Structure, physical properties, and applications of ${\mathrm{SrRuO}}_3$ thin films

${\mathrm{SrRuO}}_3$ is endowed with three remarkable features. First, it is a moderately correlated material that exhibits several novel physical properties; second, it permits the epitaxial growth of essentially single-crystal films; and third, because it is a good conductor, it has attracted interest as a conducting layer in epitaxial heterostructures with a variety of functional oxides. In this review, the present state of knowledge of ${\mathrm{SrRuO}}_3$ thin films is summarized. Their role as a model system for studying magnetism and electron transport characterized by intermediate electron correlation and large magnetocrystalline anisotropy is demonstrated. The materials science of ${\mathrm{SrRuO}}_3$ thin film growth is reviewed, and its relationship to electronic, magnetic, and other physical properties is discussed. Finally, it is argued that, despite all that has been learned, a comprehensive understanding of ${\mathrm{SrRuO}}_3$ is still lacking and challenges remain.

Figure 1

Schematic view of the orthorhombic unit cell of ${\mathrm{SrRuO}}_3$. From 59.

Figure 2

A sequence of phase transitions of unstrained bulk ${\mathrm{SrRuO}}_3$ from orthorhombic to tetragonal and then cubic symmetry at $547°\mathrm{C}$ and $677°\mathrm{C}$, respectively. The unit cell of the orthorhombic ${\mathrm{SrRuO}}_3$ consists of four formula units of the ideal cubic perovskite structure. The atoms of Ru occupy high-symmetry positions with respect to the orthorhombic shape of the cell. The atoms of O and Sr are displaced from their high-symmetry positions due to the octahedral tilting. The tetragonal ${\mathrm{SrRuO}}_3$ is a one-tilt system, where ${\mathrm{RuO}}_6$ octahedra are rotated only about the [001] direction. The cube corresponds to the unit cell of each ${\mathrm{SrRuO}}_3$ form. Gray, black, and white balls represent Ru, O, and Sr atoms, respectively. From 29.

Figure 3

Temperature dependence of the unit-cell volume of ${\mathrm{SrRuO}}_3$. The solid line represents the contribution of the phonons fitted by the Debye function with $\Theta$ of 525.5 K, $V(T=0\mathrm{K})$ of $240.9{\AA }^3$, and $9\gamma N{k}_B/B$ of $0.0281{\AA }^3/\mathrm{K}$. From 125.

Figure 4

Schematic low-spin one-electron energy level diagram for a perovskite ruthenate $A{\mathrm{RuO}}_3$. The degeneracies of the bands indicated in square brackets are multiplied by 2 to allow for spin degeneracy. The correlation lines indicate the dominant atomic parentage of the band states. From 34.

Figure 5

Electronic density of states of ferromagnetic ${\mathrm{SrRuO}}_3$. Majority spin is plotted upward, minority spin downward. The cell contains four formula units. From 7.

Figure 6

Magnetic ordering temperature $T_C$ and Curie-Weiss temperature vs Ca concentration $x$. The inset shows an expanded view of the presumed spin-glass-ordering regime (273). From 23.

Figure 7

Resistivity vs temperature for ${\mathrm{SrRuO}}_3$. From 7.

Figure 8

High-resolution TEM images showing (a) the ${\mathrm{BaTiO}}_3/{\mathrm{SrRuO}}_3$ and (b) the ${\mathrm{SrRuO}}_3/{\mathrm{GdScO}}_3$ interfaces. Dashed lines mark the positions of the interfaces. From 30.

Figure 9

A typical AFM scan of an HF-treated ${\mathrm{SrTiO}}_3$ substrate. After chemical etching, the surface is ${\mathrm{TiO}}_2$ terminated with steps edges of one unit-cell height.

Figure 10

A scanning tunneling microscopy scan of a 30-nm-thick ${\mathrm{SrRuO}}_3$ film on ${\mathrm{SrTiO}}_3$. Although the termination of the substrate was ${\mathrm{TiO}}_2$, as shown in Fig. 9, before the sample was heated in the deposition system, Sr diffused to the surface and moved to the step edges. On the SrO-terminated areas, ${\mathrm{SrRuO}}_3$ grew more slowly than on the ${\mathrm{TiO}}_2$-terminated areas, resulting in the trenches clearly seen in the STM image. At the same time, on the flat areas, unit-cell high steps can still be observed.

Figure 11

Typical AFM micrograph ($1\times 1\mu {\mathrm{m}}^2$) of a 50-nm-thick ${\mathrm{SrRuO}}_3$ film.

Figure 12

RHEED intensity at different deposition temperatures on vicinal ($\alpha =0.11°$) ${\mathrm{TiO}}_2$-terminated ${\mathrm{SrTiO}}_3$ substrates (a) The dotted lines indicate the time where completion of one unit-cell layer is expected at $700°\mathrm{C}$ and should be used as a guide for the eye. (b) RHEED intensity during the growth of ${\mathrm{SrRuO}}_3$ on SrO-terminated ${\mathrm{SrTiO}}_3$.

Figure 13

AFM images of ${\mathrm{SrRuO}}_3$ on ${\mathrm{TiO}}_2$-terminated ${\mathrm{SrTiO}}_3$ taken at the first minimum (a) and first maximum (b) of the RHEED intensity as presented in Fig. 12a at $700°\mathrm{C}$. From 208.

Figure 14

RHEED patterns recorded before (a) and (b), and after (c) and (d) deposition of ${\mathrm{SrRuO}}_3$. The azimuthal angle was set to 0° in (a) and (c), and to 10° in (b) and (d).

Figure 15

RHEED specular spot intensity variation during ${\mathrm{SrRuO}}_3$ growth (shown after deposition of $\sim 60\mathrm{nm}$) sequenced by interruptions, after 13 and 4 min of interruption (left and right parts of the graph, respectively). The inset at the bottom shows an enlargement of the former growth cycle. From 13.

Figure 16

Simulated RHEED intensity variations during growth of five unit-cell layers on substrates with different vicinal angles of 0.45° (a), 0.6° (b), and 1.0° (c). The deposition temperature was set to $600°\mathrm{C}$, $E_S=0.75\mathrm{eV}$, and $E_N=0.6\mathrm{eV}$, the pulse $\mathrm{\text{repetition rate}}=2\mathrm{Hz}$, and the number of pulses needed for completion of one unit-cell layer is 20.

Figure 17

Simulated surface morphology after five unit-cell layers on substrates with a vicinal angle of 0.6°. The advancing steps, indicated by the solid lines, coalesce with the growing islands on the terraces. In this simulation, the deposition temperature was set to $600°\mathrm{C}$, $E_S=0.75\mathrm{eV}$, and $E_N=0.6\mathrm{eV}$, the pulse $\mathrm{\text{repetition rate}}=2\mathrm{Hz}$, and the number of pulses needed for completion of one unit-cell layer is 20.

Figure 18

Schematics of possible surface configurations at room temperature and after annealing to $300–500°\mathrm{C}$ and $600–700°\mathrm{C}$ for air-exposed ${\mathrm{SrRuO}}_3$ films (a) in high vacuum (below ${10}^{-7}\mathrm{Torr}$), (b) in high ${\mathrm{O}}_2\mathrm{\text{−}}{\mathrm{O}}_3$ pressure ($\sim 10\mathrm{mTorr}$, $\sim 7\%$ ozone), and (c) in high vacuum (below ${10}^{-7}\mathrm{Torr}$) after annealing in ${\mathrm{O}}_2\mathrm{\text{−}}{\mathrm{O}}_3$. From 236.

Figure 19

A schematic of the ${\mathrm{SrRuO}}_3$ distorted orthorhombic crystal structure as it grows on ${\mathrm{SrTiO}}_3$ at room temperature, with a view along the [001] direction. The orthorhombic cell parameters $a$ and $b$ are indicated as well as the distortion angle $\gamma =89.4°$. The in-plane $c$ lattice parameter is strained to ${\mathrm{SrTiO}}_3$ and 7.81 Å in length. Note that the [110] axis is not perfectly parallel to the surface normal.

Figure 20

(a) Temperature dependence of in-plane and out-of-plane lattice parameters of a compressively strained ${\mathrm{SrRuO}}_3$ thin film grown on an ${\mathrm{SrTiO}}_3$ substrate. Transition temperatures for unstrained bulk ${\mathrm{SrRuO}}_3$ are displayed for comparison. (b) Temperature dependence of the orthorhombic lattice parameters $a_o$ and $b_o$ of an ${\mathrm{SrRuO}}_3$ film grown on an ${\mathrm{SrRuO}}_3$ substrate. (c) The normalized integral intensity of the $(113{)}_o$ XRD reflection as a function of temperature. The insets show 2D images of the $(113{)}_o$ peak obtained at different temperatures. (d) Normalized integral intensity of the $(01/2)$ RHEED pattern as a function of temperature with insets of RHEED images obtained at different temperatures. From 29.

Figure 21

Intensity of the ${\mathrm{SrRuO}}_3$ (211) peak as a function of temperature. The nonzero intensity indicates that ${\mathrm{SrRuO}}_3$ possesses a tetragonal symmetry up to $730°\mathrm{C}$. From 266.

Figure 22

Schematic diagram of a vicinal ${\mathrm{SrTiO}}_3$ (001) substrate showing miscut angle $\alpha$ and miscut direction $\beta$, as well as the epitaxial arrangement of two types of step-flow growth of $(110{)}^o$ ${\mathrm{SrRuO}}_3$ domains.

Figure 23

Typical XRD $\varphi$ scans indicating a single-domain structure of ${\mathrm{SrRuO}}_3$ on vicinal (0.2°) ${\mathrm{SrTiO}}_3$. The twofold symmetry in (a) and the absence of peaks in (b) indicate a single-domain structure.

Figure 24

A SEM picture of a ruthenium rich ${\mathrm{SrRuO}}_3$ thin film with the associated elemental maps as obtained with Auger electron spectroscopy. The precipitations show up clearly in all the scans and contain no strontium, but seem ruthenium rich and oxygen poor. The precipitations are almost certainly ${\mathrm{RuO}}_2$ and might show up as oxygen poor due to a change in the sensitivity factor between ${\mathrm{SrRuO}}_3$ and ${\mathrm{RuO}}_2$.

Figure 25

Susceptibility along the crystallographic directions $[100]({\chi }_a)$ and $[010]({\chi }_b)$ as a function of temperature, on a semilogarithmic plot. The values are multiplied by $R_s$, whose temperature dependence is expected to be smooth. The error bars for $R_s{\chi }_a$ reflect an uncertainty of up to 2° in $\theta$. The dashed lines are guides to the eye. The inset shows the ratio ${\chi }_b/{\chi }_a$ for $165<T<300\mathrm{K}$. The solid curve is a fit to $(T-T_{c,a}^{\mathrm{MF}})/(T-T_{c,b}^{\mathrm{MF}})$ with $T_{c,a}^{\mathrm{MF}}=109\mathrm{K}$ and $T_{c,b}^{\mathrm{MF}}=150.5\mathrm{K}$. From 110.

Figure 26

Magnetoresistance as a function of temperature with a field of 0.5 T applied along the different crystallographic directions (the values are normalized to the values at 180 K). The inset shows the magnetization (${\mu }_0{R}_{s}M$) and MR ($\Delta \rho$) as a function of a field (applied along the $b$ direction, at $T=170\mathrm{K}$). The solid curve is a fit to $\Delta \rho \propto -M^2$. From 110.

Figure 27

Temperature dependences of the in-plane, out-of-plane, and total remanent magnetizations of a ${\mathrm{SrRuO}}_3$ film. The film was cooled in a saturating field down to 5 K and the magnetization was measured upon warming after removing the applied field. The temperature dependence of the angle between the magnetic moment and the normal to the film plane is also shown. From 129.

Figure 28

Sequence of video images with Lorentz transmission electron microscopy during cooling of the ${\mathrm{SrRuO}}_3$ film. The initial faint stripe structure (a) increases rapidly in contrast as the magnetization increases (b). Pairs of black-and-white domain walls annihilate to increase the average wall spacing (c). This process continues for about 15 K below $T_C$ (d), and the wall structure remains unchanged with further cooling down to about 100 K. From 168.

Figure 29

STM measurement demonstrating the spatial evolution of the DOS within a “gapped strip” in the ${\mathrm{SrRuO}}_3$. (a) A schematic crossed Andreev reflection diagram. (b) $260\times 260{\mathrm{nm}}^2$ topographic image of a 18-nm-thick ${\mathrm{SrRuO}}_3/(100)\mathrm{YBCO}$ bilayer. (c) Tunneling spectra taken sequentially at fixed steps along the center of the gapped strip [white arrow in (b)]. (d) Tunneling spectra acquired across the gapped strip [white arrow in (b)]. From 11.

Figure 30

Resistivity curves of ${\mathrm{SrRuO}}_3$ films 1000 Å thick: (a) and (b) are on miscut ${\mathrm{SrTiO}}_3$ substrates and the current is perpendicular to the $c$ axis, (c) is on a regular ${\mathrm{SrTiO}}_3$ substrate, (d) is on a ${\mathrm{LaAlO}}_3$ substrate, and (e) is on a ytrria-stabilized zirconia (YSZ) substrate. From 129.

Figure 31

(a) $dR/dT$ with currents in the [001] and [110] directions; the stronger divergence is in the [110] direction. Iron data are shown for comparison, shifted with a constant of $0.5\mu \Omega \mathrm{cm}$. The inset shows a larger temperature range that enables an estimate of the nonmagnetic part in $dR/dT$. (b) Log-log plot of $d{R}_m/dT$ with slopes of 0.1 (which is expected), 0.5 (not expected; the Gaussian limit), and iron data for comparison. From 130.

Figure 32

Plot of the resistivity against the temperature for (a) two samples cooled down to room temperature at different rates (A, slow; B fast). (b) The two samples were grown on two ${\mathrm{SrTiO}}_3$ substrates having different miscut angles (A, $\alpha =0°$; B, $\alpha =2°$). In both panels, fittings to a model described by 77 are plotted, showing excellent agreement with the experimental data. The temperatures at which the minima appear are written next to the corresponding curves. From 77.

Figure 33

Extraordinary Hall effect ${\rho }_{rxy}^{\mathrm{EHE}}$ (due to the spontaneous magnetization) as a function of temperature. The inset shows the longitudinal resistivity $\rho$ as a function of temperature. From 109.

Figure 34

Hysteresis loops of resistivity vs applied field for current parallel and perpendicular to the domain walls at $T=5\mathrm{K}$. At the starting point with $H=0$ (marked by a full circle), the sample is in its domain structure. Increasing the field annihilates the domain wall, and when the field is set back to zero the magnetization of the sample remains saturated. The difference between the initial zero-field resistivity and the subsequent zero-field resistivities is identified as the domain-wall resistivity. From 134.

Figure 35

Current-induced hysteresis loop with current pulses (100 ms) at $T=140\mathrm{K}$ and $H=0$ measured with the normalized extraordinary Hall effect ($R_{\mathrm{EHE}}^{*}$). From 51.

Figure 36

$H_c/J_c$ as a function of temperature in ${\mathrm{SrRuO}}_3$ (circles), permalloy (Py, triangle), and ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ (squares). From 51.

Figure 37

(a) Optical conductivity of ${\mathrm{SrRuO}}_3$ at $T=40$, 80 (solid curve), 105, 125, 145 (solid curve), 165, 185, 205, 225, and 250 K (dashed curve). Transport measurements at $\omega =0$ are also shown for $T=145$ (△) and 250 K (+), and the top curve is given by ${\sigma }_1(\omega )=c/\sqrt{\omega }$ with $c=1.265\times {10}^5{\Omega }^{-1}{\mathrm{cm}}^{-1/2}$. (b) Frequency-dependent scattering rate $1/\tau (\omega )$ evaluated with Eq. (4), for the same temperatures. From 141.

Figure 38

Dynamical conductivity of ${\mathrm{SrRuO}}_3$ at $T=8$, 40, 60, and 80 K. Dashed lines extending over $6–36{\mathrm{cm}}^{-1}$ show terahertz measurements and solid lines extending over $26–80{\mathrm{cm}}^{-1}$ show infrared measurements performed on the same sample, a ${\mathrm{SrRuO}}_3$ film on an ${\mathrm{NdGaO}}_3$ substrate. The solid line extending over $124–2440{\mathrm{cm}}^{-1}$ shows the results of 140 with a 420 nm ${\mathrm{SrRuO}}_3$ film deposited on ${\mathrm{SrTiO}}_3$. Thin dotted lines show fits of Eq. (5) to the complex conductivity obtained from terahertz spectroscopy. The inset shows $1/\tau (T)$, together with a fit to Eq. (6). From 42.

Figure 39

Atomic motions for the 14 $A_g$ and $B_{2g}$ Raman-active phonon modes. Phonon frequencies obtained from lattice dynamical calculations are listed in parentheses below the associated mode; Raman line assignments are listed below these. All frequencies are given in wave numbers. From 83.

Figure 40

Room-temperature optical conductivity of (a) ${\mathrm{Y}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$, (b) ${\mathrm{CaRuO}}_3$ and ${\mathrm{SrRuO}}_3$, and (c) ${\mathrm{Bi}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$. Peak labels correspond to interband transitions shown schematically in Fig. 41. From 148.

Figure 41

Generic electronic structure for ${\mathrm{Y}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$, ${\mathrm{CaRuO}}_3$, ${\mathrm{SrRuO}}_3$, and ${\mathrm{Bi}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$, shown together with optical transitions assigned in Fig. 40. The specific case of ${\mathrm{CaRuO}}_3$ is shown, although qualitatively similar behavior is expected for the other compounds. From 148.

Figure 42

(a) Optical conductivity ${\sigma }_{xx}(\omega )$ and (b) magneto-optic conductivity ${\sigma }_{xy}(\omega )$. Experimental measurements are shown as discrete markers, ◯ for ${\sigma }_{1xx}$ and ${\sigma }_{2xy}$, and □ for ${\sigma }_{2xx}$ and ${\sigma }_{1xy}$; theoretical calculations in the local density approximation are shown as solid lines for ${\sigma }_{1xx}$ and ${\sigma }_{2xy}$, and dashed lines for ${\sigma }_{2xx}$ and ${\sigma }_{1xy}$. Experimental values for ${\sigma }_{xx}$ were taken at room temperature, while those for ${\sigma }_{xy}$ were taken at $T=65\mathrm{K}$ and scaled up using the known $M(T)$ to the value expected at $T=0$. From 41.

Figure 43

Time-resolved magneto-optical measurements of ferromagnetic resonance in ${\mathrm{SrRuO}}_3$ at $T=5\mathrm{K}$. (a) Change in the magneto-optic Kerr rotation angle $\Delta {\theta }_K$ as a function of time delay following pulsed excitation with a femtosecond laser, and for several values of applied magnetic field. (b) Fourier transforms of the time traces shown in (a); the inset shows the ferromagnetic resonance frequency as a function of applied magnetic field. From 145.

Figure 44

Ru $3d$ XPS spectra of ${\mathrm{RuO}}_2$, ${\mathrm{Bi}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$, ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, ${\mathrm{SrRuO}}_3$, ${\mathrm{CaRuO}}_3$, and ${\mathrm{Y}}_2{\mathrm{Ru}}_2{\mathrm{O}}_7$. $s$ and $u$ denote screened and unscreened peaks, respectively. All the spectra are aligned by the unscreened-peak positions of Ru $3d_{(5/2)}$. From 120.

Figure 45

Ru $3d$ and Sr $3p$ core-level photoemission spectra of ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x{\mathrm{RuO}}_3$. From 254.

Figure 46

UPS and O $1s$ XAS spectra of ${\mathrm{SrRuO}}_3$ compared with the band DOS in the ferromagnetic state. The band DOS has been broadened as described in the text. For the XAS spectra, the oxygen $p$ partial DOS is compared. From 54.

Figure 47

Surface (circles) and bulk (triangles) spectral functions of (a) ${\mathrm{CaRuO}}_3$ and (b) ${\mathrm{SrRuO}}_3$. Closed symbols represent spectra at 300 K and the open ones represent spectra at 48 and 35 K for ${\mathrm{CaRuO}}_3$ and ${\mathrm{SrRuO}}_3$, respectively. (c) High-resolution He I spectra of ${\mathrm{SrRuO}}_3$. The dashed, solid, and dot-dashed lines represent the spectrum at 133, 81, and 42 K, respectively. The inset shows the expanded view of the same spectra near the Fermi level. From 163.

Figure 48

Top: Angular dependence of Ru $4d$ spectra for (a) ${\mathrm{SrRuO}}_3$ films and (b) ${\mathrm{SrTiO}}_3/{\mathrm{SrRuO}}_3$ bilayers, where the 70° spectra are more surface and interface sensitive. Bottom: (a) Bulk and surface spectra extracted from the PES spectra for ${\mathrm{SrRuO}}_3$ films and (b) bulk and interface spectra of ${\mathrm{SrTiO}}_3/{\mathrm{SrRuO}}_3$ bilayers. From 142.

Figure 49

Resistivity as a function of temperature of ${\mathrm{SrRuO}}_3$ and ${\mathrm{CaRuO}}_3$ thin films grown on different substrates. ${\mathrm{SrRuO}}_3$ on ${\mathrm{DyScO}}_3$ and ${\mathrm{CaRuO}}_3$ on ${\mathrm{SrTiO}}_3$ layers affected by a higher tensile strain are tetragonal and exhibit larger resistivity values, while orthorhombic ${\mathrm{SrRuO}}_3$ on ${\mathrm{SrTiO}}_3$ and ${\mathrm{CaTiO}}_3$ on ${\mathrm{NdGaO}}_3$ layers show smaller resisitivity values. From 267.

Figure 50

Temperature dependence of in-plane and out-of-plane lattice parameters of the strained ${\mathrm{SrRuO}}_3$ film grown on a GSO substrate. The insets show RHEED images obtained at different temperatures. From 29.

Figure 51

The resistivity vs temperature curves for both a strained and a strain-relaxed ${\mathrm{SrRuO}}_3$ thin film. The arrows indicate the Curie temperature $T_C$. From 58.

Figure 52

Magnetic hysteresis loops of strained and strain-free ${\mathrm{SrRuO}}_3$ films on ${\mathrm{SrTiO}}_3$ (STO) and on ${\mathrm{Ba}}_{(1-x)}{\mathrm{Sr}}_x{\mathrm{TiO}}_3$ (BSTO) with $x=0.75$ and 0.5, respectively. The magnetic field was applied (a) parallel and (b) perpendicular to the sample surface. The measurements were done at 10 K. The compressively strained ${\mathrm{SrRuO}}_3$ (SRO) film shows the largest magnetization and the smallest coercivity, indicating that the easy axis of magnetization is more out of plane. From 257.

Figure 53

Film magnetic moment vs applied field measured with a SQUID magnetometer. Samples were 24-nm-thick (001)-, (110)-, and (111)-oriented ${\mathrm{SrRuO}}_3$ films on ${\mathrm{SrTiO}}_3$. From 65.

Figure 54

Oxygen pressure dependence of resistivity vs temperature curves for ${\mathrm{SrRuO}}_3$ thin films grown at $640°\mathrm{C}$ on ${\mathrm{SrTiO}}_3$ (001) single-crystal substrates. From 81.

Figure 55

Comparison of $\theta \mathrm{\text{−}}2\theta$ XRD scans of two thick (330 nm) films grown by PLD and MBE. The fringes indicate good crystalline quality of the films, and the shift in peak position shows that the PLD film has a larger out-of-plane lattice parameter (110 direction). From 239.

Figure 56

A comparison between the volume of the ${\mathrm{SrRuO}}_3$ unit cell in thin films on ${\mathrm{SrTiO}}_3$ substrates grown by either MBE or PLD and their transport properties: room-temperature and low-temperature resistivity on the right $y$ axis and residual resistance ratio on the left $y$ axis. The dashed lines are guides to the eye. From 239.

Figure 57

UPS spectra at room temperature of three ${\mathrm{SrRuO}}_3$ films: a MBE film, a ruthenium poor MBE film, and a PLD film. All samples show states at the Fermi edge and a Ru $t_{2}g$ peak close to the Fermi level. The spectra have been normalized on the $t_{2g}$ peak. From 239.

Figure 58

A schematic diagram for ${\mathrm{SrTi}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_3$. As $x$ decreases, (a) DOS of a correlated metal ($1-x$), shows (b) suppression in the correlated quasiparticle peak first due to disorder (a disordered metal, $x\sim 0.7$). With further decrease of $x$, (c) mobility edges are formed near $E_F$ (an Anderson insulator, $x\sim 0.5$), and (d) the increased Coulomb interaction results in a soft Coulomb gap at $E_F$ (a soft Coulomb gap insulator, $x\sim 0.4$). (e) Finally the disorder-induced correlation opens a hard gap (a disordered correlation insulator, $x\sim 0.2$). And further decrease of $x$ makes the system (f) a band insulator with a wide optical gap ($x\sim 0$). From 121.

Figure 59

A combined plot of the valence-band spectra and the O $1s$ XAS spectra of ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x{\mathrm{RuO}}_3$. The dashed curve shows how the O $2p$ band has been subtracted to obtain the Ru $4d$ band. From 254.

Figure 60

Cross-sectional high-resolution TEM images from left to right of $n=1–5$ ${\mathrm{Sr}}_{n+1}{\mathrm{Ru}}_n{\mathrm{O}}_{3n+1}$ films. The two adjacent white rows in the images correspond to the [100] projections of the rocksalt SrO layers. Between the double SrO layers lies the [100] projection of the ${\mathrm{SrRuO}}_3$ perovskite sheet. From 258.

Figure 61

Magnetization as a function of temperature of $n=1–5$ ${\mathrm{Sr}}_{n+1}{\mathrm{Ru}}_n{\mathrm{O}}_{3n+1}$ films and an $n=\infty$ ${\mathrm{Sr}}_{n+1}{\mathrm{Ru}}_n{\mathrm{O}}_{3n+1}$ film. Note that the $n=3$, 4, 5, and $\infty$ samples show ferromagnetism, while no sign of ferromagnetism is observed for the $n=1$ and 2 samples. The inset shows a plot of the ferromagnetic transition temperatures of the $n=3$, 4, 5, and $\infty$ ${\mathrm{Sr}}_{n+1}{\mathrm{Ru}}_n{\mathrm{O}}_{3n+1}$ samples vs $n$. For comparison, the metamagnetic phase transition temperature 1.1 K of the $n=2$ ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ single crystal in a magnetic field of 7.9 T data from 64 is also shown. From 258.

Figure 62

(a) In situ valence-band spectra of ${\mathrm{SrRuO}}_3$ thin films with varying nominal film thickness. (b) The photoemission spectra near $E_F$ in an enlarged binding energy scale. From 261, 260.

Figure 63

Thickness dependencies of (a) the saturated Kerr signal (▪) at the lowest temperature; (b) Curie temperature $T_C$ (▴), extrapolated Curie temperature $T_e$ (●), and resistivity anomaly (□); and (c) the angle $\Phi$ (▾) between film normal and magnetic easy axis at the lowest temperature. The dashed line in (a) is the linear fit of the data point between 4 and 22 ML. The inset in (b) shows how $T_C$ and $T_e$ are determined. From 283.

Figure 64

Schematic illustration of the capacitor test structure that was used by 47.

Figure 65

(a) The pulse train used to measure the effective read cycle discrimination. (b) Remnant polarization vs number of fatigue cycles at 10 V for the ${\mathrm{SrRuO}}_3/\mathrm{PZT}/{\mathrm{SrRuO}}_3$ and ${\mathrm{SrRuO}}_3/\mathrm{PZT}/{\mathrm{SrRuO}}_3/\mathrm{YSZ}/\mathrm{Si}$ structures, compared with data for a typical polycrystalline ferroelectric layer on a Pt base electrode. The solid line is a guide to the eye based on behavior reported in the literature (230). From 47.

Figure 66

Schematic of the $\mathrm{PZT}/{\mathrm{SrTiO}}_3$ heterostructure. With the use of an AFM with a metallized tip, ferroelectric domains can be polarized by applying a voltage between the tip and ${\mathrm{SrRuO}}_3$ film that exceeds the coercive field of the PZT layer, resulting in a local, nonvolatile change in the electronic properties of the underlying film. From 4.

Figure 67

Spatially resolved correlation between the onset of polarization reversal (a) and a change in electrical conductance (b). A change in the polarization contrast in (a) illustrates polarization reversal under an incrementally changing tip bias. Dashed lines indicate where the bias is changing. The change in PFM contrast correlates with the transition from low current (dark contrast) to high current (bright contrast). From 66.

Figure 68

Evolution of the energy as a function of the soft-mode distortion $\xi$. First-principles results (symbols) and electrostatic model results (lines) are shown for different thicknesses of the ferroelectric thin film: $m=2$ (◯, full line), $m=4$ (▵, dotted line), $m=6$ (⋄, short-dashed line), $m=8$ (□, dot-dashed line), and $m=10$ (▽, long-dashed line). The magnitude of $\xi$ is reported as a percentage of the bulk soft-mode displacements of ${\mathrm{BaTiO}}_3$ atoms ($\xi =1$ corresponds to the distortion of the bulk tetragonal ferroelectric phase). The energy of the paraelectric phase is taken as reference. The inset shows the evolution of the spontaneous polarization $P_s$ with thickness. For each thickness, $P_s$ is deduced from the amplitude of $\xi$ at the minimum. From 103.

Figure 69

Schematic of the carrier-mediated magnetoelectricity mechanism. The accumulation of up-spin electrons adjacent to the positive face of the dielectric, and their depletion from the negative face, leads to the net magnetization change $\Delta M$. From 211.