Capacitance Dilatometry Research Articles

Strong uniaxial pressure dependencies evidencing spin-lattice coupling and spin fluctuations in Cr2Ge2Te6

Single crystals of Cr$_2$Ge$_2$Te$_6$ were studied by high-resolution capacitance dilatometry to obtain in-plane ($B\parallel ab$) and out-of-plane ($B\parallel c$) thermal expansion and magnetostriction at temperatures between 2 and 300 K and in magnetic fields up to 15 T. The anomalies in both response functions lead to the 'magnetoelastic' phase diagrams and separate the paramagnetic (PM), ferromagnetic low-temperature/low-field (LTF) and aligned ferromagnetic (FM) phases. The presence of two distinct thermal expansion anomalies at small fields $B\parallel ab$ of different magnetic field dependence clearly supports the scenario of an intermediate region separating PM and LTF phases and is indicative of a tricritical point. Simulations of the magnetostriction using the Stoner-Wohlfarth model for uniaxial anisotropy demonstrate that the observed quadratic-in-field behavior in the LTF phase is in line with a rotation of the spins from the preferred $c$ direction into the $ab$ plane. Both the LTF and the PM phase close to T$_{\rm C}$ exhibit very strong pressure dependencies of the magnetization, ${\partial}\ln{M_{\rm ab}}/{\partial}p_{\rm ab}$, of several hundred %/GPa and also the transition from the LTF to the FM phase strongly depends on $p_{\rm ab}$ ($\sim -$280%/GPa), indicating a strong decrease of the uniaxial anisotropy under applied in-plane pressure. Our data clearly demonstrate the relevance of critical fluctuations and magnetoelastic coupling in Cr$_2$Ge$_2$Te$_6$.

Role of magnetoelastic coupling and magnetic anisotropy in MnTiO3

We report the thermodynamic properties studied by thermal expansion, magnetostriction, magnetisation, and specific heat measurements as well as the low-energy magnetic excitations of \mto\ and investigate how magneto-elastic coupling and magnetic anisotropy affect the evolution of long-range order and the magnetic phase diagram. Specifically, we utilise high-resolution capacitance dilatometry and antiferromagnetic resonance (AFMR) studies by means of high-frequency electron spin resonance (HF-ESR) spectroscopy. The role of anisotropy is reflected by spin-reorientation at $B_{\rm{SF}}$~$\simeq 6$~T and a corresponding sign change in $\partial T_{\rm N}/\partial B$. Analysis of the AFMR modes enables us to establish the zero-field excitation gap $\Delta$ as well as its temperature dependence. We derive the effective anisotropy field $B_\mathrm{A} = 0.16(1)$~T which predominately originates from out-of-plane nearest-neighbour dipole-dipole interactions. Despite the nearly fully quenched orbital moment, our data show pronounced thermal expansion and magnetostriction anomalies at $T_{\rm N}$ and $B_{\rm{SF}}$ , respectively, which allows the experimental determination of sizable uniaxial pressure dependencies, i.e., $\partial B_{\rm SF}/\partial p_{\rm c} = -0.20(2)$~T/GPa, $\partial T_{\rm N}/ \partial p_b = 0.69(12)$~K/GPa, and $\partial T_{\rm N}/ \partial p_c = -2.0(4)$~K/GPa. Notably, short-range magnetic order appears up to at least 3$T_{\rm N}$ , as indicated by anisotropic lattice distortion, the violation of a constant Gr\"uneisen behavior, and the presence of local magnetic fields detected by HF-ESR.

Strong effects of uniaxial pressure and short-range correlations in Cr2Ge2Te6

Cr$_2$Ge$_2$Te$_6$ is a quasi-2D semiconducting van der Waals ferromagnet down to the bilayer with great potential for technological applications. Engineering the critical temperature to achieve room temperature applications is one of the critical next steps on this path. Here, we report high-resolution capacitance dilatometry studies on Cr$_2$Ge$_2$Te$_6$ single crystals which directly prove significant magnetoelastic coupling and provide quantitative values of the large uniaxial pressure effects on long-range magnetic order (${\partial}T_{\mathrm{C}}/{\partial}p_{\mathrm{c}}$ = 24.7 K/GPa and ${\partial}T_{\mathrm{C}}/{\partial}p_{\mathrm{ab}}$ = $-$15.6 K/GPa) derived from thermodynamic relations. Moderate in-plane strain is thus sufficient to strongly enhance ferromagnetism in Cr$_2$Ge$_2$Te$_6$ up to room temperature. Moreover, unambiguous signs for short-range magnetic order up to 200~K are found.

Linear magnetoelastic coupling and magnetic phase diagrams of the buckled-kagomé antiferromagnet [Formula: see text

Single crystals of Cu_3Bi(SeO_3)_2O_2Cl were investigated using high-resolution capacitance dilatometry in magnetic fields up to 15 T. Pronounced magnetoelastic coupling is found upon evolution of long-range antiferromagnetic order at T_{mathrm {N}} = 26.4(3) K. Grüneisen analysis reveals moderate effects of uniaxial pressure on T_{mathrm {N}}, of 1.8(4) K/GPa, -0.62(15) K/GPa and 0.33(10) K/GPa for p parallel a, b, and c, respectively. Below 22 K Grüneisen scaling fails which implies the presence of competing interactions. The structural phase transition at T_{mathrm {S}} = 120.7(5) K is much more sensitive to uniaxial pressure than T_{mathrm {N}}, with strong effects of up to 27(3) K/GPa (p parallel c). Magnetostriction and magnetization measurements reveal a linear magnetoelastic coupling for Bparallel c below T_{mathrm {N}}, as well as a mixed phase behavior above the tricritical point around 0.4 T. An analysis of the critical behavior in zero-field points to three-dimensional (3D) Ising-like magnetic ordering. In addition, the magnetic phase diagrams for fields along the main crystalline axes are reported.

Magnetic phase diagram, magnetoelastic coupling, and Grüneisen scaling in CoTiO3

High-quality single crystals of ${\mathrm{CoTiO}}_{3}$ are grown and used to elucidate in detail structural and magnetostructural effects by means of high-resolution capacitance dilatometry studies in fields up to 15 T which are complemented by specific heat and magnetization measurements. In addition, we refine the single-crystal structure of the ilmenite ($R\overline{3}$) phase. At the antiferromagnetic ordering temperature ${T}_{\mathrm{N}}$ pronounced $\ensuremath{\lambda}$-shaped anomaly in the thermal expansion coefficients signals shrinking of both the $c$ and $b$ axes, indicating strong magnetoelastic coupling with uniaxial pressure along $c$ yielding six times larger effect on ${T}_{\mathrm{N}}$ than pressure applied in-plane. The hydrostatic pressure dependency derived by means of Gr\"uneisen analysis amounts to $\ensuremath{\partial}{T}_{\mathrm{N}}/\ensuremath{\partial}p\ensuremath{\approx}2.7(4)\phantom{\rule{4pt}{0ex}}\mathrm{K}/\mathrm{GPa}$. The high-field magnetization studies in static and pulsed magnetic fields up to 60 T along with high-field thermal expansion measurements facilitate in constructing the complete anisotropic magnetic phase diagram of ${\mathrm{CoTiO}}_{3}$. While the results confirm the presence of significant magnetodielectric coupling, our data show that magnetism drives the observed structural, dielectric, and magnetic changes both in the short-range ordered regime well above ${T}_{\mathrm{N}}$ as well as in the long-range magnetically ordered phase.

Magnetoelastic coupling and phases in the skyrmion lattice magnetGd2PdSi3discovered by high-resolution dilatometry

We report detailed thermodynamic studies on high-quality single crystals of the centrosymmetric skyrmion-hosting intermetallic Gd2PdSi3 by means of high-resolution capacitance dilatometry in fields up to 15 T which are complemented by specific heat and magnetization studies. Our dilatometric measurements show magnetoelastic effects associated with antiferromagnetic order at TN1 = 22.3 K and TN2 = 19.7 K, as well as strong field effects in an applied magnetic field of 15 Tup to 200 K (150 K) for B||c (B||a*, i.e. B perp c). The data allow us to complete the magneticphase diagram, including a new feature at T* approx 12 K below which a new degree of freedom becomesrelevant. For the first time, the magnetic B vs. T phase diagram for the a*-axis is also reported. Gr\"uneisen analysis shows the onset of magnetic contributions around 60 K, i.e., well above TN1. Uniaxial pressure dependencies of opposite sign, -1.3 K/GPa and 0.3 K/GPa, are extracted for the out-of-plane and in-plane directions at TN1. For T* we obtain dT*/dpc= 1.4 K/GPa. In particular we elucidate thermodynamic properties of the recently discovered skyrmion lattice phase and show that it is strongly enhanced by uniaxial pressure.

Revisiting the phase diagram of LaFe1−xCoxAsO in single crystals by thermodynamic methods

In this work we revisit the phase diagram of Co-doped LaFeAsO using single crystals and thermodynamic methods. From magnetic susceptibility studies we track the doping evolution of the antiferromagnetic phase, revealing a continuous suppression of $T_\mathrm{N}$ up to 5$\%$ Co doping. In order to study the evolution of the so-called nematic phase, the temperature dependence of the lengths changes along the $a$ and $b$ orthorhombic directions, $\Delta L/L_0$, was determined by high-resolution capacitance dilatometry. The results clearly show a gradual reduction of the orthorhombic distortion $\delta$ and of $T_\mathrm{S}$ with increasing Co content up to 4.5$\%$, while it is completely suppressed for 7.5$\%$ Co. Bulk superconductivity was found in a small doping region around 6$\%$ Co content, while both $T_\mathrm{c}$ and the superconducting volume fraction rapidly drop in the neighbouring doping regime. Ultimately, no microscopic coexistence between the superconducting and magnetic phases can be assessed within our resolution limit, in sharp contrast with other iron-pnictide families, e.g., electron- and hole-doped BaFe$_2$As$_2$.

Magnetoelastic coupling and Grüneisen scaling in NdB4

We report high-resolution capacitance dilatometry studies on the uniaxial length changes in a NdB$_4$ single crystal. The evolution of magnetically ordered phases below $T_{\rm N}$= 17.2~K (commensurate antiferromagnetic phase, cAFM), $T_{\rm IT}$= 6.8~K (intermediate incommensurate phase, IT), and $T_{\rm LT}$= 4.8~K (low-temperature phase, LT) is associated with pronounced anomalies in the thermal expansion coefficients. The data imply significant magneto-elastic coupling and evidence of a structural phase transition at $T_{\rm LT}$ . While both cAFM and LT favor structural anisotropy $\delta$ between in-plane and out-of-plane length changes, it competes with the IT-type of order, i.e., $\delta$ is suppressed in that phase. Notably, finite anisotropy well above $T_{\rm N}$ indicates short-range correlations which are, however, of neither cAFM, IT, nor LT-type. Gr\"uneisen analysis of the ratio of thermal expansion coefficient and specific heat enables the derivation of uniaxial as well as hydrostatic pressure dependencies. While $\alpha$/$c_{\rm p}$ evidences a single dominant energy scale in LT, our data imply precursory fluctuations of a competing phase in IT and cAFM, respectively. Our results suggest the presence of orbital degrees of freedom competing with cAFM and successive evolution of a magnetically and orbitally ordered ground state.

Metal matrix composites based on valence-unstable systems

The work is focused on the thermal expansion of composites based on valence-unstable systems. The main motivation was to create invar-like materials of a new type and to develop approaches to the quantitative description of coefficients of thermal expansion (CTE) of both the composite itself and its key component - a material with a negative contribution to thermal expansion due to valence fluctuations. The experimental data on the linear CTE of Al/SmB6 composite was performed by capacitive dilatometry in the temperature range 5-220K. It turned out that this composite shows invar properties up to 60K. Several models were used to describe thermal expansion in Al/SmB6. A quantitative approach is proposed for describing the negative magnetic contribution and the lattice contribution to the CTE of systems based on intermediate-valence samarium hexaboride.

Near zero thermal expansion in metal matrix composites based on intermediate valence systems: Al/SmB6

This work is focused on the fabrication and characterization of a new type of composite invar materials combining near-zero thermal expansion and functional properties that are important for applications. This is accomplished through the use of particles of SmB6, an intermediate valence system with negative thermal expansion, embedded in Al matrix. The composite based on SmB6-21 vol% was fabricated by hot pressing and was characterized by XRD, optical/electron microscopy, X-ray computed tomography and capacitive dilatometry. The study of thermal expansion revealed that the sample exhibits invar behaviour up to ~60 K with a zero value of the coefficient of thermal expansion near 45 K. In comparison to pure aluminum, the temperature range has increased by about 20 K. A quantitative analysis of dilatometric experimental data performed on the basis of widely used theoretical models showed that the thermal expansion of the Al/SmB6 composite was well reproduced within the Turner model.

Magnetic field dependence of low-energy magnons, anisotropic heat conduction, and spontaneous relaxation of magnetic domains in the cubic helimagnet ZnCr2Se4

Anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr2Se4 in the single-domain spin-spiral state are investigated by a combination of neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and nonmonotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A tiny spin gap of the pseudo-Goldstone magnon mode, observed at wave vectors that are structurally equivalent but orthogonal to the propagation vector of the spin helix, vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T < 2 K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results can be generalized to a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order.

The Complex Electronic Phase Diagram of Single-Crystalline R2PdSi3(R = Ho, Dy) Studied by Thermal Expansion and Magnetostriction

Thermal expansion and magnetostriction of single-crystalline R2PdSi3 (R = Ho, Dy) have been investigated by means of high-precision capacitance dilatometry and by specific heat studies. Pronounced ...

High magnetic field phase diagram and failure of the magnetic Grüneisen scaling in LiFePO4

We report the magnetic phase diagram of single-crystalline LiFePO$_4$ in magnetic fields up to 58~T and present a detailed study of magneto-elastic coupling by means of high-resolution capacitance dilatometry. Large anomalies at \tn\ in the thermal expansion coefficient $\alpha$ imply pronounced magneto-elastic coupling. Quantitative analysis yields the magnetic Gr\"uneisen parameter $\gamma_{\rm mag}=6.7(5)\cdot 10^{-7}$~mol/J. The positive hydrostatic pressure dependence $dT_{\rm N}/dp = 1.46(11)$~K/GPa is dominated by uniaxial effects along the $a$-axis. Failure of Gr\"uneisen scaling below $\approx 40$~K, i.e., below the peak temperature in the magneto-electric coupling coefficient [\onlinecite{toft2015anomalous}], implies several competing degrees of freedom and indicates relevance of recently observed hybrid excitations~[\onlinecite{yiu2017hybrid}]. A broad and strongly magnetic-field-dependent anomaly in $\alpha$ in this temperature regime highlight the relevance of structure changes. Upon application of magnetic fields $B||b$-axis, a pronounced jump in the magnetisation implies spin-reorientation at $B_{\rm SF} = 32$~T as well as a precursing phase at 29~T and $T=1.5$~K. In a two-sublattice mean-field model, the saturation field $B_{\rm sat,b} = 64(2)$~T enables the determination of the effective antiferromagnetic exchange interaction $J_{\rm af} = 2.68(5)$~meV as well as the anisotropies $D_{\rm b} = -0.53(4)$~meV and $D_{\rm c} = 0.44(8)$~meV.

Thermal expansion of organic superconductor α-(BEDT-TTF)2 NH4Hg(SCN)4

The temperature dependence of the linear thermal expansion coefficients (LTEC) of a single crystal of α-(BEDT-TTF)2NH4Hg(SCN)4 where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene was studied by the meth­od of precision capacitive dilatometry in the temperature range 2-250 K along the crystallographic direction b (per­pendicular to the crystal layers). Negative values of LTEC were found below 4 K. Probably it is due to charge fluc­tuations as the temperature approaches the temperature of transition to the superconducting state Tc. It has been suggested that the bends on temperature dependence of LTEC observed in the temperature range 25-45 K are relat­ed to order-disorder arrangement of NH4+ ions. Weak maximum of the LTEC, detected at a temperature of about 200-220 K, can be caused by the processes of charge redistribution and the associated intermolecular interaction fluctuations.

Thermal expansion of organic superconductor κ-(D4-BEDT-TTF)2Cu{N(CN)2}Br. Isotopic effect

Linear thermal expansion coefficient (LTEC) of single crystal κ-(D4-BEDT-TTF)2Cu[N(CN)2]Br was studied across the crystal layers in the temperature range 2–290 K using the method of precise capacitive dilatometry. Below Tc = 11.6 K the LTEC of the sample had a small negative value, which is apparently due to the transition from the paramagnetic metal in the superconducting state. There was a bend of temperature dependence of the LTEC, which shows broad peak around 40 K and can be attributed to the elastic lattice anomaly around the end-point of Mott boundary. A sharp jump in the LTEC values and hysteresis was observed in the area of Tg ∼ 75–77 K, what is likely explained by the transition in a glass-like state. The isotope effect in the thermal expansion is discusses, which manifested itself in a shift of the phase transitions in comparison with fully deuterated BEDT-TTF sample.

Methods of dilatometric investigations under extreme conditions and the case of spin-ice compounds

We give an overview on how dilatometric methods have been developed in the last decade. The concept of capacitive dilatometry was successfully adapted to dilution refrigerators with a resolution of 10−9. Miniaturized dilatometers with an overall diameter of 18 mm or less are optimally suited for measuring longitudinal and transversal components of the striction tensor. Going to another extreme, to the highest (pulsed) fields, optical methods, such as the FBG technology, were developed for investigations up to 100 T.As examples for utilizing dilatometry at low temperatures we show results for the spin-ice materials Dy2Ti2O7 and Ho2Ti2O7. To characterise the magneto-elastic coupling in these materials, we investigated the thermal expansion and magnetostriction between 80 mK and 15 K and in magnetic fields aligned along the [111] direction and found field-induced phases and strong correlations below 500 mK. Our data demonstrate, that the formation of the field-induced phase is strongly influenced by lattice distortions: any change in interatomic distances will result in a variation of the exchange couplings.

Anisotropic Thermal Expansion of α-YbAlB4

Thermal expansion measurements were performed for α-YbAlB4 using powder X-ray diffraction and our high resolution capacitance dilatometry. Highly anisotropic thermal expansion, which is much larger along the c-axis compared to the a- and b-axes, was observed. In addition, high resolution capacitance dilatometry revealed negative thermal expansion appears below 90 K only along the a-axis, not along the c-axis. The observation is consistent with anisotropic hybridization stronger in the ab-plane, suggesting the formation of anisotripic heavy fermion well below the valence fluctuation temperature scale of 200 ∼ 300 K. Furthermore, linear thermal expansion coefficient along the a-axis starts to decrease below 115 K. The characteristic temperature scale of 90 - 115 K may correspond to the crystal electric field excited level. The in-plane negative thermal expansion can be regarded as a development of anisotropic hybridization due to |Jz = ±5/2 > crystal electric field ground states which becomes dominant on cooling below the excited states.

Peculiarities of thermal expansion of quasi-two-dimensional organic conductor κ-(BEDT–TTF)2Cu[N(CN)2]Cl

Linear coefficient of thermal expansion α(T) of single crystal (BEDT–TTF)2Cu[N(CN)2]C1 was studied along the crystal layers using the method of precise capacitive dilatometry in the temperature range 2–285 K. It is positive in this direction over the entire temperature range. Anomalies of thermal expansion were observed at 29–30 K and 74–80 K. The anomaly near 30 K is, apparently, due to the transition between the paramagnetic phase and the antiferromagnetic insulator state. Peak of α(T) at 78 K corresponds to a phase transition related to orientational disordering of ethylene groups in dimers of BEDT–TTF. A broad maximum of α(T) in the temperature range 40–70 K, is apparently explained by fluctuations of charge within the dimers, and by spin fluctuations, which first increase with increasing temperature, and then decrease in process of thermal disordering of dimers.

Processing and characterization of a Ni-Co ferrite for sensor applications

AbstractNi-Co ferrites are magnetostrictive ceramics that have potential application in magnetostrictive/ magnetoelastic sensors, as well as in magnetoelectric composites. Ni-rich Ni-Co spinel ferrite samples were processed by the ceramic method and bulk samples were sintered at 1350 ºC in the solid state and at 950 ºC with Bi2O3 liquid phase. The sintered samples were characterized by light microscopy, scanning electron microscopy, Raman spectroscopy, vibrating sample magnetometry and capacitance dilatometry. With Bi2O3 additions as small as 0.6 mol% it was possible to sinter the Ni-Co ferrite at 950 ºC, obtaining high-density samples; however, such liquid-phase sintered samples presented iron oxide particles. The studied samples presented magnetoelastic sensitivities very close to CoFe2O4, with significantly lower magnetic hysteresis. The results thus indicate that the magnetic properties of the samples analyzed are suitable for applications in magnetomechanical sensors.

Thermal avalanches near a Mott transition

We probe the volume collapse transition (ΔV/Vo ∼ 15%) between the isostructural γ and α phases (T ∼ 100 K) of Ce0.9Th0.1 using the Hall effect, three-terminal capacitive dilatometry, and electrical resistivity measurements. Hall effect measurements confirm the itinerant ground state as the carrier concentration increases by a factor of 7 in the α phase, γ phase (nH = 5.28 × 1026 m−3), and the α phase (nH = 3.76 × 1027 m−3). We were able to detect a noise spectrum consisting of avalanches while slowly varying the temperature through the hysteretic region. We surmise that the avalanches originate from intergranular stresses at the interfaces between partially transformed high-volume and low-volume phases. The statistical distribution of avalanches obey power laws with energy exponent ϵ ≃ 1.5. Hall effect measurements, combined with universal critical exponents, point to short electron mean-free percolation pathways and carrier localization at phase interfaces. Carrier localization was predicted many years ago for elemental cerium by Johansson (1974 Phil. Mag. 30 469).