Schottky Anomaly Research Articles

Thermo-Magnetic properties of non-relativistic particles under the effect of energy-dependent Hellmann potential

This manuscript presents an analysis of the thermal and magnetic properties of particles moving in two dimensions under the influence of an external magnetic field and Aharanov-Bohm flux, considering an energy-dependent Hellmann potential. The energy eigenvalue is obtained using the asymptotic iteration method. Next, we model the system as a canonical ensemble and derive the partition function to acquire analytical expressions for the Helmholtz free energy, entropy, mean energy, and specific heat. We observe that an increase in the external magnetic field and AB flux generally increases the energy eigenvalues, with a stronger effect at lower flux values, while energy eigenvalues decrease with an increase in the screening parameter. Additionally, Helmholtz free energy and entropy functions are sensitive to temperature, particularly in the low-temperature regime, while specific heat exhibits a Schottky anomaly. We also compute the magnetisation and susceptibility functions, finding that both magnetisation and susceptibility increase with the external magnetic field strength and the AB flux.

Non-linear charged dS spacetime and its thermodynamics and Schottky Anomaly

Abstract In this paper, firstly, the conditions and existence region for the coexistence of the black hole and cosmological horizons in Non-linear charged dS (NLC-dS) spacetime are discussed, subsequently, the thermodynamic quantities for which the boundary conditions are satisfied in spacetime in the coexistence region of the two horizons are discussed, and the effective thermodynamic quantities in the NLC-dS spacetime in the coexistence region with two horizons are presented. Based on these, the heat capacity in the coexistence region with two horizons is addressed, the behavior of the heat capacity in the NLC-dS spacetime in the aforementioned region is found to exhibit the characteristics of Schottky specific heat. In order to investigate the intrinsic reason of the heat capacity in spacetime, regarding the two horizons in the NLC-dS spacetime as two distinct energy levels, consequently, the microscopic particles at different horizons exhibit disparate energies. Using the heat capacity relationship between the two-energy level in an ordinary thermodynamic system, the heat capacity in dS spacetime is discussed, it is observed that the behavior of the heat capacity is analogous to that of the two-energy levels in an ordinary thermodynamic system. The number of microscopic particles in the two-level system is approximated by comparing the maximum value of the heat capacity of the system with the maximum value obtained by treating the two horizons in the NLC-dS spacetime as a two-energy-level system of two distinct energies. This conclusion reflects the quantum properties of the coexistence region with two horizons in the NLC-dS spacetime. It provides a new avenue for further study of the thermodynamic properties of black holes and the quantum properties of de Sitter spacetime.

Thermodynamic functions of Tm<sub>2</sub>O<sub>3</sub>‧2HfO<sub>2</sub> solid solution and Shottky anomaly

The molar heat capacity of the solid solution Tm2O3‧2HfO2 has been determined for the first time by relaxation, adiabatic and differential scanning calorimetry, the temperature dependences of entropy and enthalpy increment in the temperature region 0–1800 K have been calculated, and the contribution to the heat capacity of the Schottky anomaly at 0–300 K has been evaluated.

Electronic heat capacity in bilayer P6 mmm borophene: Effects of a perpendicular electric field, excitonic effects, and dopants

In this work, we aim to control the electronic heat capacity (EHC) of bilayer P6 mmm borophene through a perpendicular electric field, excitonic effects, and external dopants. To achieve this, we employ the tight-binding model within a semi-classical framework. Our findings reveal a decrease in EHC under all stimuli due to decreased total electronic states in the system, while the coexistence of electric field and excitonic effects leads to an enhancement of EHC in the strong regime. Additionally, our study highlights a shift in the Schottky anomaly peak at low temperatures only in the strong regime of stimuli. This study is crucial for the design of thermoelectric materials based on borophene.

Computation insights of kagome structure for probing electronic and thermodynamic properties by applying external factors such as strain, spin-orbital coupling, and external magnetic field

In this study, we explored the electronic properties of a two-dimensional (2D) kagome lattice in the presence of an external magnetic field, spin-orbit coupling (SOC), and strain. Our focus was on investigating the energy-dependent behavior of the electronic heat capacity and paramagnetic spin susceptibility in response to changing factors. Employing the Green's function approach, we successfully determined the energy dependence of the electronic heat capacity and paramagnetic susceptibility using the tight-binding model. Notably, at low energies, the electronic heat capacity almost reaches the Schottky anomaly peak, while the paramagnetic susceptibility sharply decreases. Furthermore, we conducted a detailed investigation of the energy-dependent paramagnetic susceptibility and electronic heat capacity of a kagome lattice monolayer, considering the influences of SOC and magnetic field factors. Our investigation of the density of states (DOS) in the presence of SOC suggests that semimetal-to-insulator phase transitions occur. Additionally, throughout our study, we observed variations in the DOS spectrum, indicating the influence of both compressive and tensile strains. We found that these alterations, along with the splitting of levels under different conditions, led to changes in the material's electrical properties.

Tailoring thermoelectric properties through carbon doping and magnetic field variation: A comparative study in 2D h-BN and h-SiC

The purpose of this work is to study the effects of carbon doping on the thermoelectric properties of monolayer hexagonal boron nitride (h-BN) and hexagonal silicon carbide (h-SiC) in the presence of a magnetic field. We use a tight-binding model and Kubo formalism to calculate the effects of doping concentration, dopant type and applied magnetic field on the heat capacity, electrical conductivity, magnetic susceptibility, and thermoelectric figure of merit. Heat capacity displays a Schottky anomaly that is more prominent at lower dopant concentrations. In the presence of the magnetic field, the Schottky anomaly shifts to lower temperature and its intensity is reduced. The magnetic susceptibility of the doped structures is enhanced by both doping and a magnetic field. The p-type doped structures exhibit higher magnetic susceptibility intensity compared to the n-type doped structures, especially for h-SiC structure. The electrical and thermal conductivities rise from zero at low temperatures, with higher intensity for p-doped structures. Doped h-SiC has higher conductivity at low temperatures, but doped h-BN exceeds it at higher temperatures. A comparison of p- and n-doped h-SiC and h-BN reveals enhanced thermoelectric performance for p-doped structures, further improved by lower dopant concentrations and applied magnetic fields. Overall, the work provides new insights into optimizing the thermoelectric properties of doped h-BN and h-SiC nanostructures through doping and external fields.

Tuning the electronic heat capacity and thermal Schottky anomaly of monolayer [formula omitted]-borophene via adsorbed gas molecules

Owing to the inherent inversion symmetry between five atoms {a,b,c,d,e} and metallic phase, β12-borophene possess fantastic physical properties, such as various electronic phase transitions in the presence of external perturbations. Here, the effect of adsorbed gas molecules (NH3, NO, NO2, and CO) on the electronic heat capacity (EHC) and thermal Schottky anomaly of β12-borophene is calculated employing the tight-binding model and the Green’s function approach. The results show that the gas-adsorbed EHC is enhanced with the dominant contribution of NO on individual {a,b,d,e} atoms, while it is NO2 on c atoms. However, EHC is suppressed when the molecule is adsorbed on the pair of boron atoms. Moreover, the enhancement of EHC is dominated by the simultaneous adsorption of NH3 on all atoms. On average, the pristine Schottky anomaly moves to the higher thermal energies upon the adsorption of gas molecules. These distinct differences originate from the generation of various new energy levels. This study provides a detailed understanding of β12-borophene response to the gas molecules for tuning field effect transistor-based gas sensors.

Heat Capacity and Thermodynamic Functions of Ho2O3·2HfO2 Solid Solution

Isobaric heat capacity measurements in the range 2.4–1807 K have been performed by relaxation calorimetry, adiabatic calorimetry, and differential scanning calorimetry on a Ho2O3‧2HfO2 solid solution sample prepared and characterized by X-ray powder diffraction, electron microscopy, and chemical analysis, and thermodynamic functions have been calculated. The Schottky anomaly contribution has been determined in the range 2.4–300 K.

Magnetic Property, Heat Capacity and Crystal Structure of Mononuclear Compounds Based on Substitute Tetrazole Ligand.

Three mononuclear compounds formulated as {M[(2-1H-tetrazol-5-yl)pyridine]2(H2O)2} (M = FeII (1), CoII (2), CuII (3)) were reported and synthesized. Their space group is monoclinic, P21/c, revealed by single-crystal X-ray diffraction. Antiferromagnetic interactions exist in Compounds 1, 2 and 3, as evidenced by magnetic and low-temperature heat capacity measurements. In addition, their thermodynamic functions were determined by a relaxation calorimeter, indicating that Compound 1 exhibits a Schottky anomaly in low-temperature heat capacity. This work can provide an important fundamental basis for the research of the thermophysical properties of molecular-based magnetic materials.

Ab Initio Modeling on The Thermodynamic and Temperature-Dependent Elastic Properties of Subsystems of The FCC FeNiCoCr Medium Entropy Alloys (MEAs)

The stability, phonon spectra, thermodynamic, and temperature-dependent elasticity of subsystems of the FCC FeNiCoCr MEAs are systematically studied by the ab initio approach. Especially, the quasi-harmonic approximation (QHA) and the innovative Zentropy theory were utilized to predict the thermodynamic properties and elastic properties of FeNi, NiCo, FeNiCo, and FeNiCoCr MEAs with the consideration of magnetic transition. With the ensemble of the partition function based on the multiplicity of each magnetic configuration, the current work successfully reproduced the Curie temperature and the Schottky anomaly of heat capacity of these four MEAs purely based on the ab initio input. Meanwhile, the elastic properties of these alloys at finite temperatures are also successfully predicted with the consideration of magnetic transition. The overall results agree well with the available experimental data and CALPHAD prediction.

External magnetic field effects on the thermoelectric and thermodynamic properties of doped monolayer S-graphene: A theoretical study

This study explores the electronic, thermoelectric, and thermal properties of S-Graphene, a unique graphene allotrope with two Dirac cones and zero band gap, in the presence of magnetic field and doping. A full tight-binding model and Green function approach are utilized to study the effects of robustness, magnetic field, and doping on the thermoelectric properties of S-Graphene, including the heat capacity C(T), magnetic susceptibility χ(T), thermoelectric figure of merit ZT(T), and Seedbeck coefficients S(T) and the results are compared with those for T-Graphene. To including the robustness effects, four S1–S4 structures with different hopping parameters are selected. The results demonstrate that the temperature dependent of thermal properties of S-Graphene are strongly affected by the external parameters such as external field, chemical potential and Robustness effects. The C(T) exhibits a Schottky anomaly whose position is dependent on the magnetic field and doping parameters. Pure cases demonstrate minimum values for C(T) and χ(T), while electron/hole doping leads to increase their intensity due to enhanced density concentration of charge carriers. Additionally, the behavior of ZT(T) and S(T) depends on the structure type of S-Graphene and displays intriguing features in different temperature regions. The magnetic field significantly affects the number, position and intensity of peaks in S(μ). These findings provide important insights into the electronic, thermoelectric, and thermal properties of S-Graphene and offer possibilities for future device applications.

Structure driven magnetic properties and magnetodielectric coupling in a mixed metal oxide NdCr0.5Co0.5O3

Mixed-metal oxides provide a vast playground to enhance and tune their functional properties, as compared to the respective parent oxides. In this context, we report the magnetic, thermal, dielectric, and magnetodielectric properties of NdCr0.5Co0.5O3. Three magnetic transitions, T N1 –antiferromagnetic ordering of Cr3+ cations from paramagnetic state, T N2—spin reorientation of these Cr3+ cations, and T N3—due to Nd ordering induced by the Cr sub-lattice; have been observed due to a reduction in orthorhombic distortion. Modification of magnetic interactions is also noted because of the presence of Co cations in NdCrO3 matrix. The reduction in Nd3+-Cr3+ interactions is further concluded from the Schottky anomaly in the heat capacity, which arises due to Zeeman splitting of the ground state Kramer’s doublet of Nd3+ cations. The presence of significant magnetodielectric coupling (∼4%) below T N2 has been observed. Additionally, double relaxor-like behaviour around 176 and 230 K, with activation energy ∼0.24 and 0.32 eV, is observed due to charge carrier hopping at Cr/Co-site. Our studies indicate that structure-driven modifications of Cr3+-Cr3+ and Nd3+-Cr3+ interactions are responsible for enhanced value of magnetic transitions and magnetodielectric coupling in NdCr0.5Co0.5O3, as compared to its respective parent compounds.

Ab initio studies on structural and thermodynamic properties of magnetic Fe

The present work systematically investigates the total energy, phonon spectra, and thermodynamic properties of different polymorphs of pure Fe, i.e., FCC, BCC, and HCP, with the ab initio approach, considering various magnetic configurations. In general, the calculated energy vs. volume curves and phonon spectra agree well with previous calculations and the experimental data. In addition, their thermodynamic properties are estimated by the quasiharmonic approximation (QHA). Specifically, a superposition approach based on the latest Zentropy theory was utilized to predict magnetic transition temperatures and thermodynamic properties of pure Fe. With the ensemble of the partition function considering the multiplicity of each magnetic microstate, the current work successfully reproduced the Curie/Néel temperature and the Schottky anomaly of heat capacity in FCC, BCC, and HCP Fe purely based on the ab initio input, which exhibits good agreement with the experimental data and CALPHAD modeling.

ВЛИЯНИЕ ВНЕШНЕГО МАГНИТНОГО ПОЛЯ НА МАГНИТНЫЕ СВОЙСТВА КВАЗИОДНОМЕРНЫХ ХАЛДЕЙНОВСКИХ МАГНЕТИКОВ (Y1-XNDX)2BANIO5 (X = 0.25 И 0.04)

In the compounds of the (Y1-xNdx)2BaNiO5 family, the paradoxical coexistence of the Haldane phase and spin waves is realized. The magnetic ordering in the system is caused by the interaction of Nd3+ ions through spin fluctuations of a nickel chain, which remains internally disordered. Nd3+ magnetic moments do not deviate from the c axis of the crystal even in the presence of an external magnetic field. In this paper, for compounds (Y1-xNdx)2BaNiO5 with x = 0.25 and x = 0.04, an experimental study of the field dependence of the magnetization M(B) and the temperature dependence of the heat capacity C( T ), measured in fields B = 0; 2 and 5 T. For compounds with x = 0.25 on the dependence M(B) measured at T = 4.2 K, an anomaly was detected indicating a metamagnetic transition. Changes in the parameters of the magnetic interaction between the magnetic moments Nd along the c axis of the crystal leads to the periorientation of the magnetic moments of all Nd3+ ions along the direction of the external field B||c. For the connection with x = 0.04, no anomalies were detected on the dependence M(B), the magnetic moments of both neodymium sublattices lie along the direction of the applied magnetic field. The presence of a Schottky anomaly on the dependence C( T ) at B =0 indicates the existence of an internal magnetic field acting on the Nd3+ ion from the side of the nickel subsystem, and leading to the splitting of the main Kramers doublet of the Nd3+ ion. For a connection with x = 0.04, the Schottky anomaly shifts towards higher temperatures with an increase in the external magnetic field, and for a connection with x = 0.25, the Schottky anomaly shifts towards low temperatures only in the field B = 5 T. The displacement of the Schottky anomaly in the presence of a field is due to the ratio between the magnitude of the applied magnetic field and the component of the internal magnetic field fields с along the c axis of the crystal. For connection with x = 0.25 , the magnetic moments of the two neodymium sublattices are oppositely directed, and the Schottky anomaly of the 1st sublattice shifts towards higher temperatures, and the Schottky anomaly of the 2nd sublattice shifts towards lower temperatures. For connection with x = 0.04 с The magnetic moments of the two neodymium sublattices are directed towards the applied field, and the Schottky anomaly of both sublattices shifts towards higher temperatures, which is consistent with the experimen

On the nature of the Schottky anomaly in endohedral water.

In this work, we study the heat capacity contribution of a rigid water molecule encapsulated in C60 by performing six-dimensional eigenstate calculations with the inclusion of its quantized rotational and translational degrees of freedom. Two confinement model potentials are considered: in the first, confinement is described using distributed pairwise Lennard-Jones interactions, while in the second, the water molecule is trapped within an eccentric but isotropic 3D harmonic effective confinement potential [Wespiser et al., J. Chem. Phys. 156, 074304 (2022)]. Contributions to the heat capacity from both the ortho and para nuclear spin isomers of water are considered to enable the effects of their interconversion to be assessed. By including a symmetry-breaking quadrupolar potential energy term in the Hamiltonian, we can reproduce the experimentally observed Schottky anomaly at ∼2K [Suzuki et al., J. Phys. Chem. Lett. 10, 1306 (2019)]. Furthermore, our calculations predict a second Schottky anomaly at ∼0.1K resulting from the H configuration, a different orientational arrangement of the fullerene cages in crystalline solid C60. Contributions from the H configuration to CV also explain the second peak observed at ∼7K in the experimentally measured heat capacity.

Magnetoelastic Coupling and Cryogenic Magnetocaloric Effect in Two-Site Disordered GdSrCoFeO6 Double Perovskite

The development of new magnetic refrigerants demands an effective investigation of materials with a large magnetocaloric effect in a wide temperature range. Herein, we report on the structural, magnetic, and magnetocaloric properties of the two-site disordered double perovskite GdSrCoFeO6 prepared by the modified solid-state synthesis method. Temperature-dependent synchrotron X-ray diffraction analysis revealed that GdSrCoFeO6 crystallizes in the orthorhombic phase (Pnma), with Gd3+/Sr2+ and Co2+/3+/Fe3+/4+ ions randomly distributed on the A- and B-sites, respectively. An observed lattice parameter anomaly around 60 K indicates the occurrence of the magnetoelastic coupling, which coincides with the presence of ferro/ferrimagnetic (FM/FiM) ordering below TC ≈ 65 K from the magnetic measurements. These results match well with our first-principles calculation prediction of low-temperature magnetic (FM/FiM) and electronic (insulating/metal) transitions related to a combined effect of Co and Fe short- and long-range competitions, crossings of spin state at Co ions, and the hybridization degree between Gd-4f and Co-3d states. Additionally, a modified Arrott plot and Kouvel–Fisher analysis were used to establish the nature of the magnetic phase transition in GdSrCoFeO6, yielding the critical exponent β = 1.46(6)/1.45(6), γ = 1.48(5)/1.17(2), and δ = 2.01(3)/1.80(5), respectively. The specific heat analysis reveals two well-defined broad peaks (∼10 and ∼70 K), which match well with a Schottky anomaly (Gd-4f) and the magnetic transition of FM/FiM to paramagnetic order, respectively. The magnetocaloric effect (MCE) analysis reveals a maximum magnetic entropy change ΔSMmax ≈ 13 J kg–1 K–1 (at ∼8 K) under a field of 0–7 T. These results evidence that the Schottky anomaly and the magnetoelastic coupling seem to be key factors for driving further enhancements to the MCE in GdSrCoFeO6, making it a possible candidate for cryogenic applications.

Influence of crystalline electric field on the magnetic properties of CeCd3X3(X=P,As)

CeCd$_3$P$_3$ and CeCd$_3$As$_3$ compounds adopt the hexagonal ScAl$_3$C$_3$-type structure, where magnetic Ce ions on a triangular lattice order antiferromagnetically below $T_\text{N} \sim$0.42~K. Their crystalline electric field (CEF) level scheme has been determined by fitting magnetic susceptibility curves, magnetization isotherms, and Schottky anomalies in specific heat. The calculated results, incorporating the CEF excitation, Zeeman splitting, and molecular field, are in good agreement with the experimental data. The CEF model, with Ce$^{3+}$ ions in a trigonal symmetry, explains the strong easy-plane magnetic anisotropy that has been observed in this family of materials. A detailed examination of the CEF parameters suggests that the fourth order CEF parameter $B_{4}^{3}$ is responsible for the strong CEF induced magnetocrystalline anisotropy, with a large $ab$-plane moment and a small $c$-axis moment. The reliability of our CEF analysis is assessed by comparing the current study with earlier reports of CeCd$_{3}$As$_{3}$. For both CeCd$_{3}X_{3}$ ($X$ = P and As) compounds, less than 40 \% of $R\ln(2)$ magnetic entropy is recovered by $T_\text{N}$ and full $R\ln(2)$ entropy is achieved at the Weiss temperature $\theta_{p}$. Although the observed magnetic entropy is reminiscent of delocalized 4$f$-electron magnetism with significant Kondo screening, the electrical resistivity of these compounds follows a typical metallic behavior. Measurements of thermoelectric power further validate the absence of Kondo contribution in CeCd$_{3}X_{3}$.

Metal-semiconductor transition in Ψ-graphene

The effect of hydrogenation on the density of states (DOS), band structure, Pauli magnetic susceptibility (PMS), and electronic heat capacity (EHC) of Ψ -graphene is investigated within the nearest neighbor tight-binding model. Two different hydrogenation process of Ψ -graphene is examined: half hydrogenation ( Ψ -graphone) and full hydrogenation ( Ψ -graphane). It was observed that Ψ -graphone, like Ψ -graphene, exhibits metallic behavior, but it has sharp peaks in the DOS and corresponding flat bands in the band structure near the Fermi level, due to unpaired and localized electrons in its structure. Whereas, because of the strong σ bonds in the Ψ -graphane structure, a bandgap is created in its energy spectra. It can also be seen that with the hydrogenation of Ψ -graphene, the van-Hove singularities in the DOS and the number of sub-band in the band structures increased due to the greater overlap of the orbitals. These lead to the crossovers in the PMS and the Schottky anomaly peaks in the EHC, which both of these peaks are observed in the Ψ -graphane curve at a higher temperature than the other two structures. These results indicate that the hydrogenation of Ψ -graphene leads to a metal-to-semiconductor transition.

Critical behavior of the specific heat in Ti-Si amorphous alloys at the metal-insulator transition

In this paper, we report the measurements of specific heat of an amorphous $Ti_{9.5}Si_{90.5}$ alloy located very close to the critical point of the metal-insulator transition. In the presence of a magnetic field, the specific heat is dominated by the Schottky anomaly caused by magnetic moments associated with the dangling bonds in the matrix of amorphous Si. Subtraction of this contribution exposes the behavior of the electronic specific heat coefficient $\gamma$. The coefficient is temperature-independent above 2 K and is, in order of magnitude, close to the value expected in the absence of electron-electron interactions. In the temperature range 0.4-1.5 K, the coefficient $\gamma$ shows an anomalous downturn, which can be approximated by the dependence $\gamma\left(T\right)=\gamma_0ln{(T/T_0)}$, with $T_0\approx0.2$ K . In a companion paper, we found that the Hall coefficient in Ti-Si alloys is affected by the electron-electron interaction up to much higher temperature of 150 K and also varies critically across the metal-insulator transition. We compare our results with theoretical predictions for three models, which can potentially explain the anomalous behavior of the specific heat: generalized non-linear $\sigma$ model, Coulomb glass, and many-body localization.

Strain effect on the electronic properties of graphdiyne

In this theoretical study, within the nearest neighbor tight-binding model and Green’s function technique, the density of states (DOS), electronic heat capacity (EHC), and Pauli magnetic susceptibility (PMS) of graphdiyne system under different strain values (5%, 9%, and 15%) are calculated and the results are compared with those of a graphdiyne monolayer without any strain. It is observed that with increasing strain, the band gap near the Fermi level of graphdiyne increases monotonously due to the decreased orbital overlap between C atoms. In addition, the intra-bandgaps and the van-Hove singularities are seen in the DOS curves of all systems. These lead to the Schottky anomaly peaks in the EHC and the crossovers in the PMS curves, which are divided into two low and high temperature regions. At vicinity of zero temperatures, with increasing strain, the EHC and PMS decrease. From the theoretical stand point, this phenomenon stems from the proportional relationship of the PMS and EHC with DOS.