A compact and miniaturized high resolution capacitance dilatometer for measuring thermal expansion and magnetostriction

A high resolution dilatometer using optical fiber interferometer

We introduce a high-performance differential dilatometer based on an all-fiber Michelson interferometer at cryogenic temperature with 10-10 resolution in δL/L. It resolves the linear thermal expansion coefficient by measuring the oscillating changes of sample thickness and sample temperature with the interferometer and in situ thermometer, respectively. By measuring the linear thermal expansion coefficient α near the antiferromagnetic transition region of BaFe2As2 as a demonstration, we show that our dilatometer is able to measure thin samples with sub-pm-level length change resolution and mK-level temperature resolution. Despite the residual background thermal expansion of a few nm/K in the measurement results, our new dilatometer is still a powerful tool for the study of phase transition in condensed matter physics, especially has significant advantages in fragile materials with sub-100 μm thickness and being integrated with multiple synchronous measurements and tuning thanks to its extremely high resolution and contactless nature. The prototype design of this setup can be further improved in many aspects for specific applications.

Magnetostriction measurements at milli-kelvin temperatures using a Fabry-Pérot interferometer

This paper demonstrates an optical technique to measure magnetostrictive strain in a cryogenic environment using a Fabry-Pérot resonator spaced by crystal samples. Optical measurement techniques are calibration-free and highly sensitive. This technique was used to measure the magnetostrictive strain of neodymium gallate at a temperature of 49 mK to be λ = 1.3 × 10-5 at 3 T, with a sensitivity of 3.0 × 10-8. We highlight the interesting properties of the crystal's magnetic ordering. The sensitivity of this technique was limited by the wavemeter used to measure the laser frequency, and significant improvements in the sensitivity should be possible.

Advanced technique for measuring relative length changes under control of temperature and helium-gas pressure

We report the realization of an advanced technique for measuring relative length changes ΔL/L of mm-sized samples under the control of temperature (T) and helium-gas pressure (P). The system, which is an extension of the apparatus described in the work of Manna et al. [Rev. Sci. Instrum. 83, 085111 (2012)], consists of two ⁴He-bath cryostats, each of which houses a pressure cell and a capacitive dilatometer. The interconnection of the pressure cells, the temperature of which can be controlled individually, opens up various modes of operation to perform measurements of ΔL/L under the variation of temperature and pressure. Special features of this apparatus include the possibility (1) to increase the pressure to values far in excess of the external pressure reservoir, (2) to substantially improve the pressure stability during temperature sweeps, (3) to enable continuous pressure sweeps with both decreasing and increasing pressure, and (4) to simultaneously measure the dielectric constant of the pressure-transmitting medium, viz., helium, ε_r ^He(T,P), along the same T-P trajectory as that used for taking the ΔL(T, P)/L data. The performance of the setup is demonstrated by measurements of relative length changes (ΔL/L)_T at T = 180 K of single crystalline NaCl upon continuously varying the pressure in the range 6 ≤ P ≤ 40 MPa.

Detection of relativistic fermions in Weyl semimetal TaAs by magnetostriction measurements

Thus far, a detection of the Dirac or Weyl fermions in topological semimetals remains often elusive, since in these materials conventional charge carriers exist as well. Here, measuring a field-induced length change of the prototype Weyl semimetal TaAs at low temperatures, we find that its c-axis magnetostriction amounts to relatively large values whereas the a-axis magnetostriction exhibits strong variations with changing the orientation of the applied magnetic field. It is discovered that at magnetic fields above the ultra-quantum limit, the magnetostriction of TaAs contains a linear-in-field term, which, as we show, is a hallmark of the Weyl fermions in a material. Developing a theory for the magnetostriction of noncentrosymmetric topological semimetals and applying it to TaAs, we additionally find several parameters characterizing the interaction between the relativistic fermions and elastic degrees of freedom in this semimetal. Our study shows how dilatometry can be used to unveil Weyl fermions in candidate topological semimetals.

Detecting Weyl or Dirac charge carriers in topological semimetals is challenging due to the presence of their conventional counterparts. In this manuscript, the authors show that magnetostriction offers clearly distinguishable conventional and Weyl or Dirac charge carrier contributions when the latter are in their quantum limit.

Sapphire dilatometer cell for measuring the thermal expansion of solids

Capacitive-based dilatometry is used to determine the thermal expansion of solid specimens over a broad temperature range and for the study of structural and thermodynamic phase transitions. It can detect length changes of 0.1 Å or better. Dilatometer cells have been constructed of metals, such as copper or silver, and non-metals, such as silicon and fused silica. Sapphire is a good candidate for the construction of a dilatometer cell. It has excellent thermal conductivity, a well-behaved thermal expansion of moderate magnitude, especially below ∼60 K, and is readily available. The design, fabrication, and testing of a sapphire dilatometer cell are described herein.

Anisotropy-driven quantum criticality in an intermediate valence system

Intermetallic compounds containing f-electron elements have been prototypical materials for investigating strong electron correlations and quantum criticality (QC). Their heavy fermion ground state evoked by the magnetic f-electrons is susceptible to the onset of quantum phases, such as magnetism or superconductivity, due to the enhanced effective mass (m^*) and a corresponding decrease of the Fermi temperature. However, the presence of f-electron valence fluctuations to a non-magnetic state is regarded an anathema to QC, as it usually generates a paramagnetic Fermi-liquid state with quasiparticles of moderate m^*. Such systems are typically isotropic, with a characteristic energy scale T₀ of the order of hundreds of kelvins that require large magnetic fields or pressures to promote a valence or magnetic instability. Here we show the discovery of a quantum critical behaviour and a Lifshitz transition under low magnetic field in an intermediate valence compound α-YbAlB₄. The QC origin is attributed to the anisotropic hybridization between the conduction and localized f-electrons. These findings suggest a new route to bypass the large valence energy scale in developing the QC.

The nature of quantum criticality in intermetallic f-electron compounds exhibiting valence fluctuations is not well understood. Here, using a combination of experimental techniques, the authors attribute quantum criticality in YbAlB₄ to the anisotropic hybridization between the conduction and f-electrons.

Magnetostrictive alloys: Promising materials for biomedical applications

Magnetostrictive alloys have attracted increasing attention in biomedical applications because of the ability to generate reversible deformation in the presence of external magnetic fields. This review focuses on the advances in magnetostrictive alloys and their biomedical applications. The theories of magnetostriction are systematically summarized. The different types of magnetostrictive alloys and their preparation methods are also reviewed in detail. The magnetostrictive strains and phase compositions of typical magnetostrictive alloys, including iron based, rare-earth based and ferrite materials, are presented. Besides, a variety of approaches to preparing rods, blocks and films of magnetostriction materials, as well as the corresponding methods and setups for magnetostriction measurement, are summarized and discussed. Moreover, the interactions between magnetostrictive alloys and cells are analyzed and emphasis is placed on the transduction and transformation process of mechanochemical signals induced by magnetostriction. The latest applications of magnetostrictive alloys in remote microactuators, magnetic field sensors, wireless implantable devices and biodegradable implants are also reviewed. Furthermore, future research directions of magnetostrictive alloys are prospected with focus on their potential applications in remote cell actuation and bone repair.

Field-induced transition within the superconducting state of CeRh2As2

Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh₂As₂ Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

A temperature-modulated dilatometer by using a piezobender-based device

We report a new design of a temperature-modulated dilatometer, which obtains the linear thermal expansion coefficient by measuring the oscillating changes of the sample's length and temperature by using a piezobender and a thermocouple, respectively. Using an iron-based superconductor KFe₂As₂ as an example, we show that this device is able to measure thin samples with high resolutions at low temperatures and high magnetic fields. Despite its incapability of giving absolute values, the new dilatometer provides a high-resolution method to study many important physical properties in condensed matter physics, such as thermal and quantum phase transitions and vortex dynamics in the superconducting state. The prototype design of this device can be further improved in many aspects to meet particular requirements.

Tuning the Structural and Optoelectronic Properties of Cs2 AgBiBr6 Double-Perovskite Single Crystals through Alkali-Metal Substitution

Lead-free double perovskites have great potential as stable and nontoxic optoelectronic materials. Recently, Cs₂ AgBiBr₆ has emerged as a promising material, with suboptimal photon-to-charge carrier conversion efficiency, yet well suited for high-energy photon-detection applications. Here, the optoelectronic and structural properties of pure Cs₂ AgBiBr₆ and alkali-metal-substituted (Cs_{1- x} Y_x )₂ AgBiBr₆ (Y: Rb⁺ , K⁺ , Na⁺ ; x = 0.02) single crystals are investigated. Strikingly, alkali-substitution entails a tunability to the material system in its response to X-rays and structural properties that is most strongly revealed in Rb-substituted compounds whose X-ray sensitivity outperforms other double-perovskite-based devices reported. While the fundamental nature and magnitude of the bandgap remains unchanged, the alkali-substituted materials exhibit a threefold boost in their fundamental carrier recombination lifetime at room temperature. Moreover, an enhanced electron-acoustic phonon scattering is found compared to Cs₂ AgBiBr₆ . The study thus paves the way for employing cation substitution to tune the properties of double perovskites toward a new material platform for optoelectronics.

Negative Thermal Expansion in the Plateau State of a Magnetically Frustrated Spinel

We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr_{2}O_{4}. Using dilatometry, we precisely map the phase diagram at fields of up to 30 T and identify a strong NTE associated with the collinear half-magnetization plateau for B>27  T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly localized band of spin excitations in the plateau phase. These results provide useful guidelines for the discovery of new NTE materials.

Magnetic-Field Tuning of Hydrogen Bond Order-Disorder Transition in Metal-Organic Frameworks

The ordering of polar hydrogen bonds may break space inversion symmetry and induce ferroelectricity or antiferroelectricity. This process is usually immune to external magnetic fields so that magnetic control of hydrogen bonds is very challenging. Here we demonstrate that the ordering of hydrogen bonds in the metal-organic frameworks [(CH_{3})_{2}NH_{2}]M(HCOO)_{3} (M=Fe, Co) can be manipulated by applying magnetic fields. After cooling in a high magnetic field, the order-disorder transition of hydrogen bonds shifts to a lower or higher temperature, depending on antiferroelectricity or ferroelectricity induced by hydrogen bond ordering. Besides, the order-disorder transition leads to a giant thermal expansion, exceeding ∼3.5×10^{4} and ∼2×10^{4}  ppm for M=Fe and Co, respectively, which is much higher than that of inorganic ferroelectrics. The influence of magnetic field on hydrogen bond ordering is discussed in terms of the magnetoelastic coupling.

Tracking Structural Phase Transitions in Lead-Halide Perovskites by Means of Thermal Expansion

The extraordinary properties of lead-halide perovskite materials have spurred intense research, as they have a realistic perspective to play an important role in future photovoltaic devices. It is known that these materials undergo a number of structural phase transitions as a function of temperature that markedly alter their optical and electronic properties. The precise phase transition temperature and exact crystal structure in each phase, however, are controversially discussed in the literature. The linear thermal expansion of single crystals of APbX₃ (A = methylammonium (MA), formamidinium (FA); X = I, Br) below room temperature is measured using a high-resolution capacitive dilatometer to determine the phase transition temperatures. For δ-FAPbI₃ , two wide regions of negative thermal expansion below 173 and 54 K, and a cascade of sharp transitions for FAPbBr₃ that have not previously been reported are uncovered. Their respective crystal phases are identified via powder X-ray diffraction. Moreover, it is demonstrated that transport under steady-state illumination is considerably altered at the structural phase transition in the MA compounds. The results provide advanced insights into the evolution of the crystal structure with decreasing temperature that are essential to interpret the growing interest in investigating the electronic, optical, and photonic properties of lead-halide perovskite materials.

Influence of magnetic field on electrical and thermal transport in the hole doped ferromagnetic manganite: La0.9Na0.1MnO3

We report the magnetization (M), magnetostriction, electrical resistivity (ρ), thermal conductivity (κ) and thermopower (S) of polycrystalline La_0.9Na_0.1MnO₃ over a wide temperature range of 5 to 360 K. This sample undergoes a paramagnetic to ferromagnetic transition around T _C = 274 K and electrical resistivity ρ shows an insulator-metal transition around T _IM = 292 K. The sign of thermopower S is positive in the entire temperature range which indicates that majority charge carriers are holes. Thermopower exhibits a peak and thermal conductivity shows a dip at T _C in the absence of magnetic field. Large difference between the experimentally determined activation energies of ρ and S in the insulating state indicates small polaron hopping dominant conduction above T _IM. Polaron formation above T _C, was further confirmed from the anomaly observed in thermal expansion (ΔL/L ₀) which shows a change in slope at T _IM. In the vicinity of T _C at 3 T applied field, magneto-thermopower (∼61.5%) is larger than magnetothermal conductivity (∼12.7%) and magnetoresistance (∼49%).

Note: Optical filter method for high-resolution magnetostriction measurement using fiber Bragg grating under millisecond-pulsed high magnetic fields at cryogenic temperatures

High-resolution magnetostriction measurement of ΔL/L ∼ 10^-6 at a speed of 5 MHz is performed using the optical filter method as the detection scheme for the fiber Bragg grating (FBG) based strain monitor under 35-ms pulsed high magnetic fields up to 45 T at 2.2 K. The resolution of magnetostriction is about the same order as the conventionally reported value from FBG based magnetostriction measurement systems for millisecond pulsed magnetic fields. The measurement speed is ∼100 times the conventional ones. The present system can be a faster alternative for the conventional FBG based magnetostriction measurement system for millisecond pulsed high magnetic fields.

Breakdown of Magnetic Order in the Pressurized Kitaev Iridate β-Li_{2}IrO_{3}

Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate β-Li_{2}IrO_{3} is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Néel temperature of β-Li_{2}IrO_{3} increases with the slope of 0.9  K/GPa upon initial compression, but the reduction in the polarization field H_{c} reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition, giving way to a new ground state marked by the coexistence of dynamically correlated and frozen spins. This partial freezing in the absence of any conspicuous structural defects may indicate the classical nature of the resulting pressure-induced spin liquid, an observation paralleled to the increase in the nearest-neighbor off-diagonal exchange Γ under pressure.

Fiber Bragg Grating Dilatometry in Extreme Magnetic Field and Cryogenic Conditions

In this work, we review single mode SiO₂ fiber Bragg grating techniques for dilatometry studies of small single-crystalline samples in the extreme environments of very high, continuous, and pulsed magnetic fields of up to 150 T and at cryogenic temperatures down to <1 K. Distinct millimeter-long materials are measured as part of the technique development, including metallic, insulating, and radioactive compounds. Experimental strategies are discussed for the observation and analysis of the related thermal expansion and magnetostriction of materials, which can achieve a strain sensitivity (ΔL/L) as low as a few parts in one hundred million (≈10⁻⁸). The impact of experimental artifacts, such as those originating in the temperature dependence of the fiber’s index of diffraction, light polarization rotation in magnetic fields, and reduced strain transfer from millimeter-long specimens, is analyzed quantitatively using analytic models available in the literature. We compare the experimental results with model predictions in the small-sample limit, and discuss the uncovered discrepancies.

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 CeRhIn5. 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 [dL/L=(L−L0)/L0] on the order of 10−7. 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.

Cascade of Magnetic-Field-Induced Lifshitz Transitions in the Ferromagnetic Kondo Lattice Material YbNi_{4}P_{2}

A ferromagnetic quantum critical point is thought not to exist in two- and three-dimensional metallic systems yet is realized in the Kondo lattice compound YbNi_{4}(P,As)_{2}, possibly due to its one-dimensionality. It is crucial to investigate the dimensionality of the Fermi surface of YbNi_{4}P_{2} experimentally, but common probes such as angle-resolved photoemission spectroscopy and quantum oscillation measurements are lacking. Here, we study the magnetic-field dependence of transport and thermodynamic properties of YbNi_{4}P_{2}. The Kondo effect is continuously suppressed, and additionally we identify nine Lifshitz transitions between 0.4 and 18 T. We analyze the transport coefficients in detail and identify the type of Lifshitz transitions as neck or void type to gain information on the Fermi surface of YbNi_{4}P_{2}. The large number of Lifshitz transitions observed within this small energy window is unprecedented and results from the particular flat renormalized band structure with strong 4f-electron character shaped by the Kondo lattice effect.

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.

Breakdown of Hooke's law of elasticity at the Mott critical endpoint in an organic conductor

The Mott metal-insulator transition, a paradigm of strong electron-electron correlations, has been considered as a source of intriguing phenomena. Despite its importance for a wide range of materials, fundamental aspects of the transition, such as its universal properties, are still under debate. We report detailed measurements of relative length changes ΔL/L as a function of continuously controlled helium-gas pressure P for the organic conductor κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl across the pressure-induced Mott transition. We observe strongly nonlinear variations of ΔL/L with pressure around the Mott critical endpoint, highlighting a breakdown of Hooke's law of elasticity. We assign these nonlinear strain-stress relations to an intimate, nonperturbative coupling of the critical electronic system to the lattice degrees of freedom. Our results are fully consistent with mean-field criticality, predicted for electrons in a compressible lattice with finite shear moduli. We argue that the Mott transition for all systems that are amenable to pressure tuning shows the universal properties of an isostructural solid-solid transition.

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.

Characteristic signatures of quantum criticality driven by geometrical frustration

Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid-like state.

Persistent Detwinning of Iron-Pnictide EuFe_{2}As_{2} Crystals by Small External Magnetic Fields

Our comprehensive study on EuFe_{2}As_{2} reveals a dramatic reduction of magnetic detwinning fields compared to other AFe_{2}As_{2} (A=Ba, Sr, Ca) iron pnictides by indirect magnetoelastic coupling of the Eu^{2+} ions. We find that only ∼0.1  T are sufficient for persistent detwinning below the local Eu^{2+} ordering; above T_{Eu}=19  K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190 K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetry-breaking external force.

Thermodynamic evidence for valley-dependent density of states in bulk bismuth

Electron-like carriers in bismuth are described by the Dirac Hamiltonian, with a band mass becoming a thousandth of the bare electron mass along one crystalline axis. The existence of three anisotropic valleys offers electrons an additional degree of freedom, a subject of recent attention. Here, we map the Landau spectrum by angle-resolved magnetostriction, and quantify the carrier number in each valley: while the electron valleys keep identical spectra, they substantially differ in their density of states at the Fermi level. Thus, the electron fluid does not keep the rotational symmetry of the lattice at low temperature and high magnetic field, even in the absence of internal strain. This effect, reminiscent of the Coulomb pseudogap in localized electronic states, affects only electrons in the immediate vicinity of the Fermi level. It presents the most striking departure from the non-interacting picture of electrons in bulk bismuth.