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We present results from an experimental technique used to estimate the strength of Ta at extreme pressures (150 GPa) and strain rates (${10}^{7}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$). A graded-density impactor (GDI) was fabricated using sputter deposition to produce an approximately $40\ensuremath{-}\ensuremath{\mu}\mathrm{m}$-thick film containing alternating layers of Al and Cu. The thicknesses of the respective layers are adjusted to give an effective density gradient through the film. The GDIs were launched with a 2-stage light gas gun, and shock-ramp-release velocity profiles were measured over timescales of $\ensuremath{\sim}10$ ns. Results are presented for the direct impact of the film onto LiF windows, which allows for a dynamic characterization of the GDI, as well as from impact onto thin ($\ensuremath{\sim}40\ensuremath{\mu}\mathrm{m}$) sputtered Ta samples backed by a LiF window. The measurements were coupled with mesoscale numerical simulations to infer the strength of Ta, and the results agree well with other high-pressure platforms, particularly when strain-rate, microstructural, and thermodynamic-path differences are considered.

${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ is a Mott system with a structurally driven metal-insulator transition at ${T}_{\mathrm{MI}}=357$ K and N\'eel temperature at ${T}_{N}=110$ K. Slight substitution of trivalent La for divalent Ca in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ drastically reduces ${T}_{\mathrm{MI}}$ and the electrical resistivity, simultaneously precipitating robust ferromagnetism in the antiferromagnetic host. ${T}_{C}$ is conspicuously and consistently lower than ${T}_{\mathrm{MI}},$ suggesting that the metal-insulator transition is not driven by the magnetic instability. The La substitution also results in a rapid increase in both the Pauli susceptibility and electronic specific heat coefficient, and a crossover from hopping conductivity to disordered metallic behavior at low temperatures. These dramatic changes underline the subtlety of the competition between the antiferromagnetic and ferromagnetic coupling and a near degeneracy of the ground state in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}.$

We report a first-order phase transition at ${T}_{M}=357\mathrm{K}$ in single-crystal ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4},$ an isomorph to the superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ The discontinuous decrease in electrical resistivity signals the near destruction of the Mott insulating phase and is triggered by a structural transition from the low-temperature orthorhombic to a high-temperature tetragonal phase. The magnetic susceptibility, which is temperature dependent but not Curie-like decreases abruptly at ${T}_{M}$ and becomes less temperature dependent. Unlike most insulator to metal transitions, the system is not magnetically ordered in either phase, though the Mott insulator phase is antiferromagnetic below ${T}_{N}=110\mathrm{K}.$

The results of angle-resolved de Haas--van Alphen oscillations in $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_{3}$ single crystals are reported. At least six fundamental frequencies of oscillation are detected between 100 and 11 000 T. The effective mass of the charge carriers is measured for each orbit and ranges from 4.1 to $6.9\phantom{\rule{0.3em}{0ex}}{m}_{e}$. The mean free path length of the charge carriers is between 640 and 5500 \AA{} or roughly 100--1000 times the unit cell dimensions. The measured frequencies are compared to the Fermi surface calculated by Santi and Jarlborg.

The magnetization, resistivity, and magnetoresistance (MR) of single crystals of $\mathrm{Gd}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ and $\mathrm{Eu}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ are measured over a wide range of dc magnetic fields (up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{T}$) and temperature. In $L\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ $(L=\mathrm{Gd},\mathrm{Eu})$, the Co ions are trivalent and can exist in three spin states, namely, the $S=0$ low-spin (LS) state, the $S=1$ intermediate-spin (IS) state, and the $S=2$ high-spin (HS) state. We confirm that $\mathrm{Gd}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ and $\mathrm{Eu}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ have a metal-insulator transition accompanied by a spin-state transition at ${T}_{MI}\ensuremath{\approx}365$ and $335\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ respectively. The data suggest an equal ratio of LS $(S=0)$ and IS $(S=1)$ ${\mathrm{Co}}^{3+}$ ions below ${T}_{MI}$, with no indication of additional spin state transitions. The low-field magnetization shows a transition to a highly anisotropic ferromagnetic phase at $270\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, followed by another magnetic transition to an antiferromagnetic phase at a slightly lower temperature. The magnetization data are suggestive of weak correlations between the Gd spins but no clear signature of ordering is seen for $Tg2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Significant anisotropy between the $a\text{\penalty1000-\hskip0pt}b$ plane and $c$ axis was observed in magnetic and magnetotransport properties for both compounds. For $\mathrm{Gd}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$, the resistivity and MR data imply a strong correlation between the spin-order and charge carriers. For $\mathrm{Eu}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$, the magnetic phase diagram is very similar to its Gd counterpart, but the low-$T$ MR with current flow in the $a\text{\ensuremath{-}}b$ plane is positive rather than negative as for Gd. The magnitude and the hysteresis of the MR for $\mathrm{Eu}\mathrm{Ba}{\mathrm{Co}}_{2}{\mathrm{O}}_{5.5}$ decrease with increasing temperature, and at higher $T$ the MR changes sign and becomes negative. The difference in the behavior of both compounds may arise from a small valence admixture in the nonmagnetic Eu ions, i.e., a valence slightly less than $3+$.

We report magnetic and transport properties of single-crystal ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7},$ a bilayered orthorhombic system with Bbca symmetry. Our study reveals that ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ is a ferromagnetic insulator with a Curie temperature of ${T}_{C}=285\mathrm{K}$ and a small ordered magnetic moment. The saturation moment ${\ensuremath{\mu}}_{S}$ is found to be less than $0.04{\ensuremath{\mu}}_{B}/\mathrm{Ir}$ or 4% of the expected moment for a localized spin $S=\frac{1}{2}.$ For fields larger than 1 T the magnetic susceptibility is the superposition of a Curie law (with negligible Weiss temperature) and a constant term. Surprisingly, at low temperatures (20 K) the magnetization is opposite to the applied magnetic field when ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ is cooled in a modest magnetic field (\ensuremath{\leqslant}0.2 T). The resistivity $\ensuremath{\rho}(T)$ measured from 1.7 to 1000 K along two principal crystallographic directions exhibits insulating behavior with anomalies corresponding to the magnetic properties. Both the magnetization and the resistivity are strongly anisotropic as a consequence of the layered structure. Possible crystalline field and band scenarios are briefly discussed.

We report the observation of superconductivity in high-quality ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ single crystals with room-temperature pyrochlore structure. Resistivity and ac susceptibility measurements establish an onset transition temperature ${T}_{c}^{\mathrm{onset}}=1.47 \mathrm{K}$ with transition width $\ensuremath{\Delta}{T}_{c}=0.25 \mathrm{K}.$ In applied magnetic field, the resistive transition shows a type-II character, with an approximately linear temperature-dependence of the upper critical field ${H}_{c2}.$ The bulk nature of the superconductivity is confirmed by the specific heat jump with $\ensuremath{\Delta}C=37.9 \mathrm{mJ}/\mathrm{m}\mathrm{o}\mathrm{l}\ensuremath{-}\mathrm{K}.$ Using the \ensuremath{\gamma} value extracted from normal-state specific heat data, we obtain $\ensuremath{\Delta}C/\ensuremath{\gamma}{T}_{c}=1.29,$ close to the weak coupling BCS value. In the normal state, a negative Hall coefficient below 100 K suggests electronlike conduction in this material. The resistivity exhibits a quadratic T dependence between 2 and 60 K, i.e., $\ensuremath{\rho}={\ensuremath{\rho}}_{0}{+AT}^{2},$ indicative of Fermi-liquid behavior. The values of the Kadowaki-Woods ratio $\mathrm{A}/{\ensuremath{\gamma}}^{2}$ and the Wilson ratio are comparable to that for strongly correlated materials.

Polycrystalline samples of the lanthanide ruthenate series ${L}_{2}{\mathrm{RuO}}_{5}$ $(L=\mathrm{Pr},$ Nd, Sm, Gd, and Tb) magnetically order in the range $8lTl24\mathrm{K}$ with the ordering involving both the $L$ and Ru cations. The series has a complex orthorhombic structure (space group $Pnma)$ possessing chains of ${\mathrm{RuO}}_{5}$ five oxygen coordinated square pyramids which are corner-sharing and two inequivalent seven coordinated L sites which are edge-sharing. At ${T}_{M}$ a weak ferromagnetic moment emerges upon cooling, most likely due to a canted antiferromagnetic spin configuration. Isothermal dc and pulsed field magnetization for $Tl{T}_{M}$ reveal field induced magnetic transitions for $Hl5\mathrm{T}$ but the approach to full free ion magnetic saturation is incomplete even at fields to 60 T due to the influence of crystalline electric fields on the L ions. The low temperature linear specific heat coefficient, \ensuremath{\gamma}, for four compounds is anomalously large, ranging from $\ensuremath{\gamma}=229$ to 774 mJ/mole ${\mathrm{K}}^{2}$, for $L=\mathrm{Nd}$ and $L=\mathrm{Gd},$ respectively. These values are comparable to those for heavy fermion systems, yet all five members of the ${L}_{2}{\mathrm{RuO}}_{5}$ series exhibit semiconducting to insulating behavior. Isomorphic ${\mathrm{Gd}}_{2}{\mathrm{TiO}}_{5},$ where Ti with no unpaired d electrons ${(4d}^{0}$ configuration) replaces Ru ${(4d}^{4}$ configuration), has a vanishingly small \ensuremath{\gamma}, indicating that the thermodynamic properties of ${L}_{2}{\mathrm{RuO}}_{5}$ are dominated by unpaired $4d$ electrons. The $4d$ electrons significantly enhance the $L\ensuremath{-}L$ interaction, as demonstrated by the dramatic increase in ordering temperature for ${\mathrm{Gd}}_{2}{\mathrm{RuO}}_{5}$ ${(T}_{M}=10\mathrm{K})$ compared to ${\mathrm{Gd}}_{2}{\mathrm{TiO}}_{5}$ which does not appear to order magnetically.

The percolation behavior of films of thickness $d$ composed of a compact mixture of conducting (concentration $p$) and insulating (concentration $1\ensuremath{-}p$) beads is studied by measuring their conductivity $\ensuremath{\sigma}(d, p)$. A theoretical model based on a renormalization operation to the thickness of the film leads to predictions on the threshold ${p}_{c}(d)$, the crossover values between two- and three-dimensional behavior ${p}_{\ifmmode\pm\else\textpm\fi{}}(d)$, and the amplitude of the conductivity above threshold. The experiments are analyzed in terms of the model and lead to the determination of several critical exponents.

The density of states for thermal vibrations on a fractal is calculated with careful attention paid to the normalization condition. It is found that at the crossover between Debye-type excitations (long wavelength) and "fracton" excitations (short-length scale) the density of states is discontinuous. The size of the discontinuity is related to the ratio of the fracton dimensionality to the Euclidean dimensionality. Application is made to percolating structures. A set of missing modes is identified which may be the origin of the two-level systems hypothesized for amorphous structures. The specific heat of epoxy resin exhibits a crossover from a Debye-type region ($Tl8$ K) to a region (8-50 K) where the vibrational density of states depends linearly on the frequency. Over the same frequency regime, the thermal conductivity exhibits an effective phonon mean free path of the order of (or less than) a lattice constant. We interpret this behavior in terms of quantized fractons, with an energy range 8-50 K, and we suggest that these fracton states are localized. This is consistent with the usual interpretation of a precipitous drop in the phonon mean free path at the crossover energy of 8 K. Analogous behavior is argued for the thermal properties of glasses which exhibit a similar structure in the thermal conductivity. Recent neutron-irradiated quartz experiments tend to confirm this interpretation.

The effect of critical fluctuations on the resistivity near magnetic and order-disorder phase transitions is discussed. It is shown that in all magnetic and electronic systems the asymptotic high-momentum spin correlation functions dominate the temperature dependence of the resistivity sufficiently close to the transition. The dependence on the parameters of the system of the critical behavior and the way in which this behavior is approached is discussed in detail. In particular, the importance of the transition from a classical to a proper critical behavior, for the interpretation of experimental results, is emphasized, and recent renormalization-group results for the form of the correlation functions are utilized. For semiconductors the effects of fluctuations on the band gap are also calculated. It is suggested that the Fisher-Langer relation between the temperature derivative of the resistivity and the specific heat should be valid over a considerable temperature range outside the critical region. Theoretical predictions are compared with available experimental results on the resistivity and band gaps. It is shown that these results can all be understood, at least qualitatively, in the Born approximation by using only the most general known properties of the system.

Spectral diffusion on a one-dimensional chain with a random distribution of interruptions is considered. An exact solution for the time decay of the initial excitation is computed. The solution exhibits an exponential behavior initially, diffusion (${t}^{\frac{\ensuremath{-}1}{2}}$) behavior at intermediate times, and a long time decay $\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{(\ensuremath{\lambda}t)}^{\frac{1}{3}}]$. The relationship of this problem to the vibrating chain with some infinite masses, and to a related band-structure problem, is discussed. The possibility of observing the predicted behavior in fluorescent-line-narrowing experiments is also discussed, and some limits on the relevant parameters are given.

Relaxation processes are calculated for the emission and absorption of localized vibrational quanta by a localized electronic state. Vibrational localization can be geometrical in origin (as on a fractal network, with fractons being the quantized vibrational states) or as a consequence of scattering (analogous to Anderson localization, with localized phonons being the quantized vibrational states). The relaxation rate is characterized by a probability density which is calculated here for both classes of localization for two extreme limits: (a) the sum of the electronic and vibrational energy widths independent of the spatial distance between the electronic and vibrational states, and (b) the sum of the energy widths equal to the relaxation rate itself. The time profile of the initial electronic state population is calculated for both cases. The profile for interaction with fractons for case (a) is proportional to , where ${c}_{1}$ is a constant, D is the fractal dimensionality, and ${d}_{\ensuremath{\varphi}}$ is defined by the range dependence of the fracton wave ). This decay is faster than any power law but slower than exponential (or stretched exponential). The time profile for the interaction with fractons for case (b) is proportional to const+${c}_{2}$(1/t)(lnt${)}^{(D/{d}_{\ensuremath{\varphi}})\mathrm{\ensuremath{-}}}$ 1, where ${c}_{2}$ is another constant. This expression shows that some sites do not relax in this limit. The average relaxation rate is calculated for both cases, along with its frequency and temperature dependence.

Solutions of the linearized Landau-Ginzburg equations on networks of thin wires are studied. We derive linear-difference equations for the value of the order parameter at the junctions of the net with the use of the explicit form of the solutions on the wires. The technique is shown to be applicable to the diffusion equation, to harmonic lattice vibrations, and to the Schroedinger equation and results in equations similar to tight-binding equations. The equations are solved and the upper critical field is determined for some simple finite nets, for the infinite square net, and for the triangular Sierpinski gasket. Dead-end side branches are shown to lead to a mass renormalization. On the square net the equations map on the Azbel-Hofstadter-Aubry model. When the coherence length is small, vortex cores can be accommodated in the holes of the net and there is no upper critical field. The equations on the Sierpinski gasket are solved by an iterative decimation process. The process determines a new length scale proportional to a power of the bare coherence length. The upper critical field is studied for a finite gasket and for a lattice of gaskets. With the use of scaling arguments the results are applied tomore » percolation clusters. Far from the percolation threshold the results are described by a renormalized correlation length of standard form. When this length becomes shorter than the correlation length for the percolation problem the critical field is shown to be constant or decreasing as the threshold is approached. Existing experiments are discussed and the importance of high-field-susceptibility measurements is emphasized.« less

We demonstrate that vibrational overtone (second-harmonic) absorption must be treated as a resonance in the presence of vibrational two-exciton band excitations, as outlined earlier by two of us (T.H. and R.O.) in a manuscript with Luiz C. Scavarda do Carmo and Fritz L\"uty. Explicit calculations are made for a three-dimensional body-centered cubic and a one-dimensional lattice. The behavior of the position and intensity of the overtone absorption with exciton bandwidth and vibrational anharmonicity is studied in detail. Substantial cooperative vibrational absorption intensity is seen to be inconsistent with significant overtone splitting on the scale of the cooperative vibrational absorption bandwidth. Because no extrinsic impurity is required to provide a matrix element for two-exciton absorption, we suggest that the exciton band absorption associated with overtone absorption may be a very clean technique to observe exciton dispersion in solids.

The two localized-vibrational quanta (Raman) relaxation process is calculated for a localized electronic state. The calculation is expected to be relevant to relaxation at elevated temperatures where the principal vibrational excitations are of high energy (and hence of short length scale). Localization of the vibrational eigenstates is most likely for this regime. Vibrational localization can be geometrical in origin (as on a fractal network, with the quantized vibrational states fractons), or as a consequence of scattering (analogous to Anderson localization, with the quantized vibrational states localized phonons). The relaxation rate is characterized by a probability density which is calculated for both classes of localization under the assumption that the electronic and vibrational energy widths are larger than the maximum electronic relaxation rate. The time profile of the initial elec- tronic state population is calculated. The long-time behavior begins as ${t}^{[1/2(a\mathrm{\ensuremath{-}}1)]}$exp[-${c}_{1}$(t${)}^{1\phantom{\rule{0ex}{0ex}}/(a\mathrm{\ensuremath{-}}1)}$], where a=4q+2d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{} and 4q+2d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{}-2 for Kramers and non-Kramers transitions, respectively. Here, d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{} is the fracton dimensionality and q=d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{}${d}_{\ensuremath{\varphi}}$/D. The fractal dimensionality is D, and ${d}_{\ensuremath{\varphi}}$ is defined by the range dependence of the fracton wave ). The long-time behavior thus begins as a stretched exponential. After a crossover time, the long-time behavior varies as (lnt${)}^{\ensuremath{\eta}\mathrm{\ensuremath{-}}1/2}$${t}^{\mathrm{\ensuremath{-}}{c}_{1}}$(ln t${)}^{2\ensuremath{\eta}}$ where ${c}_{1}$ is a constant and \ensuremath{\eta}=D/${d}_{\ensuremath{\varphi}}$. This portion of the time decay is faster than any power law but slower than exponential or stretched exponential.In the presence of rapid electronic cross relaxation, the time profile is exponential, with a low-temperature relaxation time 1/${T}_{1}^{\mathrm{ave}}$ proportional to ${T}^{2d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{}[1+2({d}_{\ensuremath{\varphi}}/D)]\mathrm{\ensuremath{-}}1}$ and ${T}^{2d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{}[1+2({d}_{\ensuremath{\varphi}}/D)]\mathrm{\ensuremath{-}}3}$ for Kramers and non-Kramers transitions, respectively. These results may explain recent fractional temperature exponents found for electronic spin-lattice relaxation in macromolecules and nuclear spin-lattice relaxation in glasses.

An inhomogeneously broadened spectral line, for a spatially random site distribution with dipole-dipole coupling to first-neighbor sites, is studied using a Monte Carlo Technique. The site-site coupling is chosen at random according to the probability density function for first-neighbor dipolar interactions $\frac{[\mathrm{exp}(\ensuremath{-}\frac{1}{{X}^{\frac{1}{2}}})]}{{X}^{\frac{3}{2}}}$; where $X$ is the transfer rate proportional to $\frac{1}{{r}^{6}}$, and $r$ is the spatial separation of the interacting sites. This form is appropriate for a dilute concentration of sites on a three-dimensional random lattice. We arrange the sites in a linear array, and the spectral diffusion equation (including back transfer) is solved iteratively. We show that this is an adequate description of the three dimensional system at short and intermediate times for the dilute concentrations considered in this study. A group of sites with a specific energy is excited at (time) $t=0$. The time development of the excitation profile is then studied. For very short times, the decay of the initial excitation is linear in time, appropriate to the largest value of $X$ (near neighbor site). For longer times, but over a fairly narrow time interval, the decay proceeds as $\mathrm{exp}(\ensuremath{-}a{t}^{\frac{1}{2}})$, as calculated by Inokuti and Hirayama for dipolar coupling in the absence of back transfer. At the longest times, the decay follows the one-dimensional diffusion result, ${t}^{\ensuremath{-}\frac{1}{2}}$. The intermediate-time regime, covering most of the decay of the initial excitation profile, does not seem to follow any simple time dependence.

Previous work on anomalous transport is extended to two and three dimensions. Using critical-path analysis it is shown that random-hopping models always lead to a finite dc conductivity and diffusion constant and thus to normal asymptotic behavior above 1D. For RT models anomalous behavior is shown to be possible with indices in agreement with the Scher-Lax theory, above 2D. It is also pointed out that such behavior is to be expected for an exponential tail of traps and the temperature dependence is predicted.

It is shown that the master equation for a general diffusion problem with exclusion and symmetric binary transfer rates can be mapped exactly on the Schr\"odinger equation for an equivalent Heisenberg ferromagnet. Quantities of physical interest, e.g., the site occupation probability, are related to the lowest eignstates of the ferromagnet which play no thermodynamic role. The thermodynamics is only reflected in unobservable quantities such as the joint occupation probability of all sites. An additional result, obtained by elementary considerations, is the exact equation for the time evolution of the site-occupation probabilities. For symmetric transfer rates the equation reduces to a linear form in which exclusion effects are no longer present.

The diffusion of a labeled particle on a one-dimensional chain is discussed. It is shown that the long-time behavior is dominated by density fluctuations leading to a ${t}^{\frac{1}{2}}$ dependence of the mean-square deviation in agreement with Monte Carlo results of Richards.