Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Low-temperature anomalies in MgB<Subscript>2</Subscript> thermal expansion

The thermal expansion coefficient α(T) of MgB₂ was measured at low temperatures both in a zero magnetic field and at H=36 kOe. As in the oxide HTSCs, a region of anomalous (negative) thermal expansion and a strong effect of magnetic field on α(T) were revealed. The results obtained indicate the anomalous properties of MgB₂ and the oxide HTSCs to follow a common pattern.     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

Thermophysical study of structural phase transitions in Na<Subscript>0.95</Subscript>Li<Subscript>0.05</Subscript>NbO<Subscript>3</Subscript> solid solution

Temperature dependences of specific heat C_p(T) and coefficient of thermal expansion ;(T) for Na_0.95Li_0.05NbO₃ sodium-lithium niobate ceramic samples are investigated in the temperature range of 100–800 K. The C_p(T) and α(T) anomalies at T₃ = 310 ± 3 K, T₂ = 630 ± 8 K, and T₁ = 710 ± 10 K are observed, which correspond to the sequence of phase transitions N ? Q ? S(R) ? T2(S). The effect of heat treatment of the samples on the sequence of structural distortions was established. It is demonstrated that annealing of the samples at 603 K leads to splitting of the anomaly corresponding to the phase transition Q → R/S in two anomalies. After sample heating to 800 K, the only anomaly is observed in both the C_p(T) and ;(T) dependence. Possible mechanisms of the observed phenomena are discussed.     

Specific features in thermal expansion of <Emphasis Type="Italic">R</Emphasis>Fe<Subscript>11</Subscript>Ti single crystals

Thermal expansion and its anomalies in the vicinity of spin-reorientation phase transitions in single crystals of RFe₁₁Ti (R=Y, Tb, Dy, Ho, and Er) compounds are investigated by the tensometric technique in the temperature range 77–400 K. The temperature dependences of the thermal expansion coefficient α(T) are obtained. It is found that the YFe₁₁Ti and HoFe₁₁Ti uniaxial magnetic materials exhibit pronounced anomalies in the α coefficient at T=200 and 290 K. For the TbFe₁₁Ti single crystal, the α coefficient is close to zero in the vicinity of the spin-reorientation phase transition (at T=325 K). For the DyFe₁₁Ti single crystal, which is characterized by two spin-reorientation phase transitions (at T=120 and 250 K), no features in the α(T) dependence are revealed in the region of the low-temperature spin-reorientation phase transition. In the ErFe₁₁Ti single crystal, the specific feature of thermal expansion is observed at T ～ 220 K.     

Crystallographic characteristics and phase transitions in the [N(C<Subscript>2</Subscript>H<Subscript>5</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CdBr<Subscript>4</Subscript> crystal in the low-temperature range

The results of x-ray structural studies of the [N(C₂H₅)₄]₂CdBr₄ crystal at low temperatures are presented. The unit cell parameters and the thermal expansion coefficients along the main crystallographic directions are measured at temperatures in the range from 90 to 320 K. The integrated intensities of the diffraction reflections are investigated as a function of the temperature. It is shown that the curves a = f(T), c = f(T), I ₅₀₀ = f(T), and I ₀₀₆ = f(T) at temperatures T ₁ ≈ 174 K and T ₂ ≈ 226 K exhibit anomalies in the form of abrupt changes in the lattice parameters and the diffraction reflection intensities. This indicates that the [N(C₂H₅)₄]₂CdBr₄ crystal undergo phase transitions at these temperatures. Moreover, there is an anomaly in the form of a small maximum at the temperature T ₃ = 293 K.     

Nature of low-temperature phase transitions in CaMn<Subscript>7</Subscript>O<Subscript>12</Subscript>

New data on the specific heat, thermal expansion, and magnetization of the CaMn₇O₁₂ phase require a revision of the current concepts of the sequence of phase transitions in this compound. It is found that a spin-glass phase transition occurs in CaMn₇O₁₂ at T _M = 49 K, whereas the transition at T _S = 89 K exhibits the features of a first-order phase transition and thereby is apparently of structural origin. In the range T _M < T< T _S , the CaMn₇O₁₂ compound exhibits negative thermal expansion, which is also indicative of structural changes.     

Thermal expansion behaviour and phase stability of AFe<Subscript>2</Subscript>As<Subscript>2</Subscript> (A = Ca,Sr and Eu) using powder diffraction technique

The thermal expansibilities and phase stabilities of AFe ₂As ₂ (A = Ca, Sr and Eu) have been investigated by powder diffraction techniques in the temperature range 5–600 K. We found the anisotropic thermal expansivities with temperature for all the compounds. The lattice parameter in the tetragonal phase ( A_T) of CaFe ₂As ₂ contracts with increasing temperature, whereas C_T expands. The rate of contraction in A_T is lower than the rate of expansion in C_T. Other compounds show normal thermal expansion behaviour along both a- and c-axes. In-plane expansion (i.e., along the a-axis) is found to be the smallest for EuFe ₂As ₂ and the highest for BaFe ₂As ₂. However, the rate of change of thermal expansivities along out-of-plane (i.e., along the c-axis) is higher as we go from Ba, Sr, Eu and Ca, respectively. Above 600 K, we notice the appearance /disappearance of certain reflections which suggest that tetragonal phase is not stable above this temperature for these compounds.     

Spin dynamics and phase transitions in quasi-2D antiferromagnets <Emphasis Type="Italic">R</Emphasis><Subscript>2</Subscript>CuO<Subscript>4</Subscript> (<Emphasis Type="Italic">R</Emphasis>=Pr,Nd, Sm,Eu, Gd)

The spin and lattice dynamics of the R₂CuO₄ quasi-2D antiferromagnetic crystals (R=Pr, Nd, Sm, Eu, Gd) were studied in the millimeter-range electromagnetic wave band. Strong variations of the absorption coefficient were observed to occur at temperatures T≈T₀. Absorption lines of electrical nature due to lattice dynamics were also revealed near the T₀ temperatures. The observed anomalies are assumed to originate from phase transitions at T≈T₀, which entail changes in the structural and magnetic properties.     

Phase transitions in a MgB<Subscript>2</Subscript> granular BCS superconductor in weak magnetic fields

The character of temperature dependences of the electric conductivity of MgB₂ granular BCS superconductors at temperatures of ~35–45 K in external magnetic fields H _ext of up to ~2 kOe is studied. An increase in the superconducting transition width ΔT _c with an increase in Hext is found. The presence of a system of weak links in MgB₂-based granular superconductors is established. On the basis of experimental data, MgB₂ granular superconductor is assigned to two-level superconducting systems and the H–T phase diagram is constructed.     

Low-temperature thermal-expansion anomaly in Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CuO<Subscript>6</Subscript>

Single-crystal samples of the Bi_{2 + x}Sr_{2 ? x ? y}Cu_{1 + y}O_{6 + δ} system revealed anomalous (negative) thermal expansion in the temperature range 10–20 K. Magnetic fields of 1–3 T were found to strongly affect the position and width of the anomaly region. A thermal-expansion singularity was detected at temperatures T≈30–50 K, which may be related to the formation of a pseudogap.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

On electron transport in ZrB<Subscript>12</Subscript>, ZrB<Subscript>2</Subscript>, and MgB<Subscript>2</Subscript> in normal state

We report on measurements of the temperature dependence of resistivity, ρ(T), for single-crystal samples of ZrB₁₂, ZrB₂, and polycrystalline samples of MgB₂. It is shown that the cluster compound ZrB₁₂ behaves as a simple metal in the normal state, with a typical Bloch-Grüneisen ρ(T) dependence. However, the resistive Debye temperature, T_R=300 K, is three times smaller than T_D obtained from specific heat data. We observe the T² term in ρ(T) of all these borides, which could be interpreted as an indication of strong electron-electron interaction.     

Metamagnetic effects in epitaxial BaFe<Subscript>1.8</Subscript>Cr<Subscript>0.2</Subscript>As<Subscript>2</Subscript> thin films

Epitaxial BaFe_1.8Cr_0.2As₂ thin films with the tetragonal c-axis perpendicular to the thin film surface were grown on (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7 (LSAT) single crystalline substrates using pulsed laser deposition (PLD). Resistive measurements indicate the existence of two transitions at temperatures of about 80 K and 40 K. The transition at 80 K is attributed to the structural transition from the high temperature tetragonal phase to the low temperature orthorhombic phase accompanied with the magnetic transition from a paramagnetic to an antiferromagnetic state as known for doped bulk systems. Below T ≈ 40 K the magnetization curves measured perpendicularly to the orthorhombic c-axis in fields up to 9 Tesla show two inflexion points indicating metamagnetic transitions.     

Pressure-induced superconductivity and structural transitions in Ba(Fe<Subscript>0.9</Subscript>Ru<Subscript>0.1</Subscript>)<Subscript>2</Subscript>As<Subscript>2</Subscript>

Electrical transport and structural characterizations of isoelectronically substituted Ba(Fe_0.9Ru_0.1)₂As₂ have been performed as a function of pressure up to ～ 30 GPa and temperature down to ～ 10 K using designer diamond anvil cell. Similar to undoped members of the AFe₂As₂ (A = Ca, Sr, Ba) family, Ba(Fe_0.9Ru_0.1)₂As₂ shows anomalous a-lattice parameter expansion with increasing pressure and a concurrent ThCr₂Si₂ type isostructural (I4/mmm) phase transition from tetragonal (T) phase to a collapsed tetragonal (cT) phase occurring between 12 and 17 GPa where the a is maximum. Above 17 GPa, the material remains in the cT phase up to 30 GPa at 200 K. The resistance measurements show evidence of pressure-induced zero resistance that may be indicative of high-temperature superconductivity for pressures above 3.9 GPa. The onset of the resistive transition temperature decreases gradually with increasing pressure before completely disappearing for pressures above ～ 10.6 GPa near the T-cT transition. We have determined the crystal structure of the high-T _c phase of Ru-doped BaFe₂As₂ to remain as tetragonal (I4/mmm) by analyzing the X-ray diffraction pattern obtained at 10 K and 9.7 ± 0.7 GPa, as opposed to inferring the structural transition from electrical resistance measurement, as in a previous report [S.K. Kim, M.S. Torikachvili, E. Colombier, A. Thaler, S.L. Bud’ko, P.C. Canfield, Phys. Rev. B 84, 134525 (2011)].     

The influence of magnetic and structural heterogeneity on thermopower,magnetothermopower, electrical resistivity,and magnetoresistivity of Nd<Subscript>0.5</Subscript>Sr<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> manganite

The thermopower, S, magnetothermopower, ΔS/S, resistivity, ρ, and magnetoresistivity, Δρ/ρ, depending on the temperature T and magnetic field H, have been studied in an Nd_0.5Sr_0.5MnO₃ single crystal consisting of three types of clusters: an antiferromagnetic CE-type with charge-orbital ordering (below the Neel temperature T_NCE ~ 145 K) and an A-type with T_NA ~ 220 K; a ferromagnetic at 234 ≤ T ≤ 252 K, and a ferromagnetic metal phase below the Curie temperature T_C = 248 K. The thermopower was found to be negative, indicating the dominance of the electronic type of conductivity. In the S(T) curves, a sharp minimum is observed in the temperature range of 100 K ≤ T ≤ 133 K, close to T_NCE, where the absolute S value attains 53 μV/K. With a further increase in temperature, the absolute S value decreases rapidly; at 200 K it is equal to 7 μV/K. It then slightly increases, reaching its maximum value of 15 μV/K at a temperature of 254 K, which is close to T_C. The absolute thermopower decreased under the influence of the magnetic field; i.e., a negative magnetothermopower occurs. In {ΔS/S}(T) curves, a sharp minimum is observed at T = 130 K close to T_NCE, where the magnetothermopower reaches a huge value of ~45% at H = 13.23 kOe. A broad minimum in the {ΔS/S}(T) curves is observed near the Curie temperature and its value is also high, viz., ~15% in the maximum measuring magnetic field of 13.23 kOe. The extremely high magnetothermopower values mean that the charge-orbital ordered nanoclusters or ferron type make the main contribution to the thermopower of the entire sample. The behavior of the ρ(T) and {Δρ/ρ}(T) curves is similar to that of the S(T) and {ΔS/S}(T) dependencies, which is in agreement with this conclusion.     

Nonergodic state of relaxation ferroelectric Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> in a constant electric field

The temperature dependence of the residual polarization of the nonergodic relaxation state (NERS) obtained from the measurements of pyroelectric current during zero-field heating (ZFH) in the temperature interval from 10 to 295 K is investigated for the Cd₂Nb₂O₇ relaxation system in two cases: (1) after sample cooling in a constant electric field E (FC) from T = 295 K to a preset temperature, which is much lower than the “freezing” temperature of the relaxation state (T _f ≈ 182 K), field removal, and subsequent cooling in zero field (ZFC) to T = 10 K and (2) after ZFC from T = 295 K to the same temperature below T _f , application of the same field, and FC to T = 10 K. The behavior of the P _r ^FC (T) and P _r ^ZFC (T) dependences is analyzed. In the field E < 2 kV/cm, the P _r ^ZFC curves as functions of 1/T have a broad low-intensity peak in the region T ≈ T _f , which vanishes in stronger fields, when the P _r ^FC (1/T) curves intersect at T ≈ T _f and have no anomalies. The difference in the behavior of P _r ^ZFC (T) and P _r ^FC (T) indicates the difference in the nature of NERS formed during ZFC and FC of the system upon a transition through T _f . In the ZFC mode, NERS exhibits glasslike behavior; in the FC regime, features of the ferroelectric behavior even in the weak field. Analogous variations of P _r ^ZFC (T) and P _r ^FC (T) in a classical ferroelectric KDP are also given for comparison.     

Optical studies of phase transitions in the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>Ti(O<Subscript>2</Subscript>)F<Subscript>5</Subscript> crystal

Polarization-optical study of twinning and measurements of the Raman spectra and birefringence in oxyfluoride (NH₄)₃Ti(O₂)F₅ were carried out over the temperature range 90–350 K. Phase transitions were detected at temperatures T ₀₁ = 266 K (second-order transition) and T ₀₂ = 225 K (first order). It is assumed that the crystal symmetry is changed as follows: Fm3m ? I4/mmm ? I4/m. Anomalies of the spectral parameters are established in the frequency range of internal vibrations of ammonium ions and Ti(O₂)F₅ complexes. An analysis of the results shows that the transition at T ₀₁ is likely due to small shifts of the tetrahedral groups from their position on the triad axis and that the transition at T ₀₂ is due to fluorine-oxygen ordering of Ti(O₂)F₅ complexes.     

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.