Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films

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Thesis

Reference

Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films

SEIRO, Silvia Susana

Abstract

The transition from insulating to metallic-like behavior in La[1-x]Ca[x]MnO[3] (X~0.33) films is studied by scanning tunnelling spectroscopy (STS). The dependence on substrate-induced strain on the transition temperature and the apparent gap measured by transport is characterized for different film thickness. STS measurements on highly and weakly strained films using a home-made setup showed no evidence of a bimodal distribution of zero-bias conductance (ZBC) values, precluding a static phase separation over lengthscales of 10-100 nm. ZBC follows the trend of macroscopic conductivity, increasing (decreasing) on cooling at low (High) temperatures. At high temperatures, ZBC follows an activated behavior and normalized conductance presents a depletion at low energies, features consistent with a gapped density of states. However, the depletion does not disappear on cooling below the transition temperature. A possible explanation in terms of antiferromagnetic/charge order (AFCO) correlations, which are present both in the ferromagnetic and paramagnetic phases, is provided.

SEIRO, Silvia Susana. Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films . Thèse de doctorat : Univ. Genève, 2008, no. Sc.

3995

URN : urn:nbn:ch:unige-6197

DOI : 10.13097/archive-ouverte/unige:619

Available at:

http://archive-ouverte.unige.ch/unige:619

Disclaimer: layout of this document may differ from the published version.

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UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Section de physique

Département de physique de la matière condensée Professeur Ø. Fischer

Scanning tunneling spectroscopy across the insulator-to-metal transition

in strained manganite films

THÈSE

présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention physique

par

Silvia Susana SEIRO

de

San Carlos de Bariloche (Argentine) Alberobello et Recanati (Italie)

Vrtojba (Slovénie)

Thèse No 3995

GENÈVE

Atelier de reproduction de la Section de physique 2008

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Motivation

The transition-metal-oxide family, of which high-critical-temperature supercon- ducting cuprates are prominent members, provide an inexhaustible playground for studying strongly correlated electrons. In particular, manganese oxides with perovskite structure (manganites) have attracted enormous interest in the last fifteen years. The complex interplay of competing interactions coupling lattice, charge, orbitals and spin gives rise to extremely rich phase diagrams spanning insulating, metallic, charge- and orbitally-ordered, ferro- and antiferromagnetic, antiferroelec- tric, and even multiferroic phases, as well as phase separation phenomena.

Not only are manganites worth studying from a fundamental point of view, but they also exhibit an extremely interesting potential for technologic applications. In particular, a huge effort has been devoted to understanding the “colossal” decrease in resistivity upon application of a magnetic field, that can reach several orders of magnitude, and the spin polarization of carriers, fundamental for spintronic devices.

In this context, a good knowledge of manganite thin film growth is essential.

Thin films are the cornerstone of device fabrication, but they also allow the modification of properties through substrate-induced strain, the presence of interfaces and finite size effects. In addition, changes in oxygenation or isotope substitution are more accessible in films than in bulk single crystals.

The driving force of this thesis was the discovery of inhomogeneities in manganites, explained theoretically by an intrinsic tendency towards “electronic” phase separation. These inhomogeneities have been proposed to play a major role in insulator-to-metal transitions through temperature- or magnetic-field-induced percolation of highly conducting domains in a weakly conducting matrix. A scanning tunneling microscope (STM) appears as the ideal tool to study this problem since it provides space-resolved characterization of local electronic properties.

In addition to imaging an eventual coexistence of phases at the sub-micron scale, scanning tunneling spectroscopy can provide valuable information about the properties of the individual phases in a wide energy range, in particular at the binding energy of polarons, electrons trapped in a self-induced lattice distortion.

Although polaron hopping has been identified as the dominant transport mechanism in the insulating phase, the role played by these quasiparticles in the metallic phase is still unclear.

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Motivation

A few STM studies on manganite films have been published since the late 1990’s, but their results were often in contradiction. The quality of manganite thin films, which plays a preeminent role, has greatly improved over the last decade. A comprehensive study, however, was still missing. Therefore, an ambi- tious program was set for this thesis. As a first step, the construction of a variable temperature and magnetic field atmosphere-controlled STM setup with the possibility of potentiometry measurements. Secondly, the growth and characterization of high quality epitaxial manganite films. And finally, the measurement of their spatially-resolved local electronic properties at the nanoscale.

This thesis is organized as follows: A brief introduction to manganite physics and tunneling spectroscopy is given in Chapters 1 and 2. The construction of the STM setup is reported in Chapter 3. Thin film growth and characterization techniques are introduced in Chapter 4. The effect of substrate-induce strain on structure and transport properties of La1−xCaxMnO3 films is the subject of Chapter 5. Space-resolved STM studies on structurally homogeneous samples as a function of temperature are reported in Chapters 6 and 7. Chapter 8 provides a comparison of the tunneling data with recently reported Monte Carlo simulations.

Finally, Chapter 9 summarizes the main conclusions of this work.

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Chapter 1

An introduction to manganites

Although manganites were discovered in the 1950’s [1], they have arisen enormous interest in the last decade, triggered by the discovery of the “colossal” magnetoresistance effect [2]. As shown in Fig. 1.1, a decrease in resistivity of several orders of magnitude was obtained by applying a magnetic field near the ferromagnetic ordering temperature, TC. As TC is not far from room temperature, the phenomenon presents a great potential for fabrication of devices such as magnetic memory read-heads. At zero field, a transition from an insulating (dρ/dT < 0) to a metallic (dρ/dT >0) state takes place aroundTC. The effect of applying a magnetic field is to stabilize the metallic ferromagnetic phase by shifting TC to higher temperatures: At temperatures close toTCa decrease in resistivity follows from the increased magnetic order. In addition, the transition is accompanied by changes in the lattice, see Fig. 1.1, underlining the strong coupling between charge, lattice, orbital and spin degrees of freedom in these materials.

This interplay between the different degrees of freedom gives rise to complex phase diagrams [4, 5, 6], spanning phases with different structure, magnetic order and electronic properties, see Fig. 1.2(a). In this Chapter, a brief survey of the properties of manganites is presented.

1.1 Structural properties

The structure of rare-earth manganese oxides (manganites) is based on the AMO3

perovskite¹ common to many transition-metal oxides. It consists of an array of MO6 vertex-sharing octahedra, with the larger A cation at the body-center position as shown in Figs. 1.2. In the case of manganites, M=Mn and A is a trivalent rare earth (e.g. La or Pr) that can be partially or totally substituted by a divalent

1By intercalation of rocksalt AO layers, Ruddlesden-Popper structures AO·(AMO3)ncan be formed [8]. Although similar physics is found in manganites with different number of layers, we will refer in the following to the3Dstructure (n=∞) unless otherwise stated.

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1.1. Structural properties

Figure 1.1: Left: Temperature dependence of the magnetoresistance ratio(RH−R0)/RH, resistivity (ρ) and magnetization (M) for a 1000 Å La0.67Ca0.33MnOx film grown on LaAlO3, from Ref. [2]. R0 is the resistance at zero field andRH the resistance at 6 T.

Right: Average Mn-O-Mn bond length as a function of temperature for La0.75Ca0.25MnO3, from Ref. [3].

Table 1.1: Ionic radii taken from Ref. [13]

Ion La⁺³ Ca⁺² Sr⁺² Mn⁺³ Mn⁺⁴ O⁻² Radius (Å) 1.50 1.48 1.58 0.785 0.670 1.21

alkali (e.g. Ca or Sr). Although often considered as pseudocubic, manganites in general exhibit a complex structure.

Structural distortions in these materials can be roughly divided in three groups:

Cooperative tilting of the octahedra, changing the M-O-M bond angles, octahedral deformations that modify O-M-O distances and displacements of the cations from their central position in the oxygen octahedra².

The basic perovskite structure can accommodate a variety of cations on A and M sites, as well as both oxygen and cation vacancies by introducing some degree of structural modification [11]. For example, a smaller cation in the A site induces a tilting of the MO6octahedra that reduces the volume of the cube formed by the M cations until it fits the volume of the A cation [12]. The tendency to create octahedral tilts is measured through the tolerance factor t = dA−O/(√

2dM−0), where dA−O and dM−O are the average bond lengths between the A cation and oxygen, and between the M cation and oxygen [8]. The ideal cubic structure presents³ t = 1. These distances can be estimated at room temperature from standard tabulated ionic radii, such as shown in Table 1.1.

The stabilization of a given tilt pattern, and its ensuing structural symmetry

2For example, the Ti displacements occurring in ferroelectric BaTiO3 [9]. This kind of displacement is negligible in La0.67Ca0.33MnO3 [10] and will not be further discussed.

3A-O and M-O bonds have in general different thermal expansion and compressibility, making ta function of both temperature and applied pressure [8].

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CHAPTER 1. An introduction to manganites

Figure 1.2: (a) Phase diagram of La1−xCaxMnO3reproduced from Ref. [6]. R stands for the rhombohedral structure, O forP bnmorthorhombic, and O’ for the Jahn-Teller-distorted structures (see text). CAF refers to the canted antiferromagnetic, F to the ferromagnetic and P to the paramagnetic phase. CO indicates charge order and the suffixes I and M stand for insulating and metallic behavior respectively. (b) AMO3 cubic perovskite structure.

MO6 octahedra are formed by a central M cation surrounded by six oxygen atoms that are shared with neighboring octahedra. (c)P bnm orthorhombic symmetry generated by rotation of the MO6octahedra. Images in (b) and (c) are reproduced from Ref. [7].

depends on a balance of Coulomb interactions between the ions, electron exchange and covalent bonding [14, 15]. Although the particular crystallographic group cannot be determined from the tolerance factor alone, some global trends are observed: t < 1 gives tetragonal, rhombohedral or orthorhombic structures and t >1 rhombohedral or hexagonal structures [7]. In doped manganites, as shown in Fig. 1.3, the effect of increasing the average cation size in the A site at a constant Mn⁺³/Mn⁺⁴ ratio is a change of symmetry from orthorhombic P bnm to rhombohedral R-3c as t increases towards unity. Notably, the tilting modifies the Mn-O-Mn bond angle and has important consequences for both transport and magnetism, as shown in Section 1.2.

Further changes in structural symmetry superimposing on octahedral tilting may come from cooperative displacements of the oxygen atoms with respect to the center of the M-O-M bond, such as Jahn-Teller distortions occurring around

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1.1. Structural properties

Figure 1.3: Lattice parameters and structural symmetry in La0.6−xPrxSr0.4MnO3 as a function of the average A-site cation radius,rA, from Ref. [16]. A smallerrA corresponds to a smaller tolerance factor and a more pronounced octahedral tilting.

Mn⁺³ in manganites. The Jahn-Teller coupling between orbital occupation and structural deformation is treated in further detail in Section 1.2. In LaMnO3, the low-temperature O’ orthorhombic phase in Fig. 1.2(a) is a realization of long-range ordered (cooperative) Jahn-Teller octahedral distortions. The structure presents alternating short and long O-Mn-O bonds in theab plane in such a way that an octahedron compressed alongaand expanded alongbis surrounded by octahedra expanded alongaand compressed alongb, while the O-Mn-O bonds alongcare of intermediate length [8]. On increasing Ca-doping the ratio of Jahn-Teller-active Mn⁺³ to non-Jahn-Teller Mn⁺⁴ decreases, reducing the stability of the O’ phase until a transition occurs to a more symmetric orthorhombic (pseudotetragonal) O phase. It must be noticed that a remnant Jahn-Teller distortion is still observed in the O phase [3].

As can be seen in Fig. 8.1, on increasing temperature from the O phase, a transition to a rhombohedral structure takes place. This structure imposes a unique Mn-O distance and precludes cooperative Jahn-Teller deformations, although local or dynamical (time-dependent) octahedral distortions cannot be ruled out [3].

Jahn-Teller distortions are also strongly suppressed for intermediate Ca-doping (0.2.x.0.5) as transport becomes metallic below the ferromagneticTC.

In addition to cation substitution, a means of modifying the structure is by the application of external forces (hydrostatic pressure, uni- or bi-axial strain), that presents the advantage of keeping chemical composition constant. A low hydrostatic pressure tends to compress the Mn-O bond, while pressures above∼2GPa give rise to a Jahn-Teller splitting in Mn-O bonds [17]. Increasing pressure above

∼4GPa favors octahedral tilting, while Jahn-Teller distortions remain practically

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CHAPTER 1. An introduction to manganites unchanged [17]. Another possibility is to induce biaxial strain by epitaxially grow- ing a thin film on a lattice-mismatched substrate. The sign of the strain can be changed by choosing a substrate with a larger or smaller lattice parameter than the bulk manganite. The average strain on the film for a given substrate decreases on increasing thickness [18], although strain relaxation does not always occur ho- mogeneously throughout the film [19]. The effect of substrate-induced strain on La0.67Ca0.33MnO3thin films is a part of the work carried out in this thesis and is reported in detail in Chapter 5.

1.2 Electronic properties

The interesting physical properties in manganites are to a considerable extent related to the Mn cation and its surrounding O octahedron⁴. For an isolated Mn ion the3dlevels present a five-fold degeneracy, but in a manganite crystal six oxygen ions form an octahedron around the Mn. The effect of the crystal field is to partially lift the degeneracy into at2g triplet (dxy,dyzanddzx) and aneg doublet (d_x²_−y² and d_3z²_−r²) as shown in Fig. 1.4⁵. The energy of the t2g levels is lower than for theeg, the difference being of the order of 1-2 eV [6]. This energy difference stems from the Coulomb interaction between Mn3delectrons and oxygen ions: t2g

orbitals point away from the oxygens whileeg extend in the direction of oxygens.

Due to the strong Coulomb interactions within t2g levels, double occupation is deterred and a high-spin state is favored. In practice, the three spin-polarizedt2g

electrons are treated as a single localized3/2 “core spin” [4, 5, 6].

In the undoped compound LaMnO3, Mn ions present a valence +3. As a fraction xof the trivalent rare-earth is replaced by a divalent alkali, a fractionx of Mn³⁺ turns into Mn⁺⁴ to satisfy a valence -2 for the oxygen (the oxygen 2p levels can be considered as completely filled). There are, thus,4−x3d-electrons per Mn in the doped compound. For Mn³⁺ one of the eg levels is occupied and a spontaneous deformation of the octahedron (i.e. a displacement of the oxygen ions surrounding a Mn) lifts the degeneracy of eg levels, decreasing the energy of the occupied eg orbital. This is called the Jahn-Teller (JT) effect and the eg

level splitting is of the order of tenths of eV. The distortion partially removes the degeneracy oft2g levels as well. An example of Jahn-Teller distortion is shown in Fig. 1.4, where an electron in ad3z²−r² level induces an elongation of the Mn⁺³O6

octahedron along z, decreasing the energy of the orbital pointing along the z direction by moving oxygens away inz and bringing them closer in thexyplane.

Since the deformation of an octahedron also affects its neighbors, “cooperative”

or “coherent” Jahn-Teller distortions can give rise to a global change in the crystal

4It should be noticed that there is a considerable overlap of Mndwith Opstates [20], so this description should be understood in terms of “effective” degrees of freedom, expressed in the language of Mn d orbitals, containing the O degrees of freedom [21].

5The ligand field due to the overlap with oxygen states reinforces theeg-t2g splitting: Since the overlap is small for thet2g, the energy shift induced by hybridization is much smaller than for theeg [22].

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1.3. Magnetism and transport properties

Figure 1.4: Schematic representation of the electronic configuration of Mn: Isolated, in aM n⁺⁴O6 octahedron and in a Jahn-Teller-distortedM n⁺³O6octahedron.

structure, as in the O’ phase of La1−xCaxMnO3 (x < 0.2), see Fig. 1.2. The structure of the O’ phase exhibits alternate short and long O-Mn-O distances in theab plane, while all distances are equal alongc.

1.3 Magnetism and transport properties

Zener explained the correlation between transport properties and magnetic ordering like that shown in Fig. 1.1, as the result of double-exchange interactions [23].

The double-exchange mechanism is pictured in Fig. 1.5. The process of an eg

electron hopping to a neighboring Mn site can be visualized as the simultaneous transfer of the electron into an O2porbital and of an O2pelectron to the neighboring Mn site, hence the name “double exchange”. Since strong intrasite Coulomb repulsion discourages doubleeg occupancy, the electron transfer can only be re- alized into sites whereeg levels are not occupied (i.e. Mn⁺⁴ sites)⁶. As seen in

6In Zener’s double exchange picture, the oxygens have a nominally closed shell (O⁻²) and do not play an active role. However, electron energy loss spectroscopy measurements have shown that on doped compounds O 2p holes contribute significantly to the conduction mechanism [24].

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Figure 1.5: Double exchange mechanism as pictured in Ref. [4]

the previous section, the presence of Mn⁺⁴ requires a finite dopingx. Therefore, within the double-exchange model, the undoped compound is an insulator.

Since the spin of the eg electron is conserved in the hopping process and it couples to the localizedt2g spin⁷, an effective ferromagnetic coupling results between the spins of neighboring Mn. If classical spins are considered, the transfer probabilityti,jbecomesti,j ∝cos(θi,j/2), whereθi,jis the angle between localized spins in sitesiandj [4, 25]. The stabilization of a metallic phase on increasingx can be then qualitatively explained: Once holes are introduced, eg electrons can hop depending on the alignment of the local spins, with a maximum probability for ferromagnetic alignment. As temperature is raised above T_C spins disorder, reducing the effective hopping and increasing resistivity. Slightly aboveTC, spins are relatively easily ordered by a magnetic field and resistivity decreases as the transfer integral increases. This explains, at least qualitatively, the negative magnetoresistance observed experimentally (see Fig. 1.1).

The tilting of the MnO6 octahedra affects the overlap of orbitals on adjacent sites. The interplay between charge localization and octahedral distortion has

7In-site Hund’s coupling (∼2−3eV) [4] is much larger than the hopping parameter (a fraction of eV, according to Ref. [5]).

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Figure 1.6: Phase diagram of temperature vs. tolerance factor at constant dopingx= 0.3 reproduced from Ref. [26]. The transition temperature was estimated from magnetization (open symbols) and resistivity measurements (closed symbols).

been shown by Hwang and coworkers [26], who studied the variation ofTC with the size of the A-site cation for a fixed dopingx= 0.3, see Fig. 1.6. On reducing ra, the average ionic radius of the A-site cation, the bending of the Mn-O-Mn bond angle produces a decreased orbital overlap, loweringTC. Similar results have been reported for other doping levels [16, 27].

Besides ferromagnetism, antiferromagnetic order of different kinds is often found in manganites, see Fig. 1.2(a). Goodenough [28] showed that the sign of the magnetic interaction between neighboring Mn depends on the nature and occupation of orbitals and gives rise to different types of magnetic order, for example A-type at x = 0 (antiferromagnetically coupled ferromagnetic planes), and CE- type atx= 0.5 (depicted in Fig.1.8).

1.3.1 Electron-phonon coupling: Polarons

Double exchange alone failed to explain the experimental observations quantitatively, in particular the large resistivity atT> TCand its sharp decrease on cooling throughT_C. The missing ingredient was found to be the electron-phonon interaction, related at least partly to the Jahn-Teller effect [29]. Pioneering experimental evidence for strong coupling with the lattice was provided by the observation of a shift inTC of∼20K through isotopic substitution of¹⁶O by¹⁸O [30].

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CHAPTER 1. An introduction to manganites It was proposed [31] that a strong electron-phonon coupling⁸localizes the conduction electrons as polarons at T> TC. The concept of polaron was originally introduced by Landau [34] to describe an electron moving in a ionic lattice and interacting with the electric polarization generated by the displacement of the positive and negative ions due to the presence of the electron. It has since been gener- alized to other types of materials with different forms and ranges electron-phonon interaction, and it signifies a composite entity made of an electron surrounded by a self-induced lattice deformation [35]. A polaron is characterized by its binding energy Eb, its effective mass m^∗ and its response to external electric fields [36].

Depending on their spatial extension, polarons can be qualitatively classified in large andsmall.

Small (or Holstein) polarons are localized over distances of roughly a unit cell [37]. They can move from site to site by thermal excitation⁹ and resistivity can be expressed, in the adiabatic limit¹⁰, as [39]:

ρ= T

AexpEa/kT , (1.1)

whereA= ^e_ak²^νx(1−x)for a simple cubic lattice withathe distance between sites and ν the frequency of the longitudinal optical phonon that carries the polaron through the lattice [40]. The activation energy, Ea, is related to the polaron binding energyEB through¹¹ Ea≈Es+Eb/2.

Above the metal-insulator transition temperature in manganites, the carriers were proposed to localize as (small) polarons, opening a gap in the quasiparti- cle excitation spectrum of the order ofEB [31]. Thus, polaron hopping through thermal excitation gives rise to the activated behavior of resistivity observed experimentally [41]. The presence of polarons at T> TC has been confirmed by a number of techniques including neutron diffraction [42, 43], resistivity and ther- mopower [41], and optical spectroscopy [44, 45]. The activation energy, obtained from resistivity measurements atT> TC, decreases as the ratio of non-JT Mn⁺⁴to JT-active Mn⁺³increases, either by increasing Ca doping in La1−xCaxMnO3[46], see Fig. 1.7(a), or by changing the oxygen content of the sample [47]. A higher activation energy, and thus a higher binding energy, makes the localization of electrons more stable and entails a reduction ofTC. Figure 1.7(b) shows the correlation between the transition temperature and the polaronic activation energy for thin film samples deposited on different substrates and subject to different annealing treatment.

8The importance of including lattice effects in addition to double exchange interactions for successful theoretical modelling was confirmed by further studies [32, 33].

9They can also move by tunneling, but this process involves quantum tunneling of atoms from their equilibrium positions for an electron occupying a certain site to the equilibrium positions for the electron occupying a neighboring site, which gives rise to a huge polaronic effective mass, comparable to atomic masses [37]. This process is disturbed by the scattering with phonons and only effective at very low temperatures [38]. It is also extremely sensitive to atomic disorder [38].

10Adiabatic means here that electronic motion is much faster than atomic motion.

11Es.10meV [41].

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Figure 1.7: (a) Polaron activation energy vs. Ca content in La1−xCaxMnO3 [46]. The activation energy decreases on increasing doping, implying a collapse of Jahn-Teller like distortions as the proportion of non-Jahn-Teller Mn⁺⁴to Jahn-Teller Mn⁺³increases. (b) Correlation of the insulator-to-metal transition temperature,Tp, with polaronic activation energy,Ehop, from Ref. [48].

As temperature decreases, the kinetic energy increases due to spin ordering.

It was proposed that kinetic energy eventually becomes more important than the polaron binding energy, giving rise to a gapless metallic state [31]. Strikingly, neutron diffraction studies showed that a remnant local polaronic distortion was still present belowTC[49]. This was interpreted as a crossover from small- to large- polaron behavior on cooling throughTC, with a coexistence of both small and large polarons in the temperature region around the transition [49]. On the other hand, recent optical conductivity measurements on thin films point out that the nature (small or large) of polarons depends on the particular crystal structure and does not alter acrossTC[45]: Orthorhombic Ca-doped LaMnO3, exhibits small-polaron characteristics in optical conductivity while Sr-doped LaMnO₃, with rhombohedral structure, shows large-polaron-like characteristics [45].

Large (or Fröhlich) polarons can extend over several lattice sites and are gen- erally quite mobile [37]. For moderate coupling, the carrier is not trapped in the adiabatic sense, the atoms can move in response to the electron motion, resulting in almost free electron behavior. The mobility of large polarons is expected to decrease as the number of phonons in the crystal increases [36]. From the mobility obtained in Ref. [50], the resistivity at low temperatures for a large polaron can be written as:

ρ=ρ₀~ω

kT exp−~ω/kT . (1.2) Note that Eq. 1.2 only takes into account the phonon scattering, and other terms (such as scattering with impurities) may dominate at low temperatures. Alterna- tively, other authors explain the change in resistivity on cooling throughTCas the

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Figure 1.8: Sketch of the CE phase in thexy plane reproduced from Ref. [57]. The structure consists of ferromagnetic zigzag chains of alternating Mn⁺³/Mn⁺⁴ sites. The chains are antiferromagnetically coupled in thexyplane and along thez-direction.

unbinding, induced by magnetic order, of localized polaron-pairs (or bipolarons) into coherent small polarons [51, 52, 53].

Although the application of the concept of polarons to manganite physics is quite widespread in literature, what is actually meant by a “polaron” is often more complex than in the early models of a single electron moving in a polarizable con- tinuum. In manganites, there is not only a charge-lattice interaction but spins and orbitals play a considerable role as well. In addition, the density of carriers is often quite high (0.33 holes per site in La0.67Ca0.33MnO3) and correlation effects are important [21]. Short-range polaronic correlations are observed in neutron/x-ray scattering experiments at wave vectors corresponding to the superlattice reflections of the so-called CE-type charge-orbital-spin ordered structure commonly found in half-doped manganites [54, 55, 56, 21], see Fig. 1.8. The scattering intensity follows the behavior of resistivity [54, 55], suggesting that the observed correlations come from nanoscale regions with local CE order and that they play a major role in transport properties.

1.4 Phase separation

A coexistence of conducting and insulating domains stemming from the competi- tion of ferromagnetic-metallic and antiferro- or paramagnetic-insulating phases has been obtained in many theoretical models [5]. Intrinsic phase separation is believed to be one of the key features of manganites: The relative fraction of the phases is assumed to be temperature- and field-dependent, and the transition to macroscopic metallic transport would result from the percolation of metallic domains inside the insulating matrix [5]. Although the phase separation scenario has gained popularity in recent years, it is predominantly supported by results from

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1.5. An open door for STM

macroscopic techniques [5] where it is not easy to distinguish ‘intrinsic’ from ‘ex- trinsic’ sources of inhomogeneity [58]. Such a scenario appears to apply for certain compounds but its general application to all manganites exhibiting CMR remains an open question [59].

1.5 An open door for STM

In spite of extensive experimental and theoretical work on manganites during the last fifteen years a number of questions still remain open, such as the presence and role played by polarons on cooling below the insulator-to-metal transition temperature. Is percolation of metallic regions inside a non-conducting matrix responsible for the sharp decrease in resistivity atTC?

A problem concerning electronic properties and their spatial distribution appears tailor-made for scanning tunneling microscopy (STM), but only a few studies on paradigmatic La1−xCaxMnO3 in the ferromagnetic region have been reported.

Some of them claim electronic phase separation [60, 61, 62, 63], but a strong influence of chemical and structural disorder present in the samples cannot be ruled out. In contrast, a recent study in a fully-relaxed film reports homogeneous conductance maps [64]. These results stress the importance of appropriate sample characterization, and the need of studies as a function of both temperature an magnetic field on the same sample. On the other hand, the characterization of polaronic properties and their temperature evolution from tunneling spectra has been rewarded only little attention [65, 66]. A comprehensive study on the polaronic characteristics and their spatial dependence as a function of temperature is reported in Chapters 6 and 7. The experimental data is compared to results from Monte Carlo simulations in Chapter 8.

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Chapter 2

Scanning Tunneling

Microscopy: Theory and experiment

Tunneling is a purely quantum phenomenon. A particle wave function extends into the potential barrier separating two allowed regions in space, thus giving a finite probability for the particle to tunnel through the classically forbidden zone into an available state at the other side of the barrier. The tunnel probability decreases exponentially with barrier width, making experimental observation of tunneling phenomena only possible for extremely stable barrier widths in the nanometer scale. Esaki studied tunneling phenomena across p−n junctions and proposed an expression for the tunnel current as the energy integral of the density of states of each electrode, with level occupation given by Fermi functions, times a tunnel probability coefficient [67]. The relationship between tunnel current and density of states was beautifully demonstrated a few years later by Giaever in metal- insulator-superconductor and superconductor-insulator-superconductor junctions [68]. Esaki and Giaever’s work was rewarded with the 1973 Nobel Prize in Physics.

Tunneling through vacuum was only achieved a decade later, when Young and coworkers mounted one of the electrodes on a piezoelectric drive and studied both tunneling into vacuum (field-emission regime) and metal-vacuum-metal tunneling [69]¹. The experimental setup was greatly improved a decade later by Binnig and coworkers [71] who, thanks to efficient mechanical decoupling, achieved atomic resolution in topographic imaging [72]. In 1986, Binnig and Rohrer were awarded the Physics Nobel Prize for their design of the scanning tunneling microscope

1Although their experimental setup allowed lateral scanning of the surface with piezoelectric drives, and a feedback loop was applied to keep current constant, the lack of a logarithmic amplifier for feedback control and the absence of a vibration isolation system made their tunnel current extremely unstable [70].

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2.1. Tunneling from a theoretical viewpoint

Figure 2.1: Schematic representation of the tunnel effect. A particle incident from the left with an energyE < V0 has a finite probability density across and on the other side of the barrier.

(STM). Though mechanical vibrations still haunt the tunneling microscopist to this day, the technique remains a powerful tool that has been successfully employed to study a variety of issues such as the surface structure of semiconductors [73, 74], adsorbates on metals [73, 74], micromagnetic domains [75] and vortices in superconductors [73, 74, 76], to cite but a few examples.

This chapter presents in its first part a brief review of the theoretical description of tunneling phenomena (in particular in the context of STM) and in its second part a description of STM experiments and related techniques.

2.1 Tunneling from a theoretical viewpoint

The essential properties of tunneling are contained in the solution of the Schrödinger equation for a simple one-dimensional rectangular potential barrier of height V0

and widtha, such as shown in Fig. 2.1. The transmission probability, |T|², of a particle of energyE < V0incident on a barrier can be readily calculated by match- ing the plane wave solutions at either side of the barrier with the exponentially decreasing solutions inside the barrier [77]:

|T|²= (2kκ)²

(2kκ)²+ (k²+κ²)²sinh²κa, (2.1)

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment where k² = 2mE/~² andκ= 2m(V0−E)/~². For weak transmission (κaÀ1), Eq. 2.1 yields

|T|²'1 2

µ 2kκ k²+κ²

¶₂

exp (−2κa), (2.2)

which is a rapidly-varying function of the barrier width and the energy difference with respect to the barrier potential. Rewriting Eq. 2.2 we obtain

log|T|²' −2κa+ 2 log

√2kκ

k²+κ², (2.3)

where the first term is dominant in most cases, so that²

|T|²'exp

"

−2ap

2m(V0−E)

~

#

. (2.4)

This exponential dependence lies at the heart of the STM technique. The tunnel current,I, flowing between the two electrodes (tip and sample) roughly decays, in accordance to Eq. 2.4, in an exponential way with the barrier widtha:

I∝exp µ

−2a

~ p2mφ

¶

. (2.5)

When the barrier is vacuum, the barrier potential is given by the work functionφ, which is the energy necessary to remove an electron from the material³. For typical work function values of ∼5eV the tunnel current decreases roughly by an order of magnitude for every 1 Å increase of separation between the electrodes. This extreme sensitivity of current to changes in the electrode separation is exploited by STM to image the topography of the sample as explained in Section 2.2.

A schematic representation of a tunneling junction is presented in Fig. 2.2: By applying a bias voltage V between the two electrodes their Fermi levels will be shifted by eV (withe the elementary charge) so that electrons within eV below the Fermi level on the negative side will be able to tunnel to empty states within eV above the Fermi level on the positive side, thus giving rise to the tunneling current.

2For an arbitrarily shaped potential barrier, the transmission coefficient can be calculated through the Wentzel-Kramers-Brillouin(WKB) approximation. The potential is approximated by a juxtaposition of rectangular barriers and, for weak tunneling, the total transmission coefficient is the product of the individual transmission coefficients for each section. In the limit of infinitely narrow individual barriers,

|T|²≈exp

½

−2 Z

dx q

(2m/~²)[V(x)−E]

¾ . whereV(x)contains the spatial dependence of the potential barrier.

3In general, the work functions of the two electrodes are different. In that case, transfer of charge from one to the other will occur until thermodynamic equilibrium is reached and both Fermi levels are lined up, leading to an approximately linear dependence of the barrier potential.

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Figure 2.2: Representation of tip-to-sample electron tunneling. A positive bias V is applied on the sample electrode, making empty states above Fermi level in the sample accessible to tunneling tip electrons.

2.1.1 The transfer Hamiltonian approach

Within this approach the tunnel junction is described by a HamiltonianH=H0+ HT, where the electrodes are supposed to be independent so thatH0 is the sum of the Hamiltonians for each (isolated) electrode. The transfer HamiltonianHT = P

µ,νMµνc^†_µcν +h.c., where indices µ, ν run over states in the first and second electrode, describes the tunneling process. If the potentialV applied between the electrodes is small compared to the barrier height, then to lowest order inHT the tunneling current is given by [76]:

I(V) = 2eπ/~

Z

dω[f(ω−eV)−f(ω)]X

µ,ν

|Mµν|²Aµ(ω)Aν(ω−eV), (2.6) wheref is the Fermi function, andA are the spectral function of the electrodes.

Bardeen proposed an expression forMµ,ν in terms of the current density operator in the barrier region [78]:

Mµν =−(~²/2m) Z

dS·[ψ_µ^∗∇ψν−ψν∇ψ_µ^∗], (2.7) whereSis an arbitrary surface separating the two electrodes.

The evaluation of Eq. 2.7 for a STM configuration was first addressed by Tersoff and Hamann [79]. They considered spherical-wave states for a tip electrode with a center of curvature at −→ro and a radius of curvature R, which gives rise to a

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment s-state like decay of the wave functions outside the tip. The sample electrode was taken as a flat surface, for which the wave functionsψν can be expressed as Bloch waves in the plane of the surface and exponentially-decaying plane waves inside the barrier. They found that Mµν ∝ ψν(−→ro), and as a result could express the tunneling current at zero temperature for a bias voltageV ¿φas:

I(V) = 8π³e²~³ m² R²exp

µ2R

~

p2mφ

¶

V ρt(EF)ρs(EF,−→ro), (2.8) where ρt is the density of states of the tip per unit volume and ρs(EF,−→ro) = P

ν|ψν(−→ro)|²δ(Eν−E)is the local density of states of the sample, evaluated at the Fermi energy and at the center of curvature of the tip. Note that the exponential dependence of the current on the tip-sample distance is contained in ρs(EF,−→ro), through the exponential decay ofψν outside the sample.

In the spirit of Esaki’s work [67], Selloni and coworkers proposed to rewrite Eq. 2.8 for moderate (though smaller thanφ) bias voltage in the phenomenological form [80]:

I(V) = Z _eV

0

ρs(E)ρt(eV −E)T(E, eV)dE, (2.9) which at finite temperature becomes:

I(V) = Z

ρs(E)ρt(eV −E)T(E, eV)[f(E−eV)−f(E)]dE, (2.10) where f(E) is the Fermi function, ρs is the sample density of states and the exponential dependence on the barrier width is absorbed by a tunnel coefficient T, which in the spirit of Eq. 2.4, is often assumed to take the form⁴:

T(E, eV) = exp Ã

−2a√ 2m

~ r

φ˜+eV 2 −E

!

, (2.11)

withφ˜the average work function of sample and tip. Differentiation of Eq. 2.9 with respect to applied voltage yields [81]:

dI

dV =ρs(eV)ρt(0)T(eV, eV) + Z _eV

0

ρs(E)ρt(eV −E)dT(E, eV)

dV dE. (2.12) ForeV ¿φ,˜ Tin Eq. 2.11 can be assumed constant, so that if the energy range of interest is small, as it is the case for superconductors, the tunneling barrier is only a minor effect anddI/dV ∝ρ_s(eV). However, the voltage-dependence of the

4In their original formulation Selloni and coworkers proposed asT(E, eV)the transmission coefficient for a triangular barrier in the Wentzel-Kramers-Brillouin approximation [80], which is probably more adequate for applied voltages of the order of the workfunction.

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tunneling barrier cannot be neglected in the case of semiconductors, where the energy range of interest can extend to the eV range.

To extract a measure of the sample density of states from experimental I(V) curves, Stroscio and coworkers [82] proposed to calculate the ratio of differential to total conductance:

dI/dV

I/V = dlogI

dlogV ∝ρs(eV). (2.13)

They observed that this phenomenological procedure provided a barrier-independent measure of the surface density of states on Si and Ni samples measured at different tip-sample distances. Unfortunately, the procedure fails for systems with a large gap because near band edgesI/V drops to zero more rapidly thandI/dV, giving rise to an artificial divergence of the normalized conductance [83]. The transmission factor T in Eq. 2.9 should remain finite at energies close and smaller than the gap, but in this energy range current is zero, so the estimation ofTbyI/V is no longer valid. The solution is to find a well-behaved function to estimateTat low bias. This can be done, for example, by adding a small constant toI/V or by replacingI/V in Eq. 2.13 by a ‘smeared’ function [83, 84] such as:

I/V = exp(a⁰|V|) Z _∞

−∞

[I(V⁰)/V⁰] exp

µ−|V⁰−V|

∆V

¶

exp(−a⁰|V⁰|)dV⁰ (2.14) where the exponential weight factor witha⁰ ∼d(logI)/dV (atV much larger than the gap) is there to assure thatI/V ∼(I/V)at voltages above the gap, and the broadening width ∆V should be comparable to the gap value. A more recent procedure proposed normalizing dI/dV with a WKB-like tunnel coefficient (like that in Eq. 2.11), fitted to the experimental data, which also yields tip-sample separation and the work function [85].

The parameters of the WKB transmission coefficient can also be obtained from independent measurements of current as a function of tip-sample distance, and then be used to calculateρs by replacing the explicit form ofTfrom Eq. 2.11 in Eq. 2.12 [86]:

ρs(eV) = 1 T(eV, eV)

½dI dV + z

2α√ φ

h 1 +³

2p

φz+ 3´

V²/96φ²i I(V)

¾

(2.15) In spite of the widespread use of these phenomenological descriptions, and of the transfer-Hamiltonian approach in general, several difficulties arise in the attempt to compare quantitatively experimental STM data with theoretical pre- diction. A non-exhaustive list is given below:

• Electrode configuration: Most implementations of Bardeen’s approach as- sume planar tunneling, where the momentum k_k parallel to the interface

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment is conserved. Since the exponential decay of the wavefunctions across the barrier is of the form ∼exph

−2a/~p

2m(φ−Ez)i

, the tunnel current will be dominated by contributions from the states with largerk⊥ (and smallest kk). Harrison [87] claimed that in such a situation the contribution of the density of states to the tunneling current is completely cancelled out by the tunneling matrix element. On the other hand, in a STM configuration the tip electrode is laterally confined, so tip states do not have a well definedk_k and nok-selection takes place.

• Potential barrier: When the tunneling distance is of the order of a few Å the effective barrier is strongly modified from that expected from considerations of the work functions of the two electrodes. Image potential effects ‘round it off’ close to the electrodes, decreasing the effective barrier height asI(V) characteristics become increasingly nonlinear [88].

• Tip states: Tersoff and Hamman’s Eq. 2.8 corresponds to s-states of the tip, but many of the materials used as STM tips such as iridium or platinum present a strong d-character. The influence of the angular momentum was studied by Chen [89], who found that tunneling matrix elements for a simple metallic surface are proportional to partial spatial derivatives of the sample wavefunction.

2.2 The scanning tunneling microscope

As mentioned above, in a STM experimental setup the sample to be studied is one of the junction electrodes, while the second electrode is a sharp metallic tip, usually made of Ir, Pt, W or Au. The electrodes are usually separated by vacuum, but operation in exchange gas or even a liquid medium are also possible [75]. The tunnel current depends, as shown in Section 2.1, on the tip-sample distance and the bias voltage applied between the electrodes. Experimentally, the absolute value of the electrode separation is a priori not known, and the tunnel current and bias voltage values are the control parameters, fixed in such a way thatI/V ∼1GΩ.

As shown in Fig. 2.3 for Binnig and coworkers’ STM, the tip is mounted on a set of piezoelectric drives: Pz controls the electrode separations and Px and Py

scan the tip over the sample surface. In theconstant current modea feedback loop is used to keep the tunnel current constant as the tip is swept over the sample, compensating the variations in current due to the change in sample height by adjusting the voltage Vp applied toPz. By recordingVp as a function of lateral position, an image of the sample topography can be obtained. Topographic images on different surfaces are shown in Fig. 2.4.

Though closely related, the topography does not render the sample’s geometri- cal morphology but the surface of constant wavefunction overlap between sample and tip states [90] and the difference between topography and geometry can be

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2.2. The scanning tunneling microscope

Figure 2.3: Principle of operation of a scanning tunneling microscope, reproduced from Ref. [72]. Piezoelectric drives Px and Py scan the metal tip laterally over the surface.

The control unit (CU) adjusts the voltageVp applied to thePzpiezoelectric drive, which controls the tip-sample separation sso that the tunnel currentJT is constant at a bias voltageVT. The broken line represents a scan along y, passing by a step A and a zone C with lower work function .

striking in some cases [91, 75]. Images at positive and negative sample bias can differ significantly whenever there is a spatial variation of empty and occupied states across the sample surface, in particular in the presence of defects such as vacancies [92]. Topography can also be distorted by hysteresis, creep and thermal derive of the piezoelectric drives.

Theconstant-current mode allows to measure surfaces with large variations in height, but the finite response time of the feedback loop limits the scan speed.

Faster measurements can be made in the constant height mode, in which the feedback loop is not active and the exponential variations in tunnel current directly reflect the variations in spacing between tip and sample created by the morphology of the surface. However, a major disadvantage of the constant-height mode is that direct contact between sample and tip is likely to occur on surfaces of a certain roughness.

The exponential dependence of tunnel current on tip-sample distance allows subatomic vertical resolution, which is limited experimentally by the stability of the tip-sample distance. The lateral resolution at the atomic scale is determined by the sharpness of the tip and the tip-sample distance. Both vertical and lateral resolution are of course also dependent on the resolution of the voltage applied to the piezoelectric drives.

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment

Figure 2.4: Topographs over different surfaces: (a) Si(111)7×7 from Ref. [93]. (b) Submonolayer of Au grown on a Ru(0001) surface from Ref. [94]. (c) Carbon nanotube from Ref. [95].

Figure 2.5: Simultaneously acquired1µm×1µmconstant-current topographic image (a) and barrier height map (b) of a 250 nm WOs film, reproduced from Ref. [96].

2.2.1 Work function

A STM can also be used to obtain the local tunneling barrier height, which is related to the work functions of both the tip and the sample. This can be done by recording the tunnel current as the tip is moved vertically. From Eq. 2.5, the barrier heightφcan be obtained from the slope of the semi-logarithmic plot of I vs. a. Simultaneous topographic and barrier height measurements obtained with this method are shown in Fig. 2.5.

This method assumes the validity of Eq. 2.5, which is not always satisfied. In particular, when the tip gets too close to the surface (experimentally, this occurs when a moderate to high value of current is demanded for a small applied bias voltage) other forces between tip and sample come into play such as van der Waals, electrostatic or magnetic, so that d(logI)/dz is no longer proportional to the square-root of the work function [74].

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Figure 2.6: Spectroscopic measurements on the vortex lattice of MgB2 from Ref. [97]:

(a) Conductance map over a single vortex at 0.05 T. (b) Vortex lattice at 0.2 T. (c) Tunnel conductance curves along the white line in (a).

2.2.2 Spectroscopy

Although spectroscopic measurements can be performed with rigid barriers such as in metal-oxide-metal trilayers, scanning tunneling spectroscopy (STS) has the advantage of nanopositioning which allows to probe surface spectroscopic properties with a high spatial resolution and to control the barrier width. The theory underlying scanning spectroscopy experiments has been presented in Section 2.1.

The idea of STS is to extract a measure of the density of states of the sample from the bias-voltage dependence of the tunneling current. This allows, in particular, the distinction of zones of the sample with different spectroscopic characteristics, as vortices in superconductors, see Fig. 2.6.

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment

Figure 2.7: Scanning tunneling potentiometry setup. A lateral voltageVS is applied across the sample. The local potential dropVLOCat a pointxof the surface with respect to a reference pointxois measured by the shift in the zero-tunnel-current voltage.

In its simplest implementation, called CITS (for Current Imaging Tunneling Spectroscopy) the tip is scanned over the surface with the feedback loop active as in the constant current topography mode [81]. This sets the tip-sample separation.

At each point, the feedback loop is interrupted to acquire tunnel current as bias voltage is ramped. The feedback loop is then restored and the scanning proceeds.

As a result, topography and a map of I(V) characteristics are simultaneously obtained.

Several variations exist, such as obtaining directly maps of dI/dV at a given voltage by superposing a AC signal to the constant bias voltage [76], or increasing tip-sample separation as bias voltage is increased to allow acquisition of current in a current range of several orders of magnitude [84].

However, one has to keep in mind when comparing experimental STM results to bulk properties that STM probes the density of states at the surface, which may be significantly different from that of the bulk due to surface reconstruction, contamination or degradation. Moreover, the electronic structure of the surface may be locally modified by the presence of the tip (tip-induced localized states, band bending) [98, 99].

2.2.3 Potentiometry

The potentiometry technique, developed by Muralt and Pohl [100], allows to image electrical transport at the nanoscale. A current is established through the sample by applying a difference of potential between opposite edges. At each location on

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Figure 2.8: Topography (A) and local potential image (B) of a granular La0.7Sr0.3MnO3

film grown on MgO, reproduced from Ref. [103]. The images were acquired simultaneously over an area of2000×2000Å².

the sample, the local voltage can be determined using an STM by measuring its influence on the tunneling current.

A schematic picture of the technique, as applied by Kirtley and coworkers [101], is shown in Fig. 2.7. The tip is grounded and a floating potential differenceVS is applied between the sample terminals. A potentiometer is connected in parallel to the sample, with the “wiper” terminal connected to the bias voltage, V, well defined with respect to ground. The potentiometer is set so that at a given point x0on the sample surface, the local potential is equal toV. The bias voltage is then ramped and the tunnel currentIis acquired through the tip. Atx0,I(V = 0) = 0.

When the tip is moved to a new locationxthe potential drop across the sample modifies the local potential seen by the tip, so that the acquired I(V) curve is offset by the local voltage dropVLOC with respect tox0. Knowing that the tunnel current atxis zero forV =−V_LOC,V_LOC can thus be obtained and mapped over the surface.

Since a I(V) curve is measured, conductance (in particular at zero bias) can be simultaneously obtained. IfVLOC is much smaller than the regulation voltage, topographic images will not be substantially distorted by the local potential drop.

In this way, topography, spectroscopy and local potential can be simultaneously acquired and compared.

The resolution is limited by the maximum VS that can be applied through the sample. To enhance sensitivity the contacts on the sample should be located as close as possible. The limit is then given by the sample resistance, because at a constantVS the dissipated power increases as the distance between contacts (and thus the total resistance) is decreased and sample heating effects can be important. In particular, for manganites at T . TC, self heating effects can induce the transition from the metallic to the insulating state [102]. This problem is often overcome by using patterned tracks of thin film materials with a small cross section to keep resistance high and power low.

The potentiometry method has been successfully applied to the study of gran-

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CHAPTER 2. Scanning Tunneling Microscopy: Theory and experiment ular manganite films at room temperature [103, 104]. Figure 2.8 shows both topographic and potentiometric measurements performed simultaneously on a La_0.7Sr_0.3MnO₃/MgO film. The local potential drop is small and homogenous inside the grains, while sudden drops are observed across some grain boundaries, signature of a bad grain connectivity.

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Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films

Thesis

Reference

Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films

SEIRO, Silvia Susana

SEIRO, Silvia Susana. Scanning tunneling spectroscopy across the insulator-to-metal transition in strained manganite films . Thèse de doctorat : Univ. Genève, 2008, no. Sc.

3995

URN : urn:nbn:ch:unige-6197

DOI : 10.13097/archive-ouverte/unige:619

Scanning tunneling spectroscopy across the insulator-to-metal transition

in strained manganite films

THÈSE

Silvia Susana SEIRO

Contents

Motivation

Chapter 1

An introduction to manganites

1.1 Structural properties

1.2 Electronic properties

1.3 Magnetism and transport properties

1.3.1 Electron-phonon coupling: Polarons

1.4 Phase separation

1.5 An open door for STM

Chapter 2

Scanning Tunneling

Microscopy: Theory and experiment

2.1 Tunneling from a theoretical viewpoint

2.1.1 The transfer Hamiltonian approach

2.2 The scanning tunneling microscope

2.2.1 Work function

2.2.2 Spectroscopy

2.2.3 Potentiometry