From chessboard of bipolarons of size 4a in cubic La7/8Sr1/8MnO3 to stripes of the same bipolarons in layered high Tc cuprates

Abstract

The compound La1-xSrxMnO3 exhibits a charge order (CO) state at $x\approx 1/8$ and $T<T_{co}$, which recalls the CO state with a decrease in the temperature of the superconducting transition, $T_c$, observed in all cuprates at this doping value. Local excitations of lattice and magnetic origins measured in the two-dimensional metallic state of La7/8Sr1/8MnO3 reveal the existence of bipolarons of size $4a$ resulting from structural and antiferromagnetic pairings of hole-rich orbital polarons of size $2a$. They are intertwined with hole-poor domains in a disordered state at $T>T_{co}$ which become ordered on a chessboard organized in a 3D-order state of ferromagnetically paired polarons at $T<T_{co}$. Applied to the CuO$_2$ planes of the cuprates of the "214" family, this model produces stripes of bipolarons intertwined with stripes of antiferromagnetically arranged spins, hole-poor, both of size $4a$, leading to a spin density wave with a wave vector $δ=1/8$, a charge density wave with $q=1/4$, the Yamada laws $δ(x)=x$ and $T_c\propto δ$ and a decrease of $T_c$ at x=1/8. This work invokes relevance of a bipolaronic origin of high $T_c$ superconductivity, in which bipolarons of size $4a$ can play a major role.

Figures (20)

• Figure 1: a) Magnetic spectrum along [110] at T$>T_{co}$ (full red circles) and along [111] at T$<T_{co}$ (empty blue triangles). At $T>T_{co}$ we have checked that the [110] direction is equivalent to the [111] direction which was used in the highest energy range to open the available energy window. The two (four) branches observed along [110] ([111]) arise from AF paired (F paired) hole-rich domains fluctuating between the diagonals of squares (cubes). b) Phonon spectrum determined at $T=300K$ along [110]. The rectangle outlines the additional excitation observed between LA and TA at q=0.125 rlu. The anomalous increase of their intensity is shown in the raw data of panel c). In all excitation spectra, the vertical lines are error bars and the continuous and dashed lines are guides to the eye.
• Figure 2: Magnetic spectrum along the MnO bond directions. a) at $T<T_{co}$ E(q) branches of the magnetic spectrum adapted from Ref.Hennion05 showing a dip at $q=7/16$ rlu in the $E=LA$ and $E=LO$ branches corresponding to the "in-plane" magnetic fluctuations. The upper energy branch occurring at $E=LO'$ at $T<T_{co}$ has been omitted for clarity. b) Quadratic law $Dq^2$ measured at T=150K ( blue circles) adapted from Ref.Hennion06 showing an energy gap at $q=1/8$ rlu outlined by an arrow and compared to the $Dq^2$ measured at T=169K (red circles). c) Maximum of energy observed at $q=0.45$ rlu in the upper energy branches of the magnetic fluctuations. The $q'$ scale is defined by $q'=(0.83)^{-1}q$ (see the text). The E(0) branch, also observed in lattice excitations, but not displayed, can be attributed to a binding energy of the bipolaron to the latticeHennion19. $\Gamma$ is the energy line-width.
• Figure 3: The dispersion branches sketched by continuous lines reveal four distinct experimental situations. a) an F coupling at the interface between two neighboring F domains, each of size $a\sqrt{3}$ along [111], b) a F coupling between adjacent F domains of size $2a$ showing a period $8a$. c) a AF coupling at the interface between two neighboring F domains, each of size $a\sqrt{2}$ along [110] d) an AF coupling at the interface between two neighbor F domains of size $2a'$ with $a'=0.25/0.3 a$ and $q'$=$q$ x $0.3/0.25$ along the MnO directions of the planes (see the text).
• Figure 4: 3D superstructure of orbital bipolarons. a): 3D ferromagnetic orbital polaron $2a$x$2a$x$2a$ defined by the orbitals $T^x$, $T^y$ and $T^z$ lying at the center of each face and pointing to the $Mn^{4+}$ site in an ionic picture (cyan circle), adapted from Ref.Mizokawa00. b) Cubes of side $4a$ containing eight charges (octopolarons) defined 1) from magnetic excitations that reveal F domains on the scale $4a\sqrt 3$ along the four [111] directions resulting from the F pairing of domains of size $2a\sqrt 3$ along these directions. They are observed thanks to orbital fluctuations that occur during their motion 2) from the additional lattice excitations that reveal bipolaronic domains of size $4a$ along the 3 MnO directions (12 links) observed during their short lifetime. c) 3D charge order defined by two families of columns of identical cubes of side $4a$ sketched with red and blue colors corresponding to a translation by $+a$ or $-a$ along $c$ axis. Each cube is connected to cubes of same family by its four diagonals [111] (see the two dotted-dashed lines along one diagonal [111] of each family). d) Projection in (a, b) planes of the two families of cubes with bases respectively at the coordinates $z_1$ and $z_2=z_1-a$ or $z_2=z_1+a$. e) Chessboard of hole-rich and hole-poor domains of size $4a$ with alternation along the $\bf c$ axis determined by the 3D charge order. The white circles indicate Mn sites. The large blue circles visualize the center of the hole-rich polarons in a given MnO plane. The green line indicates a CDW of period $4a$ along one MnO bond direction of the planes intertwined with the chessboard of bipolarons also inferred from our experiments. The CDW of period $4a\sqrt 2$ also observed along the [110] direction is not shown. The large red circle enhances the small red one. The charge density extends up to the oxygen sites sketched by filled brown circles.
• Figure 5: Phonon spectra along [100] determined in longitudinal (red and green color) and transverse (blue color) configurations with: in a) at 15K ($T<T_{co}$) one additional branch labeled TA', and, in b), at 300K and 180K ($T>T_{co}$) four additional branches labeled LO' and LA' ($q_{min}\approx 0.3$ rlu), TA' and TA" ($q_{min}\approx 0.15$ rlu). The $q'$ wave-vector is defined by $q'=(0.3/0.25)^{-1}q$ (see the text). The dashed area indicates that the LA(q) branch splits into three branches at $q\le 0.15$ rlu. In a) and b), the continuous and dotted lines are guides to the eye. The dotted vertical lines point to the characteristic values $q_{min}$=0.125 and $q=0.25$ rlu for TA' ($T<T_{co}$) and $q_{min}$=0.15 for TA' and TA" , $q_{min}$=0.3 for LO' and LA' ($T>T_{co}$). The horizontal arrows represent their estimated error.