3.2.1 ARPES

As early as 1964, Kane argued that the momentum-dependent band structure could be mapped from the angle and energy dependence of the photoemission spectra. However, during the formative years of photoemission, all experiments were exclusively angle-integrated. In the early 1970s, work began in earnest on measuring the angular distribution of the photoelectrons. It was not until 1974 that the first angular dependent band-mapping was performed using photoemission by Traum, Smith, and DiSalvo (1974), which also used two-dimensional (2D) layered compounds TaS₂ and TaSe₂ to avoid the complications of the uncertainty in the transverse momentum, k_z, and were able to show good agreement with band structure calculations.

The energy resolution of photoemission experiments in the late 1970s and 1980s was in the order of 100 meV. In contrast, the thermodynamic properties of solids are determined by the electronic states within a thin strip of energy about k_BT wide where k_B is Boltzmann’s constant, around the Fermi energy. At room temperature, this corresponds to a thermal energy of 30 meV, but at low temperatures where phenomena such as superconductivity occur (~ 10 K), this corresponds to an energy of roughly 1 meV. Therefore, an energy resolution of 100 meV (corresponding to roughly 1000 K, in the order of the melting temperature of most solids) was clearly insufficient to address anything beyond the gross electronic structure of solids. However, substantial advances in detector technology in the late 1990s and early 2000s resulted in order-of-magnitude improvements in the energy and angular resolutions, along with the data acquisition efficiency. At present, multichannel angular and energy detection in normal ARPES experiments typically occur using ∆E ~ 5 meV, ∆θ ~ 0.2°, and with over 100 angular channels acquired simultaneously. Using the latest generation of analyzers and laser-based light sources, sub-meV energy resolutions have recently been demonstrated (Kiss et al. 2008).

Figure 3.1 shows the energetics of the photoemission process in a simplified density-of-states picture. Within the solid, there is an electronic density of states governed by the intrinsic band structure and interaction effects, where states are filled up to the Fermi energy. There is a finite potential energy barrier between the first occupied electronic state (at T = 0) at E_F, and the vacuum level (the potential energy zero infinitely far away from the sample), which is the work function of the material, Φ, and this is what holds the electrons inside the crystal. Therefore, when an electron absorbs a photon (and does not experience any inelastic losses), the binding energy of the electron in the initial state relative to the Fermi energy, E_B, can be related to the measured kinetic energy, E_kin, by hv – Φ – E_F. The work function in question is that of the detector, since all materials have slightly different work functions depending on the characteristics of the surface. If the work function of the sample and detector are different, then a potential will be set up between the sample and detector.

To relate the relationship of the photoelectron momentum to the momentum of the photohole left in the crystal, we consider an electron in a crystal with a well-defined quasimomentum K, and energy E_B. If the incident photon has enough energy to promote the electron above E_vac, then the electron can be photoemitted into free space. Because the electron has to propagate a macroscopic distance (~1 m) to the detector, it can essentially be treated as a free plane wave with E = hk²/2 m. Therefore, by knowing the takeoff angles of the electron relative to the crystal axes and the detector, we can determine the momentum wavevector of the outcoming photoelectron. The geometrical considerations for the photoemission process are illustrated in Fig. 3.2. From this we can use momentum conservation to relate this to the quasimomentum of the electron in the initial state. We can roughly generalize the real situation to a semi-infinite crystal (infinite in the lateral directions, but with a discontinuous step – the crystal surface – in the z direction). In this case, the momentum in the lateral direction, k_parallel is conserved due to translational symmetry, but the momentum in the z direction is clearly not conserved, owing to the work function step potential at the surface (the ‘lost’ k_z momentum of the photoelectron across the barrier is then taken up by a recoil of the crystal). Therefore, we can obtain an exact measure of the in-plane wavevectors of the electron in the initial state, k_parallel, but extracting k_z is more challenging. To determine k_z, one should determine the so-called ‘inner potential’ of the crystal, which is essentially determining which photoelectron kinetic energy corresponds to k_z = 0 (the (0,0,0) point) (Hufner 1995). This is typically rather involved and requires spanning a wide range of incident photon energies, hv, in real measurements.

It is generally most appropriate to view the experimentally measured photocurrent as a photoinduced transition between electron initial and final states. In UPS, the incoming photon carries negligible momentum (for hv = 10 eV, Q ~ 5 × 10^− 3 A^− 1), so all transitions are essentially direct, but this should clearly not be the case for XPS. To reach an available final state, the photoelectron should then be translated by a reciprocal lattice vector, G, so that the wavevector of the outgoing photoelectron K = k + G, demonstrating that the photoemission process requires the presence of a lattice potential to conserve momentum. The above analysis allows us to relate the photoelectrons measured at some kinetic energy and momentum to electrons with some different binding energy and momentum in the initial state, inside the crystal before the photoemission process. However, it does not tell us the direct relationship between the electronic states of the N and N–1 system. For this, one must make further assumptions beyond simple kinematics and conservation relations to obtain meaningful information about the N–1 system of the photohole from the experimentally measured photocurrent.

Rigorously speaking, the best theoretical description of the photoemission process is the so-called ‘one-step model’. In the one-step model, the photoemission process is treated as a single, entirely quantum-mechanical process. However, the phenomenological model which is nearly exclusively used in the experimental photoemission community is the ‘three-step’ model, popularized by Berglund and Spicer in 1964. The steps in the three-step model are as follows:

The independent steps in the three-step model are shown in Fig. 3.3. In this semiclassical picture, only the first step is treated quantum mechanically, and the three steps are treated as independent of one another, in contrast to the correct quantum-mechanical one-step approach. The beauty of the three-step model is that it actually removes the complicated photoemission process itself from photoemission. The three-step model effectively reduces the photoemission process to an optical excitation. Steps (2) and (3) in the three-step model are simply attenuation factors and kinematic considerations, respectively, leaving (1) as the only nontrivial process. Given the dramatic simplifications of the three-step model, it works remarkably well and provides surprisingly accurate results.

Here we will discuss a few additional aspects of the photoemission process. First, photoemission is a highly surface-sensitive process because of the strong Coulomb interactions between the photoelectron and the rest of the electrons left in the solid, with a typical mean free path on the order of 1 nm for photon energies in the vacuum ultraviolet (VUV). Because the mean free path depends on the cross-section of the photoelectrons to scatter with plasmons, the mean free path should be even lower for ‘bad metals’ with low plasmon energies such as many strongly correlated transition metal oxides. This high degree of surface sensitivity is the reason for extremely stringent ultra-high vacuum conditions necessary for reliable, high-resolution ARPES experiments, and experiments are typically performed at pressures of better than 5 × 10^− 11 torr. Samples are usually cleaved in situ at low temperatures and base pressure to ensure an atomically clean surface layer. Even at these pressures, we can occasionally observe surface degradation, although this varies significantly on the particular compound and contaminants in the vacuum chamber.

3.2.2 Instrumentation and light sources for high-resolution photoemission spectroscopy

ARPES experienced a renaissance in the late 1990s and early 2000s with the advent of 2D multiplexing analyzers by the Swedish company VG Scienta which could measure a range of electron kinetic energies and angles simultaneously. The way that traditional electron analyzers worked was that their angular acquisition was based on a small pinhole aperture. The position of the pinhole relative to the sample normal determined the photoelectron K, and the solid angle subtended by the pinhole determined ∆k. The problem with this approach is that all electrons outside this pinhole are discarded, and only one wavevector can be measured at a time. The great advantage of the Scienta analyzers is that the electron lens system for these analyzers allowed for parallel detection of many (~ 100) angular channels, thereby increasing the measurement efficiency by about two orders of magnitude. Today, such multiplexing analyzers are quite common and easily achieve energy resolutions of ∆E = 1 meV and simultaneously measure angular ranges greater than 30 degrees in parallel. The electrons pass through the entrance aperature, and then through a three-element lens system, through the entrance slits, and then the two concentric hemispheres housed inside the large stainless steel dome (all electron lens elements are electrostatic). The electrons are finally detected at the bottom of the analyzer, after the electron signals are amplified by a pair of microchannel plates (MCPs) and a phosphor screen. Flashes on the phosphor screen are then detected ex situ by a CCD camera looking through the window, visible at the bottom flange. An illustration of a Scienta analyzer operating at a synchrotron beamline is shown in Fig. 3.4.

A major barrier to performing UPS is the relative dearth of appropriate UV and VUV photon sources. As a result, many UPS and ARPES systems are located at synchrotrons where at undulator insertion devices, tunable photon energies can be achieved with high photon fluxes (~ 10¹² photons/s mm²) within a narrow (~ meV) energy bandwidth. Synchrotron sources remain the light source of choice for ARPES, as no other sources can match their flexibility in terms of photon energies and polarizations. However, because of the scarcity and relatively small number of synchrotrons, laboratory-based UV and VUV sources present a highly desirable alternative. These sources must exceed the energy of the work function (typically 4–5 eV), and such light sources are relatively scarce. The most common light sources for laboratory- based UPS are plasma discharge (He, Ar, Xe) lamps which have discrete emission lines with high brightness (~ 10¹²/s mm²) and narrow spectral widths (~ 1 meV). The main disadvantage to plasma discharge lamps is the lack of tunability in photon energies which can be essential for many experiments. More recently, VUV lasers which use higher harmonic generation (HHG) have come to the forefront. Although currently restricted in photon energy tunability and limited to fairly low photon energies (5–7 eV), they have the distinct advantage of superior spectral linewidths and brightness over plasma discharge lamps. In addition, laser sources can be utilized for time-resolved experiments such as pump-probe measurements. However, at present, the wavelengths available to VUV lasers is rather restricted, although this is likely to change as the technology matures.

3.3.1 SrRuO₃

SrRuO₃ has drawn wide interest for thin film studies and applications for a number of major reasons. First, SrRuO₃ is a ferromagnetic metal (T_c = 160 K) which is unusual for a 4d transition metal oxide, but also exhibits unconventional ‘bad metal’ behavior at elevated temperatures. The Ruddlesden-Popper series of layered ruthenates Sr_n + 1Ru_nO_3n + 1, of which SrRuO₃ is the three-dimensional end-member, display a remarkable evolution in magnetic and electronic properties as a function of dimensionality, n. The single layer n = 1 compound, Sr₂RuO₄, is an exotic spin triplet superconductor with a time- reversal symmetry breaking ground state (Mackenzie and Maeno 2003). The n = 2 bilayer compound, Sr₃Ru₂O₇ exhibits quantum critical metamagnetism and an apparent electronic nematicity where the magnetoresistance breaks C4 symmetry (Borzi et al. 2007). Ferromagnetic tendencies are enhanced by increasing the number n of RuO₂ sheets per unit cell. In addition, Ca substitution for Sr dramatically alters the magnetic and electronic properties of all known members of the Sr_n + 1Ru_nO_3n + 1 ruthenates, despite the fact that Ca and Sr are isovalent (for instance, CaRuO₃ is a paramagnetic metal, and Ca₂RuO₄ is an antiferromagnetic insulator). In addition, spin–orbit interactions and 4d orbital degeneracies are known to be important factors. Therefore, SrRuO₃ and other members of the ruthenate family present a wealth of exotic electronic and magnetic behaviors which are ripe for investigation. From the thin film standpoint, SrRuO₃ is also an excellent material for investigation since epitaxial thin films of very high quality can be synthesized. Until very recently, many properties of films (such as resistivity) were found to exceed even those of the best bulk single crystals. In addition, the low resistivity of SrRuO₃ films make it an excellent candidate material for thin film applications such as electrode materials or magnetic tunnel junctions. In addition, the pseudocubic perovskite structure makes SrRuO₃ suitably lattice matched to other common transition metal oxides such as SrTiO₃, a common substrate material for SrRuO₃.

Because the electronic properties of SrRuO₃ are still not well understood, UPS and ARPES studies of SrRuO₃ are essential for answering important basic questions about the electronic structure, such as whether first-principles calculations can capture an accurate description of this complex correlated material which exhibits ferromagnetism and three-fold orbital degeneracy, or the nature of the large effective masses and the strength of electron–electron correlations. However, because of its pseudocubic structure, cleaving single crystals does not yield the flat, well-defined surfaces necessary for ARPES. Therefore, measurements of atomically flat thin film samples synthesized in situ are essential for performing ARPES measurements of the quasiparticle band structure and Fermi surface. Moreover, because of the surface sensitivity of the ARPES technique (inelastic mean free path ~ 1 nm), these thin film samples cannot be removed from ultra-high vacuum (UHV) conditions before measurement; exposure of an atomically pristine surface to atmosphere can render a surface unmeasurable within nanoseconds. Therefore, the synthesis, transfer, and measurement stages must all take place under strict UHV conditions.

The earliest UPS measurements of SrRuO₃ were performed by Fujioka et al. (1997) and Okamoto et al. (1999) on polycrystalline samples of SrRuO₃ which were sintered as pellets and scraped in situ. Based on comparisons to the density of states obtained from band structure calculations, Okamoto et al. were able to obtain a mass enhancement factor of approximately m*/m_b ~ 4.4, which appeared consistent with estimates from transport measurements. On the other hand, based on this analysis, it is difficult to determine the origin of this fairly large mass enhancement, although it has been speculated by Fujioka et al. that this may be due to electron–electron interactions. On the other hand, Mazin and Singh (1997) have argued that electron–magnon and phonon couplings in SrRuO₃ could be anomalously large due to the important role of oxygen in forming the ferromagnetic state. A major limitation of performing photoemission spectroscopy on polycrystalline samples is the lack of any momentum-resolved information. Therefore, developing a method for pursuing in situ photoemission studies of SrRuO₃ thin films will be critical for in-depth studies of the electronic structure of SrRuO₃.

Using a novel combination of both PLD and MBE, Siemons et al. (2007) were able to synthesize a variety of SrRuO₃ thin films with varying degrees of Ru stoichiometry and quantified the strong dependence of the Ru stoichiometry (deficiency) on the unit cell volume and c-axis lattice constant as well as with the residual resistivity ratio (RRR), as shown in Fig. 3.5. They determine that films grown by PLD are typically ruthenium deficient with poor (low) residual resisitivities and can have an expanded unit cell volume, and could synthesize thin films with RRRs as low as 5 or less (PLD, high oxygen pressures) or up to 40 (MBE, low oxygen pressures). It is interesting to note that the Curie temperature is only very weakly dependent on Ru stoichiometry, and therefore should not be used as a metric for determining the quality of SrRuO₃ thin films. In addition, using in situ photoemission spectroscopy, Siemons et al. clearly demonstrate that the quality of the UPS spectra of these thin films near E_F (E < 1 eV) is strongly dependent on the Ru stoichiometry. In particular, the spectral intensity near E_F (constituted primarily of the Ru d_xy, d_yz, and d_xz orbitals) is strongly suppressed with respect to the background at higher binding energies as shown in Fig. 3.6. Therefore, measurements which attempt to extract the quasiparticle mass enhancement based solely on comparisons of spectral weight intensities and comparisons with theoretical densities of states must necessarily take into account the potentially sizable effects of Ru non-stoichiometry on the photoemission spectra.

As mentioned earlier, the electronic and magnetic properties of the Ruddlesden–Popper series ruthenates are known to depend critically on dimensionality. In response to this, ultrathin films of SrRuO₃ grown on SrTiO₃ have been investigated and an evolution in their electronic and magnetic properties have been reported by increasing the SrRuO₃ film thickness within the first 10 monolayers (MLs) of growth. Xia et al. (2009) have determined through a combination of polar Kerr effect measurements and resistivity that below a SrRuO₃ film thickness of 4 MLs, the material’s ferromagnetic properties appear to be heavily suppressed, suggesting the formation of antiferromagnetism, while above 4 MLs, bulk-like behavior is reported. In conjunction with this ferromagnetic suppression, films thinner than 4 MLs exhibited insulating behavior in resistivity measurements, shown in Fig. 3.7. These findings are consistent with earlier reports by Toyota et al. (2005) which studied the evolution of the photoemission spectra of SrRuO₃ films as a function of thickness. As shown in Fig. 3.8, below approximately 6 MLs, there is little to no spectral intensity near E_F, while above 10 MLs the spectra are similar to much thicker (100 ML) films. This again points to some kind of metal–insulator transition around 4 MLs which also appears to be coincident with a dramatic change in the ferromagnetic properties of the material.

The work by Siemons and Toyota clearly establishes the importance of in situ photoemission spectroscopy on uncovering the complex electronic structure of SrRuO₃. However, there is still much to be learned about the underlying electronic structure which may come from future angle-resolved measurements as well as additional thickness dependence studies of ultrathin SrRuO₃ films. At present, angle-resolved photoemission measurements of SrRuO₃ have not yet been conducted, although these recent successes of in situ angle-integrated photoemission measurements on SrRuO₃ and in situ ARPES on other thin films such as La_1–xSr_xMnO₃ suggest that future ARPES measurements on SrRuO₃ films are not far off on the horizon. ARPES measurements will be key in answering critical questions about the intrinsic electronic structure of SrRuO₃, such as whether density functional theory can adequately predict the electronic structure of such a complex, correlated multi-band ferromagnet, or what is the true nature (electron–electron or electron–boson coupling) of the large mass renormalization observed in SrRuO₃. However, a major consideration will be that accounting for Ru stoichiometry will be particularly critical for high-quality ARPES measurements. A high concentration of Ru vacancies will introduce a large amount of scattering which would broaden and mix otherwise well-defined eigenstates in momentum space, meaning the materials requirements for ARPES will be even more stringent than for angle-integrated UPS.

3.3.2 La_1–XSr_XMnO₃

The Re_1–xAe_xMnO₃ manganites (with Re a rare earth, and Ae an alkaline earth metal) have been at the forefront of the field of strongly correlated electrons due to their host of electronic phases and dramatic phase transitions. Most well known amongst these properties is colossal magnetoresistance (CMR), where the electrical resistance can drop by more than six orders of magnitude with the application of a magnetic field. La_1–xSr_xMnO₃ (LSMO) shows excellent metallic behavior and the highest Curie temperature of all Re_1–xAe_xMnO₃ variants, and is predicted theoretically to be 100% spin polarized. Based on these properties, LSMO is a potentially ideal material for the development of new spintronics devices, particularly magnetic memory and magnetic sensors. Toward this end, CMR effects in LSMO tunnel junctions and the integration of semiconductors into LSMO-based devices have been demonstrated, and a great deal of interest and work has been devoted to synthesizing epitaxial thin films of LSMO and other manganite compounds. Recently, there has also been great activity in using LSMO as a building block for novel heterostructured materials. Cation-ordered versions of LSMO, where layers of LaMnO₃ are alternately stacked with layers of SrMnO₃, have shown new and dramatic metal–insulator transitions, increased ordering temperatures, and may generate spin-polarized two-dimensional electron gases at the LaMnO₃–SrMnO₃ interfaces.

Due to its three-dimensional pseudocubic structure, ARPES measurements of bulk single crystals of LSMO remain inaccessible because of the inability to produce a well-defined crystallographic surface upon cleaving. Therefore, like the case of SrRuO₃, atomically flat thin film samples of LSMO grown in situ using MBE or PLD provide the only route to accessing the electronic structure of these materials. The importance of understanding the complex electronic structure of this strongly correlated material has led to various research groups performing in situ ARPES studies of thin films of LSMO.

The first in situ ARPES studies of thin films of LSMO were reported by Shi et al. (2004) and later by Chikamatsu et al. (2006). Thin films were synthesized using pulsed laser deposition on SrTiO₃ substrates. Measurements were conducted using an energy resolution of 150 meV and an angular resolution of 0.5° for the work of Chikamatsu et al. and 40 meV and 0.2° for Shi et al. Chikamatsu et al. demonstrated for x = 0.4 that the valence band (within ~ 10 eV of the Fermi level) exhibits generally good agreement with band structure calculations based on a local density approximation plus on-site Coulomb interactions (LDA + U), shown in Fig. 3.9. Close to E_F (within 1 eV), only broader features with weak spectral weight could be observed near E_F. While the approximate dispersion of these features qualitatively tracked some of the LDA + U predictions, important questions persist about the nature of these near E_F states. First, the reason for the dramatically reduced near E_F spectral weight is still unclear, although it has been suggested that this spectral weight suppression could be the signature of polaronic behavior due to strong electron–phonon interactions, shown in Fig. 3.10. However, it may be conceptually challenging to reconcile small polaron formation (and subsequently very large effective masses) with its reasonably metallic behavior at low temperatures (ρ ~ 10^− 5 Ω cm).

The work by Shi et al. on films of x = 0.33 grown by PLD also revealed that the large-scale electronic structure in the valence band also agreed reasonably well with predictions, but similar to the work by Chikamatsu et al., the near E_F electronic structure remained somewhat surprising. In particular, in both Chikamatsu’s and Shi’s works, a large sheet of Fermi surface predicted by theory (a large hole-like cubic sheet centered at k = (π,π,π)) was experimentally absent. Shi et al. have suggested that strong nesting between the flat faces of this sheet could have resulted in a charge density wave instability that results in this Fermi surface being entirely gapped. While a distinct possibility, such nesting driven density wave instabilities are highly uncommon in three-dimensional compounds due to phase space considerations, as pointed out by Chikamatsu et al.

At present, the origin of the apparent discrepancy between theory and experiment for these near E_F states in LSMO is still unclear. Because it is the states near E_F that are responsible for the thermodynamic properties, determining the electronic structure of these states and the suitability of theory to describe these materials remains a critical issue. In addition, LSMO is a polar compound, and charge redistribution at the surface which could alter the doping level on the surface relative to the bulk is another potential source of the discrepancy between experiment and theoretical predictions. At present, the possibilities regarding this apparent disagreement are as follows: whether this is due to (1) a failure of the density functional theory caused by the presence of strong electron correlations and magnetism, (2) the presence of a competing density wave instability which gaps out parts of the Fermi surface, (3) an altered surface electronic structure caused by the polar redistribution of charge and the surface termination, (4) strong electron–phonon interactions which dramatically suppress the near-E_F spectral weight resulting in highly massive polaronic charge carriers, or some combination of these various factors.

These first ARPES experiments have clearly demonstrated the importance and feasibility of thin film studies of LSMO and other closely related manganite perovskites. These measurements clearly demonstrate that the high energy structure of the valence band agrees well with predictions based on density functional theory, but clear discrepancies exist between the theory and experiment regarding the Fermi surface and near E_F band structure which are still unresolved. Therefore important questions remain which must be resolved before a clear understanding of the electronic structure of LSMO can be achieved through future ARPES experiments on LSMO thin films.

Berglund, C.N., Spicer, W.E. Photoemission studies of copper and silver. Phys. Rev. A. 1964; 136:1030.

Borzi, R.A., Grigera, S.A., Farrell, J., Perry, R.S., Lister, S.J.S., Lee, S.L., Tennant, D.A., Maeno, Y., Mackenzie, A.P. Formation of a nematic fluid at high fields in Sr₃Ru₂O₇. Science. 2007; 315:214.

Chikamatsu, A., Wadati, H., Kumigashira, H., Oshima, M., Fujimori, A., Hamada, N., Ohnishi, T., Lippmaa, M., Ono, K., Kawasaki, M., Koinuma, H. Band structure and Fermi surface of La_0.6Sr_0.4MnO₃ thin films studied by in situ angle-resolved photoemission spectroscopy. Phys. Rev. B. 2006; 73:195105.

Damascelli, A., Hussain, Z., Shen, Z.X. Angle-resolved photoemission studies of cuprate superconductors. Rev. Mod. Phys. 2003; 75:473.

Fujioka, K., Okamoto, J., Mizokawa, T., Fujimori, A., Hasi, I., Abbate, M., Lin, H.J., Chen, C.T., Takeda, Y., Takano, M. ‘Electronic structure of SrRuO₃’, Phys. Rev B. 1997; 56:6380.

Hufner, S. Photoelectron Spectroscopy: Principles and Applications. New York: Springer-Verlag; 1995.

Kane, E.O. Implications of crystal momentum conservation in photoelectric emission for band structure measurements. Phys. Rev. Lett. 1964; 12:97–98.

Kiss, T., Shimojima, T., Ishizaka, K., Chainani, A., Togashi, T., Kanai, T., Wang, X.Y., Chen, C.T., Watanabe, S., Shin, S. A versatile system for ultrahigh resolution, low temperature, and polarization dependent laser-angle-resolved photoemission spectroscopy. Rev. Sci. Inst. 2008; 79:023106.

Mackenzie, A.P., Maeno, Y. The superconductivity of Sr₂RuO₄ and the physics of spin-triplet pairing. Rev. Mod. Phys. 2003; 75:657.

Mazin, I.I., Singh, D.J. Electronic structure and magnetism in Ru-based perovskites. Phys. Rev. B. 1997; 56:2556.

Okamoto, J., Mizokawa, T., Fujimori, A., Hase, I., Nohara, M., Takagi, H., Takeda, Y., Takano, M. Correlation effects in the electronic structure of SrRuO₃. Phys. Rev. B. 1999; 60:2281.

Shi, M., Falub, M.C., Willmott, P.R., Krempasky, J., Herger, R., Hricovini, K., Patthey, L. k-dependent electronic structure of the colossal magnetoresistive perovskite La_0.66Sr_0.34MnO₃. Phys. Rev. B. 2004; 70:140407.

Siemons, W., Koster, G., Vailionis, A., Yamamoto, H., Blank, D.H.A., Beasley, M.R. Dependence of the electronic structure of SrRuO₃ and its degree of correlation on cation off-stoichiometry. Phys. Rev. B. 2007; 76:075126.

Toyota, D., Ohkubo, I., Kumigashira, H., Oshima, M., Ohnishi, T., Lippmaa, M., Takizawa, M., Fujimori, A., Ono, K., Kawasaki, M., Koinuma, H. Thickness-dependent electronic structure of ultrathin SrRuO₃ films studied by in situ photoemission spectroscopy. Appl. Phys. Lett. 2005; 87:162508.

Traum, M.M., Smith, N.V., DiSalvo, F.J. Angular dependence of photoemission and atomic orbitals in the layer compound 1 T-TaSe₂. Phys. Rev. Lett. 1974; 32:1241.

Xia, J., Siemons, W., Koster, G., Beasley, M.R., Kapitulnik, A. Critical thickness for itinerant ferromagnetism in ultrathin films of SrRuO₃. Phys. Rev. B. 2009; 79:140407(R).