Efros Variable-range Hopping Research Articles

Anomalous electric transport across Verwey transition in nanocrystalline Fe3O4 thin films

Charge ordering (Fe+3/Fe+2) is a key concept in the Verwey transition of Fe3O4 because it frequently competes with functional properties (half-metallicity/ferromagnetism and structural transformation) and quantum confinement effect, especially at nanoscale dimensions. In this paper, we report the fabrication of nanocrystalline Fe3O4 thin films via two different reduction routes, namely, vacuum annealing and wet H2 annealing. While vacuum annealed films exhibit Verwey transition and resistivity values comparable to bulk Fe3O4, the same is not observed in electric transport properties of wet H2 annealed films. However, this transition was visible in the magnetic characteristics exhibited by both the films though realized via different routes. This observation indicates the possibility of charge and spin ordering as two independent phenomena, and it is a coincidence that happens at the same Verwey transition region. It is seen that a crossover from thermally activated hopping (300–120 K) to Mott variable range hopping (VRH) (across Verwey transition) and then to Shklovskii–Efros VRH hopping (70–30 K) via the conduction mechanism takes place in vacuum annealed films in contrast to the typical semiconducting behavior (300–50 K) expected of wet H2 annealed films. Different electric transport properties in both varieties of Fe3O4 films could be ascribed to the electronic disorder/defects affecting charge ordering Fe+3/Fe+2 and trimerons (Fe+3–Fe+2–Fe+3).

Interspacing dependence of spin-dependent variable range hopping for cold-pressed Fe3O4 nanoparticles

The influence of the contact between monodisperse Fe3O4 nanoparticles (NPs) on the spin-dependent transport mechanism has been investigated by only changing the cold-press pressures from 20.0 MPa to 5.0 GPa. For the sample cold-pressed under 20.0 MPa, the temperature dependence of resistivity ρ-T curve is best fitted by the log ρ ∝ T−1/2 relation, suggesting the Efros's variable range hopping (VRH) mechanism, while the ρ-T curves of the samples cold-pressed under 1.0 GPa to 5.0 GPa can be best fit with the relation of log ρ ∝ T−1/4, revealing the Mott's VRH mechanism. The different mechanisms are related to the interspacing dependence of charging energy and exchange energy between NPs. Monte Carlo simulations indicated that the charging energy plays a dominant role in the former mechanism, while the spin-dependent exchange energy is dominated in the latter one.

Polaronic transport and magnetism in Ag-doped ZnO

Magnetic polarons have been proposed to play important roles in doped wide band gap oxides that exhibit weak room temperature ferromagnetism. Here, we report the experimental evidence supporting polaronic magnetism and transport in Ag-doped ZnO. Temperature dependent resistivity data suggest the conduction mechanism of Mott and Efros variable range hopping. The observed weak ferromagnetism and its temperature dependence are explained using the percolation-based model of partially ordered bound magnetic polarons.

Variable-range hopping conductivity ofLa1 − xSrxMn1 − yFeyO3

The temperature dependence of the resistivity,ρ, of ceramicLa1 − xSrxMn1 − yFeyO3 (LSMFO)samples with x = 0.3 and y = 0.03, 0.15, 0.20 and 0.25 (or simply #03, #15, #20 and #25, respectively) is investigated between temperaturesT ∼ 5 and 310 K inmagnetic fields B up to 8 T. Metallic conductivity in #03 is changed eventually to activated in #25. In #15 and #20 the behaviorof ρ(T) is more complicated, comprising of two extremes, divided byan interval of metallic behavior in #15, and two inflections ofρ(T) in #20 withinsimilar intervals ΔT below ∼ 100 K.Mott variable-range hopping (VRH) conductivity is observed in #15 above the ferromagnetic Curie temperature,TC. In #20 the Mott VRH conductivity takes place in three different temperature intervals atT > TC,T closeto TC and T < TC. In #25, the Mott VRH conductivity is observed in two different intervals, above and belowTC, divided by an intermediate interval of the Shklovskii–Efros VRH conduction regime.Analysis of the VRH conductivity yielded the values of the localization radius,α, and thedependence of α and of the density of the localized states,g, near the Fermilevel, on B. AboveTC the localization radiusin all samples at B = 0 hassimilar values, α≈1.0–1.2 Å,which is enhanced to α≈3.3 Å (#20) and 2.0 Å (#25) below TC. The sensitivity of α and g toB dependon y andT. Thecomplicated behavior of the mechanisms of the hopping charge transfer, as well as of the microscopicparameters α and g, is attributable to different electronic and magnetic phases of LSMFO varying withtemperature and Fe doping.

Controllable spin-polarized electrical transport in wide-band-gap oxide ferromagnetic semiconductors

A family of wide-band-gap ternary oxide ferromagnetic semiconductor films with high transition metal concentration was prepared. The resistivity of these films can be changed up to four orders of magnitude by varying the composition or the concentration of the oxygen vacancies. Moreover, all these films show common features in electrical transport, i.e., Mott variable range hopping (VRH) in the lower resistivity range, Efros VRH in the middle resistivity range, and “hard gap” resistance in the higher resistivity range. The above phenomena are well understood by considering the relative magnitude of three characterization lengths, i.e., Coulomb screening length, localization length of the carriers, and optimal hopping distance. Furthermore, spin polarization ratio of these magnetic semiconductors was obtained by fitting the experimental results of electrical transport. Therefore, the wide gap oxide ferromagnetic semiconductors with controllable spin-polarized electrical transport are expected to have application in spintronics devices as a spin injection source.

Hopping conductivity in Cr-doped β-FeSi2 single crystals

The resistivity of Cr-doped p-type β-FeSi2 single crystals has been investigated in the temperature interval of T=4.2–300K. The data are analyzed within the framework of the variable-range hopping (VRH) mechanism for both the Mott and the Shklovskii–Efros regimes. With decreasing temperature a crossover between the Mott and the Shklovskii–Efros VRH conductivity regimes is observed. It is shown that the temperature dependence of the resistivity, ρ (T), of Cr-doped β-FeSi2 crystals, that follows a VRH conductivity mechanism, obeys a scaling law ln(ρ∕ρ0)=Af(T∕Tx). The values of the characteristic (T0) and the transition temperatures (Tv), as well as the width of the soft Coulomb gap Δ in the spectrum of the density of the localized states (DOS) are determined. The observed values of the VRH transition and characteristic temperatures indicate the existence of a rigid gap δ in the spectrum of the DOS in addition to Δ. This points to the polaronic nature of the charge carriers in the investigated compound.

Variable-range hopping conductivity in thin film of the ladder compound [Ca1+δCu2O3

Low-temperature charge transport in [Ca1+δCu2O3]4 films with δ=0 and 0.08 is investigated at T=1.4–290 K in magnetic fields of B=0–30 T. Between Tv≈20 and 40 K, depending on δ, and Tv′≈2–3 K three-dimensional (3D) Mott variable-range hopping (VRH) conductivity is observed. Deviations from 3D Mott VRH conductivity below Tv′ can be attributed to the onset of the Shklovskii–Efros VRH regime, accompanied by violation of the 3D hopping condition, Rh≪d (where Rh is the mean hopping length and d is the thickness of the film). The density of the localized states (DOS) at the Fermi level, g3(μ)≈4.4×1020 eV−1 cm−3, the values of the localization radius, α≈46 and 34 Å, the concentration of sites involved in hopping charge transfer, N≈9.9×1018 and 9.0×1018 cm−3, the width of the band of localized electron states, 2W≈22 and 20 meV, and the width of the Coulomb gap in the DOS spectrum, 2Δ≈1 and 1.6 meV are obtained for films with δ=0 and 0.08, respectively. These values characterize the films as being near the 3D metal–insulator transition given by the critical concentration NC≈1.3×1019 cm−3.

Transport of heavily boron-doped synthetic semiconductor diamond in the hopping regime

We report electrical transport measurements of synthetic diamonds doped with boron about 100 ppm. The resistivity has been measured in the temperature range 20--300 K by the van der Pauw method. We have also investigated infrared absorption coefficient at room temperature. Furthermore, we have studied the effect of ${\mathrm{P}}^{+9}$ ion irradiations with 150 MeV which introduce donor defects and also the influence of the annealing after the irradiation. The key features of the present measurement are as follows: (i) The observed temperature dependence of resistivity shows characteristic features of the variable-range-hopping (VRH). A crossover from ${T}^{\ensuremath{-}1/4}$ behavior of Mott VRH to the ${T}^{\ensuremath{-}1/2}$ form of Efros VRH is found to occur at 100 K. (ii) Below 50 K we have observed the hard gap ${T}^{\ensuremath{-}1}$ form. The width of the hard gap is about 10 meV. (iii) The experimental results are quantitatively explained by the theory of VRH. (iv) The observed width of the optical hard gap is equal to that of the hard gap obtained from resistivity. (v) The annealing effects appear only in the hard gap region and do not appear in the variable-range-hopping region. This result leads to the speculation that the hard gap is weakened by the lattice defects.