High-resolution Thermal Expansion Research Articles

Colossal c-Axis Response and Lack of Rotational Symmetry Breaking within the Kagome Planes of the CsV_{3}Sb_{5} Superconductor.

The kagome materials AV_{3}Sb_{5} (A=K, Rb, Cs) host an intriguing interplay between unconventional superconductivity and charge-density waves. Here, we investigate CsV_{3}Sb_{5} by combining high-resolution thermal-expansion, heat-capacity, and electrical resistance under strain measurements. We directly unveil that the superconducting and charge-ordered states strongly compete, and that this competition is dramatically influenced by tuning the crystallographic c axis. In addition, we report the absence of additional bulk phase transitions within the charge-ordered state, notably associated with rotational symmetry breaking within the kagome planes. This suggests that any breaking of the C_{6} invariance occurs via different stacking of C_{6}-symmetric kagome patterns. Finally, we find that the charge-density-wave phase exhibits an enhanced A_{1g}-symmetric elastoresistance coefficient, whose large increase at low temperature is driven by electronic degrees of freedom.

Charge density wave transitions, soft phonon, and possible electronic nematicity in BaNi2(As1−xPx)2

A detailed investigation of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ single crystals using high-resolution thermal-expansion, heat-capacity, Young's-modulus, and resistivity measurements is presented. The phase diagram of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ is shown to be much richer than suggested by the original data of Kudo et al. [Phys. Rev. Lett. 109, 097002 (2012)]. The transition to the commensurate charge density wave (C-CDW) is always preceded by a fourfold symmetry-breaking transition associated with the long-range ordering of a strongly fluctuating unidirectional incommensurate charge density wave (I-CDW). Significant precursors above the I-CDW and C-CDW transitions are seen in the thermal expansion and resistivity and are particularly evident in the temperature dependence of the $c/a$ ratio of the lattice parameters. Heat-capacity measurements of the crystals with a higher P content and a higher critical temperature of 3.2 K uncover a Debye-like behavior of a soft-phonon mode with a very low ${\mathrm{\ensuremath{\Theta}}}_{\text{Debye}}$ of roughly 50 K. Associated with this soft phonon are unusually large thermal-expansion anomalies, resulting in logarithmically diverging uniaxial phonon Gr\"uneisen parameters. Young's-modulus data of these higher-${T}_{c}$ crystals exhibit a significant softening in both ${B}_{1g}$ and ${B}_{2g}$ channels, which is argued to be incompatible with nematic criticality and is rather associated with a broad phase transition to an hitherto unknown structure. Possible origins of the increase in the superconducting critical temperature with P substitution are discussed.

Setup of high resolution thermal expansion measurements in closed cycle cryostats using capacitive dilatometers

We present high resolution thermal expansion measurement data obtained with high relative sensitivity of ΔL/L = 10−9 and accuracy of ± 2 % using closed cycle refrigerators employing two different dilatometers. Experimental details of the set-up utilizing the multi-function probe integrated with the cold head of two kinds of closed cycle refrigerators, namely, pulse tube and Gifford-McMahon cryocoolers, has been described in detail. The design consists of decoupling the bottom sample puck and taking connections from the top of the multi-function probe to mitigate the vibrational noise arising from the cold heads, using which smooth and high quality thermal expansion data could be obtained. It was found that dilatometer#2 performs a better noise mitigation than dilatometer#1 due to the constrained movement of the spring in dilatometer#2. This was confirmed by finite element method simulations that were performed for understanding the spring movement in each dilatometer using which the effect of different forces/pressures and vibrations on the displacement of the spring was studied. Linear thermal expansion coefficient α obtained using both dilatometers was evaluated using derivative of a polynomial fit. The resultant α obtained using dilatometer#2 and either of the closed cycle cryostats on standard metals silver and aluminium showed excellent match with published values obtained using wet cryostats. Finally, thermal expansion measurements is reported on single crystals of two high temperature superconductors YBa2Cu3−x Al x O6+δ and Bi2Sr2CaCu2O8+x along the c-axis with very good match found with published data obtained earlier using wet liquid helium based cryostats.

On the Order Parameter of the Continuous Phase Transition in the Classical and Quantum Mechanical Limits

The mean field theory is revisited in the classical and quantum mechanical limits. Taking into account the boundary conditions at the phase transition and the third law of the thermodynamics the physical properties of the ordered and disordered phases were reported. The equation for the order parameter predicts the occurrence of a saturation of $\Psi^2$ = 1 near $\Theta_S$, the temperature below the quantum mechanical ground state is reached. The theoretical predictions are also compared with high resolution thermal expansion data of SrTiO$_{\text{3}}$ monocrystalline samples and other some previous results. An excellent agreement has been found suggesting a universal behavior of the theoretical model to describe continuous structural phase transitions.

Structural and physical properties of trilayer nickelates R4Ni3O10 ( R=La , Pr, and Nd)

We investigate the low temperature structural and physical properties of the trilayer nickelates R4Ni3O10 (R = La, Pr and Nd) using resistivity, thermopower, thermal conductivity, specific heat, high-resolution synchrotron powder X-ray diffraction and thermal expansion experiments. We show that all three compounds crystallize with a monoclinic symmetry, and undergo a metal-to-metal (MMT) transition at 135 K (La), 156 K (Pr) and 160 K (Nd). At MMT, the lattice parameters show distinct anomalies; however, without any lowering of the lattice symmetry. Unambiguous signatures of MMT are also seen in magnetic and thermal measurements, which suggest a strong coupling between the electronic, magnetic and structural degrees of freedom in these nickelates. Analysis of thermal expansion yields hydrostatic pressure dependence of MMT in close agreement with experiments. We show that the 9-fold coordinated Pr ions in the rocksalt (RS) layers have a crystal field (CF) split doublet ground state with possible antiferromagnetic ordering at 5 K. The Pr ions located in the perovskite block (PB) layers with 12-fold coordination, however, exhibit a non-magnetic singlet ground state. The CF ground state of Nd in both RS and PB layers is a Kramers doublet. Heat capacity of R = Nd shows a Schottky-like anomaly near35 K, and an upturn below T = 10 K suggesting the presence of short-range correlations between the Nd moments. However, no signs of long-range ordering could be found down to 2 K despite a sizeable theta_p ~ -40 K. The strongly suppressed magnetic long-range ordering in both R = Pr and Nd suggests the presence of strong magnetic frustration in these compounds. The low-temperature resistivity shows a T^0.5 dependence. No evidence for the heavy fermion behavior could be found in any of the three compounds.

Synchrotron high-resolution XRD and thermal expansion of synthetic Mg calcites

The structural parameters and the thermal behavior of a complete series of Ca–Mg carbonates synthesized at high pressure and temperature (1–1.5 GPa, 1273–1373 K) in the range 0–50 mol% MgCO3 have been investigated by in situ powder synchrotron high-resolution X-ray diffraction at ambient and up to 1073 K under self-controlled CO2 partial pressure. The crystal structures are disordered Mg calcite in the range 1–41 mol% MgCO3, and Ca dolomite at 49 mol% MgCO3. New calibration curves of the cell parameters for the Mg content and thermal expansion from ambient to 1073 K are given. Short-range structural effects of cation substitution and ordering and their thermal behavior as a function of Mg content were identified from three sets of data: the peak broadening, the cell parameter strains and the Raman band enlargements. Both intra- and inter-crystalline levels of compositional heterogeneity are identified and allow splitting the Mg calcites into two groups: low- and high-Mg calcites. The low-Mg calcites (up to 22 mol% MgCO3) are homogeneous in Mg content with short-range ordering. High-Mg calcite (up to 41 mol% MgCO3) displays domains with different local ordering configurations and similar or slightly different Mg contents, and to which is added a compositional variation between crystals, as determined by EMP, of the order of ± 0.8 mol% MgCO3. The cation ordering in Ca-rich dolomites similarly occurs in high-Mg synthetic calcites. The role of (CO3)2− group ordering is shown to be an important factor in the formation of Ca–Mg carbonates.

Field-induced transitions in the Kitaev material α−RuCl3 probed by thermal expansion and magnetostriction

High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $\alpha$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the honeycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field $\mu_0H_{c1} = 7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around $\mu_0H_{c2} \approx 11$ T. The extracted Gr\"uneisen parameter shows typical hallmarks for quantum criticality near $H_{c1}$, but also displays anomalous behavior above $H_{c1}$. We compare our experimental data with linear spin-wave calculations employing a minimal Kitaev-Heisenberg model in the semiclassical limit. Most of the salient features are in agreement with each other, however, the peculiar features in the high-field region above $H_{c1}$ cannot be accounted for in our modelling and hence suggest a genuine quantum nature. We construct a phase diagram for $\alpha$-RuCl$_3$ showing two low-temperature transitions induced by an in-plane field along the Ru-Ru bonds.

Competing Electronic Phases near the Onset of Superconductivity in Hole-doped SrFe2As2

An intriguingly complex phase diagram of Na-doped SrFe2As2 is uncovered using high-resolution thermal-expansion, magnetization and heat-capacity measurements. The detailed temperature dependence of the orthorhombic distortion and the anisotropy of the uniform magnetic susceptibility provide evidence for nine distinct electronic phases near the transition region between stripe antiferromagnetism and unconventional superconductivity. In particular, we report the finding of a new magnetic phase which competes surprisingly strongly with superconductivity. From theoretical studies we propose that this phase is a double-Q phase consisting of a mixture of symmetry-distinct commensurate magnetic orders with a peculiar temperature-dependent magnetic moment reorientation.

Uniaxial and hydrostatic pressure effects in α-RuCl3 single crystals via thermal-expansion measurements

We present high-resolution thermal-expansion and specific-heat measurements of single crystalline α-RuCl3. An extremely hysteretic structural transition expanding over 100 K is observed by thermal-expansion along both crystallographic axes, which we attribute to a change of stacking sequence of the RuCl3 layers. Three magnetic transitions are observed, which we link to the different stacking sequences. Using our data and thermodynamic relations, we derive the uniaxial and hydrostatic pressure derivatives of all three magnetic transitions. Our results demonstrate that magnetic order of the major transition at ∼7 K should be totally suppressed by very moderate pressures of 0.3 GPa. Finally, we discuss why our results differ from recent hydrostatic pressure measurements and suggest a possible route to reaching the spin-liquid state in α-RuCl3.

Uniaxial stress tuning of geometrical frustration in a Kondo lattice

Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($\parallel a$). Since the Kondo coupling increases with stress, which alone would stabilize paramagnetic behavior in CeRhSn, the observed order arises from the release of geometrical frustration by in-plane stress.

An FBG Optical Approach to Thermal Expansion Measurements under Hydrostatic Pressure.

We report on an optical technique for measuring thermal expansion and magnetostriction at cryogenic temperatures and under applied hydrostatic pressures of 2.0 GPa. Optical fiber Bragg gratings inside a clamp-type pressure chamber are used to measure the strain in a millimeter-sized sample of CeRhIn. We describe the simultaneous measurement of two Bragg gratings in a single optical fiber using an optical sensing instrument capable of resolving changes in length on the order of . Our results demonstrate the possibility of performing high-resolution thermal expansion measurements under hydrostatic pressure, a capability previously hindered by the small working volumes typical of pressure cells.

The world's smallest capacitive dilatometer, for high-resolution thermal expansion and magnetostriction in high magnetic fields.

For the characterization of novel quantum phases of matter, it is often required to study materials under multi-extreme conditions, in particular down to very low temperatures and in very high magnetic fields. We developed the world's smallest high-resolution capacitive dilatometer suitable for temperatures down to 10 mK and usage in high magnetic fields up to 37.5 T. Despite the extreme miniaturization, the capacitive dilatometer can resolve length changes down to 0.01 Å. This is an unprecedented resolution in a capacitive dilatometer of this compact size. Many cryogenic devices have limited space. Due to the extremely reduced cell size (3 cm3, 12 g), implementation or new applications in many of these sample space lacking devices are now possible. As an important example, the minute device can now be rotated in any standard cryostat, including dilution refrigerators or the commercial physical property measurement system. The present super compact design provides also for high resolution thermal expansion and magnetostriction measurements in a 15.2 mm diameter tube, enabling its use in the 32 mm bore, 37.5 T Bitter magnet at the High Field Magnet Laboratory in Nijmegen down to a temperature of 300 mK.

Evidence of phase transitions in MoO2 single crystals

Abstract In this work, structural and physical properties are revisited in the MoO2 compound. MoO2 single crystals have been prepared by chemical vapor transport technique and characterized by X-ray diffraction, neutron diffraction, high-resolution thermal expansion, electrical resistance measurements, and heat capacity. Electrical resistivity, heat capacity, and thermal expansion measurements show two clear features which are related to phase transitions on the MoO2 compound. These results suggest that an electronic-type transition occurs near 220 K and a structural transition at ∼267 K.

Dilatometric study of the metamagnetic and ferromagnetic phases in the triple-layered Sr4Ru3O10 system

The Ruddlesden Popper series Sr${}_{n+1}$Ru${}_{n}$O${}_{3+n+1}$ contains highly interesting physical phenomena depending on the number of RuO${}_{2}$ layers in the unit cell, spanning from unconventional superconductivity for the $n$=1 member Sr${}_{2}$RuO${}_{4}$ to itinerant ferromagnetism in the infinite-layer system SrRuO${}_{3}$. Obviously, the unique interplay between electronic, spin, and lattice degrees of freedom in this group of correlated itinerant electron systems leads to a tremendous change of the physical properties. This is also demonstrated by anisotropic and orbital-dependent magnetism and a strong spin-phonon coupling found in many members within the series. This paper focusses on triple-layer Sr${}_{4}$Ru${}_{3}$O${}_{10}$, which becomes ferromagnetic at ${T}_{c}$$\ensuremath{\sim}$105 K and shows a metamagnetic transition below ${T}^{*}$$\ensuremath{\sim}$50 K for a magnetic field along the $a\phantom{\rule{0}{0ex}}b$ plane. The authors investigate the magnetoelastic properties of this compound as a function of temperature and magnetic field. The high-resolution thermal expansion and magnetostriction measurements indicate a highly anisotropic response with a specific rearrangement of the crystal lattice in fields parallel and perpendicular to the $c$ axis. Finally, they reconstruct the $T$-$H$ phase diagram, which shows a new feature suggestive of the multiple-orbital character of Sr${}_{4}$Ru${}_{3}$O${}_{10}$, where both the ferromagnetic (${d}_{x\phantom{\rule{0}{0ex}}y}$) and the metamagnetic orbitals (${d}_{x\phantom{\rule{0}{0ex}}z;y\phantom{\rule{0}{0ex}}z}$) coexist and interact.

A uniaxial stress capacitive dilatometer for high-resolution thermal expansion and magnetostriction under multiextreme conditions.

Thermal expansion and magnetostriction are directional dependent thermodynamic quantities. For the characterization of novel quantum phases of matter, it is required to study materials under multi-extreme conditions, in particular, down to very low temperatures, in very high magnetic fields or under high pressure. We developed a miniaturized capacitive dilatometer suitable for temperatures down to 20 mK and usage in high magnetic fields, which exerts a large spring force between 40 to 75 N on the sample. This corresponds to a uniaxial stress up to 3 kbar for a sample with cross section of (0.5 mm)(2). We describe design and performance test of the dilatometer which resolves length changes with high resolution of 0.02 Å at low temperatures. The miniaturized device can be utilized in any standard cryostat, including dilution refrigerators or the commercial physical property measurement system.

Complex phase diagram ofBa1−xNaxFe2As2: A multitude of phases striving for the electronic entropy

The low-temperature electronic phase diagram of Ba$_{1-x}$Na$_{x}$Fe$_{2}$As$_{2}$, obtained using high-resolution thermal-expansion and specific-heat measurements, is shown to be considerably more complex than previously reported, containing nine different phases. Besides the magnetic $C_{2}$ and reentrant $C_{4}$ phases, we find evidence for an additional, presumably magnetic, phase below the usual SDW transition, as well as a possible incommensurate magnetic phase. All these phases coexist and compete with superconductivity, which is particularily strongly suppressed by the $C_{4}$-magnetic phase due to a strong reduction of the electronic entropy available for pairing in this phase.

Doping dependence of the critical fluctuation regime in the Fe-based superconductorBa1−xKxFe2As2

We investigate the importance of superconducting order parameter fluctuations in the 122 family of Fe-based superconductors, using high-resolution specific heat and thermal expansion data of various Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals covering a large range of the phase diagram from the strongly underdoped to the overdoped regime. By applying scaling relations of the 3d-XY and the 3d-Lowest-Landau-Level (3d-LLL) fluctuation models to data measured in different magnetic fields, we demonstrate that a strong increase of the critical fluctuation regime is responsible for the transition broadening in magnetic fields, which is a direct consequence of a magnetic-field-induced finite size effect due to a reduction of the effective dimensionality by a decreasing magnetic length scale related to the mean vortex separation and the confinement of quasiparticles in low Landau levels. The fluctuations are stronger in the underdoped and overdoped regimes and appear to be weakest at optimal doping.

Heat capacity, thermal expansion and heat transport in the Han Blue (BaCuSi4O10): Observation of structural phase transitions

Structural phase transitions at 87K and 103K are reported for single-crystalline Han Blue (BaCuSi4O10) by means of high-resolution thermal-expansion, thermal conductivity and heat capacity measurements. The phase transition at 103K results in differing lengths of the a and b lattice parameters, and thus a lowering of the crystallographic symmetry. Negative thermal-expansion coefficients are observed perpendicular to the c-axis over a wide temperature range (108K<T<350K). The thermal conductivity is small, and decreases with temperature, both of which suggest strong scattering of heat-carrying phonons. The principle Grüneisen parameter within the plane and perpendicular to it was determined to be γ1=−1.09 and γ3=1.06 at room temperature; the bulk Grüneisen parameter is γ=0.10. The results are consistent with the presence of low-energy vibrations associated with the collective motions of CuO4 and Si4O10 polyhedral subunits.

Dilatometric Studies on Single Crystalline Barlowite – A Structurally Perfect Spin-1/2 Kagome System

We present results of high-resolution thermal expansion measurements on single crystalline barlowite – a structurally perfect spin-1/2 kagome system. The data reveal strongly pronounced and anisotropic second-order phase transition anomalies at the Néel transition at TN = 16K. From these data, together with literature results on the specific heat, the uniaxial-pressure dependences of TN are derived. We find a rather large positive pressure coefficient for uniaxial pressure along the hexagonal c axis of ∂TN/∂pc = (2.3 ± 0.2) K/GPa and smaller negative in-plane pressure coefficient of ∂TN/∂pin-plane = -(0.6 ± 0.03) K/GPa. These effects result in a small positive pressure coefficient under hydrostatic-pressure conditions of ∂TN/∂phydr = (1.1 ± 0.2) K/GPa. Bond-lengths considerations indicate that inter-layer Cu-O bonds, being larger than those typically found in stable Cu-O complexes, are responsible for this behavior.

Lattice Strain Accompanying the Colossal Magnetoresistance Effect inEuB6

The coupling of magnetic and electronic degrees of freedom to the crystal lattice in the ferromagnetic semimetal EuB(6), which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect, is studied by high-resolution thermal expansion and magnetostriction experiments. EuB(6) may be viewed as a model system, where pure magnetism-tuned transport and the response of the crystal lattice can be studied in a comparatively simple environment, i.e., not influenced by strong crystal-electric field effects and Jahn-Teller distortions. We find a very large lattice response, quantified by (i) the magnetic Grüneisen parameter, (ii) the spontaneous strain when entering the ferromagnetic region, and (iii) the magnetostriction in the paramagnetic temperature regime. Our analysis reveals that a significant part of the lattice effects originates in the magnetically driven delocalization of charge carriers, consistent with the scenario of percolating magnetic polarons. A strong effect of the formation and dynamics of local magnetic clusters on the lattice parameters is suggested to be a general feature of colossal magnetoresistance materials.