Nematic State Research Articles

Evidence for short-range magnetic order in the nematic phase of FeSe from anisotropic in-plane magnetostriction and susceptibility measurements

The nature of the nematic state in FeSe remains one of the major unsolved mysteries in Fe- based superconductors. Both spin and orbital physics have been invoked to explain the origin of this phase. Here we present experimental evidence for frustrated, short-range magnetic order, as suggested by several recent theoretical works, in the nematic state of FeSe. We use a combination of magnetostriction, susceptibility and resistivity measurements to probe the in-plane anisotropies of the nematic state and its associated fluctuations. Despite the absence of long-range magnetic order in FeSe, we observe a sizable in-plane magnetic susceptibility anisotropy, which is responsible for the field-induced in-plane distortion inferred from magnetostriction measurements. Further we demonstrate that all three anisotropies in FeSe are very similar to those of BaFe2As2, which strongly suggests that the nematic phase in FeSe is also of magnetic origin.

Orbital Order in Two-Orbital Hubbard Model

In strongly correlated multi-orbital systems, various ordered phases appear. In particular, the orbital order in iron-based superconductors attracts much attention since it is considered to be the origin of the nematic state. In order to clarify the essential condition for realizing orbital orders, we study simple two-orbital ($d_{xz}$, $d_{yz}$) Hubbard model. We find that the orbital order, which corresponds to the nematic order, appears due to the vertex corrections even in the two-orbital model. Thus, $d_{xy}$ orbital is not essential to realize the nematic orbital order. The obtained orbital order depends on the orbital dependence and the topology of fermi surfaces. We also find that another type of orbital order, which is rotated $45^\circ$, appears in the heavily hole-doped case.

Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{\vartriangle}$ and $J_{\triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $\mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{\triangledown}/J_{\vartriangle}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the "simplex" $\mathbb{Z}_{2}$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., $J_{\triangledown} \ll J_{\vartriangle}$.

Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2

The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe2As2 acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.

Elliptical vortex and oblique vortex lattice in the FeSe superconductor based on the nematicity and mixed superconducting orders

The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-Tc superconductors, regardless of cuprate or pnictide family. The nematic state in high-Tc systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films revealed the nematic superconducting state by Song et al. Here, motivated by the experiment, we construct the extended Ginzburg–Landau free energy to describe the elliptical vortex, where a mixed s-wave and d-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhances the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from C4 to C2. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble a lozenge-like vortex lattice, being well consistent with experimental results.

Pervasive electronic nematicity in a cuprate superconductor

We describe an extensive experimental study of La2-xSrxCuO4 films synthesized by molecular beam epitaxy and investigated by angle-resolved measurements of transverse resistivity (without applied magnetic field). The data show that an unusual metallic state, in which the rotational symmetry of the electron fluid is spontaneously broken, occurs in a large temperature and doping region. The superconducting state always emerges out of this nematic metal state.

133Cs-NMR study on aligned powder of competing spin chain compound Cs2Cu2Mo3O12

S = 1/2 competing spin chain compound Cs2Cu2Mo3O12 has two dominant exchange interactions of the nearest neighbouring ferromagnetic J1 = 93 K and the second nearest neighbouring antiferromagnetic J2 = +33 K, and is expected to show the nematic Tomonaga-Luttinger liquid (TLL) state under high magnetic field region. The recent theoretical study by Sato et al. has shown that in the nematic TLL state, the spin fluctuations are expected to be highly anisotropic, that is, its transverse component is suppressed. Our previous NMR study on the present system showed that the dominant contribution to nuclear spin relaxation comes from the longitudinal component. In order to conclude that the transverse component of spin fluctuations is suppressed, the knowledge of hyperfine coupling is indispensable. This article is solely devoted to investigate the hyperfine coupling of 133Cs-NMR site to prove that the anisotropic part of hyperfine coupling, which connects the nuclear spin relaxation with the transverse spin fluctuations is considerably large to be Aan = +770 Oe/μB.

Densely Packed Semiflexible Macromolecules in a Rigid Spherical Capsule

The ordering of semiflexible polymers with persistence length lp and contour length L confined in a sphere of radius R is studied by molecular dynamics simulations of a coarse-grained model. Monomer densities are chosen where the corresponding bulk lyotropic solution or melt is a well-ordered nematic, and purely repulsive walls of the rigid confining sphere are considered. It is found that polymers close to the walls are bent according to the curvature of the confining spheres with all their monomers in a few layers parallel to the sphere surface, whereas the remaining macromolecules closer to the sphere center have one chain end and their center of mass far from the surface. The latter chains are responsible for the average nematic order of the system for sufficiently stiff chains. If L exceeds R, a single transition from isotropic to nematic states is found when lp increases. However, if R is close to an even multiple of L, a second transition occurs where chain ends are enriched near the equatorial plane (and two further planes parallel to it, if R ≈ 2L); i.e., the system develops a distorted smectic structure. The order in the surface shell then is characterized by topological defects.

Mesophase study of pure and doped cyanobiphenyl liquid crystals with salen-type systems

ABSTRACTTwo salen Schiff base ligands derived from the condensation of ethylendiamine on salicylaldehyde and 5-chlorosalicylaldehyde, namely N,N′-bis(salicylidene)ethylene-diamine (L1) and N,N′-bis(5-chlorosalicylidene)ethylene-diamine (L2) as well as two of their iron(III) and nickel(II) complexes, were prepared and then used as doping agents of two thermotropic liquid crystals (LCs) of cyanobiphenyl type, namely 4-cyano-4′-n-pentyl-biphenyl (5CB) and 4-cyano-4′-n-octyl-biphenyl (8CB). The study of the mesophase of pure and doped LCs was carried out by UV–visible spectroscopy equipped with a heating compartment for precise temperature control, differential scanning calorimetry and polarised optical microscopy. The characteristic nematic/isotropic and smectic-A/nematic transition temperatures of 5CB- and 8CB-based systems were measured and then compared to those of the literature concerning pure 5CB and 8CB. Optical microscopy results revealed the existence of Schlieren and focal conic textures of the nematic and smectic states, respectively, both of pure and doped LCs. The homogeneity of the obtained guest–host systems was proven by the linear evolution of their transition temperatures as function of the solute concentration, with correlation factors close to unity.

Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State.

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.

Abrupt change of the superconducting gap structure at the nematic critical point in FeSe1−xSx

The emergence of the nematic electronic state that breaks rotational symmetry is one of the most fascinating properties of the iron-based superconductors, and has relevance to cuprates as well. FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering, providing a significant opportunity to investigate the role of nematicity in the superconducting pairing interaction. Here, to reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specific heat of FeSe1 - x S x , in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at [Formula: see text] We find that, in the whole nematic regime ([Formula: see text]), the field dependence of two quantities consistently shows two-gap behavior; one gap is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime ([Formula: see text]), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of [Formula: see text] and [Formula: see text] orbitals are enhanced equally in the tetragonal side, whereas they develop differently in the orthorhombic side. Our observation therefore directly implies that the orbital-dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction.

Signatures of electronic nematicity in (111) LaAlO3/SrTiO3 interfaces

The two-dimensional conducting gas (2DCG) that forms at the interface between ${\mathrm{LaAlO}}_{3}$ (LAO) and ${\mathrm{SrTiO}}_{3}$ (STO) has been widely studied due to the multitude of in situ tunable phenomena that exist at the interface. Recently it has been shown that nearly every property of the 2DEG that forms at the interface of (111) oriented LAO/STO is strongly anisotropic with respect to the in-plane crystal direction. This in-plane rotational symmetry breaking points to the existence of an electronic nematic phase at the interface that can be modified by an in situ electrostatic back-gate potential. Here we show that the onset temperature of the anisotropy in the longitudinal resistance is $T\ensuremath{\approx}22\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, which does not match up with any known structural transition, and coincides with the onset of anisotropy in the Hall response of the system. Furthermore, below 22 K, charge transport is activated in nature with different activation energies along the two in-plane crystal directions. Such a response implies that the band edges along the two directions are different and provides further evidence of an electronic nematic state at the interface.

Quantum Hall Ferroelectrics and Nematics in Multivalley Systems

We study broken symmetry states at integer Landau level fillings in multivalley quantum Hall systems whose low energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks twofold rotational symmetry, like in Bismuth (111) and in Sn$_{1-x}$Pb$_x$Se (001) surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existence of unusually robust skyrmion quasiparticles.

Nematic superconducting state in iron pnictide superconductors

Nematic order often breaks the tetragonal symmetry of iron-based superconductors. It arises from regular structural transition or electronic instability in the normal phase. Here, we report the observation of a nematic superconducting state, by measuring the angular dependence of the in-plane and out-of-plane magnetoresistivity of Ba0.5K0.5Fe2As2 single crystals. We find large twofold oscillations in the vicinity of the superconducting transition, when the direction of applied magnetic field is rotated within the basal plane. To avoid the influences from sample geometry or current flow direction, the sample was designed as Corbino-shape for in-plane and mesa-shape for out-of-plane measurements. Theoretical analysis shows that the nematic superconductivity arises from the weak mixture of the quasi-degenerate s-wave and d-wave components of the superconducting condensate, most probably induced by a weak anisotropy of stresses inherent to single crystals.

The Key Ingredients of the Electronic Structure of FeSe

FeSe is a fascinating superconducting material at the frontier of research in condensed matter physics. Here, we provide an overview of the current understanding of the electronic structure of FeSe, focusing in particular on its low-energy electronic structure as determined from angle-resolved photoemission spectroscopy, quantum oscillations, and magnetotransport measurements of single-crystal samples. We discuss the unique place of FeSe among iron-based superconductors, as it is a multiband system exhibiting strong orbitally dependent electronic correlations and unusually small Fermi surfaces and is prone to different electronic instabilities. We pay particular attention to the evolution of the electronic structure that accompanies the tetragonal-orthorhombic structural distortion of the lattice around 90 K, which stabilizes a unique nematic electronic state. Finally, we discuss how the multiband multiorbital nematic electronic structure impacts our understanding of the superconductivity, and show that the tunability of the nematic state with chemical and physical pressure helps to disentangle the role of different competing interactions relevant for enhancing superconductivity.

A large‐strain phase‐field model for nematic elastomers based on Landau‐de‐Gennes theory

AbstractLiquid crystal elastomers bring together the orientational properties of liquid crystals as well as elastic properties of soft rubber. Nematic elastomers are a subclass of these materials which exhibit a phase transition from high‐symmetry isotropic state to low‐symmetry nematic state, when cooled down below a material specific temperature. We present a phase–field model based on Landau‐de‐Gennes theory for the modeling of nematic elastomers. The model is implemented within finite element framework and an initial boundary value problem of isotropic‐nematic phase transition is solved. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spectra of collective excitations and low-frequency asymptotics of Green's functions for degenerate states in magnets with spin s = 1

A phenomenological description of how the non-equilibrium degenerate states of one- and multi-sublattice magnets with spin s = 1 evolve in an external field. Dynamic equations for the magnetic degrees of freedom are obtained, based on which low-frequency asymptotics of two-time Green's functions are calculated. The spectra of collective excitations for ferromagnet, quadruple magnet, and spin nematic states are found. A comparative analysis of these asymptotics of Green's functions is carried out, and the nature of the magnetic anisotropy caused by the unitary symmetry of the exchange interaction is clarified.

In-plane anisotropy of transport coefficients in electronic nematic states: Universal origin of nematicity in Fe-based superconductors

The origin of the electronic nematicity and its remarkable material-dependence are famous longstanding unsolved issues in Fe-based superconductors. To attack these issues, we focus on the in-plane anisotropy of the resistivity: In the nematic state in FeSe, the relation $\rho_x>\rho_y$ holds, where $\rho_{x(y)}$ is the resistivity along the longer (shorter) Fe-Fe axis. In contrast, the opposite anisotropy $\rho_x<\rho_y$ is realized in other undoped Fe-based superconductors. Such nontrivial material dependence is naturally explained in terms of the strongly orbital-dependent inelastic quasiparticle scattering realized in the orbital-ordered state. The opposite anisotropy between FeSe ($\rho_x>\rho_y$) and other undoped compounds ($\rho_x<\rho_y$) reflects the difference in the number of hole-pockets. We also explain the large in-plane anisotropy of the thermoelectric power in the nematic state.

Effect of proton irradiation on the normal-state low-energy excitations of Ba(Fe1−xRhx)2As2 superconductors

We present a \asnmr Nuclear Magnetic Resonance (NMR) and resistivity study of the effect of 5.5 MeV proton irradiation on the optimal electron doped ($x=$ 0.068) and overdoped ($x=$ 0.107) Ba(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ iron based superconductors. While the proton induced defects only mildly suppress the critical temperature and increase residual resistivity in both compositions, sizable broadening of the NMR spectra was observed in all the irradiated samples at low temperature. The effect is significantly stronger in the optimally doped sample where the Curie Weiss temperature dependence of the line width suggests the onset of ferromagnetic correlations coexisting with superconductivity at the nanoscale. 1/T$_2$ measurements revealed that the energy barrier characterizing the low energy spin fluctuations of these compounds is enhanced upon proton irradiation, suggesting that the defects are likely slowing down the fluctuations between ($0,\pi)$ and ($\pi$,0) nematic ground states.

Classical Spin Nematic Transition in LiGa_{0.95}In_{0.05}Cr_{4}O_{8}.

We present the results of a combined ^{7}Li-NMR and diffraction study on LiGa_{0.95}In_{0.05}Cr_{4}O_{8}, a member of the LiGa_{1-x}In_{x}Cr_{4}O_{8} "breathing" pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for LiGaCr_{4}O_{8} is replaced by a single second-order transition at T_{f}=11 K. Neutron and x-ray diffraction rule out both structural symmetry lowering and magnetic long-range order as the origin of this transition. Instead, reverse MonteCarlo fitting of the magnetic diffuse scattering indicates that the low-temperature phase may be described as a collinear spin nematic state, characterized by a quadrupolar order parameter. This state also shows signs of short-range order between collinear spin arrangements on tetrahedra, revealed by mapping the reverse MonteCarlo spin configurations onto a three-state color model.