Alexandra S. Gibbs

High-temperature phase transitions of hexagonal YMnO3

We report a detailed high-resolution powder neutron diffraction investigation of the structural behaviour of the multiferroic hexagonal polymorph of YMnO3 between room temperature and 1403 K. The study was aimed at resolving previous uncertainties regarding the nature of the paraelectric- ferroelectric transition and the possibilities of any secondary structural transitions. We observe a clear transition at 1258 +/- 14 K corresponding to a unit cell tripling and a change in space group from centrosymmetric P6_3/mmc to polar P6_3cm. Despite the fact that this symmetry permits ferroelectricity, our experimental data for this transition analysed in terms of symmetry-adapted displacement modes clearly supports previous theoretical analysis that the transition is driven primarily by the antiferrodistortive K3 mode. We therefore verify previous suggestions that YMnO3 is an improper ferrielectric. Furthermore, our data confirm that the previously suggested intermediate phase with space group P6_3/mcm does not occur. However, we do find evidence for an isosymmetric phase transition (i.e. P6_3cm to P6_3cm) at ~920 K which involves a sharp decrease in polarization. This secondary transition correlates well with several previous reports of anomalies in physical properties in this temperature region and may be related to Y-O hybridization.

Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain

Strained Superconductor Distorting a material and observing its response can allow insight into its electronic properties. Thin films can be strained by placing them on a substrate with a different lattice constant; bulk samples present more of a challenge. Hicks et al. (p. 283) designed an apparatus to apply both tensile and compressive strain and used it to study the properties of the superconductor Sr2RuO4, which has long been hypothesized to host the unusual p-wave superconductivity. The response of the superconducting transition temperature Tc to the applied strain depended on the direction in which the strain was applied, and did not exhibit a cusp predicted to occur around zero strain. As the technique leaves a surface of the probe open to external probes, it could be adopted for a wide range of methods. An apparatus that can apply both tensile and compressive strain is used to study an unconventional superconductor. A sensitive probe of unconventional order is its response to a symmetry-breaking field. To probe the proposed px ± ipy topological superconducting state of Sr2RuO4, we have constructed an apparatus capable of applying both compressive and tensile strains of up to 0.23%. Strains applied along 〈 100 〉 crystallographic directions yield a strong, strain-symmetric increase in the superconducting transition temperature Tc. 〈 110 〉 strains give a much weaker, mostly antisymmetric response. As well as advancing the understanding of the superconductivity of Sr2RuO4, our technique has potential applicability to a wide range of problems in solid-state physics.

Quantum oscillations near the metamagnetic transition in Sr3Ru2O7

We report detailed investigation of quantum oscillations in Sr3Ru2O7, observed inductively (the de Haas-van Alphen effect) and thermally (the magnetocaloric effect). Working at fields from 3 T to 18 T allowed us to straddle the metamagnetic transition region and probe the low- and high-field Fermi liquids. The observed frequencies are strongly field-dependent in the vicinity of the metamagnetic transition, and there is evidence for magnetic breakdown. We also present the results of a comprehensive rotation study. The most surprising result concerns the field dependence of the measured quasiparticle masses. Contrary to conclusions previously drawn by some of us as a result of a study performed with a much poorer signal to noise ratio, none of the five Fermi surface branches for which we have good field-dependent data gives evidence for a strong field dependence of the mass. The implications of these experimental findings are discussed.

Strong peak in Tc of Sr2RuO4 under uniaxial pressure

Squeezing out the oddness The material Sr2RuO4 has long been thought to exhibit an exotic, odd-parity kind of superconductivity, not unlike the superfluidity in 3He. How would perturbing this materials electronic structure affect its superconductivity? Steppke et al. put the material under large uniaxial pressure and found that the critical temperature more than doubled and then fell as a function of strain (see the Perspective by Shen). The maximum critical temperature roughly coincided with the point at which the materials Fermi surface underwent a topological change. One intriguing possibility is that squeezing changed the parity of the superconducting gap from odd to even. Science, this issue p. 10.1126/science.aaf9398; see also p. 133 Perturbing the electronic structure of Sr2RuO4 has profound effects on its superconductivity. INTRODUCTION A central challenge of modern condensed matter physics is to understand the range of possible collective states formed by assemblies of strongly interacting electrons. Most real materials contain high levels of disorder, which can disrupt possible ordered states and so substantially hinder the path to understanding. There is a premium, therefore, on working with extremely clean materials and identifying clean ways to tune their physical properties. Here, we show that uniaxial pressure can induce profound changes in the superconductivity of one of the model materials in the field, Sr2RuO4, and demonstrate using explicit calculations how our findings provide strong constraints on theory. RATIONALE Superconductivity remains arguably the most intriguing collective electron state. All superconductors form from the condensation of pairs of electrons into a single ground state, but in “unconventional” superconductors, a rich variety of qualitatively different ground states is possible. One of the most celebrated examples, and the one with the lowest known levels of disorder, is Sr2RuO4. Previous experimental results suggest that its superconducting condensate has odd parity, that is, its phase is reversed upon inversion of spatial coordinates. A relatively unexplored route to test this possibility is to perturb the assembly of conduction electrons through lattice distortion, which introduces no additional disorder. Electronic structure calculations suggest that if sufficient uniaxial pressure could be applied to compress the lattice along the pressure axis by about 0.8%, the largest Fermi surface of Sr2RuO4 would undergo a topological transition. One of the consequences of tuning to this transition would be to substantially lower the velocity of some of charge carriers, and because slow carriers are generally favorable for superconductivity, the superconductivity might be profoundly affected. Although this topological transition has been achieved with other experimental techniques, too much disorder was introduced for the superconductivity to survive. RESULTS Our central experimental result is summarized in the figure. We prepare the sample as a beam and use piezoelectric stacks to compress it along its length. Compressing the a axis of the Sr2RuO4 lattice drives the superconducting transition temperature (Tc) through a pronounced maximum, at a compression of ≈0.6%, that is a factor of 2.3 higher than Tc of the unstrained material. At the maximum Tc, the superconducting transition is very sharp, allowing precise determination of the superconducting upper critical magnetic fields for fields along both the a and c directions. The c-axis upper critical field is found to be enhanced by more than a factor of 20. We perform calculations using a weak-coupling theory to compare the Tc’s and upper critical fields of possible superconducting order parameters. The combination of our experimental and theoretical work suggests that the maximum Tc is likely associated with the predicted Fermi surface topological transition and that at this maximum Tc, Sr2RuO4 might have an even-parity rather than an odd-parity superconducting order parameter. The anisotropic distortion is key to these results: Hydrostatic pressure is known experimentally to decrease Tc of Sr2RuO4. CONCLUSION Our data raise the possibility of an odd-parity to even-parity transition of the superconducting state of Sr2RuO4 as a function of lattice strain and fuel an ongoing debate about the symmetry of the superconducting state even in the unstrained material. We anticipate considerable theoretical activity to address these issues, and believe that the technique developed for these experiments will also have a broader significance to future study of quantum magnets, topological systems, and electronic liquid crystals as well as superconductors. The rise and fall of Tc of Sr2RuO4. (Top left) A photograph of the uniaxial pressure apparatus. Pressure is applied to the sample by piezoelectric actuators. (Top middle) A sample, prepared as a beam and mounted in the apparatus. The susceptometer is a pair of concentric coils. (Top right) A schematic of a mounted sample. The piezoelectric actuators compress or tension the sample along its length. (Bottom) Tc of three samples of Sr2RuO4 against strain along their lengths. Negative values of εxx denote compression. Tc is taken as the midpoint of the transition, observed by ac susceptibility. Sample #1 was cracked, and so could be compressed but not tensioned. Sr2RuO4 is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (Tc) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum Tc occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, Tc = 3.4 K Sr2RuO4 has an even-parity, rather than an odd-parity, order parameter.

Quantum Oscillations and High Carrier Mobility in the Delafossite PdCoO2

We present de Haas-van Alphen and resistivity data on single crystals of the delafossite PdCoO(2). At 295 K we measure an in-plane resistivity of 2.6  μΩ cm, making PdCoO(2) the most conductive oxide known. The low-temperature in-plane resistivity has an activated rather than the usual T(5) temperature dependence, suggesting a gapping of effective scattering that is consistent with phonon drag. Below 10 K, the transport mean free path is ∼20  μm, approximately 10(5) lattice spacings and an astoundingly high value for flux-grown crystals. We discuss the origin of these properties in light of our data.

Muon-spin rotation measurements of the vortex state in Sr2RuO4 : Type-1.5 superconductivity, vortex clustering, and a crossover from a triangular to a square vortex lattice

Muon-spin rotation has been used to probe the vortex state in Sr2RuO4. At moderate fields and temperatures a lattice of triangular symmetry is observed, crossing over to a lattice of square symmetr ...

Resistivity in the Vicinity of a van Hove Singularity: Sr2RuO4 under Uniaxial Pressure

We report the results of a combined study of the normal-state resistivity and superconducting transition temperature T_{c} of the unconventional superconductor Sr_{2}RuO_{4} under uniaxial pressure. There is strong evidence that, as well as driving T_{c} through a maximum at ∼3.5  K, compressive strains ϵ of nearly 1% along the crystallographic [100] axis drive the γ Fermi surface sheet through a van Hove singularity, changing the temperature dependence of the resistivity from T^{2} above, and below the transition region to T^{1.5} within it. This occurs in extremely pure single-crystals in which the impurity contribution to the resistivity is <100  nΩ cm, so our study also highlights the potential of uniaxial pressure as a more general probe of this class of physics in clean systems.

Strong Peak in

Squeezing out the oddness The material Sr2RuO4 has long been thought to exhibit an exotic, odd-parity kind of superconductivity, not unlike the superfluidity in 3He. How would perturbing this materials electronic structure affect its superconductivity? Steppke et al. put the material under large uniaxial pressure and found that the critical temperature more than doubled and then fell as a function of strain (see the Perspective by Shen). The maximum critical temperature roughly coincided with the point at which the materials Fermi surface underwent a topological change. One intriguing possibility is that squeezing changed the parity of the superconducting gap from odd to even. Science, this issue p. 10.1126/science.aaf9398; see also p. 133 Perturbing the electronic structure of Sr2RuO4 has profound effects on its superconductivity. INTRODUCTION A central challenge of modern condensed matter physics is to understand the range of possible collective states formed by assemblies of strongly interacting electrons. Most real materials contain high levels of disorder, which can disrupt possible ordered states and so substantially hinder the path to understanding. There is a premium, therefore, on working with extremely clean materials and identifying clean ways to tune their physical properties. Here, we show that uniaxial pressure can induce profound changes in the superconductivity of one of the model materials in the field, Sr2RuO4, and demonstrate using explicit calculations how our findings provide strong constraints on theory. RATIONALE Superconductivity remains arguably the most intriguing collective electron state. All superconductors form from the condensation of pairs of electrons into a single ground state, but in “unconventional” superconductors, a rich variety of qualitatively different ground states is possible. One of the most celebrated examples, and the one with the lowest known levels of disorder, is Sr2RuO4. Previous experimental results suggest that its superconducting condensate has odd parity, that is, its phase is reversed upon inversion of spatial coordinates. A relatively unexplored route to test this possibility is to perturb the assembly of conduction electrons through lattice distortion, which introduces no additional disorder. Electronic structure calculations suggest that if sufficient uniaxial pressure could be applied to compress the lattice along the pressure axis by about 0.8%, the largest Fermi surface of Sr2RuO4 would undergo a topological transition. One of the consequences of tuning to this transition would be to substantially lower the velocity of some of charge carriers, and because slow carriers are generally favorable for superconductivity, the superconductivity might be profoundly affected. Although this topological transition has been achieved with other experimental techniques, too much disorder was introduced for the superconductivity to survive. RESULTS Our central experimental result is summarized in the figure. We prepare the sample as a beam and use piezoelectric stacks to compress it along its length. Compressing the a axis of the Sr2RuO4 lattice drives the superconducting transition temperature (Tc) through a pronounced maximum, at a compression of ≈0.6%, that is a factor of 2.3 higher than Tc of the unstrained material. At the maximum Tc, the superconducting transition is very sharp, allowing precise determination of the superconducting upper critical magnetic fields for fields along both the a and c directions. The c-axis upper critical field is found to be enhanced by more than a factor of 20. We perform calculations using a weak-coupling theory to compare the Tc’s and upper critical fields of possible superconducting order parameters. The combination of our experimental and theoretical work suggests that the maximum Tc is likely associated with the predicted Fermi surface topological transition and that at this maximum Tc, Sr2RuO4 might have an even-parity rather than an odd-parity superconducting order parameter. The anisotropic distortion is key to these results: Hydrostatic pressure is known experimentally to decrease Tc of Sr2RuO4. CONCLUSION Our data raise the possibility of an odd-parity to even-parity transition of the superconducting state of Sr2RuO4 as a function of lattice strain and fuel an ongoing debate about the symmetry of the superconducting state even in the unstrained material. We anticipate considerable theoretical activity to address these issues, and believe that the technique developed for these experiments will also have a broader significance to future study of quantum magnets, topological systems, and electronic liquid crystals as well as superconductors. The rise and fall of Tc of Sr2RuO4. (Top left) A photograph of the uniaxial pressure apparatus. Pressure is applied to the sample by piezoelectric actuators. (Top middle) A sample, prepared as a beam and mounted in the apparatus. The susceptometer is a pair of concentric coils. (Top right) A schematic of a mounted sample. The piezoelectric actuators compress or tension the sample along its length. (Bottom) Tc of three samples of Sr2RuO4 against strain along their lengths. Negative values of εxx denote compression. Tc is taken as the midpoint of the transition, observed by ac susceptibility. Sample #1 was cracked, and so could be compressed but not tensioned. Sr2RuO4 is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (Tc) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum Tc occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, Tc = 3.4 K Sr2RuO4 has an even-parity, rather than an odd-parity, order parameter.

T_c

Although Sr3Ru2O7 has not been reported to exhibit superconductivity so far, ac susceptibility measurements revealed multiple superconducting transitions occurring in the Sr3Ru2O7 region cut from Sr3Ru2O7-Sr2RuO4 eutectic crystals. Based on various experimental results, some of us proposed the scenario in which Sr2RuO4 thin slabs with a few layers of the RuO2 plane are embedded in the Sr3Ru2O7 region as stacking faults and multiple superconducting transitions arise from the distribution of the slab thickness. To examine this scenario, we measured the resistivity along the ab plane (rho_ab) using a Sr3Ru2O7-region sample cut from the eutectic crystal, as well as along the c axis (rho_c) using the same crystal. As a result, we detected resistance drops associated with superconductivity only in rho_ab, but not in rho_c. These results support the Sr2RuO4 thin-slab scenario. In addition, we measured the resistivity of a single crystal of pure Sr3Ru2O7 with very high quality and found that pure Sr3Ru2O7 does not exhibit superconductivity down to 15 mK.

of Sr

Squeezing out the oddness The material Sr2RuO4 has long been thought to exhibit an exotic, odd-parity kind of superconductivity, not unlike the superfluidity in 3He. How would perturbing this materials electronic structure affect its superconductivity? Steppke et al. put the material under large uniaxial pressure and found that the critical temperature more than doubled and then fell as a function of strain (see the Perspective by Shen). The maximum critical temperature roughly coincided with the point at which the materials Fermi surface underwent a topological change. One intriguing possibility is that squeezing changed the parity of the superconducting gap from odd to even. Science, this issue p. 10.1126/science.aaf9398; see also p. 133 Perturbing the electronic structure of Sr2RuO4 has profound effects on its superconductivity. INTRODUCTION A central challenge of modern condensed matter physics is to understand the range of possible collective states formed by assemblies of strongly interacting electrons. Most real materials contain high levels of disorder, which can disrupt possible ordered states and so substantially hinder the path to understanding. There is a premium, therefore, on working with extremely clean materials and identifying clean ways to tune their physical properties. Here, we show that uniaxial pressure can induce profound changes in the superconductivity of one of the model materials in the field, Sr2RuO4, and demonstrate using explicit calculations how our findings provide strong constraints on theory. RATIONALE Superconductivity remains arguably the most intriguing collective electron state. All superconductors form from the condensation of pairs of electrons into a single ground state, but in “unconventional” superconductors, a rich variety of qualitatively different ground states is possible. One of the most celebrated examples, and the one with the lowest known levels of disorder, is Sr2RuO4. Previous experimental results suggest that its superconducting condensate has odd parity, that is, its phase is reversed upon inversion of spatial coordinates. A relatively unexplored route to test this possibility is to perturb the assembly of conduction electrons through lattice distortion, which introduces no additional disorder. Electronic structure calculations suggest that if sufficient uniaxial pressure could be applied to compress the lattice along the pressure axis by about 0.8%, the largest Fermi surface of Sr2RuO4 would undergo a topological transition. One of the consequences of tuning to this transition would be to substantially lower the velocity of some of charge carriers, and because slow carriers are generally favorable for superconductivity, the superconductivity might be profoundly affected. Although this topological transition has been achieved with other experimental techniques, too much disorder was introduced for the superconductivity to survive. RESULTS Our central experimental result is summarized in the figure. We prepare the sample as a beam and use piezoelectric stacks to compress it along its length. Compressing the a axis of the Sr2RuO4 lattice drives the superconducting transition temperature (Tc) through a pronounced maximum, at a compression of ≈0.6%, that is a factor of 2.3 higher than Tc of the unstrained material. At the maximum Tc, the superconducting transition is very sharp, allowing precise determination of the superconducting upper critical magnetic fields for fields along both the a and c directions. The c-axis upper critical field is found to be enhanced by more than a factor of 20. We perform calculations using a weak-coupling theory to compare the Tc’s and upper critical fields of possible superconducting order parameters. The combination of our experimental and theoretical work suggests that the maximum Tc is likely associated with the predicted Fermi surface topological transition and that at this maximum Tc, Sr2RuO4 might have an even-parity rather than an odd-parity superconducting order parameter. The anisotropic distortion is key to these results: Hydrostatic pressure is known experimentally to decrease Tc of Sr2RuO4. CONCLUSION Our data raise the possibility of an odd-parity to even-parity transition of the superconducting state of Sr2RuO4 as a function of lattice strain and fuel an ongoing debate about the symmetry of the superconducting state even in the unstrained material. We anticipate considerable theoretical activity to address these issues, and believe that the technique developed for these experiments will also have a broader significance to future study of quantum magnets, topological systems, and electronic liquid crystals as well as superconductors. The rise and fall of Tc of Sr2RuO4. (Top left) A photograph of the uniaxial pressure apparatus. Pressure is applied to the sample by piezoelectric actuators. (Top middle) A sample, prepared as a beam and mounted in the apparatus. The susceptometer is a pair of concentric coils. (Top right) A schematic of a mounted sample. The piezoelectric actuators compress or tension the sample along its length. (Bottom) Tc of three samples of Sr2RuO4 against strain along their lengths. Negative values of εxx denote compression. Tc is taken as the midpoint of the transition, observed by ac susceptibility. Sample #1 was cracked, and so could be compressed but not tensioned. Sr2RuO4 is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (Tc) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum Tc occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, Tc = 3.4 K Sr2RuO4 has an even-parity, rather than an odd-parity, order parameter.