Heat capacity of the Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric system

The temperature dependences of the molar heat capacity at constant pressure, C_p, of Pb₅(Ge_1?xSi_x)₃O₁₁ crystals with x=0, 0.39, and 0.45 in the range 5–300 K, as well as of their permittivity, dielectric losses, and the pyroelectric effect, have been measured. Experimental data on the temperature behavior of the heat capacity are presented in the form of a sum of two Debye and one Einstein terms, C_p(T)=0.405C_D1(Θ_D1=160 K, T)+0.53C_D2(Θ_D2=750 K, T)+0.046C_E(Θ_E=47 K, T). Besides a peak in the region of the ferroelectric Curie point T_c=450 K for crystals with x=0, the temperature dependences of the heat capacity did not reveal any other pronounced anomalies.     

Finite size and surface effects on the magnetic properties of cobalt ferrite nanoparticles

Cobalt ferrite, CoFe₂O₄, nanoparticles in the size range 2–15 nm have been prepared using a non-aqueous solvothermal method. The magnetic studies indicate a superparamagnetic behavior, showing an increase in the blocking temperatures (ranging from 215 to more than 340 K) with the particle size, D _TEM. Fitting M versus H isotherms to the saturation approach law, the anisotropy constant, K, and the saturation magnetization, M _S, are obtained. For all the samples, it is observed that decreasing the temperature gives rise to an increase in both magnetic properties. These increases are enhanced at low temperatures (below ~160 K) and they are related to surface effects (disordered magnetic moments at the surface). The fit of the saturation magnetization to the T ² law gives larger values of the Bloch constant than expected for the bulk, increasing with decreasing the particle size (larger specific surface area). The saturation magnetization shows a linear dependence with the reciprocal particle size, 1/D _TEM, and a thickness of 3.7 to 5.1 Å was obtained for the non-magnetic or disordered layer at the surface using the dead layer theory. The hysteresis loops show a complex behavior at low temperatures (T ≤ 160 K), observing a large hysteresis at magnetic fields H > ~1000 Oe compared to smaller ones (H ≤ ~1000 Oe). From the temperature dependence of the ac magnetic susceptibility, it can be concluded that the nanoparticles are in magnetic interaction with large values of the interaction parameter T ₀, as deduced by assuming a Vogel–Fulcher dependence of the superparamagnetic relaxation time. Another evidence of the presence of magnetic interactions is the almost nearly constant value below certain temperatures, lower than the blocking temperature T _b, observed in the FC magnetization curves.     

High-temperature redistribution of cation vacancies and irreversible magnetic transitions in the Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>S nanodisks observed by the Mössbauer spectroscopy and magnetic measurements

The hexagonal pyrrhotite Fe_1?x S nanodisks with the NiAs-type structure were synthesized by thermal decomposition of ferrous chloride and thiourea in oleylamine. The Mössbauer spectroscopy and magnetic measurements data indicate that a mixture of antiferromagnetic (AFM) and ferrimagnetic (FRM) phases with the NC (N ≥ 3) and 2C-type superstructures is present in the Fe_1?x S compound at temperatures between 80 K and Néel temperature T _N. At T < 370 K, the AFM phase prevails over the FRM phase. At T > 370 K, a redistribution of iron vacancies takes place, and the vacancy ordering transforms from the NC (N ≥ 3) to 2C-type which essentially increases the magnetization with maximum value at 470 K. Heating the sample above the Néel temperature 565 K leads to a random distribution of vacancies, and this state is quenched upon subsequent cooling of the sample to 300 K. This gives rise to a pure AFM structure with a zero magnetic moment due to a total compensation of the moments in neighboring iron layers. Thus, the high-temperature redistribution of cation vacancies leads to irreversible magnetic transformations in the Fe_1?x S nanoparticles.     

Correlation between structural and giant magnetoresistance properties of Fe–Ag nanogranular films

Fe _x Ag_1?x granular thin-films, with the atomic Fe concentration, x, ranging from 0 up to 0.5, were deposited by dc magnetron co-sputtering. The giant magnetoresistance (GMR) intensity is maximum at x _I  = 0.32, while the maximum of GMR efficiency, γ, i.e., the change of GMR intensity for a unit change of reduced squared magnetization, is observed at x _γ = 0.26. Owing to the spin-dependent scattering features, the GMR intensity and γ depend on both the concentration and the arrangement of the magnetic material. Therefore, to explain the difference between x _I and x _γ and to understand how the structural properties affect the magnetoresistive behaviour, we performed magnetization, Mössbauer and X-ray diffraction measurements as a function of x. X-ray data indicate that the granular films exhibit three different regimes: for x < 0.2, they can be described as a Fe–Ag solid solution; for 0.2 < x < 0.32 the Fe–Ag solid solution is still observed and very small Fe precipitates are found; finally, for x > 0.32, a Fe–Ag saturated solid solution is detected, containing bcc Fe clusters whose size is about 10 nm. Differently, for all the concentrations, magnetization data show the presence of Fe precipitates, whose size increases with x, and the Mössbauer investigation confirms this picture. We find that the samples grown at x = x _γ display the finest Fe dispersion within the Ag matrix, as the Fe–Ag solid solution is nearly at saturation and the Fe cluster size is of the order of a few nanometers; this arrangement possibly maximizes the magnetic/non-magnetic interface extension thus enhancing the GMR efficiency. If x is slightly increased, the increase in total Fe content compensates the GMR efficiency reduction, so the GMR intensity maximum is observed.     

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2ST _H is found in the next to leading order computation in the noncommutative parameter θ (i.e. \({\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})}\)) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point T _H  = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2ST _H , where the mass (M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter–Schwarzschild geometry.     

Visualization of the magnetic flux structure in phosphorus-doped EuFe<Subscript>2</Subscript>As<Subscript>2</Subscript> single crystals

Magnetic flux structure on the surface of EuFe₂(As_1-x P _x )₂ single crystals with nearly optimal phosphorus doping levels x = 0.20 and x = 0.21 is studied by low-temperature magnetic force microscopy and decoration with ferromagnetic nanoparticles. The studies are performed in a broad temperature range. It is shown that the single crystal with x = 0.21 in the temperature range between the critical temperatures T _SC= 22 K and T _C = (18 ± 0.3) K of the superconducting and ferromagnetic phase transitions, respectively, has the vortex structure of a frozen magnetic flux, typical for type-II superconductors. The magnetic domain structure is observed in the superconducting state below T _C. The nature of this structure is discussed.     

The magnetization reversal in CoFe<Subscript>2</Subscript>O<Subscript>4</Subscript>/CoFe<Subscript>2</Subscript> granular systems

The temperature-dependent field cooling (FC) and zero-field cooling (ZFC) magnetizations, i.e., M _FC and M _ZFC, measured under different magnetic fields from 500 Oe to 20 kOe have been investigated on two exchange–spring CoFe₂O₄/CoFe₂ composites with different relative content of CoFe₂. Two samples exhibit different magnetization reversal behaviors. With decreasing temperature, a progressive freezing of the moments in two composites occurs at a field-dependent irreversible temperature T _irr. For the sample with less CoFe₂, the curves of ?d(M _FC ? M _ZFC)/dT versus temperature T exhibit a broad peak at an intermediate temperature T ₂ below T _irr , and the moments are suggested not to fully freeze till the lowest measuring temperature 10 K. However, for the ?d(M _FC ? M _ZFC)/dT curves of the sample with more CoFe₂, besides a broad peat at an intermediate temperature T ₂, a rapid rise around the low temperature T ₁~15 K is observed, below which the moments are suggested to fully freeze. Increase of magnetic field from 2 kOe leads to the shift of T ₂ and T _irr towards a lower temperature, and the shift of T ₂ is attributable to the moment reversal of CoFe₂O₄.

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Graphical abstract CoFe₂O₄/CoFe₂ composites with different relative content of CoFe₂ were prepared by reducing CoFe₂O₄ in H₂ for 4 h (S4H) and 8 h (S8H). The temperature-dependent FC and ZFC magnetizations, i.e., M _FC and M _ZFC, under different magnetic fields from 500 Oe to 20 kOe have been investigated. Two samples exhibit different magnetization reversal behaviors. With decreasing temperature, a progressive freezing of the moments in two composites occurs at field-dependent irreversible temperature T _irr. For the S4H sample, the curves of ?d(M _FC ? M _ZFC)/dT versus temperature T exhibit a broad and field-dependent relaxing peak at T ₂ below T _irr (figure a), and the moments were suggested not to fully freeze till the lowest measuring temperature 10 K. However, for the S8H sample, it exhibits the reentrant spin-glass state around 50 K, as evidenced by a peak in the M _FC curve (inset in figure b) and as a result of the cooperative effects of the random anisotropy of CoFe₂O₄, exchange–spring occurring at the interface of CoFe₂O₄ and CoFe₂ together with the inter-particle dipolar interaction (figure c); in ?d(M _FC ? M _ZFC)/dT curves, besides a broad relaxing peat at T ₂, a rapid rise around the low-temperature T ₁~15 K is observed, below which the moments are suggested to fully freeze. Increase of magnetic field from 2 kOe leads to the shift of T ₂ and T _irr towards a lower temperature, and the shift of T ₂ is attributable to the moment reversal of CoFe₂O₄.

     

Intersubband cyclotron resonance of holes in strained Ge/GeSi(111) heterostructures with germanium wide quantum wells and cyclotron resonance of 1<Emphasis Type="Italic">L</Emphasis> electrons in GeSi layers

The submillimeter (?ω=0.5–5 meV) magnetoabsorption spectra of strained Ge/Ge_1?xSi_x(111) multilayer heterostructures with thick Ge layers (d_Ge=300–850 Å, d_GeSi≈200 Å, x≈0.1) are investigated at T=4.2 K upon band-gap optical excitation. It is revealed that the absorption spectra contain cyclotron resonance lines of 1L electrons localized in GeSi solid solution layers (unlike the previously studied structures with thin Ge layers as quantum wells for 3L electrons). The absorption spectra of the samples with thick Ge layers (d_Ge=800–850 Å) exhibit cyclotron resonance lines of holes due to transitions from the lower Landau levels in the first quantum-well subband to the Landau levels belonging to the third and fifth higher subbands.     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.     

Structural Phase Transition of Perovskite-Type N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>CdBr<Subscript>3</Subscript> Studied by MAS NMR and Static NMR

The structural geometry change in the perovskite-type N(CH₃)₄CdBr₃ single crystal near the phase transition temperature of T _C = 390 K was investigated using magic angle spinning nuclear magnetic resonance techniques. For ¹H and ¹³C nuclei, the temperature dependences of their chemical shift, spectral intensity, and spin–lattice relaxation time (T _1ρ) in the rotating frame were obtained and analyzed. While the chemical shift and T _1ρ of ¹H showed change near T _C, those of ¹³C did not. In addition, the ¹¹³Cd spin–lattice relaxation time T ₁ in the laboratory frame near T _C show no evidence of anomalous change near the phase transition temperature, which coincides with the measured changes in the ¹H T _1ρ. The driving force for this phase transition was connected to the ¹H in the CH₃ groups.     

Substitution effects on the bulk and surface properties of (Li,Ni)Mn<Subscript>2</Subscript>O<Subscript>4</Subscript>

Manganese oxides of spinel structure, LiMn₂O₄, Li_1-x Ni _x Mn₂O₄ (0.25 ≤ x≤ 0.75), and NiMn₂O₄, were studied by EDS, XRD, SEM, magnetic (M-H, M-T), and XPS measurements. The samples were synthesized by an ultrasound-assisted sol-gel method. EDS analysis showed good agreement with the formulations of the oxides. XRD and Rietveld refinement of X-ray data indicate that all samples crystallize in the Fd3m space group characteristic of the cubic spinel structure. The a-cell parameter ranges from a = 8.2276 Å (x = 0) to a = 8.3980 Å (x = 1). SEM results showed particle agglomerates ranging in size from 2.3 μm (x = 0) down to 0.8 μm (x = 1). Hysteresis magnetization vs. applied field curves in the 5–300K range was recorded. ZFC-FC measurements indicate the presence of two magnetic paramagnetic-ferrimagnetic transitions. The experimental Curie constant was found to vary from 5 to 7.1 cm³ K mol^?1 for the range of compositions studied (0 ≤ x ≤ 1). XPS studies of these oxides revealed the presence of Ni²⁺, Mn³⁺, and Mn⁴⁺. The experimental Ni/Mn atomic ratios obtained by XPS were in good agreement with the nominal values. A linear relationship of the average oxidation state of Mn with Ni content was observed. The oxide’s cation distributions as a function of Ni content from x = 0 ?Li⁺[Mn³⁺Mn⁴⁺]O₄ to x = 1 \( {\mathrm{Ni}}_{0.35}^{2+}{\mathrm{Mn}}_{0.65}^{3+}\left[{\mathrm{Ni}}_{0.65}^{2+}\right.\left.{\mathrm{Mn}}_{1.35}^{3+}\right]{\mathrm{O}}_4 \) were proposed.     

Structure and stability of two-dimensional systems of C<Subscript>20</Subscript> fullerenes

Two-dimensional systems of C₂₀ fullerenes connected to each other by strong covalent bonds have been investigated. Several isomers differing in the type of intercluster bonds have been revealed. The lifetimes τ of the (C₂₀) _{M × M} complexes with M = 2 and 3 at T = 1800–3300 K have been directly calculated using the molecular dynamics method. It has been shown that these complexes lose their periodic cluster structure due usually to the coalescence of two or several neighboring C₂₀ fullerenes. The activation energy of this process determined by analyzing the τ(T) dependence appears to be E _a ≈ 2.5 eV in agreement with the calculations of the heights of the potential barriers preventing the coalescence. At high temperatures T > 2400 K, the decay of C₂₀ fullerenes entering into the complex is possible.     

(Pr–Ca) Manganites That Display Multiferroic Properties: High-Temperature Magnetic,Resistive, and Dielectric Measurements

Complex magnetic, resistive, and dielectric studies of Pr_1–xCa_xMnO₃ (х = 0.15–0.30) manganites reveal multiferroic properties at T?T_C in these solid solutions. States with local magnetization in the form of ferromagnetic clusters (nucleation temperature T* ≈ 700 K) and high dielectric constants coexist in the temperature window T_C ≤ T ≤ T*. There is a correlation between the temperature dependences of specific resistance and specific magnetization.     

Magnetic Resonance in Gadolinium Nanoparticles near the Curie Point

The Influence of temperature in the range from 275 to 320 K on ESR spectra and magnetization m of ensembles of spherical gadolinium nanoparticles with the diameter from 89 to 18 nm was studied. The particles with d = 18 nm had a cubic face centered structure and no magnetic transition. At T > T_C all particles were paramagnetic, and their g factors were g = 1.98 ± 0.02 irrespective of their size and structure. At T = T_C the particles having 28 to 89 nm in size experienced a magnetic and orientation transition; at T < T_C their m(H) dependences were described by the Langevin function, and the FMR lines broadened and shifted towards H = 0. FMR lines of the Gd particle ensembles showed a hysteresis behavior during magnetization reversal, which did not correlate with the coercivity of the particles. Dependences of the Gd nanoparticles FMR linewidth ΔH(T) changed proportionally to |T–T_C|.     

Phase transitions and magnetoelectric coupling in BiFe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> multiferroics

Multiferroic BiFe_1?xZn _x O₃ ceramics were prepared by solution combustion method. Their structure, magnetoelectric, dielectric, magnetic, thermal characteristics were studied. The magnetic M(T) and heat capacity C _p (T) measurements demonstrate an antiferromagnetic to paramagnetic phase transition (T _N ) around 635 K. The anomaly on the temperature dependence of the dielectric constant near T _N was observed, which could be induced by the magnetoelectric coupling between electric and magnetic ordering. The magnetoelectric behavior was also confirmed by the linear relation between Δε and M², which is in the agreement of the Ginzburg-Landau theory for the second-order phase transition.     

Intermediate phases in [111]- and [001]-oriented PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–29PbTiO<Subscript>3</Subscript> single crystals

Phase transformations in [111]- and [001]-oriented PbMg_1/3Nb_2/3O₃–29PbTiO₃ single crystals have been studied using dielectric and optical measurements before and after applying an electric field. It is shown that the subsequence of phase transitions rhombohedral (R)—tetragonal (T)—cubic (C) phases is observed in nonpolarized samples of both orientations as temperature increases. In the [111]-oriented crystal, an additional intermediate monoclinic phase (it is possible, M _a ) is induced after preliminary polarization at room temperature and the R–M _a –T–C phase transitions are observed on heating. In the [001]-oriented crystal, after its polarization, the monoclinic phase forms instead of the rhombohedral phase even at room temperature and the M _a –T–C transitions occur on heating. The results are discussed from the point of view of the existence polar nanoregions with different local symmetries in a glasslike matrix.     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

The Boundary Control Approach to the Titchmarsh-Weyl <Emphasis Type="Italic">m</Emphasis>–Function. I. The Response Operator and the <Emphasis Type="Italic">A</Emphasis>–Amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? _x ²  + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.