Electron–phonon heat exchange in quasi-two-dimensional nanolayers

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1 K, such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film’s surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron–phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T _e for the electrons temperature and T _ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T _e ) or (d, T _ph ), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P ∝ T _e ^3.5 – T _ph ^3.5 . From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.     

Intercluster conduction in lightly doped La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites in the paramagnetic temperature range

The magnetotransport and magnetic properties of La _{1 ? x} Ca _x MnO₃ polycrystalline samples (x = 0–0.3) annealed under vacuum and in the oxygen environment are investigated in the temperature range from 77 to 400 K. The magnetic studies of lightly doped manganites reveal persistence of short-range magnetic order up to a temperature T* ≈ 300 K, which is about 2–3 times higher than their Curie temperature T _C. The temperature dependence of the electrical resistivity measured from T* down to nearly T ≈ T _C is fitted by the relation logρ ～ T ^?1/2, which is characteristic of granular metals with electrons tunneling among nanoclusters of magnetic metals embedded in a dielectric host. The magnetoresistance of polycrystalline samples annealed in the oxygen environment has been observed to increase. The electrical, magnetic, and magnetotransport properties of the manganites can be accounted for by the formation of magnetic nanoclusters below T*, tunneling (or hopping) of carriers among the nanoclusters, variation in the magnetic cluster size, and tunneling barrier thickness with variations in temperature and magnetic field strength, as well as by the effect of annealing in different media on the cluster properties.     

Self-consistent inhomogeneity of quantum wells in II–VI semiconductors

An X-ray diffraction method that uses a slightly diverging (3′) beam and maximally attainable diffraction angles ? _B (as large as 77°) was developed to study quantum wells (QWs) with widths of 5–8 nm separated by wide (100–220 nm) barrier layers. The advantage of this method compared to the use of a parallel beam is an increase by two orders of magnitude in the intensity of the beam incident on the sample and an increase in the probability of diffraction for all QWs as a unified single crystal. It is found that the growth on GaAs substrates misoriented by 10° from the (001) plane in the [111]_II direction brings about monoclinization of crystal lattices of the QW layers and barrier layers in opposite directions. Inhomogeneity of composition over the thickness of each well is observed. In the case of growth of a ZnSe/ZnMgSSe structure in which the layers have a crystal-lattice period close to the lattice period of the GaAs substrate, the QWs are inhomogeneously doped with elements from the composition of the barrier layers. The inhomogeneity of QW composition observed in the growth of mismatched layers in ZnCdSe/ZnSSe and ZnCdS/ZnSSe structures is caused by the fact that mismatch between the lattice parameters of QWs and barriers stimulates the growth of self-consistent compositions; this occurs due to a decrease in the Cd concentration in the Zn_1?x Cd _x Se QW in the initial stages of growth compared to the Cd concentration in the flow of gases and an increase in the Zn concentration in the Cd_1?x Zn _x S QW at small values of x up to the concentration matching GaAs (x = 0.4). The mismatch stresses are partially relaxed via dislocations with the (111)_II glide planes, as a result of which is observed the combination of rotation of the crystal planes of the layers and QW around the [1\(\overline 1 \)0] axis and almost cylindrical bending of the entire sample around the perpendicular [110] axis. Mismatch between lattice parameters of the ZnMgSSe barrier layers and the substrate brings about decomposition of these layers into two phases; this decomposition is caused by thermodynamic instability of the alloy.     

Magnetic and transport properties of colossal magnetoresistance compound EuB<Subscript>6</Subscript>

The galvanomagnetic and magnetic properties of EuB₆ single crystal have been measured over wide temperature (1.8–300 K) and magnetic-field (up to 70 kOe) ranges, and the parameters of charge carriers and the characteristics of the magnetic subsystem are estimated in the paramagnetic and ferromagnetic (T < T _C ≈ 13.9 K) phases of this compound with strong electron correlations. In the temperature range T < T* ≈ 80 K, a magnetoresistance hysteresis Δρ(H)/ρ(0) is detected; it reaches a maximum amplitude of about 5% at T ≈ 12 K. The anomalies of charge transport observed in the temperature range T _C < T < T* are shown to be related to the magnetic scattering of charge carriers (m _eff = (15–30)m ₀, where m ₀ is the free-electron mass) that results from a short-range magnetic order appearing upon the formation of ferromagnetic nanoregions (ferrons).     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

The influence of magnetic and structural heterogeneity on thermopower,magnetothermopower, electrical resistivity,and magnetoresistivity of Nd<Subscript>0.5</Subscript>Sr<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> manganite

The thermopower, S, magnetothermopower, ΔS/S, resistivity, ρ, and magnetoresistivity, Δρ/ρ, depending on the temperature T and magnetic field H, have been studied in an Nd_0.5Sr_0.5MnO₃ single crystal consisting of three types of clusters: an antiferromagnetic CE-type with charge-orbital ordering (below the Neel temperature T_NCE ~ 145 K) and an A-type with T_NA ~ 220 K; a ferromagnetic at 234 ≤ T ≤ 252 K, and a ferromagnetic metal phase below the Curie temperature T_C = 248 K. The thermopower was found to be negative, indicating the dominance of the electronic type of conductivity. In the S(T) curves, a sharp minimum is observed in the temperature range of 100 K ≤ T ≤ 133 K, close to T_NCE, where the absolute S value attains 53 μV/K. With a further increase in temperature, the absolute S value decreases rapidly; at 200 K it is equal to 7 μV/K. It then slightly increases, reaching its maximum value of 15 μV/K at a temperature of 254 K, which is close to T_C. The absolute thermopower decreased under the influence of the magnetic field; i.e., a negative magnetothermopower occurs. In {ΔS/S}(T) curves, a sharp minimum is observed at T = 130 K close to T_NCE, where the magnetothermopower reaches a huge value of ~45% at H = 13.23 kOe. A broad minimum in the {ΔS/S}(T) curves is observed near the Curie temperature and its value is also high, viz., ~15% in the maximum measuring magnetic field of 13.23 kOe. The extremely high magnetothermopower values mean that the charge-orbital ordered nanoclusters or ferron type make the main contribution to the thermopower of the entire sample. The behavior of the ρ(T) and {Δρ/ρ}(T) curves is similar to that of the S(T) and {ΔS/S}(T) dependencies, which is in agreement with this conclusion.     

Spin-polaron transport and magnetic phase diagram of iron monosilicide

The study of galvanomagnetic, magnetic, and magnetooptical characteristics of iron monosilicide in a wide range of temperatures (1.8–40 K) and magnetic fields (up to 120 kOe) has revealed the origin of the low-temperature sign reversal of the Hall coefficient in FeSi. It is shown that this effect is associated with an increase in the amplitude of the anomalous component of the Hall resistance ρ_H (the amplitude increases by more than five orders of magnitude with decreasing temperature in the range 1.8–20 K). The emergence of the anomalous contribution to ρ_H is attributed to the transition from the spin-polaron to coherent regime of electron density fluctuations in the vicinity of Fe centers and to the formation of nanosize ferromagnetic regions, i.e., ferrons (about 10 Å in diameter), in the FeSi matrix at T<T_C=15 K. An additional contribution to the Hall effect, which is observed near the temperature of sign reversal of ρ_H and is manifested as the second harmonic in the angular dependences ρ_H(?), cannot be explained in the framework of traditional phenomenological models. Analysis of magnetoresistance of FeSi in the spin-polaron and coherent spin fluctuation modes shows that the sign reversal of the ratio Δρ(H)/ρ accompanied by a transition from a positive (Δρ /ρ>0, T>T_m) to a negative (Δρ/ρ<0, T<T_m) magnetoresistance is observed in the immediate vicinity of the mictomagnetic phase boundary at T_m=7 K. The linear asymptotic form of the negative magnetoresistance Δρ/ρ ∝?H in weak magnetic fields up to 10 kOe is explained by the formation of magnetic nanoclusters from interacting ferrons in the mictomagnetic phase of FeSi at T<T_m. The results are used for constructing for the first time the low-temperature magnetic phase diagram of FeSi. The effects of exchange enhancement are estimated quantitatively and the effective parameters characterizing the electron subsystem in the paramagnetic (T>T_C), ferromagnetic (T_m<T< T_C), and mictomagnetic (T<T_m) phases are determined. Analysis of anomalies in the aggregate of transport, magnetic, and magnetooptical characteristics observed in the vicinity of H_m≈35 kOe at T<T_m leads to the conclusion that a new collinear magnetic phase with M∥H exists on the low-temperature phase diagram of iron monosilicide.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Exponential Increase in the Resistivity upon Cooling and Superconductivity in Indium-Doped Pb<Subscript>0.45</Subscript>Sn<Subscript>0.55</Subscript>Te

We have analyzed the temperature and magnetic-field dependences of resistivity ρ(T, H) of semiconducting compound Pb_0.45Sn_0.55Te doped with 5 at % In under a hydrostatic compression at P < 12 kbar. It is found that the temperature dependence ρ(T) at all pressures at T < 100 K is exponential with the activation energy decreasing upon an increase in pressure; this is accompanied with a superconducting transition on the ρ(T) and ρ(H) dependences at P > 4.8 kbar at T > 1 K (T _c = 1.72 K at a level of 0.5ρ _N at P = 6.8 kbar). We consider the model describing the low-temperature “dielectrization” of the semiconducting solid solution and the formation of the superconducting state upon an increase in the hydrostatic compression P > 4 kbar.     

Variable-range hopping conduction in LaMnO<Subscript>3 + δ</Subscript>

The temperature dependence of the electrical resistivity ρ(T) for ceramic samples of LaMnO_{3 + δ} (δ = 0.100–0.154) are studied in the temperature range T = 15–350 K, in magnetic fields of 0–10 T, and under hydrostatic pressures P of up to 11 kbar. It is shown that, above the ferromagnet-paramagnet transition temperature of LaMnO_{3 + δ}, the dependence ρ(T) of this compound obeys the Shklovskii-Efros variable-range hopping conduction: ρ(T) = ρ₀(T)exp[(T ₀/T)^1/2], where ρ₀(T) = AT ^9/2 (A is a constant). The density of localized states g(?) near the Fermi level is found to have a Coulomb gap Δ and a rigid gap γ(T). The Coulomb gap Δ assumes values of 0.43, 0.46, and 0.48 eV, and the rigid gap satisfies the relationship γ(T) ≈ γ(T _v)(T/T _v)^1/2, where T _v is the temperature of the onset of variable-range hopping conduction and γ(T _v) = 0.13, 0.16, and 0.17 eV for δ = 0.100, 0.125, and 0.154, respectively. The carrier localization lengths a = 1.7, 1.4, and 1.2 Å are determined for the same values of δ. The effect of hydrostatic pressure on the variable-range hopping conduction in LaMnO_{3 + δ} with δ = 0.154 is analyzed, and the dependences Δ(P) and γ_v(P) are obtained.     

Low-temperature thermal conductivity of tellurium-doped bismuth

Phonon thermal conductivities κ₂₂ (?T ‖ C1) and κ₃₃ (? T ‖ C₃) of tellurium-doped bismuth with an electron concentration in the range 1.8 × 10¹⁹ ≤ n_L ≤ 1.4 × 10²⁰ cm^?3 were studied in the temperature interval 2 < T < 300 K. The temperature dependence of the phonon thermal conductivity obtained on doped bismuth samples of both orientations exhibits two maxima, one at a low temperature and the other at a high temperature. The effect of various phonon relaxation mechanisms on the dependence of both phonon thermal conductivity maxima on temperature, impurity concentration, and electron density is studied.     

A new critical point in the non-linear conductivity due to variable range hopping in Si

A critical point in the non-linear conductivity has been observed in epitaxial silicon in the variable range hopping regime, due to a negative differential resistance with a dc bias currentI _dc. This gives thermal breakdown via the electron-phonon coupling and circuit-limited oscillations with a frequencyf∝I _dc, below a critical temperatureT _c. This critical behaviour is intrinsic, and forR(T)=R ₀ exp(T ₀ /T)^1/2 we show thatT _c=0.00512T ₀.     

Transport properties and ferromagnetism of Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>S sulfides

We have studied the resistivity and thermoelectromotive force (thermo emf) in a temperature range of T = 80–1000 K, the magnetic susceptibility and magnetization in a temperature range of T = 4.2–300 K at an external magnetic field of up to 70 kOe, and the structural characteristics of Co _x Mn_1?x S sulfides (0 ≤ x ≤ 0.4). Anomalies in the transport properties of these compounds have been found in the temperature intervals ΔT ₁ = 200–270 K and ΔT ₂ = 530–670 K and at T ₃ ～ T _N. The temperature dependences of the magnetic susceptibility, magnetization, and resistivity, as well as the current-voltage characteristics, exhibit hysteresis. In the domain of magnetic ordering at temperatures below the Néel temperature (T _N), the antiferromagnetic Co _x Mn_1?x S sulfides possess a spontaneous magnetic moment that is explained using a model of the orbital ordering of electrons in the t _2g bands. The influence of the cobalt-ion-induced charge ordering on the transport and magnetic properties of sulfides has been studied. The calculated values of the temperatures corresponding to the maxima of charge susceptibility, which are related to a competition between the on-site Coulomb interaction of holes in various subbands and their weak hybridization, agree well with the experimental data.     

Magnetized Quark-Gluon Plasma at the LHC

In QCD, the strengths of the large scale temperature dependent chromomagnetic, B₃, B₈, and usual magnetic, H fields spontaneously generated in quark-gluon plasma after the deconfinement phase transition (DPT), are estimated. The consistent at high temperature effective potential accounting for the oneloop plus daisy diagrams is used. The heavy ion collisions at the LHC and temperatures T not much higher than the phase transition temperature T_d are considered. The critical temperature for the magnetized plasma is found to be T_d (H) ～ 110–120 MeV. This is essentially lower compared to the zero field value T_d (H=0) ～ 160–180 MeV usually discussed in the literature. Due to contribution of quarks, the color magnetic fields act as the sources generating H. The strengths of the fields are B₃(T), B₈(T) ～ 10¹⁸–10¹⁹ G, H(T) ～ 10¹⁶–10¹⁷ G for temperatures T ～ 160–220 MeV. At temperatures T < 110–120 MeV the effective potential minimum value being negative approaches to zero. This is signaling the absence of the background fields and color confinement.     

The giant volume magnetostriction and colossal magnetoresistance in Eu<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript> manganite

A doped manganite with the composition Eu_0.55Sr_0.45MnO₃ exhibits giant negative magnetostriction and colossal negative magnetoresistance at temperatures in the vicinity of the magnetic phase transformation (T～41 K). In the temperature interval 4.2 K≤T ≤40 K, the isotherms of magnetization, volume magnetostriction, and resistivity exhibit jumps at the critical field strength H_c1, which decreases with increasing temperature. At 70 K ≤T ≤120 K, the jumps on the isotherms are retained, but the shapes of these curves change and the H_c1 value increases with the temperature. At H<H_c1, the magnetoresistance is positive and exhibits a maximum at 41 K; at H>H_c1, the magnetoresistance becomes negative, passes through a minimum near 41 K and then reaches a colossal value. The observed behavior is explained by the existence of three phases in Eu_0.55Sr_0.45MnO₃, including a ferromagnetic (in which the charge carriers concentrate due to a gain in the s-d exchange energy) and two antiferromagnetic phases (of the A and CE types). The volumes of these phases at low temperatures are evaluated. It is shown that the colossal magnetoresistance and the giant volume magnetostriction are related to the ferromagnetic phase formed as a result of the magnetic-field-induced transition of the CE-type antiferromagnetic phase to the ferromagnetic state.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Properties of InGaAs/GaAs quantum wells with a δ〈Mn〉-doped layer in GaAs

A method of formation of two-dimensional structures containing a δ〈Mn〉-doped layer in GaAs and an In_xGa_1?x As quantum well (QW) separated by a GaAs spacer of thickness d = 4–6 nm is developed using laser evaporation of a metallic target during MOS hydride epitaxy. It is shown that, up to room temperature, these structures have ferromagnetic properties most likely caused by MnAs clusters. At low temperatures (T _m ～ 30 K), the anomalous Hall effect is revealed to occur. This effect is related to hole scattering by Mn ions in GaAs and to the magnetic exchange between these ions and QW holes, which determines the spin polarization of the holes. The behavior of the negative magnetoresistance of these structures at low temperatures indicates the key role of quantum interference effects.     

Room-temperature phase separation in weakly doped lanthanum manganites

The properties of single crystals of weakly doped lanthanum manganites La_1?xA_xMnO₃ (A = Ca, Ce, Sr; x = 0, 0.07?0.1) have been studied in the temperature range from 77 to 400 K. It is established that these lanthanum manganites exhibit (in addition to the well-known characteristic features observed in the region of the temperature of magnetic ordering) changes in the electrical and magnetic properties in the region of room temperature (T ≈ 270–300 K), which is about two times the Curie temperature (T ≈ 120–140 K) and is far from the temperature of structural transitions in the samples studied. The results are explained in terms of phase separation related to the formation of magnetic clusters in the nonconducting medium. The phase separation is caused by a gain in the exchange energy and by the development of elastic stresses in the crystal lattice and proceeds via combination of small-radius magnetic polarons into a large-size magnetic cluster containing several charge carriers. The short-range order in the cluster appears and the phase separation begins at a temperature T_ps, which is close to T_C ≈ 300 K, typical of doped conducting manganites. The results of magnetic measurements show that, as the temperature decreases from 300 to 190 K, the size of superparamagnetic droplets increases from about 8 to 15 Å.     

Variable-range cotunneling and conductivity of a granular metal

The Efros-Shklovskii (E-S) law for the conductivity of granular metals is interpreted as a result of a variable-range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T ≤ T _c , while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T ≥ T _c . The corresponding E-S temperature T _ES , in the latter case, is slightly (logarithmically) T dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T?T _c , while, at T > T _c , it is suppressed due to inelastic processes, which destroy the interference.