Comment on the low temperature specific heat of ferroelectrics,antiferroelectrics, and related materials

Lawless has reported accurate, low temperature (2–30°K) specific heat measurements (C_Exp) of a large number of ferroelectrics, antiferroelectrics, and related materials. A plot of C_Exp T^?3 vs. T (T is temperature) reveals an “excess’ specific heat in the 10–30K range. Lawless has interpreted and fit this excess heat with an Einstein term determining the number of oscillators and the Einstein frequence for each material. He has related these large number of extra oscillators to modes observed in some Raman experiments. Using a more realistic density of states, we suggest that the experimental data can be understood in terms of straightforward harmonic lattice dynamics and that there are no extra modes. The “extra” heat capacity merely arises from the differences between the more realistic density of states and that of a Debye solid.     

Low temperature specific heat of single-domain and polydomain ferroelectric NaNO2

The specific heat of a NaNO₂ sample has been measured between 2 K and 40 K in both single-domain and polydomain states. In this region the specific heat of the single domain sample follows exactly the T³ dependence. A clear excess contribution which in this temperature range has a temperature dependence between T and T² has been detected for the polydomain sample. It is attributed to domain walls.     

Low temperature specific heat of bi-layered manganites La2−2xSr1+2xMn2O7 (x=0.3 and 0.5)

The specific heat (C) of bi-layered manganites La_2−2xSr_1+2xMn₂O₇ (x=0.3 and 0.5) is investigated for the ground state of low temperature excitations. A T^3/2 dependent term in the low temperature specific heat (LTSH) is identified at zero magnetic field and suppressed by magnetic fields for x=0.3 sample, which is consistent with a ferromagnetic metallic ground state. For x=0.5 sample, a T² term is observed and is consistent with a two-dimensional (2D) antiferromagnetic insulator. However, it is almost independent of magnetic field within the range of measured temperature (0.6-10 K) and magnetic field (6 T).     

The specific heat of potassium holmium double tungstate

The results of measurements of thermal properties (specific heat) of potassium holmium double tungstate KHo(WO₄)₂ as a function of temperature (from 0.5 to 300?K) and magnetic field (up to 2?T) are presented. The total specific heat without the phonon and Schottky contributions is found to have the anomaly with maximum at T _SPT?～?5?K. This anomaly is likely related with the structural phase transition (SPT) caused by the cooperative Jahn–Teller effect. The increase of specific heat at very low temperatures and its shift towards high temperatures with increasing magnetic field are observed. The origin of this behaviour can be connected with possible magnetic phase transition induced by magnetic field.     

Low-temperature specific heats of lanthanum and yttrium phosphate glasses

Summary The specific heats of (R₂O₃) _x (P₂O₅)_1−x glasses containing high concentrations of La³⁺ and Y³⁺ ions have been measured between 1.5K and 30K. It is shown that, in addition to the usual Debye contribution, there is an excess specific heat arising from localized vibrational states which has been discussed in terms of two distinct models. The first predicts a maximum in the temperature dependence of the excess specific heat associated with the crossover frequency from phonon to fracton behaviour. The phonon-fracton density of states used to fit the excess specific heat gives rise to model parameters having the same magnitudes as those found previously for other glasses including samarium phosphates. The second model, formulated on the basis of soft vibrations in glasses, predicts a minimum in the excess specific heat, which is also observed. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Capanello, Italy, July 4–8, 1994.     

Non-linear temperature dependence of the low temperature specific heat of vitreous B2O3

The specific heat of virteous B₂O₃ has been measured between 50 mK and 1 K. The excess to the calculated acoustic term is found to vary as T^1.45 below 0.7K as opposed to the linear law generally observed. This may be attributed to the particular structure of this glass.     

The specific heat of CeAl2 between 0.02 and 1 K

We report specific heat measurements on a CeAl₂ single crystal between 0.02 and 1 K. Above 0.08 K, we found C₀ = γT + βT³ with γ = (130±0.5) mJ/K²mole and β = (142±1) mJ/K⁴mole in good agreement with previous results above 0.3 K. Below 0.08 K, an excess specific heat C_N = αT^?2 with α = (6.4±1) mJK/mole was detected and interpreted in terms of hyperfine splitting of the Al²⁷ nuclear states. Our results suggest that in CeAl₂ (complex) antiferromagnetism coexists with the Kondo effect at least down to 20 mK.     

On the phonon Hall effect in a paramagnetic dielectric

The phonon Hall effect in the paramagnetic dielectric garnet Tb₃Ga₅O₁₂ has been investigated. It has been found that the coefficient of the phonon Hall effect is positive and is equal to (3.5 ± 2) × 10^?5T^?1 in a magnetic field of 3 T at a temperature of 5.13 K. The results are experimental evidence of the phonon Hall effect in the paramagnetic dielectric found by C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phys. Rev. Lett. 95, 155901 (2005).     

Specific heat of La(Fe<Subscript>0.873</Subscript>Co<Subscript>0.007</Subscript>Al<Subscript>0.12</Subscript>)<Subscript>13</Subscript> compound in antiferromagnetic and ferromagnetic states

The low-temperature specific heat C _p of La(Fe_0.873Co_0.007Al_0.12)₁₃ compound has been measured in two states: (i) antiferromagnetic (AFM) with a Néel temperature of T _N = 192 K and (ii) ferromagnetic (FM). The FM order appears at T = 4.2 K in a sample exposed to an external magnetic field with induction B _C ≥ 2.5 T and is retained for a long time in a zero field at temperatures up to T*_C = 23 K. The coefficient γ_FM in the low-temperature specific heat C = γT + βT ³ in the FM state differs quite insignificantly from that (γ_AFM) in the AFM state. Contributions to the low-temperature specific heat, which are related to a change in the elastic and magnetoelastic energy caused by magnetostrictive deformations, are considered.     

Effect of magnetic annealing on phonon behaviors of nanocrystalline BiFeO3

Influence of magnetic annealing at 823 K up to 10 T (T) on the phonon behaviors of nanocrystalline BiFeO₃ was investigated by Raman spectroscopy. The frequencies of fundamental Raman modes increase obviously with increasing annealing magnetic field, and the intensity of the 1260 cm⁻¹ two-phonon mode decreases. The pronounced anomalies of Raman phonon modes under magnetic annealing are attributed to the change of the spin-phonon coupling due to the modulation of spiral spin order. Furthermore, the temperature dependence of Raman peak positions, for the two prominent modes (147 and 176 cm⁻¹), show no notable anomaly around T_N except the sample annealed under 10 T magnetic field; meanwhile, in this sample, another obvious phonon anomaly occurs at ∼150 K (another magnetic phase transition point), which indicate that stronger magnetic annealing with 10 T intensely enhances the spin-phonon coupling, and possibly increases magnetoelectric coupling of nanocrystalline BiFeO₃ due to severely modulation of spiral spin order.     

Effect of structural relaxation on low energy excitations in amorphous Zr x Cu1−x

We report on an investigation of the liquid-quenched metallic glass Zr _x Cu_1?x (0.6≦x≦0.74) subjected to heat treatments below the glass transition temperatureT _g. Annealing temperatures up to 200°C (<0.8T _g) were chosen as to achieve topological relaxation only. The superconducting transition temperaturesT _c are lowered, as already observed for other metallic glasses. Low temperature measurements of the thermal conductivity (0.5 K≦T≦15 K) and of the specific heat (0.1 K≦T≦3 K) were carried out in order to determine the effect of structural relaxation on the low energy configurational excitations characteristic of the amorphous state. The annealed samples show no detectable (<20%) change in the specific heat forT?T _c, but an increase of the thermal conductivity by a factor of 2 forT?T _c is observed. Within the tunneling model of two level systems (TLS) for the low energy excitations, this behavior can be qualitatively understood in terms of a change of the TLS relaxation time distribution upon annealing. This distribution differs from that of the commonly used standard tunneling model. The change of the phonon scattering by TLS directly observed forT?T_c is largely responsible for the enhancement of the thermal conductivity found also aboveT _c.     

Specific heat and latent heat of KMnF3 ferroelastic crystal

The specific heat and the heat flux exchanged by a single crystal of KMnF₃ have been measured simultaneously while cooling the sample at constant rate of 0·06 K/h through the phase transition at T ₀= 186 K. The phase transition is weakly first order and close to a tricritical point. The temperature dependence at T185 K of the excess specific heat and the excess entropy follow very well the predictions of a Landau potential at a tricritical point.     

Specific heat of Na1−x V2O5 single crystals

Temperature dependences of the specific heat C and the magnetic susceptibility χ of Na_1?x V₂O₅ single crystals (x=0, 0.01, 0.02, 0.03, and 0.04) are studied. In NaV₂O₅, the transition to the spin-gap state (T _c =34 K) is accompanied by a sharp decrease in χ, while C exhibits a λ-shaped anomaly. At low temperatures, the specific heat of NaV₂O₅ is approximated by the sum of phonon ～T ³ and magnon ～exp(?Δ/T) contributions, which makes it possible to estimate the Debye temperature Θ_D=336 K and the gap in the magnetic excitation spectrum Δ=112 K. With the departure from stoichiometry, the anomalies observed in the behavior of χ and C are spread and shifted to lower temperatures. The low-temperature specific heat of nonstoichiometric samples is determined by the sum of phonon and magnon components and the contribution due to the presence of defects. The values of magnetic entropy characterizing the phase transitions in Na_1?x V₂O₅ are calculated.     

单晶NdMnO3的比热研究

研究了低温下NdMnO₃单晶的比热随温度和磁场的变化(2K≤T≤200K，0T≤H≤8T ).对应于 Mn磁矩亚晶格的A型反铁磁(A-AF)相变，零场下的比热曲线在85K附近出现尖锐的λ形峰，随 着磁场的增加，此λ峰降低展宽而且平滑变化，这与此温度附近磁化强度的变化规律一致. 与磁有序相变相关的熵变约为理论值的26％，这可能是由于磁有序涨落延续在较大温区造成 的.在20K以下，比热曲线出现了明显的肩膀形状的Schottky反常，其峰值随着磁场的增加而 逐渐向高温移动.考虑了低温下比热的各种贡献，根据Nd³⁺位有效分子场(H _mf) 引起的Nd^3＋基态双重态(GSD)劈裂对上述现象进行了解释.通过对2K≤T≤2 0K，0Ｔ≤ H≤8T范围内比热数据的拟合，得到了样品的GSD劈裂，德拜温度和A-AF自旋波劲度系数以及 它们对磁场的依赖关系.发现GdFeO₃型八面体旋转引起的A-AF结构中Mn磁矩亚晶 格的铁磁成分可能是H_mf的来源. 关键词： 比热 Schottky反常 反铁磁相变     

Low temperature heat capacity and magnetic excitation of HoAl2 in a magnetic field

The specific heat of single crystalline HoAl₂ in magnetic fields up to 7.5 T has been measured for the temperature range 1.5–16 K. In addition the energy of a magnetic excitation in a magnetic field of 5 T at 4.2 K has been determined by inelastic neutron scattering. The results have been interpreted with a cubic crystalline electric field and an exchange interaction using the same parameter set B₄=-0.85×10^-4 meV, B₆=+0.71× 10^-6 meV and T_C=31.5 K previously obtained by magnetization measurements.     

A specific heat and magnetization study of highT c ceramic superconductors

From the temperature dependence of the specific heat of the semiconductor La₂CuO₄ and the high temperature superconductors La_1.8Sr_0.2CuO₄ (T _c =37.2 K) and YBa_1.9K_0.1Cu₃O_6.9 (T _c =91.5 K) in the range 1.5–30 K, a strong similarity of the lowfrequency part of their phonon density of states with a peak around 10 meV could be inferred. In the case of La_1.8Sr_0.2CuO₄ the thermodynamical critical field belowT _c has been determined and using the Rutger's formula and the BCS model, a Sommerfeld coefficient γ=9 mJ·mol^?1 K^?1 was obtained, which, taking into account recent results of band structure calculations leads to an electron-phonon enhancement factor γ=1.3, value compatible withT _c =36 K when using McMillan's formula forT _c . A systematic study of the magnetization offered evidence for strong flux trapping effects at higher fields and for Meissner shielding by superconducting Josephson currents in fields below 6 mT at 4.2 K.     

The specific heat of Y0.7Th0.3C1.58

The specific heat of the novel high temperature superconductor Y_0.7Th_0.3C_1.58 (T_c = 17.0 K) has been measured between 4 and 22 K. Unlike the other known high temperature superconductors (T_c > 16 K) which have either an A-15 or a NaCl-type structure, this material forms in the b.c.c., Pu₂C₃-type, structure. The Debye temperature, θ_D, is 346 K and the linear term coefficient, γ, of the specific heat has the value 4.66 mJ/mole-K². Thus the electronic density of states, N(0), which is proportional to γ, is quite low. The energy gap, 2Δ/kT_c, on the other hand has an anomalously high value of 5.8. Comparisons between these parameters of Y_0.7Th_0.3C_1.58 and those for some A-15 and NaCl-type superconductors are made.     

Specific heat of V6O11 between 0.4 and 50 K

The specific heat of 3 sets of V₆O₁₁ single crystals has been measured between 0.4 and 50 K. This compound is an insulator below 170 K; the specific heat shows a λ-type anomaly at 24 K, T_N and linear term above this temperature. The features of the specific heat can be understood if a model of independent antiferromagnetic chains above T_N is postulated. The λ-type anomaly arises as a consequence of the weak interactions between the chains and the one dimensional system changes to a three dimensional system.     

Features of the low-temperature specific heat in underdoped YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6 + <Emphasis Type="Italic">x</Emphasis></Subscript> single crystals

The behavior of the low-temperature specific heat C(T) for YBa₂Cu₃O_{6 + x} single crystals with the doping level corresponding to the normal phase has been studied by the relaxation technique at different values of the applied magnetic field. It has been found that the C(T)/T plot exhibits such an anomaly as a steep increase with decreasing temperature from T about 4 K down to T ≤ 2 K (the minimum temperature value accessible in the experiment). The applied magnetic field as high as 9 T inverts this anomaly and leads to a sharp drop in C(T)/T during cooling within the same temperature range. A model involving the Schottky-type centers formulated in this work and the data on spin correlation functions has allowed us to calculate the temperature dependence of the specific heat, which fits the experimental curves quite well.