Spin Stripe Research Articles

Nature of stripes in the generalized t–J model applied to the cuprate superconductors

A recent study of the transport properties on the stripe phase in La1.875Ba01.25CuO4 by Li et al (2007 Phys. Rev. Lett. 99 067001) found two-dimensional (2D) superconductivity over a wide temperature range including a Berezinski–Kosterlitz–Thouless transition at a temperature T=16 K, with 3D superconducting (SC) ordering only at T=4 K. These results contradict the long standing belief that the onset of superconductivity is suppressed by stripe ordering and suggest coexistence of stripe and SC phases. The lack of 3D SC order above T=4 K requires an antiphase ordering in the SC state to suppress the interlayer Josephson coupling as proposed by Berg et al (2007 Phys. Rev. Lett. 99 127003). Here, we use a renormalized mean field theory for a generalized t–J model to examine in detail the energetics of the spin and charge stripe ordered SC states including possible antiphase domains in the SC order. We find that the energies of these modulated states are very close to each other and that the anisotropy present in the low temperature tetragonal crystal structure favors stripe resonating valence bond states. The stripe antiphase SC states are found to have energies very close to, but always above, the ground state energy, which suggests additional physical effects are responsible for their stability.

Theoretical investigation of magnetic order inRFeAsO(R=Ce,Pr)

Density-functional theory calculations are carried out on $R\text{FeAsO}$, $R=\text{Ce}$ and Pr, the parent compounds of the high-${T}_{c}$ superconductors $R{\text{FeAsO}}_{1\ensuremath{-}x}{\text{F}}_{x}$, in order to determine the magnetic order of the ground state. It is found that the magnetic moments on the Fe sites adopt an antiferromagnetic order, with a stripelike pattern similar to the case of LaFeAsO. Within the generalized gradient approximation along with Coulomb on-site repulsion $(\text{GGA}+U)$, we show that the $R$ magnetic moments also adopt an antiferromagnetic order for which, within the $R\text{O}$ layer, the same spin $R$ sites lie along a zigzag line perpendicular to the Fe spin stripes. While within GGA the $R\text{ }4f$ band crosses the Fermi level, upon inclusion of on-site Coulomb interaction on the $R$ sites the $4f$ band splits and moves away from the Fermi level. If on-site Coulomb interaction is also included on the Fe sites, $R\text{FeAsO}$ is shown to change from a semimetal to a Mott insulator.

Commensurate Itinerant Antiferromagnetism in BaFe2As2: 75As-NMR Studies on a Self-Flux Grown Single Crystal

We report results of 75 As nuclear magnetic resonance (NMR) experiments on a self-flux grown single crystal of BaFe 2 As 2 . A first-order antiferromagnetic (AF) transition near 135 K was detected by the splitting of NMR lines, which is accompanied by simultaneous structural transition as evidenced by a sudden large change of the electric field gradient tensor at the As site. The NMR results lead almost uniquely to the stripe spin structure in the AF phase. The data of spin–lattice relaxation rate indicate development of anisotropic spin fluctuations of the stripe-type with decreasing temperature in the paramagnetic phase.

Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high-temperature superconductors

We consider incommensurate order parameters for electrons on a square lattice which reduce to $d$-density wave order when the ordering wave vector $\mathbf{Q}$ is close to ${\mathbf{Q}}_{0}=(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$, $a$ being the lattice spacing and describe the associated charge and current distributions within a single-harmonic approximation that conserves current to lowest order. Such incommensurate orders can arise at the mean-field level in extended Hubbard models, but the main goal here is to explore thoroughly the consequences within a Hartree-Fock approximation. We find that Fermi surface reconstruction in the underdoped regime can correctly capture the phenomenology of the recent quantum oscillation experiments that suggest incommensurate order, in particular the de Haas--van Alphen oscillations of the magnetization in high fields and very low temperatures in presumably the mixed state of these superconductors. For 10% hole doping in ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6+\ensuremath{\delta}}$, we find in addition to the main frequency around 530 T arising from the electron pocket and a hole frequency at around 1650 T, a new low frequency from a smaller hole pocket at 250 T for which there are some indications that require further investigations. The oscillation corresponding to the electron pocket will be further split due to bilayer coupling, but the splitting is sufficiently small to require more refined measurements. The truly incommensurate $d$-density wave breaks both time reversal and inversion, but the product of these two symmetry operations is preserved. The resulting Fermi surface splits into spin-up and spin-down sectors that are inversion conjugates. Each of the spin sectors results in a band structure that violates reflection symmetry, which can be determined in spin and angle-resolved photoemission spectroscopies. For those experiments such as the current photoemission experiments or the quantum oscillation measurements that cannot resolve the spin components, the bands will appear to be symmetric because of the equal mixture of the two spin sectors. There is some similarity of our results with the spiral spin-density wave order which, as pointed out by Overhauser, also breaks time reversal and inversion. Calculations corresponding to higher order commensuration produce results similar to antiphase spin stripes but appear to us to be an unlikely explanation of the experiments. The analysis of the Gorkov equation in the mixed state shows that the oscillation frequencies are unshifted from the putative normal state and the additional Dingle factor arising from the presence of the mixed state can provide a subtle distinction between the spiral spin-density wave and the $d$-density wave, although this is very difficult to establish precisely.

Spectral signatures of modulatedd-wave superconducting phases

We calculate, within a mean-field theory, the spectral signatures of various striped $d$-wave superconducting phases. We consider both in-phase and antiphase modulations of the superconducting order across a stripe boundary and the effects of coexisting inhomogeneous orders, including spin stripes, charge stripes, and modulated $d$-density wave. We find that the antiphase modulated $d$-wave superconductor exhibits zero-energy spectral weight, primarily along extended arcs in momentum space. Concomitantly, a Fermi surface appears and typically includes both open segments and closed pockets. When weak homogeneous superconductivity is also present, the Fermi surface collapses onto nodal points. Among them are the nodal points of the homogeneous $d$-wave superconductor, but others typically exist at positions that depend on the details of the modulation and the band structure. Upon increasing the amplitude of the constant component, these additional points move toward the edges of the reduced Brillouin zone where they eventually disappear. The above signatures are also manifested in the density of states of the clean, and the disordered system. While the presence of coexisting orders changes some details of the spectral function, we find that the evolution of the Fermi surface and the distribution of the low-energy spectral weight are largely unaffected by them.

Topological spin textures in the helimagnet FeGe

We report on the real-space observation of a type of spin texture, i.e., the Swiss-roll-like vortex, in cubic helimagnet ($B20$-type) FeGe in terms of the Lorentz electron microcopy. This structure is enabled by the weak spin anisotropy in FeGe and the two-dimensional confinement, as revealed by a theoretical analysis that takes into account the Berry phase [Proc. R. Soc. London, Ser. A 392, 45 (1984)] associated with the curved spin stripes, i.e., the change in the spiral direction.

Electronic structure of charge and spin stripe order inLa2−xSrxNiO4(x=13,12)

Electronic structure of stripe ordered ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Ni}{\mathrm{O}}_{4}$ is investigated. The system with $x=\frac{1}{3}$ is insulator, in $\mathrm{LSDA}+U$ calculations, and shows charge and spin stripe, consistent with the experimental results. A highly correlated system of $x=\frac{1}{2}$ is studied by using exact diagonalization of the multiorbital many-body Hamiltonian derived from LDA calculations and including on-site and intersite Coulomb interactions. The fluctuation of the residual spin on ${\mathrm{Ni}}^{3+}$ (hole) site couples with the charge fluctuation between ${\mathrm{Ni}}^{3+}$ and ${\mathrm{Ni}}^{2+}$ states and this correlation lowers the total energy. The resultant ground state is an insulator with charge and spin stripe of the energy gap $0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, consistent with the observed one. The on-site Coulomb interaction stabilizes integral valency of each Ni ion (${\mathrm{Ni}}^{3+}$ and ${\mathrm{Ni}}^{2+}$), but does not induce the charge order. Two quantities, intersite Coulomb interaction and anisotropy of hopping integrals, play an important role to form the charge and spin stripe order in a system of $x=\frac{1}{2}$.

MAGNETIC PHASE DIAGRAMS OF THE GENERALIZED SPIN-ONE-HALF FALICOV–KIMBALL MODEL

A combination of small-cluster exact-diagonalization calculations and a well-controlled approximative method is used to examine the ground-state phase diagrams of the spin-one-half Falicov–Kimball model extended by the spin-dependent on-site interaction (J) between localized spins and itinerant (d) electrons, as well as by external magnetic field (h). Both the magnetic ordering and metamagnetic transitions are analyzed as functions of h and the number of itinerant electrons (Nd) at selected J. Various magnetic superstructures including axial and diagonal spin stripes are observed for non-zero values of J and h. Moreover, it is shown that increasing h strongly stabilizes the fully and partially polarized states, while the non-polarized state is reduced.

Coupling of stripes to lattice distortions in cuprates and nickelates

In recent X-ray diffraction experiments on orthorhombic nickelates, we have observed a significant coupling between the stripe correlations and the lattice distortion. In particular, the diagonal charge stripes of this insulating material exhibit a preferred orientation parallel to the orthorhombic a-axis, similar to the diagonal spin stripes in La2−xSrxCuO4 below the metal-insulator transition. In the light of this finding, we draw a comparison between the lightly doped parts of the phase diagrams of La2−xSrxCuO4 with low-temperature orthorhombic (LTO) structure, and La1.8−xEu0.2SrxCuO4 with low-temperature tetragonal (LTT) structure. In La1.8−xEu0.2SrxCuO4, a local minimum in the Sr dependence of the LTO/LTT transition temperature, as well as reduced spin-glass transition temperatures, may be indicators for the presence of diagonal charge correlations. Above the metal-insulator transition the LTT phase is suited to pin parallel stripes, while below that transition the LTT phase seems instead to compete with the formation of diagonal stripes.

Spin Incommensurability and Two Phase Competition in Cobaltites

The perovskite LaCoO3 evolves from a nonmagnetic Mott insulator to a spin cluster ferromagnet (FM) with the substitution of Sr2+ for La3+ in La1-xSrxCoO3. The clusters increase in size and number with x and the charge percolation through the clusters leads to a metallic state. Using elastic neutron scattering on La1-xSrxCoO3 single crystals, we show that an incommensurate spin superstructure coexists with the FM spin clusters. The incommensurability increases continuously with x, with the intensity rising in the insulating phase and dropping in the metallic phase as it directly competes with the commensurate FM, itinerant clusters. The spin incommensurability arises from local order of Co3+-Co4+ clusters but no long-range static or dynamic spin stripes develop. The coexistence and competition of the two magnetic phases explain the residual resistivity at low temperatures in samples with metalliclike transport.

Unidirectional diagonal order and three-dimensional stacking of charge stripes in orthorhombicPr1.67Sr0.33NiO4andNd1.67Sr0.33NiO4

The interplay between crystal symmetry and charge stripe order in Pr1.67Sr0.33NiO4 and Nd1.67Sr0.33NiO4 has been studied by means of single crystal x-ray diffraction. In contrast to tetragonal La1.67Sr0.33NiO4, these crystals are orthorhombic. The corresponding distortion of the NiO2 planes is found to dictate the direction of the charge stripes, similar to the case of diagonal spin stripes in the insulating phase of La2-xSrxCuO4. In particular, diagonal stripes seem to always run along the short a-axis, which is the direction of the octahedral tilt axis. In contrast, no influence of the crystal symmetry on the charge stripe ordering temperature itself was observed, with T_CO 240K for La, Pr, and Nd. The coupling between lattice and stripe degrees of freedom allows one to produce macroscopic samples with unidirectional stripe order. In samples with stoichiometric oxygen content and a hole concentration of exactly 1/3, charge stripes exhibit a staggered stacking order with a period of three NiO2 layers, previously only observed with electron microscopy in domains of mesoscopic dimensions. Remarkably, this stacking order starts to melt about 40K below T_CO. The melting process can be described by mixing the ground state, which has a 3-layer stacking period, with an increasing volume fraction with a 2-layer stacking period.

Gapless quantum spin liquid, stripe, and antiferromagnetic phases in frustrated Hubbard models in two dimensions

Unique features of non-magnetic insulator phase are shown, and phase diagram for t-t' Hubbard model on square lattice is presented. Using the path-integral renormalization group method, we find antiferromagnetic phase for small next-nearest neighbor transfer t' and stripe (or collinear) phase for large t' in the Mott insulating region of strong on site interaction U. For intermediate t'/t~ 0.7 at large U/t>7, we find longer-period antiferromagnetic insulator phase with 2*4 structure. In the Mott insulating region, we also find quantum spin liquid (in other words, non-magnetic insulator) phase near the Mott transition to paramagnetic metals. Correlated electrons often crystallize to the Mott insulator usually with some magnetic orders, whereas the "quantum spin liquid" has been a long-sought issue. We report numerical evidences that a nonmagnetic insulating (NMI) phase gets stabilized near the Mott transition with remarkable properties: The 2D Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. It has an interpretation for an unexplored type of a quantum liquid. The present concept is useful in analyzing a variety of experimental results in frustrated magnets including organic BEDT-TTF compounds and 3He atoms adsorbed on graphite.

Charge stripes in cuprate superconductors: The middle way

Charge and spin stripe order is a type of electronic crystal observed in certain layered cuprates associated with high-temperature superconductivity. Quantum-disordered stripes could be relevant for understanding the superconductivity. Here I discuss recent experimental characterizations of the stripe-ordered state in La(1.875)Ba(0.125)CuO(4), and compare them with properties of superconducting compositions.

Universal magnetic excitation spectrum in cuprates

Abstract We have recently used inelastic neutron scattering to measure the magnetic excitation spectrum of La 1.875 Ba 0.125 CuO 4 up to 200 meV. This particular cuprate is of interest because it exhibits static charge and spin stripe order. The observed spectrum is remarkably similar to that found in superconducting YBa 2 Cu 3 O 6+ x and La 2− x Sr x CuO 4 ; the main differences are associated with the spin gap. We suggest that essentially all observed features of the magnetic scattering from cuprate superconductors can be described by a universal magnetic excitation spectrum multiplied by a spin gap function with a material-dependent spin-gap energy.

Weak ferromagnetic spin and charge stripe order inLa5∕3Sr1∕3NiO4

We present magnetization and specific heat data of a La5/3Sr1/3NiO4 single crystal in high magnetic fields. From the charge and spin stripe ordering temperatures, as well as a magnetic low temperature transition, we have constructed the electronic phase diagram for fields up to 14 Tesla. While the charge stripe ordering temperature TCO is independent of the magnetic field, there is a significant shift of the spin stripe ordering temperature TSO of about 1.5 K/ Tesla, if the magnetic fields are applied parallel to the NiO2-planes. The specific heat measurements indicate a large anomalous entropy change at TCO. In contrast, no significant entropy change is observed at the spin stripe transition. The high field magnetization experiments reveal the presence of in-plane weak ferromagnetic moments in the charge stripe ordered phase. From a phenomenological analysis, the magnetic correlation length of these moments is determined. We suggest that the weak ferromagnetism is due either to the presence of bond-centered charge stripes or to double exchange interactions across site-centered charge stripes.

Spin Dynamics in the Stripe Phase of the Cuprate Superconductors

Within a model that supports stripe spin and charge order coexisting with a d(x2-y2)-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin-wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.

Field-induced magnetic order and thermal conductivity in La 1.87Sr 0.13Cu 1− yM yO 4 (M = Zn, Ni)

We have measured the thermal conductivity in the ab plane, κ ab , of La 1.87Sr 0.13Cu 1− y M y O 4 (M = Zn, Ni; y = 0.01, 0.03, 0.10) single crystals in magnetic fields up to 14 T parallel to the c axis. By the application of magnetic field, κ ab has been found to be slightly suppressed at low temperatures for y(Zn) = 0.01 and y(Ni) = 0.01. The suppression of κ ab is smaller for y(Zn) = 0.01 than that for y(Ni) = 0.01. These results support the stripe-pinning model where the dynamically fluctuating stripes of spins and holes are regarded as being pinned by vortex cores, leading to the development of the static stripe order.

μSR and thermal conductivity studies on inhomogeneity of the impurity- and field-induced magnetism and superconductivity in high- Tc cuprates

The inhomogeneity of the impurity- and field-induced magnetic order and superconductivity has been investigated in the hole-doped La 2− x Sr x CuO 4 (LSCO), La 2− x Ba x CuO 4 (LBCO) and the electron-doped Pr 1− x LaCe x CuO 4 (PLCCO). For the hole-doped cuprates, it has been found from the muon-spin-relaxation measurements that both Zn and Ni impurities tend to develop a magnetic order and to destroy the superconductivity around themselves not only around p (the hole concentration per Cu) = 1/8 but also at x = 0.15 and 0.18 in LSCO, though the development of the magnetic order by Zn is more marked than by Ni. Moreover, it has been found from the thermal conductivity measurements that the development of the magnetic order by the application of magnetic field is marked not just at p = 1/8 but in the neighborhood of p = 1/8 in LSCO and LBCO. The impurity- and field-induced magnetic order in the hole-doped cuprates can be interpreted as being due to pinning of the dynamical stripes of holes and spins by impurities and vortex cores in the CuO 2 plane, respectively. For the electron-doped PLCCO with x = 0.14, on the contrary, no impurity-induced magnetic order has been observed. The reason is discussed.

Properties and detection of spin nematic order in strongly correlated electron systems

A spin nematic is a state which breaks spin SU(2) symmetry while preserving translational and time reversal symmetries. Spin nematic order can arise naturally from charge fluctuations of a spin stripe state. Focusing on the possible existence of such a state in strongly correlated electron systems, we build a nematic wave function starting from a t-J-type model. The nematic is a spin-2 operator, and therefore does not couple directly to neutrons. However, we show that neutron scattering and Knight-shift experiments can detect the spin anisotropy of electrons moving in a nematic background. We find the mean-field phase diagram for the nematic taking into account spin–orbit effects.

FIELD-INDUCED AND IMPURITY-INDUCED MAGNETIC ORDER IN La2-xSrxCuO4 STUDIED BY THE THERMAL CONDUCTIVITY AND μSR

Our recent experimental works on the field-induced and impurity-induced magnetic order in La 2-x Sr x CuO 4 are reviewed. The muon-spin-relaxation (μSR) measurements of La 2-x Sr x Cu 1-y M y O 4 ( M = Zn , Ni ) have revealed that both Zn and Ni impurities develop the magnetic order around x=0.115, though the effect of Zn on the development of the magnetic order is more marked than that of Ni . The field-induced magnetic order around x=0.115 pointed out from the neutron scattering experiments has also been investigated by the thermal conductivity measurements in magnetic fields. Marked suppression of the thermal conductivity by the application of magnetic fields parallel to the c-axis has been observed in x=0.10 and x=0.13, which appears to be in good correspondence to the development of the magnetic order. In conclusion, not only impurities but also vortex cores in the CuO 2 plane seem to operate to pin the dynamical stripes of spins and holes, leading to the development of the magnetic order.