which the sample could eventually become half-metallic at the surface [48].^†

1.5 Thesis goals

The main goal of this thesis is to revisit and refine the spin-resolved experiment by Park et al. [56]. To understand experimental data to full extent, however, additional questions emerge:

†It seems the sample preparation was not so complex at all. Since the sample was delivered by FedEx to the laboratory (J. W. Freeland, private communication), it needed some cleaning under ultra-high vacuum in order to make the sample ready for a photoemission experiment.

The cleaning was just a short annealing under oxygen in order to not change the sample O stoichiometry at the sample surface. However, as mentioned by Park et al. in Ref. [56], after this treatment the sample roughness allowed angle-integrated photoemission experiment only.

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1. How close to 100% are we able to measure the spin polarization?

Can our angle- and spin-resolved photoemission spectroscopy (de- noted herefater as SARPES) measurements be reconciled with the work of Park et al. [56]?

2. Is it possible to assess intrinsic effects, such as k_⊥-broadening effects, in 3D ARPES data. If yes, how are they reflected in SARPES measurements?

3. Are there some extrinsic effects, such as surface reconstruction, reflected in ARPES data?

4. Is it possible to connect ARPES and SARPES data?

5. Do ARPES data connect to bulk-band structure based on first- principle calculations?

6. How does the Fermi surface look like? Is it possible to reconcile the experimental Fermi surface with theory?

7. How are the strong electron correlations reflected in ARPES?

The first point is an extension of the work by Park et al. because our data are resolved in momentum k-space (Park’s data are not). P₀ in Eq. 1.3 relies on the assumption that the contributions of N^↑(E_F) and N^↓(E_F) are within the independent particle picture. This assumption is not evident even in “simple” itinerant ferromagnets such as Ni. So it might be not adequate for half-metallic ferromagnets as well. From this point of view, this work might trigger another view in the interpretation of spin-resolved data, especially in such a complex system like LSMO. Our results show potential new insight into the microscopic physics of this system, since the values of the spin polarization are extremely sensitive to the way how the photoelectrons are smeared out in their momentum space due to the three-dimensional (3D) LSMO band structure. This additional smearing in k-space is in agreement with experimental data based on high-resolution ARPES.

One important message from this thesis work is that it is responsible for the spin contrast reduction in SARPES due to photohole lifetime effects.

The ARPES studies focus on (100) and (110) mirror planes, which I denote henceforth as ΓX and ΓM mirror planes, respectively. Data were measured during several beam times on pulsed laser-grown La_2/3Sr_1/3MnO₃ at low temperatures.

In the Surfaces Interfaces Spectroscopy (SIS) experimental station, the sample temperature was kept at ≈ 40 K; in the COmplete PHotoEmission Experiment (COPHEE) endstation, temperatures of ≈ 60 K were achieved.

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1.6. STRUCTURE OF THE THESIS 13

1.6 Structure of the thesis

Part I of this thesis is a general background which deals with theoretical and experimental concepts used to give a consistent interpretation of the experimental data (Part II). Crystal quality is crucial for the experiments presented in this thesis. For this reason emphasis is also put on the sample growth and character- ization in Chap. 7: stoichiometry, surface reconstruction, and intrinsic epitaxial strain are addressed. Characteristic ex situ resistivities and magnetization temperature dependencies are presented. The LSMO bulk vs surface magnetism is addressed, whereby images of the spontaneous-magnetization domains, measured on the X-ray photoemission electron microscope at the Surfaces Interfaces Microscopy beam line (SIM), are presented.

In Part II, unpublished ARPES/SARPES data are presented. They connect to results of Paper A and B (the abstracts of four papers where I participated as a co-author are attached as appendices). In these papers the La_2/3Sr_1/3MnO3 band structure and photoemission simulations were not considered to such extent as presented in Paper E. A series of high-resolution ARPES spectra with a combined data processing technique is presented. I demonstrate that data processing used in this thesis unveils subtle spectral features difficult to see, or even not visible, in raw ARPES spectra. They definitively cannot be attributed to some noise because are reproducible between different ARPES spectra measured either on the same sample, or between different samples. The relevance of this data treatment is evidenced by comparison of experimental band structure between ARPES and SARPES measurements. There is a remarkable agreement between ARPES intensity simulations and ARPES data shown in the thesis. In view of the confusing results in the literature, as far as a comparison between theory and experiment is concerned, Chap. 6.1 might be a significant input to the LSMO community. It is the author’s opinion that “The case against half-metallicity in La_2/3Sr_1/3MnO₃” introduced by Nadgorny (see Ref. [47] and references therein), is based on incor- rect assumptions due to the neglect of the proper parameter in computational band structure simulations. For this reason the presented work puts emphasis also on a theoretical model of the LSMO band structure. In particular, the U parameter in our calculations was adjusted to the experimental data and can not be directly related to electron correlations, like the Hubbard’s U .

It is important to say that the presented band structure model is oversimpli- fied: it does not account for many-body effects based mainly on electron-phonon interactions –presumably a key issue in perovskite oxides. However, it is quite surprising to which extent a set of few parameters in the model, that just reflect the LSMO lattice, embodies the physics of LSMO, also recognized in the ARPES experiment. To cover these issues, a large collaboration was needed. It under- lines the importance of knowledgeable partners to find synergy between theory and experiment.

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Chapter 8 presents Fermi surface contours of the LSMO hole pockets. Up to now, such experimental data in literature were measured only for 2D LSMO system. They seem to be in excellent agreement with theoretical predictions. This surprising reconciliation is actually quite confusing, because ARPES analysis in selected mirror planes is quite deceptive and boring: only broad features without clear quasiparticles. Yet, under certain conditions, a clear metallic cutoff pops up with large emission angles, which looks like a collapse of the interpretation of the ARPES data in terms of direct transitions in photoemission. Photoemission simulations in this thesis explain that the “extra” signal at EF is intrinsic of 3D systems.

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Chapter 2 Instrumentation

2.1 The SIS beamline

The Swiss Light Source (SLS) started to be operational in August 2001. Among the first beamlines were the Surfaces and Interfaces Spectroscopy (SIS) and Sur- faces and Interfaces Microscopy (SIM) beamlines covering the photon energy range from 10 to 800 and 100 to 2000 eV, respectively [22, 65]. The SIS twin undulators (UE212, λ_u = 212 mm) were installed in a long straight section and are electromagnetic DC devices. The vertical poles are driven by two separate circuits to allow a quasiperiodic field variation in an electromagnetic undulator.

This novel design in electromagnetic undulators allows to change the amplitude difference such that the higher harmonics are suppressed to a level of 10⁻³ in the 10–30 eV energy range [70]. The twin-undulator with separate source points can match the phase to gain flux. This operation mode turned out to be difficult to maintain, mainly due to hysteresis loops in the electromagnets, and will be re- designed. Both insertion devices will merge, providing again two separate source points for the SIS beamline and its branch line for X-ray lithography. The SIM twin undulators (UE56, λ_u = 56 mm), installed in a medium straight section, are of APPLE II type. Besides circular polarization, these devices will produce rotat- able linearly polarized light by shifting the magnet arrays in opposite direction (the same concept of helicity switching have also the ID212 undulators).

The optical design is based on a SX-700 type plane grating monochromator operated in collimated light. This scheme provides a high flexibility over a large spectral range. The optical layout is shown in Fig. 2.1. The undulator radiation is collimated by a horizontal deflecting toroidal mirror (CMU) outside the shielding wall. The monochromator vessel contains two plane mirrors and three gratings.

A horizontally deflecting toroidal mirror (FMU) focuses the light to the vertical exit slit. The third toroidal mirror (RMU) is used for refocusing the intermediate

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RMU GDS

EPICSDISTRIBUTED

CONTROL

Linux,Windows, VME SETENERGY

GDS

Igor Pro

2x Undulator ID212 CMU

FMU

RMU

double slit

PGM exit slit

SETENERGY

GDS f

q t

y x

z

Figure 2.1: (Top): Synoptic view of the X09LA Surfaces Interfaces Spectroscopy (SIS) beamline. (Middle): Optical layout of the beamline showing the optical elements with their shape and positions, insertion devices, manipulator and the Gammadata Scienta (GDS) SES2002 electron analyzer. CMU, FMU, and RMU are the collimating, focusing, and refocusing mirror units, respectively. The beamline control is fully implemented in Experimental Physics and Industrial Control System (EPICS), a distributed control over computer network. (Bottom): The client applications are running on Linux consoles, the GDS analyzer is controlled from XP-Windows personal computer due to vendor specific implementation of the analyzer. The GDS EPICS control allows to implement arbitrary photoemission experiment as a sequence of operations on the manipulator and beamline. The ARPES images are sequentially saved to Igor Pro files (WaveMetrics), which contain all data needed for k-space mapping, along with other relevant data like temperatures and pressures, slit openings, and storage ring current.

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2.2. CONTROL 17

focal points to the sample. An energy resolution down to 12 meV has been reached at low photon energies (≈ 50 eV).

2.2 Control

The Cathedral & the Bazaar is an essay by Raymond (O’Reilly Media, 1990) on software engineering methods, based on his observations of the Linux operating system development process. In the “Cathedral” model the source code is available with each software release, but code developed between releases is restricted to an exclusive group of software developers. In the “Bazaar” model the code is developed over the Internet in view of the public.

One of the most significant decisions to build up the Swiss Light Source control system was to use EPICS (Experimental Physics and Industrial Control System).

It is a distributed Open Source software based on soft real-time control which fits into the “Bazaar” model. The beamline control, like the machine, is based on a combined use of EPICS and Equipment Protection System (EPS). The EPS controls cooling, valves, shutters, temperatures, pressures and their interlocks. At the beamlines, the EPICS control focuses on the optical elements and detector readouts; it also provides a set of “Bazaar” device controls for a full control the beamline optical elements.

2.2.1 Monochromator and insertion device

The most important control aspect of the beamline is the “SET ENERGY”

command which allows simultaneous control of the monochromator and both insertion devices (Fig. 2.1). The precision of the energy setting is limited by the PGM monochromator. The in-vacuum encoders with very accurate direct angular readout (±0.06 arcsec) allows in principle a very accurate positioning.

However, mechanical vibrations induced mainly by mirror cooling system set the limit in energy readback to ≈ 10 meV.

2.2.2 Manipulator

Main features. Figure 2.2(a) shows the manipulator used in this thesis inside the analysis chamber (AC). It allows to cover 0–360^◦ azimuthal scans combined with 0–80^◦ polar angles. In addition, it allows to optimize the emission angles with additional x-y translations, as schematically seen in Fig. 2.1. The vertical translation z was used to transport the sample from the preparation chamber (PC) to AC. By design of the manipulator, polar angle change pulled the sample azimuth. This required a compensation of the sample φ-positions depending on θ, which imposed quite sophisticated control and calibration.

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q

f t

GX

(a) (b)

(c)

Figure 2.2: (a) Manipulator designed by University of Fribourg with two performance examples: (top) X-ray photoelectron diffraction map of the O 1s states from a SrTiO3 substrate;

(bottom) Fermi surface map of Cu(110) (see text). (b) Novel state-of-the-art CARVING manipulator designed by L. Patthey in collaboration with van der Waals–Zeeman Institute, with additional tilt motion τ (angular interval of ≈ 30^◦). (c) Control panel of the CARVING manipulator indicating sample temperature, pressures, and individual axis motion. Three control buttons [go to PC], [transfer AC/PC] and [go to AC] allow safe automated sample transfer between AC and PC chambers. The x, y, z, and θ axes with absolute encoders indicate positions that are surveyed by interlocks for safe manipulation.

Two test case examples. The correct functioning of the manipulator in Fig. 2.2(a) has been extensively tested. Two examples are shown in the insets. First, on top there is an X-ray photoelectron diffraction map of the O 1s state from the SrTiO₃ (STO) substrate on which the LSMO films were grown (Sec. 7.1). The signal was integrated over a ≈ 10 eV energy window on the O 1s state. The ±6^◦ angular acceptance of the Gammadata Scienta (GDS) analyzer was further sliced such that the 1743 angular settings increased to 6974 in the final X-ray photoelectron diffraction map.

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2.2. CONTROL 19

Another example is the Fermi surface map from Cu(110), seen in the bottom inset of Fig. 2.2(a). Here 2700 angular settings revealed the surface state indicated by arrow at the Y point of the surface Brillouin zone (BZ) [52]. Both examples give a fairly good picture of the overall manipulator performance with θ-φ angular precision of ≈ 0.1^◦.

The CARVING novel design. Figure 2.2(b) shows a novel manipulator design developed in collaboration with van der Waals–Zeeman Institute (Amsterdam), with additional tilt (τ ) angular setting within a range of 0–30^◦, θ-φ angular precision ≈ 0.05^◦ and a sample cooling below 10 K. Figure 2.2(c) is the graphical user interface (GUI) panel to the fully controlled manipulator operation.

2.2.3 Gammadata Scienta electron analyzer

Spectrometer lens modes. The GDS analyzer has a capability of measuring kinetic energy and momentum of photoelectrons with high energy and angular resolutions. This is a major breakthrough in design of state-of-the-art spectrom- eters which simplified ARPES experiments dramatically. The GDS spectrometer (SES2002) has wide angle lens where photoelectrons from an acceptance cone of

≈ ±6^◦are passed through the multi-element lens system. In addition to the angle integrated mode the analyzer features also an angle-resolved mode. All ARPES spectra presented in this thesis were measured in this mode.

EK

q - line

sample

q-line

(a) (b)

x

z

Figure 2.3: (a) Schematic layout of the GDS analyzer. The incoming electrons with angular acceptance of ≈ ±6^◦ are mapped into an ARPES image. (b) Ray-tracing calculations of the GDS lens system in angular mode: the angles of the photoelectrons ejected from the sample at different distances x are mapped onto the θ-line. The energy dispersive direction EK is perpendicular to the lens axis z (courtesy L. Patthey).

Angular mapping mode. For the angular mapping mode a special set of lens parameters has to be selected so that all electrons which leave the sample at a given angle but at different locations at the sample will be imaged at the exit slit at same angular position. Figure 2.3(a) illustrates the mapping of angles along the θ-line which is perpendicular to the energy dispersion direction E_K. Panel (b)

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shows ray-tracing calculations of electrostatic lens in angular mode. Photoelec- trons entering the analyzer from a sample position x are guided through the multi-element lens system where the angular spread of the electrons is imaged along a line perpendicular to lens axis z. Besides this, the lens system transmits the electrons to the spectrometer entrance slit and also decelerates the electrons to the pass energy E_p of the hemispheres. The purpose of decelerating the electrons is to increase the resolution. The hemispheres select the electron kinetic energy of interest and passes these electrons through the exit slit to the detection system. Roughly speaking, a selected pass energy Ep allows to collect ≈ 10% of the photoelectron kinetic energies given by Eq. 4.1. At the same time transmission decreases quadratically as the pass energy decreases. The presented ARPES spectra were recorded with Ep = 5 eV. The energy dispersion takes place inside the hemispheres perpendicular to the plane that define the angle [Fig. 2.3(b)]. The intensity distribution of electrons is measured with a 2D electron detector/video system at the analyzer exit plane. More specifically, there is a multichannel plate, which counts electrons in the non-dispersive plane (θ-line) by subdividing the ±6^◦ into up to 127 slices and sorting the electrons according their kinetic energy into (up to) 470 channels.

Computer control. The computer control, as proposed by Gammadata Scienta, was problematic. The main reason was that vendor supplied control concept was based exclusively on the “Cathedral” model (Sec. 2.2) that simply did no fit into a distributed control based on EPICS devices spread out across computer network. Luckily the essential control of the GDS analyzer is “packed” inside a Windows-based dynamically loadable library (known as DLL). The nice EPICS feature is that the core Input-Output-Controller code is platform independent and is available also on Windows. This was used for developing the GDS analyzer EPICS device control model, where (i) a complete set of EPICS channels define a GDS region [some of the region parameters are seen in the GUI panel Fig. 2.1 (bottom)]; (ii) a set of commands like “Start” and “Stop” are available;

(iii) a special EPICS “Idle-Busy” channel notifies when a spectrum acquisition (region execution) is done. Having all these functionalities packed in the GDS device support (the blue GDS frame in the control scheme in Fig. 2.1), an arbitrary photoemission experiment can be then implemented as a sequential execution of GDS regions and manipulator/beamline settings. To do this, the users just prepare an Excel spreadsheet which is then loaded in a client application con- nected to instrumentation via EPICS channels. Its main task is to: (i) execute the configured sequence; (ii) collect ARPES spectra together with beamline and manipulator settings; (iii) save all data into Igor Pro format for off-line analysis during the experiment.

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Chapter 3 LSMO: theoretical insights

3.1 Introduction

There are numerous approaches in solid-state physics capable to explain physical properties of simple metals, semiconductors, and insulators. But materials with open d and f shells, where electrons occupy narrow orbitals have properties that are referred to strongly interacting or correlated electrons. For transition metal oxides, such as La_2/3Sr_1/3MnO3, these strong correlations cannot be described as embedded in a static mean field generated by other electrons.

The effect of correlations is very profound. Schlapbach opened the conference “World of Perovskites” in EMPA D¨ubendorf (2005) with the words: “This is a conference on how to engineer d electrons”. What he meant is depicted in Fig. 3.1^∗: the interplay of the d-electrons internal degree of freedom –spin, charge, and orbital moment– can exhibit a zoo of exotic ordering phenomena at low temperature. This interplay makes strongly correlated electron systems extremely sensitive to small perturbations in external parameters such as pressure, temperature, magnetic field, doping or even light irradiation. Consequently dramatic change in electrical or magnetic properties might be induced. For the studies made in this thesis, the effect of the tensile strain due to lattice mismatch between STO and LSMO, grown by pulsed laser deposition, is briefly discussed.

3.2 Description of manganese oxide perovskites

The physics of manganese oxide perovskites keeps the physicists busy more than half century. This section is a brief summary of the main issues and ideas which drive the theoretical understanding of these complex systems.

∗From http://www.aist.go.jp/aist e/research units/research center/cerc/cerc main.html.

21

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charge

spin orbital

electric field, photon

pressure magnetic

field electron materials^correlated

magnetic control electric control photonic control

Figure 3.1: The term correlated electrons represents the state of matter where many electrons are strongly interacting with each other, forming the liquid-, solid-, and liquid-crystal-like state of electrons. Those electronic phases can be switched by external stimuli, which causes drastic changes in magnetic, electrical, and optical properties. Such a phase switching can be as fast as one picosecond or less.

Mn O

La/Sr a

c

Figure 3.2: Manganites cubic crys- talline structure. The octahedra are formed by six oxygen atoms at the ver- tices and one manganese atom in their center. The octahedra are slightly tilted due to the different sizes of La and Sr cations. a and c are the lattice parameters. For STO, a = c ≈ 3.902 ˚A. A LSMO film grown on STO substrate with thickness of ∼ 100 nm is tetragonally distorted (c/a ≈ 0.99) due to the tensile strain at the STO- LSMO interface, which has its origin in the small difference between the STO and LSMO lattice constants.

First the concepts of the mixed valency is explained based on the thesis work of Prieto [64]. As a closing parenthesis to this brief description of the relevant generally-accepted physics I quote Coey [9], who puts serious question marks on the concepts based on mixed valency. In author’s opinion this has important ram- ifications also on the generally accepted double-exchange model for manganese oxide perovskites.

3.2.1 Mixed valency

In La_2/3Sr_1/3MnO₃ the oxygen, being in a O²⁻ state, has a full outer shell (2p).

On the other hand Mn is present in two oxidation states Mn⁴⁺and Mn³⁺. LSMO is a mixed valency compound: La³⁺_1−xSr²⁺_x Mn³⁺_1−xMn⁴⁺_x O²⁻₃ . In order to get charge neutrality, the ratio Mn³⁺/Mn⁴⁺ is equal to the ratio La³⁺/Sr²⁺. The extreme compounds x = 0 and x = 1 are not mixed-valent. Therefore, doping with Sr is equivalent to change the valence of the Mn ions from +3 to +4. Mn ions have an incomplete d shell (Mn: [Ar]3d⁵4s²). Thus the mixed-valent manganites are solid solutions: compositionally random mixtures of two perovskite-structure oxides that have the general formula ABO₃ (see Fig. 3.2). An equivalent way to think on the doping with divalent alkaline such as Sr²⁺ is that the system gets doped with holes.

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3.2. DESCRIPTION OF MANGANESE OXIDE PEROVSKITES 23

d

Mn4+ Mn³⁺

3z -r² ²

x -y² ²

zx yz xy

e orbitals_g

t_2gorbitals ^x y

e_g z

t_2g

x -y² ² 3z -r² ²

xy

yz, zx

(a) (b)

Figure 3.3: The outer shell of the Mn ions is 3d. (a) The five d levels are split in eg (two degenerate levels: d_x2−y² and d_3z2−r²) and t2g (three degenerate levels: dxy, dyz, and dzx), due to the cubic crystal field. (b) Jahn–Teller distortions act on Mn³⁺leading to a further splitting.

The t2g levels are also split due to Jahn–Teller distortions but this has no relevance for the system as the electrons living there are completely localized. Only the majority spins levels are shown.

According to Hund’s rule, in order to minimize the energy of the Mn ions, all the unpaired electrons in the outer Mn d shell have their spins parallel to one another. Thus, only the five d levels corresponding to the majority spin are accessible. Hund’s rule is implied by two interactions: Coulomb repulsion makes electrons to be in a different d orbital each; Hund’s coupling obliges the electrons spins to be parallel. Due to the cubic symmetry in which manganites crystallize, the five d orbitals are not degenerate but they split in three t_2g (d_xy, d_yz and d_zx) and two e_gstates (d_x²_−y² and d_3z²_−r²) as seen in Fig. 3.3(a). They are further split in energy due to Jahn–Teller distortion, as schematically seen in Fig. 3.3(b). t_2g orbitals are lower in energy than e_g orbitals because the latter are aligned with the O p levels leading to a larger Coulomb repulsion than in other directions.

Mn⁴⁺ has three electrons in the outer d shell that can be considered as localized in the three t_2g levels giving a total spin S = 3/2 (core spin). The two e_g levels remain empty. On the other hand, Mn³⁺has an extra electron that fills one of the eg levels (S = 2). The eglevels are the active ones for conductivity that hybridize with O p levels, constituting the conduction band whose bandwidth depends on the overlap between the Mn e_g and O p orbitals. The minority (antiparallel) spin levels are very high in energy. This implies that only majority spins can conduct.

For this reason, manganites are called half-metals (Fig. 1.5).

3.2.2 LaMnO3: a Mott insulator

In strongly correlated systems, the failure of band theory was first noticed in insulators such as nickel oxide and manganese oxide. Band theory incorrectly predicts them to be metallic in paramagnetic state. Mott first noted that such insulators are better understood from a simple, real-space picture of the solid

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as a collection of localized electrons bound to atoms with open shells, such as manganese. Adding and removing electrons from such atoms leaves them in an excited configuration. Because the internal spin and orbital degrees of freedom in the remaining atoms scatter the excited configurations, these states propagate through a crystal incoherently and broaden to form bands, called the lower and upper Hubbard bands, which are the basis of the Hubbard model [38]. It accounts for the magnetic ground state through a balance of two competing energies under constraint of the Pauli exclusion principle. First, the hopping energy t which involves motion of electrons of the same spin between different atoms. This favors delocalized or band-like behavior. Second, the Coulomb interaction experienced by electrons of opposite spin on the same atom keeps the electron apart, confined by other atoms (Ref. [76] p. 194). This favors the formation of localized moments and the repulsion between them is expressed with a Hubbard potential U .

LaMnO₃ is a Mott insulator with spin S = 2 and the orbital degrees of freedom. The spin S = 2 can be represented by the t_2g spin 3/2 strongly coupled to the e_g spin 1/2 with ferromagnetic J_H (Hund’s coupling) as schematically seen in Fig. 3.3. There are only Mn³⁺ ions in the system, hence the conduction band is full and the system is a Mott insulator. A Mott insulator is fundamentally different from a conventional (band) insulator. In the latter system, conductivity is blocked by the Pauli exclusion principle. When the highest occupied band contains two electrons per unit cell, electrons cannot move because all orbitals are filled. In a Mott insulator, charge conduction is blocked instead by electron-electron repulsion. The LaMnO₃ ground state at low temperatures is antiferromagnetic, in particular, it has A-type antiferromagnetism. Every Mn ion in the system suffers a static Jahn–Teller distortion and orbital ordering in such a way that ferromagnetic planes are antiferromagnetically coupled.

LaMnO₃ is the La_2/3Sr_1/3MnO₃ parent compound. For intermediate values of x, Mn³⁺ and Mn⁴⁺ are present and metallic behavior is possible. This is correlated with a ferromagnetic state because the carriers carry their spin without change as they move from atom to atom and Hund’s rule makes very expensive for a carrier to move between atoms with different core spin orientations. One moves away from the Mott insulator limit. The system is made up of electrons that are neither fully itinerant and described by Bloch waves, nor fully localized on their atomic sites. It is a system with charge-orbital-spin competing interactions. It is argued that the orbital ordering and electron-electron correlations are at the heart of the CMR phenomenon in this “anomalous” metal. Dagotto [10] explains that CMR is a percolative process which implies certain orbital disorder. The results discussed in Chap. 12 support this picture.

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3.2. DESCRIPTION OF MANGANESE OXIDE PEROVSKITES 25

3.2.3 Double-exchange model

The correlation between ferromagnetism and metallic conductivity in manganites was first described by Zener [88] to an indirect coupling of the incomplete d shells of the Mn via the carriers. Apart from this indirect coupling there is superexchange coupling among t_2g levels of Mn nearest neighbor ions. Superex- change is mediated by the non magnetic ion (oxygen). According to Zener, the hopping of the carriers from one Mn to another leads to an indirect ferromagnetic exchange interaction between the localized spins, called double exchange. Hence, if the carriers were localized, superexchange would dominate. Zener visualized the electron transfer from one Mn ion to an adjacent Mn ion as the transfer of an electron from one Mn to the oxygen, which is in the middle, simultaneously with the transfer of an electron from the central oxygen to the other Mn ion. As two simultaneous processes are involved, this model has been called double exchange.

There are then two states which are degenerate in energy: Ψ1(Mn³⁺O²⁻Mn⁴⁺) and Ψ₂(Mn⁴⁺O²⁻Mn³⁺). A necessary condition for this degeneracy (and, hence, metallic conductivity) is that the spins of their respective d shells point in the same direction because the carrier spin does not change in the hopping process and Hund’s coupling punishes anti-alignment of unpaired electrons. The parallel coupling is of the order of magnitude of the hopping. These ideas were formal- ized by Anderson and Hasewaga [1]. They calculated the interaction for a pair of Mn ions with general spin, transfer integral t, and internal exchange integral J_H (Hund’s coupling). However, the double-exchange model alone cannot account on the CMR effect. Millis et al. [46] extended the double-exchange model and proposed that, in addition to double-exchange physics, a strong electron-phonon interaction arising from the Jahn–Teller splitting of the outer Mn d level plays a crucial role.

3.2.4 Estimation of couplings

There are numerous model Hamiltonians used in the physics of manganites. Ac- cording to Dagotto (Ref. [10], p. 75), a simple but realistic model Hamiltonian can be written as:

H = H_kin+ H_Hund+ H_AF + H_el−ph+ H_el−el , (3.1) where H_kinis the kinetic energy of the e_g electrons, H_Hundis the Hund’s coupling between the e_g and t_2g spins, H_AF is the antiferromagnetic exchange coupling, H_el−ph is the electron-phonon coupling and H_el−el is the Coulomb interaction between the e_g electrons. The model is simplified such that the interactions beyond the on-site terms are just a “screening” effect. To solve such a problem is, however, a formidable task. For this reason simplifications are needed which often reduce to “key” parameters in a model Hamiltonian. For doing this, the

Angle- and spin-resolved photoemission on La 2/3 Sr 1/3 MnO 3

Universit´e de Cergy-Pontoise

TH` ESE

pour obtenir le titre de

Docteur de l’Université de Cergy-Pontoise (Spécialité : Physique)

pr´esent´ee par

Juraj K REMPASK´ Y