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Pronounced interplay between intrinsic phase-coexistence

The date of: 2022-08-29
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Pronounced interplay between intrinsic phase-coexistence and octahedral tilt magnitude in hole-doped lanthanum cuprates




Definitive understanding of superconductivity and its interplay with structural symmetry in the hole-doped lanthanum cuprates remains elusive. The suppression of superconductivity around 1/8th doping maintains particular focus, often attributed to charge-density waves (CDWs) ordering in the low-temperature tetragonal (LTT) phase. Central to many investigations into this interplay is the thesis that La1.875Ba0.125CuO4 and particularly La1.675Eu0.2Sr0.125CuO4 present model systems of purely LTT structure at low temperature. However, combining single-crystal and high-resolution powder X-ray diffraction, we find these to exhibit significant, intrinsic coexistence of LTT and low-temperature orthorhombic domains, typically associated with superconductivity, even at 10 K. Our two-phase models reveal substantially greater tilting of CuO6 octahedra in the LTT phase, markedly buckling the CuO2 planes. This would couple significantly to band narrowing, potentially indicating a picture of electronically driven phase segregation, reminiscent of optimally doped manganites. These results call for reassessment of many experiments seeking to elucidate structural and electronic interplay at 1/8 doping.


The prospect of room-temperature superconductivity (SC) has provided a tantalising target1 to chemists and physicists alike for some 35 years since the discovery of high-temperature SC in La2−xBaxCuO4. Yet, despite the extensive research efforts drawn by this and the range of compounds that followed, understanding of the origin and mechanism of the SC and competing electronic phenomena, including charge-density wave (CDW) and spin-ordered (SO) states, remains limited to the electronic context2,3 and unification with the structural behaviour has proved elusive4. In this context, a comprehensive understanding of the microscopic structure–property relationship in these compounds is highly desirable and would further illuminate the path to enhanced critical temperatures (TC) for three-dimensional (3D) SC in these and similar materials.

At high temperature, the Ruddlesden-Popper An+1BnO3n+1 (n = 1) cuprate perovskites crystallise in the high-temperature tetragonal (HTT), I4/mmm phase (Fig. 1a), wherein only two internal degrees of freedom are allowed, perturbing the A-site cation and apical oxygen atoms along the crystallographic c axis5. In general, as these samples are cooled, they undergo a phase transition (defined as occurring at TLTO) to an orthorhombic, Bmab supercell (basis w.r.t HTT: ([1 −1 0], [1 1 0], [0 0 1]) with no change of origin). In this so-called low-temperature orthorhombic (LTO) phase (Fig. 1b,c), additional degrees of freedom are realised which transform as the irreducible representation (irrep) X3+(a;0) of I4/mmm and correspond to the BO6 octahedra tilting off the crystallographic c axis by rotation about the a axis of the low-temperature supercell (Fig. 1e). This results in all Cu–O–Cu bonds buckling to an equal degree in an alternating fashion above and below the (2 0 0) planes. It is in this LTO phase that 3D SC is understood to arise at certain doping levels of the parent lanthanum cuprate phase.

(a) Representation of the HTT structure of the Ruddlesden-Popper n = 1 cuprates, packed according to the low-temperature supercell and showing its relationship to the I4/mmm aristotype unit-cell (for LTO and LTT, a = aHTT − bHTT, b = aHTT + bHTT and c = cHTT); A-site cation (e.g., La, Ba,…) in green, copper (B-site) in blue and oxygen in red. (b) and (c) show representations of the LTO structure (A-site cations omitted for clarity) viewed just off (a) and (b), respectively. (d) Presents a similar depiction of the LTT phase viewed just off (a). Note how, in LTO (b, c), the sense of the distortion is such that they propagate solely along (b) and all Cu–O–Cu bonds are buckled while, in the LTT phase (d), distortions propagate along alternating diagonals in adjacent layers, [1 1 0] at z = 0 and [1 −1 0] at z = 0.5 with respect to the super-cell, and so buckle only half the Cu–O–Cu bonds, along orthogonally alternating vectors in each layer. (e) and (f) show the CuO6 octahedra in the ab planes of the LTO and LTT phase, respectively, viewed parallel to (c); black arrows depict the direction in which the tilts occur, i.e., their ‘sense’, and the blue dashed lines the associated ‘buckles’ in the CuO2 planes.

In the case of La2−xBaxCuO4, the temperature/doping phase diagram exhibits two pronounced regions of superconductivity, with TC peaking at c.a. x = 0.095 and 0.155, either side of a pronounced dip at 1/8th doping6. This suppression of TC is understood to be coincident with the occurrence of a second structural phase transition, with TLTT commencing below 80 K and forming the low-temperature tetragonal (LTT) phase (P42/ncm) that may be expressed in the same supercell setting as for LTO. In this arrangement, tilt degrees of freedom now correspond to an order parameter direction of X3+(a;a), wherein the sense of the octahedral tilting is described by equal magnitudes in both a and b with respect to the low-temperature supercell (Fig. 1f) and the resulting rotations propagating along orthogonally alternating diagonals in adjacent CuO2 layers (Fig. 1d). This results in only half of the Cu–O–Cu interactions—those along the [1 1 0] and [1 −1 0] directions of the supercell for the different layers centred at z = 0 and ½—buckling out of the (2 0 0) planes with O atoms alternating above and below the CuO2 plane. Perpendicular to these within each layer, the Cu–O–Cu interactions adopt linear configurations that form 1D chains. It is important to note that, although 3D SC is typically suppressed in the LTT phase, two-dimensional (2D) superconductivity is understood as being able to coexist with the CDW state7.

Unlike the second-order HTT → LTO phase transition, which in La2−xBaxCuO4 (x = 0.125; LBCO) occurs upon cooling below ~ 210 K8, there is no group-subgroup relationship between the LTO and LTT phases, requiring the phase transition to be first-order in nature. A second-order transition pathway could only be envisaged if the system passed continuously through a lower symmetry phase that formed a subgroup of both LTT and LTO phases. In this context, evidence of such an intervening ‘low-temperature, less-orthorhombic’ (LTLO) phase (in Pccn) has been seen in rare-earth doped systems, including La2−y−xNdySrxCuO49 and La2−ySmyCuO410. Surprisingly, these transitions still appear to proceed with clear elements of first-order character and pronounced coexistence of orthorhombic phases, presenting further unexplained complexities to the structural behaviour of this family of materials.

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