Schottky Anomaly Research Articles

Heat capacity, electrical and thermal conductivity of silicene

We investigate the electronic heat capacity, electrical and thermal conductivity of monolayer planar and buckled silicon sheets (silicene) through tight binding approximation and Kubo-Greenwood formula. Applying and increasing dopant atoms to the system leads to opening a gap in the band structures and density of states that causes to decrease (increase) the heat capacity before (after) the Schottky anomaly. The electrical and electronic thermal conductivity of doped silicene reduces with increasing impurity strength.

Role of Spin–Orbit Interaction and Impurity Doping in Thermodynamic Properties of Monolayer MoS2

Using linear response theory, a tight-binding Hamiltonian model, and the Green’s function technique, the influences of spin–orbit interaction (SOI) and impurity doping on the electronic heat capacity (EHC) and magnetic susceptibility (MS) of monolayer MoS2 have been investigated. The effect of scattering on dilute charged impurities is discussed in terms of the self-consistent Born approximation. We have calculated the temperature dependence of the EHC and MS for different values of SOI, concentration, and scattering strength of dopant impurity. The results show that, in the presence of impurities, the heat capacity of MoS2 decreases (increases) before (after) the Schottky anomaly, as does the MS. It is also found that the EHC and MS of the doped MoS2 reduce with the SOI in all temperature ranges.

Magnon heat capacity and magnetic susceptibility of the spin Lieb lattice

Using linear response theory, Heisenberg model Hamiltonian and Green's function technique, the influences of Dzyaloshinskii–Moriya interaction (DMI), external magnetic field and next-nearest-neighbor (NNN) coupling on the density of magnon modes (DMM), the magnetic susceptibility (MS) and the magnon heat capacity (MHC) of a spin Lieb lattice, a face-centered square lattice, are investigated. The results reveal a band gap in the DMM and we witness an extension in the bandwidth and an increase in the number of van-Hove singularities as well. As a notable point, besides the magnetic nature which includes ferromagnetism in spin Lieb-based nanosystems, MS is investigated. Further, we report a Schottky anomaly in the MHC. The results show that the effects of the magnetic field on the MHC and MS have different behaviors in two temperature regions. In the low temperature region, MHC and MS increase when the magnetic field strength increases. On the other hand, the MHC and MS reduce with increasing the magnetic field strength in the high temperature region. Also comprehensive numerical modelling of the DMM, the MS and the MHC of a spin Lieb lattice yields excellent qualitative agreement with the experimental data.

Low-temperature specific heat and magnetic properties of the filled skutterudite ferromagnet NdRu4As12

Abstract We present the low-temperature specific heat and magnetic properties of the filled skutterudite compound NdRu4As12 that exhibits a ferromagnetic transition at T C ≃ 2.3 K . Magnetic entropy considerations point at a quartet ground state of the Nd 3 + ions. Deep in the ferromagnetic state, the heat capacity shows a Schottky anomaly that we ascribe to the Zeeman splitting in the presence of a molecular field. Comparison of the specific heats of NdRu4As12 and its Os-based homologue near their Curie temperatures supports our earlier observation suggesting an unusual lowering of the Th cubic point symmetry in the latter filled skutterudite.

Internal field emission nature of the fine structure of tunnel spectra in icosahedral quasicrystals

Calorimetric and tunnel data for the icosahedral phases of the Al–Cu–Fe system have been jointly analyzed. It has been found that the field-dependent part of the tunnel conductance can be represented as the sum of elementary terms similar in nature to thermal Schottky anomalies. As a result, the features of the fine structure of tunnel spectra in the form of zero-bias anomalies, peaks, and humps can be due to the internal field emission and can indicate a wide distribution of two-level electron traps in the electronic structure of quasicrystals. It was previously assumed that these features constitute a direct image of the density of single-electron states of the conduction band.

Thermal properties of the Nd1−xCaxBaCo2O5.5 compositions (0 ≤ x ≤ 0.2)

Layered cobaltites RBaCo2O5.5, considered for application as cathodes of fuel cells, exhibit a rich spectrum of magnetic and electronic properties. Taking advantage of the fact that Nd3+ and Ca2+ ions have nearly identical ionic radii, by synthesizing the Nd1−xCaxBaCo2O5.5 compounds (for x=0, 0.02, 0.06, 0.08, 0.16, and 0.2), a hole doping was realized, without significant disturbing the crystalline structure and the ordering of oxygen vacancies. In order to study the influence of the hole doping on thermal properties of these compositions, specific heat studies were performed over the temperature range from 2 to 395 K. The main, i.e., lattice, magnon and Schottky, contributions to the specific heat were separated from the total specific heat measured and described theoretically. In particular, the lattice contribution was described by combining the Debye and the Einstein models, whereas the magnon specific heat was described in frames of a model developed for anisotropic magnetic materials (A. I. Akhiezer et al., Sov. Phys. Usp. 3 (1961) 567). Changes of width and height of a specific heat anomaly accompanying the insulator-metal phase transition, appearing unmonotonously as a function of x, were ascribed to small deviations of the oxygen content from the assumed stoichiometry and to non-uniformity of the oxygen content over the sample volume. Smearing of specific heat anomalies related to magnetic phase transitions was found and attributed tentatively to disorder introduced by nonuniform distribution of the calcium ions within (Nd,Ca)–O planes. An impact of the calcium substitution on the position of the Schottky anomaly, related to thermal excitations of the Nd3+ ions, was found and interpreted qualitatively as a side effect of the hole doping, which causes also deformations of the crystalline structure and affects the magnetic structure of the Co sublattice.

Schottky anomaly in a repulsive lattice polymer

We examine the specific heat of a self-avoiding polymer on a square lattice with repulsive interactions, which exhibits the Schottky anomaly, a peak in the low-temperature region without a divergence in the thermodynamic limit. The low-temperature tail of the specific heat can be explained by the bending energy imposed due to repulsive next-nearest-neighbor interactions, which play the role of local interactions along the chain. For comparison, the specific heat of a polymer without nonlocal self-exclusion is also considered, wherein only the bending energy is present, which is analytically solvable. The specific heat of the self-avoiding repulsive next-nearest-neighbor polymer is also shown to be robust with respect to the addition of repulsive nearest-neighbor interactions, which act only as nonlocal perturbations causing a slight change in the specific heat in the high-temperature region. We also discuss the relevance of the lattice effect in the context of real polymers.

Electronic heat capacity and thermal conductivity of armchair graphene nanoribbons

Using the Green’s function formalism and tight-binding Hamiltonian model in the band representation, for various widths of armchair graphene nanoribbons, the band structure, density of states, and temperature dependence of the heat capacity and thermal conductivity are considered for the electronic contribution per single width of the ribbons. Observed for various widths are similar peaks of Schottky anomaly, but with a tiny departure toward higher temperatures and a slight decline (rise) before (after) it for wider ribbons. Furthermore, the thermal conductivity decreases as the width of the ribbon gets larger, owing to the overlap between the nonhybridized \(p_{z}\) orbitals which provide literal paths across the ribbon to distract a part of the electron’s drift from the axial direction.

Schottky anomaly and hadronic spectrum

We show that the hadronic "heat capacity" calculated as a function of temperature may be used to infer the possible presence of different scales underlying the dynamical structure of hadronic resonances using the phenomenon of Schottky anomaly. We first demonstrate this possibility with well known meson spectrum in various channels and comment on the possibility of using this method as a diagnostic to distinguish the exotic states.

Analytic model of the Schottky anomaly and phase transition

The Schottky anomaly is a peak in the specific heat at low temperatures without divergence, in contrast to a phase transition which is characterized by a singularity of a physical quantity. A model with the analytic form of a density function, where both the phase transition and the Schottky anomaly appear depending on the limit of the model parameters, is presented. The model allows a unified analytic treatment of the phase transition and the Schottky anomaly.

Low-lying magnetic excitations and magnetocaloric effect of molecular magnet K6[V15As6O42(H2O)] · 8H2O

Low-temperature heat capacity measurements were performed on the molecular nanomagnet (V15). The low-lying magnetic excitations are clearly evidenced by the Schottky anomalies in the specific-heat data. The energy levels determined from the low-temperature observables agree well with the three-spin model for V15. The magnetocaloric effect of V15 is examined. The maximum entropy change of is found for a field change of at . In spite of the low ground-state spin of V15, a drastic entropy change of is observed for a field change of at 0.4 K, which is comparable to the entropy change of some high-spin sub-kelvin magnetic coolers at such low temperatures. Anisotropy and consequent zero-field splitting result in this characteristic of V15 and may open new possibilities in the design of ultra-low-temperature molecular coolers.

Electronic, magnetic, transport, and thermal properties of single-crystallineUFe2Al10

The valence and core-level x-ray photoemission spectra (XPS), performed on an $\mathrm{UF}{\mathrm{e}}_{2}\mathrm{A}{\mathrm{l}}_{10}$ single crystal, were measured using the Al K\ensuremath{\alpha} radiation. The results of valence XPS show practically two separate regions of spectral intensity, one just at the Fermi level $({E}_{\mathrm{F}})$ and the other one being a wide content with its maximum at about $0.8\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ below ${E}_{\mathrm{F}}$. These give rise to two electronic configurations of the $5f$ states in the studied aluminide, itinerant and localized ones, i.e., their dual character. In such a situation the corresponding valence spectra, calculated within the local density approximation (LDA), well explain the former configuration, being responsible for a metallic behavior of the studied compound. Moreover, this behavior is confirmed clearly also by our results of magnetotransport measurements. On the other hand, the obtained magnetic susceptibility, specific heat, electrical resistivity, and thermoelectric power data support very well the local character of the $5{f}^{2}$-electron configuration of the ${\mathrm{U}}^{4+}$ ion in $\mathrm{UF}{\mathrm{e}}_{2}\mathrm{A}{\mathrm{l}}_{10}$ having the orthorhombic and cage-type crystal structure. Based on that configuration, the magnetic and thermal characteristics of the compound were modeled by the effective crystal field (CF) potential in the intermediate coupling scheme using initial parameters obtained by the angular overlap model (AOM). The obtained final CF parameters yielded the CF level scheme, composed of only singlets, proper for orthorhombic symmetry. Such a set of singlets reproduces in a satisfactory way both the strongly anisotropic temperature variations of the magnetic susceptibility, measured along the three main crystallographic directions, as well as the Schottky anomaly, evaluated using specific heat results of isomorphic $\mathrm{ThF}{\mathrm{e}}_{2}\mathrm{A}{\mathrm{l}}_{10}$ as a phonon reference. Also, the strongly anisotropic behavior of the Seebeck coefficient and its low temperature maxima observed for the compound studied here have been explained roughly by the CF effect.

Magnetic susceptibility and heat capacity of graphene in two-band Harrison model

Using a two-band tight-binding Harrison model and Green's function technique, the influences of both localized σ and delocalized π electrons on the density of states, the Pauli paramagnetic susceptibility, and the heat capacity of a graphene sheet are investigated. We witness an extension in the bandwidth and an increase in the number of Van-Hove singularities as well. As a notable point, besides the magnetic nature which includes diamagnetism in graphene-based nanosystems, a paramagnetic behavior associated with the itinerant π electrons could be occurred. Further, we report a Schottky anomaly in the heat capacity. This study asserts that the contribution of both σ and π electrons play dominant roles in the mentioned physical quantities.

Thermal properties of [Cr(NH3)6](BF4)3 studied by adiabatic and relaxation calorimetry

Four (solid–solid) phase transitions were detected in the temperature range of (9 to 300)K in polycrystalline [Cr(NH3)6](BF4)3 at TC1=240.7K, TC2=108.0K, TC3=91.9K, and TC4=61.3K by adiabatic calorimetry. The measurements by relaxation calorimetry were followed on lowering temperature from 20K down to 0.35K under six different external magnetic field values (9, 7, 5, 3, 1 and 0)T. For non-zero values of applied magnetic field well-defined Schottky anomaly appears. Magnetic heat capacity was calculated assuming the zero-field splitting for the decoupled Cr(III) ions. There is no discrepancy between the observed and calculated values. Isothermal magnetization curve recorded up to 5T was measured at temperature of 1.8K.

Thermodynamic properties of multiferroic Mg doped YbMnO3

Calorimetric studies of polycrystalline samples Yb1−xMgxMnO3 with x=0.0 and 0.05 are reported. It is revealed that the Mg doping raises the antiferromagnetic ordering temperature, TN, from 83K for x=0.0 to 86K for x=0.05. A ferromagnetic ordering is also observed around 3K. The broad feature in the specific heat data just above ferromagnetic ordering, is attributed to the Schottky anomaly. The estimated effective molecular fields from the Schottky analysis are Hmf=3.0 and 3.5T for YbMnO3 and Yb0.95Mg0.05MnO3, respectively. High temperature shift of Schottky anomaly with Mg doping indicates increase in effective molecular field of Mn at the Yb 4b site. The data supports that the idea that although molecular field is mainly responsible for the Schottky anomaly in Yb1−xMgxMnO3 and Mn3+ spin ordering also affects it. Magnetic part of the specific heat is obtained by subtracting the lattice contribution estimated using two Debye temperatures. The magnetic entropy change (ΔSmag) for pure and doped samples are 2.0Jmol−1K−1 and 2.1Jmol−1K−1 respectively, while the relative cooling power (RCP) calculate 26.1J/mol, 27.2J/mol for a field change of 10T.

Crystal growth and magnetic properties of equiatomic CeAl

Single crystal of CeAl has been grown by flux method using Ce-Al self-flux. Several needle like single crystals were obtained and the length of the needle corresponds to the [001] crystallographic direction. Powder x-ray diffraction revealed that CeAl crystallizes in orthorhombic CrB-type structure with space group Cmcm (no. 63). The magnetic properties have been investigated by means of magnetic susceptibility, isothermal magnetization, electrical transport, and heat capacity measurements. CeAl is found to order antiferromagnetically with a Neel temperature TN = 10 K. The magnetization data below the ordering temperature reveals two metamagentic transitions for fields less than 20 kOe. From the inverse magnetic susceptibility an effective moment of 2.66 μB/Ce has been estimated, which indicates that Ce is in its trivalent state. Electrical resistivity data clearly shows a sharp drop at 10 K due to the reduction of spin disorder scattering of conduction electrons thus confirming the magnetic ordering. The estimated residual resistivity ratio (RRR) is 33, thus indicating a good quality of the single crystal. The bulk nature of the magnetic ordering is also confirmed by heat capacity data. From the Schottky anomaly of the heat capacity we have estimated the crystal field level splitting energies of the (2J + 1) degenerate ground state as 25 K and 175 K respectively for the fist and second excited states.

Lattice vacancies responsible for the linear dependence of the low-temperature heat capacity of insulating materials

The linear dependence on temperature $(\ensuremath{\gamma}T)$ of the heat capacity at low temperatures $(Tl15\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ is traditionally attributed to conduction electrons in metals; however, many insulators also exhibit a linear dependence that has been attributed to a variety of other physical properties. The property most commonly used to justify the presence of this linear dependence is lattice vacancies, but a correlation between these two properties has never been shown, to our knowledge. We have devised a theory that justifies a linear heat capacity as a result of lattice vacancies, and we provide measured values and data from the literature to support our arguments. We postulate that many small Schottky anomalies are produced by a puckering of the lattice around these vacancies, and variations in the lattice caused by position or proximity to some form of structure result in a distribution of Schottky anomalies with different energies. We present a mathematical model to describe these anomalies and their distribution based on literature data that ultimately results in a linear heat capacity. From these calculations, a quantitative relationship between the linear term and the concentration of lattice vacancies is identified, and we verify these calculations using values of $\ensuremath{\gamma}$ and vacancy concentrations for several materials. We have compiled many values of $\ensuremath{\gamma}$ and vacancy concentrations from the literature which show several significant trends that provide further evidence for our theory.

Investigating spin reversal and other anomalies in magnetic, transport and specific heat measurements of NdFeO3 and NdFe0.5Ni0.5O3 ortho-perovskites

Specific heat versus temperature. Lower inset: zero-field data with the fitting result. Upper inset: specific heat versus temperature at different magnetic fields near a Schottky anomaly in (a) NFO and (b) NFNO.

Phase transition properties of the Bell-Lavis model.

Using Monte Carlo calculations we analyze the order and the universality class of phase transitions into a low-density (honeycomb) phase of a triangular antiferromagnetic three-state Bell-Lavis model. The results are obtained in a whole interval of chemical potential μ corresponding to the honeycomb phase. Our results demonstrate that the phase transitions might be attributed to the three-state Potts universality class for all μ values except for the edges of the honeycomb phase existence. At the honeycomb phase and the low-density gas phase boundary the transitions become of the first order. At another, honeycomb-to-frustrated phase boundary, we observe the approach to the crossover from the three-state Potts to the Ising model universality class. We also obtain the Schottky anomaly in the specific heat close to this edge. We show that the intermediate planar phase, found in a very similar antiferromagnetic triangular Blume-Capel model, does not occur in the Bell-Lavis model.

Generalized Schottky anomaly

The Schottky anomaly in the specific heat is one of the most universal phenomena in nature. The generalized Schottky anomaly for the combined system of two Hamiltonians \(\mathcal{H}_1 = - \mu B\sum\nolimits_i {\sigma _i }\) (B: magnetic field) and \(\mathcal{H}_2 = - J\sum\nolimits_{\left\langle {i,j} \right\rangle } {\sigma _i \sigma _j }\) (J: coupling constant), both showing the Schottky anomaly, is systematically investigated for the first time. For a small magnetic field, we find the new fact that the maximum of the Schottky anomaly increases sharply and the Schottky temperature falls and then rises (making a sharp v shape) as the magnetic field B is increased. For a large magnetic field, as B increases, the maximum of the Schottky anomaly decreases, and the Schottky temperature increases gradually, in agreement with recent experimental measurements.