Schottky Specific Heat Research Articles

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.

Low-temperature physical properties of a new orthorhombic compound Ce2Ir3Sb4

We have synthesized polycrystalline samples of a new orthorhombic compound Ce2lr3Sb4 and investigated their physical properties by measuring the magnetization, the electrical resistivity, and the specific heat down to 0.4 K. From the results of electrical resistivity measurements, it was found that Ce2Ir3Sb4 is a Kondo lattice compound. We found that Ce2Ir3Sb4 does not show any phase transition down to 0.4 K. The specific heat peak at 1.3 K is not due to a phase transition but due to the Schottky specific heat caused by the crystalline electric field splitting of the 4f level of Ce ions.

Change of electronic state in the noncentrosymmetric superconductor Th7Fe3

57Fe Mössbauer spectroscopy and specific heat measurements were performed for the noncentrosymmetric superconductor Th7Fe3. An explicit increase in the center shift δCS(T), normalised spectral area A(T)/A(1.5 K) and electric quadrupole splitting ΔEQ(T) is observed below 60 K. The temperature dependencies of δCS(T) and A(T)/A(1.5 K) follow the Debye model for , whereas ΔEQ(T) can be described by an empirical T3/2 equation in both two temperature ranges 2 K–T* and T*–300 K. The behaviour of ΔEQ(T) can more willingly be interpreted in terms of the Fe3+ charge distributions on the singlet (dxy) ground state, the doublet (dxz, dzy) of T2g and doublet () of Eg excited states, characterised by respective splitting energies Δ1 and Δ2. It is shown that the excited energies deduced from the 57Fe Mössbauer data are in good agreement with those of Schottky specific heat. We argue that the anomaly detected in hyperfine parameters and specific heat substantially associates with change in the electronic state of the Fe atoms. We are convinced that a precursor crystal-electric field (CEF) effect has undergone before the onset of superconductivity sets in at lower temperature and the present results would spur new interest to researchers about the interplay between CEF and superconductivity in noncentrosymmetric materials.

Schottky specific heat of the lightly Mn-substituted electron-doped SrTiO3

Large changes in the low-temperature specific heat (low-T C) by applying magnetic fields up to 9 Tesla were found in the lightly Mn-substituted electron-doped perovskites Sr1−xLaxTiO3. The changes in the low-T C are qualitatively well explained by the Schottky specific heat (CSch) of localized spins of the Mn 3d electrons in weak internal magnetic fields via itinerant electrons. According to the analysis by using the conventional model, the doped Mn ions are apparently not Mn4+ (S = 3/2) ions, but are Jahn-Teller active Mn3+ (S = 2) ions or mixtures of Mn3+ and Mn2+ ions. However, the actual numbers of localized spins estimated from CSch are about 30% smaller than the expected values. Part of the localized spins of the Mn 3d electrons may disappear due to Kondo coupling with the itinerant electrons, leading to the observed enhancement of the electronic specific heat coefficients.

Crystalline electric field schemes of Ce2NiGe6 and Ce2NiGe3

The splitting levels and corresponding wave functions of rare earth compounds Ce2NiGe6 and Ce2NiGe3 have been presented by taking into account the crystalline electric field. The influences of Ge content on rare earth ion ground state splitting also have been analysed. The first excited energy and overall splitting energy of Ce2NiGe3 coincides with the ones calculated by simulating Schottky specific heat.

Schottky effect in thei-Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant

The analysis of low-temperature specific heat of rare-earth (RE)-containing quasicrystals and periodic approximants and consequent interpretation of their electronic properties in the $T\ensuremath{\rightarrow}0$ limit is frequently hampered by the Schottky effect, where crystalline electric fields lift the degeneracy of the RE-ion Hund's rule ground state and introduce additional contribution to the specific heat. In this paper we study the low-temperature specific heat of a thulium-containing $i$-Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant, both being classified as ``Schottky'' systems. We have derived the crystal-field Hamiltonian for pentagonal symmetry of the crystalline electric field, pertinent to the class of Tsai-type icosahedral quasicrystals and their approximants, where the RE ions are located on fivefold axes of the icosahedral atomic cluster. Using the leading term of this Hamiltonian, we have calculated analytically the Schottky specific heat in the presence of an external magnetic field and made comparison to the experimental specific heat of the investigated quasicrystal and approximant. When the low-temperature specific heat $C$ is analyzed in a $C/T$ versus ${T}^{2}$ scale (as it is customarily done for metallic specimens), the Schottky specific heat yields an upturn in the $T\ensuremath{\rightarrow}0$ limit that cannot be easily distinguished from a similar upturn produced by the electron-electron interactions in exchange-enhanced systems and strongly correlated systems. Our results show that extraction of the electronic properties of RE-containing quasicrystals from their low-temperature specific heat may be uncertain in the presence of the Schottky effect.

Anomaly of Specific Heat in High Quality Single Crystal of PrAg2In

PrAg2In has a non-Kramers doublet Λ3 ground state, which is expected to show a quadrupolar phenomena. Although many studies have been devoted to investigate the novel features of PrAg2In, there is no clear result how to remove the degeneracy of quadrupolar moment because this compound has a Heusler structure, in which the substitution between Pr and In ions is inevitable. We therefore prepare a high quality single crystal of PrAg2In with the residual resistivity ratio of 14, which is much larger than that of the previous samples. We measure the magnetic susceptibility with the SQUID magnetometer down to T = 0.4 K and the specific heat in the magnetic fields up to H = 8T along [100] crystal direction down to T =0.1 K. The susceptibility is consistent with the CEF calculation. The specific heat shows a sharp peak at around Tp = 0.33 K. When the magnetic field is applied, the peak at TP does not move up to H = 2.5 T. In contrast, it shifts to higher temperatures with broadening above H = 2.5 T. The broad peak above H = 2.5 T is well reproduced by the Schottky specific heat due to the splitting of the Λ3 doublet in the magnetic fields. From these results, we conclude that a phase transition related to the r3 doublet occurs at around TP.

Anomalous Elastic Softening due to the Crystal Electric Field Effect and Successive Phase Transitions in the Yb-Based Heavy-Fermion Antiferromagnet YbIrGe

To investigate the crystal electric field effect and antiferromagnetic transitions at 2.4 and 1.4 K, we carried out ultrasonic measurements on the Yb-based heavy-fermion antiferromagnet YbIrGe. We found characteristic softening of the elastic moduli originating from a quadrupole interaction. By theoretical analyses of the transverse elastic moduli, the magnetic susceptibility, and the Schottky specific heat between 10 and 300 K, we determined the crystal electric field: the ground doublet and an excited doublet separated by 138 K. The moduli exhibit elastic hardening below both 2.4 and 1.4 K, suggesting a strong coupling between a strain and magnetic order parameters. We estimated the strain dependence of the transition temperature at 2.4 K along the a- and c-axes from the Ehrenfest relation for the first time.

Anomalous Schottky Specific Heat and Structural Distortion in FerromagneticPrAl2

Unique from other rare earth dialuminides, PrAl(2) undergoes a cubic to tetragonal distortion below T = 30 K in a zero magnetic field, but the system recovers its cubic symmetry upon the application of an external magnetic field of 10 kOe via a lifting of the 4f crystal field splitting. The nuclear Schottky specific heat in PrAl(2) is anomalously high compared to that of pure Pr metal. First principles calculations reveal that the 4f crystal field splitting in the tetragonally distorted phase of PrAl(2) underpins the observed unusual low temperature phenomena.

Magnetic behavior of single-crystalline RPd 3 S 4 (R=Ho and Er)

Abstract The magnetic properties of single-crystalline RPd 3 S 4 (R=Ho, Er) have been examined by the measurements of the specific heat C ( T , B ), magnetization M ( T , B ) and magnetic susceptibility M / B ( T ). The previous study using polycrystalline samples has reported that HoPd 3 S 4 and ErPd 3 S 4 show successive phase transitions above 0.5 K. However, the present measurements using the single-crystalline samples have revealed that HoPd 3 S 4 and ErPd 3 S 4 compounds do not show any phase transitions down to 0.5 K. The anomalies appeared in C ( T , B ) of both compounds could be understood as a Schottky specific heat of R nuclei and 4 f electrons.

Magnetic and Fermi Surface Properties in PrRh3B2

We have grown a single crystal of PrRh 3 B 2 with the hexagonal structure and measured the electrical resistivity, specific heat, de Haas–van Alphen oscillation, magnetic susceptibility, high-field magnetization, thermal expansion and magnetostriction. PrRh 3 B 2 is not a simple ferromagnet as reported previously, but a ferrimagnet with an ordering temperature T ord =3.6 K. The Schottky specific heat observed around 25 K and the large anisotropy of the magnetic susceptibility and magnetization are found to be well explained by the crystalline electric field (CEF) with a large overall CEF-splitting energy of 1080 K and a strong ferromagnetic exchange interaction along the [0001] direction. The topology of the Fermi surface in PrRh 3 B 2 is similar to that of the non-4 f reference compound LaRh 3 B 2 , exhibiting a quasi-one-dimensional character of the electronic states.

INFLUENCE OF CRYSTAL FIELD EXCITATIONS COUPLED TO LATTICE VIBRATIONS ON THERMODYNAMICAL PROPERTIES OF A TWO-LEVEL PARAMAGNET

A two-level crystal field model in the presence of the phonon field is considered. Spins are arranged on a lattice and weakly coupled to the lattice oscillations of small amplitudes. The anticommutator Green function perturbative method up to the second order in the coupling constant is applied to find thermodynamical quantities. The magnetic spectral function, describing the crystal field excitations, influences these quantities. The effect is studied numerically and illustrated in figures. In particular, the influence of the coupling on the Schottky specific heat is shown.

Magnetic Properties of the Pseudo-Ternary System Pr1-xNdxNiAl4

The magnetization and specific heat of the pseudo-ternary system Pr1-xNdxNiAl4 were studied using single crystals with x=0.0, 0.3, 0.5, 0.7 and 1.0. Experimental results reveal that there are two magnetic states in PrNiAl4 with transition temperatures, TN=8.1 K and T'N=6.9 K. The substitution of Nd for Pr in PrNiAl4 lowers TN. The lowest TN was found at x=0.7. The suppression of TN can be explained by the competing magnetic anisotropies of Pr and Nd ions. The specific heat of NdNiAl4 in high magnetic fields is quantitatively explained in terms of the Schottky specific heat anomaly.

Schottky Specific Heat due to the Tunneling Rotation of Methyl Groups in Deuterated (DMe-DCNQI)2Cu System

In the course of studies on thermal properties of (DMe-DCNQI) 2 Cu systems that exhibit a reentrant metal-insulator transition, we discovered a Schottky type of specific heat with a peak around 8 K. The peak value exceeds 25 J/mol·K. This type of anomaly is observed only on samples composed of molecules containing partially deuterated methyl groups, and was found to be originated from the rotation of deuterated methyl groups that occurs by quantum tunneling. From an analysis of the specific heat curve, we obtained information concerning the low lying energy level scheme of deuterated methyl group CH 2 D. It has a non-degenerated ground state and doubly degenerated first excited states located about 20 K above the ground state.

The estimation of the heat capacity of NpO2

The heat capacity Cp, mof NpO2was estimated for temperatures between 300 K and 1400 K. The Cp, mwas evaluated as a sum of three terms, phonon vibration Cph, m, dilation Cd, m, and Schottky specific heat Cs, m. The Cph, mand Cd,mwere calculated using the Debye temperature, Grüneisen constant and thermal expansion data obtained by high-temperature X-ray diffractometry. The coefficient of the linear thermal expansion (l.t.e.) for NpO2was given as a polynomial function up to T= 1573 K. The estimated Cp,mwas compared with that of previous studies. The present result at T= 300 K was 66.87 J · K−1· mol−1, which agreed well with previous results, 66.22 J · K−1· mol−1, measured by using calorimetry. The thermodynamic functions were given as a function of temperature.

Crystal-field effect on the hyperfine splittings, Mössbauer spectra and specific heat of Er 3+ in pyrogermanate and diglycollate hosts

Hyperfine splittings and the Mössbauer spectra (MS) of the two isomers 166Er and 167Er in the pyrogermanate (or ErPG) and diglycollate (or ErDG) hosts were calculated using the previously determined values of the crystal field (CF) parameters and the CF levels. MS for the 166 isomer in both the hosts show only 5 lines, whereas 27 lines are expected for the 167 isomer. In case of ErDG, the quadrupole interaction P increased considerably between 300 and 4 K, i.e., from 1.5 to 21.3 MHz in case of 166Er and from −1.0 to −14.0 MHz in 167Er. However for ErPG, the corresponding changes in P for both the isomers are insignificant ∼1 MHz. The hyperfine magnetic fields H hf in ErDG and ErPG were found to be nearly the same being equal to 4.4±0.01 MG because the g ∥-values are close, i.e., 10.31 and 10.58, respectively. Specific heat C p of ErPG was measured between 30 and 0.65 K and a sharp λ peak was detected with a transition temperature T N=0.95±0.01 K. The calculated hyperfine and Schottky specific heat components, C hf, and C sch, respectively showed peaks at 32 mK and 110 K. From the experimental results of C p , the lattice specific heat C L/ R in ErPG was found to be 3.34×10 −5 T 3 and the thermal characteristics of the magnetic specific heat C M was determined. The internal energy U M( T) was obtained from C M by numerical integration and its change Δ E/ R=[ U M(∞)/ R– U M(0)/ R] was found to be 1.02 K and the corresponding value of the Weiss constant θ in the ordered state was 2.01 K. The value of the exchange interaction constant | J ex/ k| and the dipole–dipole interaction constant for nearest neighbours were found to be ∼0.5 and ∼1.03 K, respectively. The molecular field ( H mol) for ErPG was equal to 4.1 kG. From future epr and MS measurements, interesting results are expected regarding the magnetic ordering in ErPG and the phase change in ErDG.

An examination of the estimation method for the specific heat of TRU dioxides: evaluation with PuO 2

This work set out to study the estimation method of the specific heat, C p, for the dioxides of the transuranic elements. C p was evaluated as a sum of three terms, contributions of phonon vibration, C ph, dilation, C d, and Schottky specific heat, C s, C ph and C d were calculated using the Debye temperature and Grüneisen constant obtained by high-temperature X-ray diffractometry. The method was applied to PuO 2. The estimated C p was in good accordance with the reported one measured using a calorimeter. The error in the estimation was small compared to that which arises from using the conventional method based on C p(298) and the melting temperature.

Measurements of the magnetic susceptibility and anisotropy of Tb 2Ge 2O 7 single crystal

Magnetic susceptibilities χ a and the anisotropy χ a − χ c =Δ χ in the ac-plane of the tetragonal crystal of Tb 2Ge 2O 7 or TbPG were measured between 300 and 23 K. The crystal field (CF) at the site of the Tb 3+ ion has a unique D 5h symmetry and the D 5h axis coincides with the c-axis of the tetragonal (D 4 4) crystal, which permitted easy determination of the thermal characteristics of molecular susceptibilities K ‖, K ⊥, K ̄ and the anisotropy Δ K= K ⊥− K ‖. It was found that at 300 K, Δ K was 31.3% of K ̄ and increased by 34.5 times at 23 K, becoming 107% of K ̄ , suggesting strong CF effect in TbPG. For analysing these results and the optical spectra reported earlier, the total Hamiltonian, consisting of the atomic and CF interactions, was diagonalized considering 66 intermediately coupled (IC) basis states of the 4f 8 ground configuration of Tb 3+ in the PG host, allowing J-mixing between the IC states. The best-fitted values of the atomic and CF parameters were E 1=6030, E 2=35, E 3=605, ξ so=1749, α=18, β=−673, γ=1918, B 20=470, B 40=571, B 60=2500, B 65=915 (all in cm −1). The lowest CF level was found to be a singlet followed by a doublet at 19.5 cm −1 above and the total CF splitting of the 7 F 6 ground term was 280 cm −1. The calculated value of the nuclear quadrupole splitting 〈Δ E Q〉 of the ground nuclear level of 159 Tb in TbPG changed from 3.186×10 −4 cm −1 (=0.204 mm/s) to 89.65×10 −4 cm −1 between 300 and 2 K. The Schottky specific heat C sh showed a maximum at 26 K and a hump is expected around 14 K in the C p versus T curve, calculated by substituting the value of the lattice component C L/ R=3.2±0.2 T 3×10 −5 of GdPG.

Study of the magnetic susceptibility and anisotropy properties of Tm 3+ diglycollate crystal for evaluating crystal field effects

The thermal characteristics between 300 and 26 K of the molecular magnetic susceptibilities K ∥ and K ⊥, obtained from the experimental studies of susceptibility K ̄ of the powdered sample and the anisotropy Δ K= K ⊥− K ∥ of a single crystal of Tm diglycollate (TmDG), were utilised to determine the crystal field parameters (CFP) and thereby to calculate the CF levels of the visible and UV spectra, electronic Schottky specific heat and the nuclear quadrupole splitting of 169Tm in TmDG. No phase change was observed up to 26 K.

Optical absorption spectra of doped in yttrium pyrogermanate crystal

This paper reports the low temperature absorption and Zeeman spectra of doped in yttrium pyrogermanate (YPG), which were studied for the first time. In this compound the site symmetry of , or the crystal field (CF) symmetry, was found to be , as present in other rare earth pyrogermanates, and not . The spectral results were analysed by diagonalizing the total Hamiltonian consisting of the atomic (electrostatic, spin-orbit and configuration interactions) and the CF interactions, in a basis of states spanning the entire ground configuration of in the intermediate coupling formalism, including J-mixing under CF. The best fitted free ion and CF parameters obtained were and (all in ). Using these parameters the thermal characteristics of molar magnetic susceptibilities , their anisotropy and the Schottky specific heat of in YPG were calculated. It was found that the calculated values of between 300 and 152 K but on cooling further was observed, i.e. the sign of was reversed below . The calculated values of exhibited a sharp peak at 24 K and a broad maximum at 156 K. These characteristics were similar to other compounds studied earlier.