Measurement of the B1g and B2g components of the elastoresistivity tensor for tetragonal materials via transverse resistivity configurations

Emergent tetragonality in a fundamentally orthorhombic material

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe3, for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.

Comparison of temperature and doping dependence of elastoresistivity near a putative nematic quantum critical point

Strong electronic nematic fluctuations have been discovered near optimal doping for several families of Fe-based superconductors, motivating the search for a possible link between these fluctuations, nematic quantum criticality, and high temperature superconductivity. Here we probe a key prediction of quantum criticality, namely power-law dependence of the associated nematic susceptibility as a function of composition and temperature approaching the compositionally tuned putative quantum critical point. To probe the ‘bare’ quantum critical point requires suppression of the superconducting state, which we achieve by using large magnetic fields, up to 45 T, while performing elastoresistivity measurements to follow the nematic susceptibility. We performed these measurements for the prototypical electron-doped pnictide, Ba(Fe_1−xCo_x)₂As₂, over a dense comb of dopings. We find that close to the putative quantum critical point, the elastoresistivity appears to obey power-law behavior as a function of composition over almost a decade of variation in composition. Paradoxically, however, we also find that the temperature dependence for compositions close to the critical value cannot be described by a single power law.

Evidence for quantum criticality in Fe-based superconductors is still being accumulated. Here, the authors observe power-law behavior of the elastoresistivity as a function of composition in Ba(Fe_1−xCo_x)₂As₂ near a putative nematic quantum critical point, consistent with expectations for quantum criticality, while the temperature dependence near the critical doping deviates from a power law.

The transport-structural correspondence across the nematic phase transition probed by elasto X-ray diffraction

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and X-ray diffraction measurements with in-situ tunable strain (elasto X-ray diffraction) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of Ba(Fe_0.96Co_0.04)₂As₂. The ratio of transport to structural quantities is nearly temperature independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto X-ray diffraction is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of the mean-field description reveals the intertwined nature of nematicity.

Evolution of the Nematic Susceptibility in LaFe_{1-x}Co_{x}AsO

We report a systematic elastoresistivity study on LaFe_{1-x}Co_{x}AsO single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss-like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of LaFe_{1-x}Co_{x}AsO.

Sixfold enhancement of superconductivity in a tunable electronic nematic system

The electronic nematic phase-in which electronic degrees of freedom lower the crystal rotational symmetry-is commonly observed in high-temperature superconductors. However, understanding the role of nematicity and nematic fluctuations in Cooper pairing is often made more complicated by the coexistence of other orders, particularly long-range magnetic order. Here we report the enhancement of superconductivity in a model electronic nematic system that is not magnetic, and show that the enhancement is directly born out of strong nematic fluctuations associated with a quantum phase transition. We present measurements of the resistance as a function of strain in Ba_1-x Sr _x Ni₂As₂ to show that strontium substitution promotes an electronically driven nematic order in this system. In addition, the complete suppression of that order to absolute zero temperature leads to an enhancement of the pairing strength, as evidenced by a sixfold increase in the superconducting transition temperature. The direct relation between enhanced pairing and nematic fluctuations in this model system, as well as the interplay with a unidirectional charge-density-wave order comparable to that found in the cuprates, offers a means to investigate the role of nematicity in strengthening superconductivity.

Divergence of the quadrupole-strain susceptibility of the electronic nematic system YbRu2Ge2

A wide range of strongly correlated quantum materials, including some high-temperature superconductors, exhibit “electronic nematic” phases, in which the electronic properties spontaneously break the rotational symmetry of the crystal. However, the role that the corresponding nematic fluctuations play in these complicated systems is unclear, motivating the search for simpler model systems. Here, we identify a particular 4f intermetallic material which exhibits ferroquadrupole order, YbRu2Ge2, as just such a model system. We also provide a robust and accurate method to probe the divergence of an important associated quantity, the quadrupole-strain susceptibility. The temperature dependence of this quantity provides insight into the nature of the interactions that lead to ferroquadrupole order, in this case, magnetoelastic coupling.

Ferroquadrupole order associated with local 4f atomic orbitals of rare-earth ions is a realization of electronic nematic order. However, there are relatively few examples of intermetallic materials which exhibit continuous ferroquadrupole phase transitions, motivating the search for additional materials that fall into this category. Furthermore, it is not clear a priori whether experimental approaches based on transport measurements which have been successfully used to probe the nematic susceptibility in materials such as the Fe-based superconductors will be as effective in the case of 4f intermetallic materials, for which the important electronic degrees of freedom are local rather than itinerant and are consequently less strongly coupled to the charge-carrying quasiparticles near the Fermi energy. In the present work, we demonstrate that the intermetallic compound YbRu2Ge2 exhibits a tetragonal-to-orthorhombic phase transition consistent with ferroquadrupole order of the Yb ions and go on to show that elastoresistivity measurements can indeed provide a clear window on the diverging nematic susceptibility in this system. This material provides an arena in which to study the causes and consequences of electronic nematicity.

Measurement of elastoresistivity at finite frequency by amplitude demodulation

Elastoresistivity, the relation between resistivity and strain, can elucidate the subtle properties of the electronic structure of a material and is an increasingly important tool for the study of strongly correlated materials. To date, elastoresistivity measurements have predominantly been performed with quasi-static (DC) strain. In this work, we demonstrate a method using AC strain in elastoresistivity measurements. A sample experiencing AC strain has a time-dependent resistivity, which modulates the voltage produced by an AC current; this effect produces time-dependent variations in resistivity that are directly proportional to the elastoresistivity, and which can be measured more quickly, with less strain on the sample, and with less stringent requirements for temperature stability than the previous DC technique. Example measurements between 10 Hz and 3 kHz are performed on a material with a large, well-characterized and temperature dependent elastoresistivity: the representative iron-based superconductor Ba(Fe_0.975Co_0.025)₂As₂. These measurements yield a frequency independent elastoresistivity and reproduce results from previous DC elastoresistivity methods to within experimental accuracy. We emphasize that the dynamic (AC) elastoresistivity is a distinct material-specific property that has not previously been considered.

Determination of the resistivity anisotropy of orthorhombic materials via transverse resistivity measurements

Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often suffer very significant systematic errors. Here we describe a novel approach to measuring the resistivity anisotropy of orthorhombic materials, using a single crystal and a single measurement that is derived from a π4 rotation of the measurement frame relative to the crystallographic axes. In this new basis, the transverse resistivity gives a direct measurement of the resistivity anisotropy, which combined with the longitudinal resistivity also gives the in-plane elements of the conventional resistivity tensor via a 5-point contact geometry. This is demonstrated through application to the charge-density wave compound ErTe₃, and it is concluded that this method presents a significant improvement on existing techniques, particularly when measuring small anisotropies.