Dirty Regime Research Articles

Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime.

Studying the mechanisms of the spin Hall effect (SHE) is essential for the fundamental understanding of spintronic physics. By now, despite the intensive studies of SHE on heavy metal (HM)/metallic magnet heterostructures, the SHE on HM/ferrimagnetic insulator (FMI) heterostructures still remains elusive. Here, we study the mechanism of SHE in the Pt/Tm3Fe5O12 (TmIG) heterostructure. We first tune the crystallinity and resistivity of Pt by an annealing method, and then study the spin-orbit torque (SOT) in the tuned-Pt/TmIG devices. The SOT generation efficiency per unit electric field and spin Hall angle were obtained, which are insensitive to the annealing temperature. We further demonstrate that the intrinsic contribution in the moderately dirty regime is responsible for the SHE in our Pt/TmIG bilayer. Our study provides an important piece of information for the SHE in FMI-based spintronic physics.

Scattering-dependent transport of SrRuO3 films: From Weyl fermion transport to hump-like Hall effect anomaly

Recent observation of quantum transport phenomena of Weyl fermions has brought much attention to $4d$ ferromagnetic perovskite ${\mathrm{SrRuO}}_{3}$ as a magnetic Weyl semimetal. Additionally, the hump-like Hall effect anomaly, which might have a topological origin, has been reported for this material. Here, we show that the emergence of such phenomena is governed by the degree of scattering determined by the defect density (Ru-deficiency- and/or interface-driven-defect scattering) and measurement temperature (phonon scattering), where the former is controlled by varying the growth conditions of the ${\mathrm{SrRuO}}_{3}$ films in molecular beam epitaxy as well as the film thickness. The resulting electronic transport properties can be classified into three categories: clean, intermediate, and dirty regimes. The transport of Weyl fermions emerges in the clean regime, whereas that of topologically trivial conduction electrons in the ferromagnetic metal state prevails in the intermediate and dirty regimes. In the clean and intermediate regimes, anomalous Hall resistivity obeys a scaling law incorporating the intrinsic Karplus-Luttinger and extrinsic side-jump mechanisms. The hump-like Hall effect anomaly is observed only in the dirty regime, which is contrary to the scaling law between anomalous Hall resistivity and longitudinal resistivity. Hence, we conclude that this anomaly is not inherent to the material and does not have a topological origin. We also provide defect- and temperature-dependent transport phase diagrams of stoichiometric ${\mathrm{SrRuO}}_{3}$ and Ru-deficient ${\mathrm{SrRu}}_{0.7}{\mathrm{O}}_{3}$ where the appearance of Weyl fermions and hump-like Hall effect anomaly is mapped. These diagrams may serve as a guideline for designing $\mathrm{Sr}\phantom{\rule{0.16em}{0ex}}{\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{O}}_{3}$-based spintronic and topological electronic devices.

Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy

Epitaxial Mn4N films with different thicknesses were fabricated by facing-target reactive sputtering and their anomalous Hall effect (AHE) is investigated systematically. The Hall resistivity shows a reversed magnetic hysteresis loop with the magnetic field. The magnitude of the anomalous Hall resistivity sharply decreases with decreasing temperature from 300 K to 150 K. The AHE scaling law in Mn4N films is influenced by the temperature-dependent magnetization, carrier concentration and interfacial scattering. Different scaling laws are used to distinguish the various contributions of AHE mechanisms. The scaling exponent γ > 2 for the conventional scaling in Mn4N films could be attributed to the residual resistivity ρ xx0. The longitudinal conductivity σxx falls into the dirty regime. The scaling of is used to separate out the temperature-independent ρ xx0 from extrinsic contribution. Moreover, the relationship between ρ AH and ρxx is fitted by the proper scaling to clarify the contributions from extrinsic and intrinsic mechanisms of AHE, which demonstrates that the dominant mechanism of AHE in the Mn4N films can be ascribed to the competition between skew scattering, side jump and the intrinsic mechanisms.

Effect of a conductive layer on Fabry-Pérot resonances

Using terahertz spectroscopy, we investigate resonant transmission through a dielectric slab with a conducting layer of varied mobility on one side. We observe the well-known Fabry-P\'erot resonances in the transmission. Two fundamentally different regimes of the electrodynamic response of the system are established. In the clean limit, when the radiation frequency exceeds the carrier relaxation rate, $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\gg}1$, the system exhibits a plasmonic response. As a result, there is a continuous shift in the Fabry-P\'erot resonances with respect to the system parameters. By contrast, in the dirty regime, when $\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\ll}1$, there is an abrupt $\ensuremath{\pi}$ shift in the resonance frequency, as the renormalized film resistance matches the impedance of free space. We find that under this condition, Fabry-P\'erot oscillations disappear entirely over a broad frequency range. Such a matching effect might be of interest in various terahertz applications, for example, involving broadband filters or absorbers.

Path dependence, self-fulfilling expectations, and carbon lock-in

Growing under the incumbent dirty regime might generate inertia against switching to a clean alternative and lead to the carbon lock-in. I analyze the economics of carbon lock-in through the lens of path dependence and self-fulfilling expectation. The incumbent dirty regime, as the first mover, accumulates an installed base of household users during early lead periods. The installed base generates an effect of path dependence that incentives upcoming households to keep on joining the incumbent dirty regime rather than switch to the clean alternative. Switching could be an expectation-driven selection outcome if expectations are formed about an expanding clean regime which outweighs the path dependence effect. Switching is a welfare-improving outcome if welfare gains by upcoming households switching to the clean regime offset welfare losses by installed-base households locked in the dirty one.

Crossover of the intrinsic spin Hall effect in the presence of lattice expansion

We report the robustness of the intrinsic spin Hall effect in Pt against a change in the lattice constant. We measure spin-torque ferromagnetic resonance for $\mathrm{Pt}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ bilayers, where the lattice constant and carrier scattering time of the Pt layer are varied by incorporating the nitrogen atoms as interstitial impurities. We find that the spin Hall angle is enhanced by a factor of 3 as the resistivity of the Pt layer is increased by the nitrogen incorporation. The variation of the spin Hall conductivity is consistent with the prediction of the crossover of the intrinsic spin Hall effect from the moderately dirty regime to the dirty-metal regime. This result demonstrates the variation of the intrinsic spin Hall conductivity in Pt is dominated by the change in the scattering time, rather than the change in the band structure, under a few percent change in the lattice constant.

Higgs-mode resonance in third harmonic generation in NbN superconductors: Multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence

We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurity scatterings. Using the estimated pairing interactions with multiband impurity scattering rates being varied from clean to dirty regimes, we calculate the THG susceptibility for NbN in a channel-resolved manner by means of the BCS and self-consistent Born approximations. In the dirty regime, which is close to the experimental situation, the leading contribution is given by the paramagnetic channel of the Higgs mode having almost no polarization-angle dependence, while the second leading contribution comes from the paramagnetic channel of quasiparticles generally showing significant polarization-angle dependence. The result is consistent with the recent experimental observation of no polarization-angle dependence of THG, giving firm evidence that the Higgs mode dominantly contributes to the THG resonance in NbN superconductors.

Superconductivity in Y7Ru4InGe12

We report a type-II intermetallic superconductor ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$ with a transition temperature $({T}_{\mathrm{c}})$ of \ensuremath{\sim}5.8 K, which is confirmed by zero resistivity, diamagnetic magnetic susceptibility, and specific-heat jump. Single crystals of ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$ were grown from a reactive indium flux. ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$ crystallizes in the tetragonal space group $P4/m$ and features a $[\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}]$ polyanionic network with Y atoms located in three different channels. The upper critical fields of ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$ at 0 K are determined to be \ensuremath{\sim}5.3 and 2.4 T along the $c$ axis and the $ab$ plane, respectively. The estimated coherence length along the $c$ axis (\ensuremath{\sim}174 \AA{}) is much larger than the estimated mean free path along the $c$ axis (\ensuremath{\sim}29 \AA{}) in ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$, placing its superconductivity in the so-called dirty regime. The compound exhibits a large superconducting specific-heat jump $\phantom{\rule{4pt}{0ex}}\frac{\mathrm{\ensuremath{\Delta}}C}{{\ensuremath{\gamma}}_{e}{T}_{\mathrm{c}}}\ensuremath{\approx}2.4$, significantly well above the weak-coupling Barden-Cooper-Schrieffer theoretical value of 1.43 and pointing to a strong-coupling scenario in ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$. Density-functional-theory calculations show that the density of states in ${\mathrm{Y}}_{7}\mathrm{R}{\mathrm{u}}_{4}\mathrm{InG}{\mathrm{e}}_{12}$ exhibits a broad peak near the Fermi level which mainly derives from $\mathrm{Y}\text{\ensuremath{-}}4d,\mathrm{Ru}\text{\ensuremath{-}}4d$, and $\mathrm{Ge}\text{\ensuremath{-}}4p$ states.

Clean to dirty limit and Tc suppression in NdFeAsO0.7F0.3 studied by Hc2 analysis

In this work, we investigate the temperature dependence of the upper critical field, dHc2/dT, in an increasingly disordered NdFeAsO0.7F0.3 (NdFeAs(O,F)) single crystal that has been progressively irradiated up to a 5.25 × 1016 cm−2 total α-particle dose. For the H∣∣ab-plane, dHc2/dT does not vary remarkably with irradiation, while for the H∣∣c-axis it increases sharply after the first irradiation of 3.60 × 1015 cm−2 and then more gradually with further irradiation doses. Focusing on the H∣∣c-axis, we develop a phenomenological analysis of the Hc2 slope which allows us to inspect the crossover from the clean to the dirty regime. From the Hc2 slope normalized to the critical temperature and to its clean limit value, we extract the ratio of the coherence length ξBCS to the mean free path and we find that when Tc is reduced by a factor of four from its pristine value, ξBCS/ becomes as large as ∼7 and reaches values of ∼1.8 nm, indicating that NdFeAs(O,F) is well into the dirty regime. Our analysis of the Hc2 slope also allows us to compare the pair-breaking effectiveness of scattering in different superconductors, showing similarity between unconventional NdFeAs(O,F) and moderate-Tc phonon-mediated devices, such as MgB2 and A15 compounds, but much a stronger difference with YBa2Cu3O7-δ. This work thus shows that dHc2/dT is a reliable parameter, providing an alternative to residual resistivity, for investigating the pair-breaking mechanism induced by impurity scattering in superconductors.

Parallel Critical Field in Thin Niobium Films: Comparison to Theory

For the first time, a comparison to the predicted behavior for parallel critical field is carried out for the model of Kogan and the model of Hara and Nagai. In this study, thin niobium films in the moderately dirty regime were considered. Experimental values of the $-C_{2}$ term are seen to be lower than those from the model of Hara and Nagai. A possible reason for this could be not including the non spherical Fermi surface of niobium into the model. There is clearly disagreement with the model of Kogan as the films get cleaner and thinner, and two films which should be below his critical thickness still show positive values of $-C_{2}$, in disagreement with his theory.

La macroeconomía de la flotación sucia en una economía primario exportadora: el caso del Perú

The current Peruvian exchange regime is neither pegged nor free-floating. The Peruvian Central Bank sails against the wind in the exchange market, tending to buy dollars when the exchange rate falls, and tending to sell when the exchange rate rises. It is a dirty float regime. In this paper we present a simple macroeconomic model where the central bank fixes the interest rate and maintains a dirty floating exchange rate regime, assuming a small, open, and partiallydollarized economy that exports raw materials, faces imperfect capital mobility, and has a structural fiscal deficit limit as a rule for its fiscal policy. The predictions of the model are consistent with the rule of foreign exchange intervention by the Central Bank and the main stylized facts of the Peruvian economy since the decline in the international price of raw materials in late 2011: drastic fall in private investment, decline of GDP growth, rising nominal exchange rate and reduction of international reserves.

Abrikosov vortices in SF bilayers

We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or by changing an exchange field in a ferromagnet. We argue that the origin of this effect is due the phase shift between singlet and triplet order parameter components induced in the F-layer. Possible ways of experimental detection of the predicted effect are discussed.

Effective numbers of charge carriers in doped graphene: Generalized Fermi liquid approach

The single-band current-dipole Kubo formula for the dynamical conductivity of heavily doped graphene from Kup\v{c}i\'{c} [Phys. Rev. B 91, 205428 (2015)] is extended to a two-band model for conduction $\pi$ electrons in lightly doped graphene. Using a posteriori relaxation-time approximation in the two-band quantum transport equations, with two different relaxation rates and one quasi-particle lifetime, we explain a seemingly inconsistent dependence of the dc conductivity $\sigma^{\rm dc}_{\alpha \alpha}$ of ultraclean and dirty lightly doped graphene samples on electron doping, in a way consistent with the charge continuity equation. It is also shown that the intraband contribution to the effective number of conduction electrons in $\sigma^{\rm dc}_{\alpha \alpha}$ vanishes at $T=0$ K in the ultraclean regime, but it remains finite in the dirty regime. The present model is shown to be consistent with a picture in which the intraband and interband contributions to $\sigma^{\rm dc}_{\alpha \alpha}$ are characterized by two different mobilities of conduction electrons, the values of which are well below the widely accepted value of mobility in ultraclean graphene. The dispersions of Dirac and $\pi$ plasmon resonances are reexamined to show that the present, relatively simple expression for the dynamical conductivity tensor can be used to study simultaneously single-particle excitations in the dc and optical conductivity and collective excitations in energy loss spectroscopy experiments.

A Topographical Approach to Re-Reading Books about Islands in Digital Literary Spaces

This article takes a topographical approach to re-reading print books in digital literary spaces through a discussion of a web-based work of digital literature, …and by islands I mean paragraphs (Carpenter 2013). In this work, a reader is cast adrift in a sea of white space extending far beyond the bounds of the browser window, to the north, south, east and west. This sea is dotted with computer-generated paragraphs. These fluid texts call upon variable strings containing words and phrases collected from a vast literary corpus of books about islands. Individually, each of these textual islands represents a topic—from the Greek topos, meaning place. Collectively they constitute a topographical map of a sustained practice of reading and re-reading and writing and re-writing on the topic of islands. This article argues that, called as statement-events into digital processes, fragments of print texts are reconstituted as events occurring in a digital present which is also a break from the present. A new regime of signification emerges, in which authorship is distributed and text is ‘eventilized’ (Hayles). This regime is situated at the interface between an incoherent aesthetics, one which tends to unravel neat masses, including well-known works of print literature; and an incoherent politics, one which tends to dissolve existing institutional bonds, including bonds of authorship and of place. Galloway terms this regime of signification the ‘dirty regime of truth’.DOI: http://dx.doi.org/10.14195/2182-8830_4-1_5

Anomalous Hall Effect of the Co Thin Film Deposited by High-Pressure Magnetron Sputtering

In this paper, we studied the dependence of temperature and weak localization (WL) effect on the anomalous Hall effect (AHE) in strong disordered and poorly crystallized metal Co thin film deposited by high-pressure magnetron sputtering. The temperature coefficients of resistivity is positive at high temperatures and becomes negative at low temperatures, which is the typical characteristic of weak localization effect in dirty metal regime due to the strong disorder. The saturation anomalous Hall resistivity (ρAxy) have no scaling relation between ρxy and ρxx in weak localization region with temperature below 50 K. In metal region, temperature ranged from 50 K to 300 K, the relation between ρAxy and ρxxis ρAxy=A+bρ2xx, which indicates that the AHE in this Co thin film is scattering-independence at high temperature. The results also shows that the WL effect have a significant impact on the AHE of the Co thin film at low temperature.

Scaling of anomalous Hall effect in amorphous CoFeB films with accompanying quantum correction

Abstract Scaling of anomalous Hall effect in amorphous CoFeB films with thickness ranging from 2 to 160 nm has been investigated. We have found that the scaling relationship between longitudinal (ρxx) and anomalous Hall (ρAH) resistivity is distinctly different in the Bloch and localization regions. For ultrathin CoFeB films, the sheet resistance (Rxx) and anomalous Hall conductance (GAH) received quantum correction from electron localization showing two different scaling relationships at different temperature regions. In contrast, the thicker films show a metallic conductance, which have only one scaling relationship in the entire temperature range. Furthermore, in the dirty regime of localization regions, an unconventional scaling relationship σ A H ∝ σ x x α with α=1.99 is found, rather than α=1.60 predicted by the unified theory.

Anomalous Nernst effect ofFe3O4single crystal

We report a complete characterization of the anomalous Nernst effect (ANE) and its relationship with the anomalous Hall effect (AHE) in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. By combining full thermoelectric and electric transport measurements as a function of temperature, we have verified that the universal scaling relation between the anomalous Hall and diagonal conductivities (${\ensuremath{\sigma}}_{zy}\ensuremath{\propto}{\ensuremath{\sigma}}_{zz}^{1.6}$), observed in materials with bad-metal-hopping type of conduction, is also applicable to the thermoelectric transport. We further show that the ANE and AHE are commonly related through the Mott relation, therefore demonstrating its validity for anomalous transport phenomena in materials with conduction in the the dirty regime.

Scaling of the thickness dependent anomalous Hall effect in amorphous ferromagnetic thin films

We testified the scaling theory of room temperature anomalous Hall effect in amorphous Co90Zr10 ferromagnetic thin films with the thickness between 5 nm to 600 nm. The experiment results did not meet the theory expectation if we simply put σxy and σxx into a log-log plot, because a negative exponent in σxy = σxxβ appeared for the films thicker than 100 nm. We removed the thickness independent bulk contribution to the scattering, and rebuilt the scaling relation by using only the surface/interface contribution. A crossover from the intrinsic moderately dirty regime, where β = 0.82 to the dirty regime, where β = 1.76, had been observed, which matched previous results and theory expectations. Therefore, it is necessary to remove the bulk contribution in establishing the AHE scaling relation when using the thickness to tune the transportation properties of ferromagnetic thin films.

Self-consistent electronic structure of multiquantum vortices in superconductors at T ≪ Tc

We investigate the multiquantum vortex states in a type-II superconductor in both ‘clean’ and ‘dirty’ regimes defined by impurity scattering rate. Within a quasiclassical approach we calculate self-consistently the order parameter distributions and electronic local density of states (LDOS) profiles. In the clean case we find the low temperature vortex core anomaly predicted analytically by Volovik (1993 JETP Lett. 58 455) and obtain the patterns of LDOS distributions. In the dirty regime multiquantum vortices feature a peculiar plateau in the zero energy LDOS profile, which can be considered as an experimental hallmark of multiquantum vortex formation in mesoscopic superconductors.

Unconventional scaling of the anomalous Hall effect accompanying electron localization correction in the dirty regime

Scaling of the anomalous Hall conductivity to longitudinal conductivity, has been observed in the dirty regime of two-dimensional weak and strong localization regions in ultrathin, polycrystalline, chemically disordered, ferromagnetic FePt films. The relationship between electron transport and temperature reveals a quantitatively insignificant Coulomb interaction in these films while the temperature dependent anomalous Hall conductivity experiences quantum correction from electron localization. At the onset of this correction, the low-temperature anomalous Hall resistivity begins to be saturated when the thickness of the FePt film is reduced, and the corresponding Hall conductivity scaling exponent becomes 2, which is above the recent unified theory of 1.6 (\sigma_AH \propto \sigma^1.6_xx). Our results strongly suggest that the correction of the electron localization modulates the scaling exponent of the anomalous Hall effect.