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Collective dynamics often play an important role in determining the stability of ground states for both naturally occurring materials and metamaterials. We studied the temperature dependent dynamics of antiferromagnetically ordered superdomains in a square artificial spin lattice using soft x-ray photon correlation spectroscopy. We observed an exponential slowing down of superdomain wall motion below the AF onset temperature, similar to the behavior of typical bulk antiferromagnets. Using a continuous time random walk model we show that these superdomain walls undergo low-temperature ballistic and high-temperature diffusive motions., 5 pages, 4 figures

The metal-insulator phase transition in magnetite, known as the Verwey transition, is characterized by a charge-orbital ordering and a lattice transformation from a cubic to monoclinic structure. We use $x$-ray photon correlation spectroscopy to investigate the dynamics of this charge-orbitally ordered insulating phase undergoing the insulator-to-metal transition. By tuning to the Fe ${L}_{3}$ edge at the $(00\frac{1}{2})$ superlattice peak, we probe the evolution of the Fe ${t}_{2g}$ orbitally ordered domains present in the low temperature insulating phase and forbidden in the high temperature metallic phase. We observe two distinct regimes below the Verwey transition. In the first regime, magnetite follows an Arrhenius behavior and the characteristic timescale for orbital fluctuations decreases as the temperature increases. In the second regime, magnetite phase separates into metallic and insulating domains, and the kinetics of the phase transition is dictated by metallic-insulating interfacial boundary conditions.

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in ${\mathrm{La}}_{1.825}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_{4}$ by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu ${L}_{3}$ edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to $2\text{ }\textthreequarters{}\text{ }\text{ }\mathrm{h}$. We discuss the implications of these results for some of the competing theories.

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾ h. We discuss the implications of these results for some of the competing theories.

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

We present an element selective resonant magnetic x-ray scattering study of ${\mathrm{NdFe}}_{3}({\mathrm{BO}}_{3}{)}_{4}$ as a function of temperature and applied magnetic field. Our measurements show that the magnetic order of the Nd sublattice is induced by the Fe spin order. When a magnetic field is applied parallel to the hexagonal basal plane, the helicoidal spin order is suppressed and a collinear ordering, where the moments are forced to align in a direction perpendicular to the applied magnetic field, is stabilized. This result excludes a noncollinear spin order as the origin of the magnetically induced electric polarization in this compound. Instead our data imply that magnetic frustration results in a phase competition, which is the origin of the magnetoelectric response.

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

Recently, charge density wave (CDW) order in the ${\mathrm{CuO}}_{2}$ planes of underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\ensuremath{\delta}}$ was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.75}$ with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice reflection at $Q=[0.33\text{ }0\text{ }L]$ whose energy and polarization dependence agrees with expectations for oxygen ordering and a spatial modulation of the Cu valence in the chains. Incommensurate peaks at [0.30 0 $L$] and [0 0.30 $L$] from the CDW order in the planes are shown to be distinct in $Q$ as well as their temperature, energy, and polarization dependence, and are thus unrelated to the structure of the chain layer. Moreover, the energy dependence of the CDW order in the planes is shown to result from a spatial modulation of energies of the Cu $2p$ to $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ transition, similar to stripe-ordered 214 cuprates.

We present an element selective resonant magnetic x-ray scattering study of NdFe3(BO3)4 as a function of temperature and applied magnetic field. Our measurements show that the magnetic order of the Nd sublattice is induced by the Fe spin order. When a magnetic field is applied parallel to the hexagonal basal plane, the helicoidal spin order is suppressed and a collinear ordering, where the moments are forced to align in a direction perpendicular to the applied magnetic field, is stabilized. This result excludes a noncollinear spin order as the origin of the magnetically induced electric polarization in this compound. Instead our data imply that magnetic frustration results in a phase competition, which is the origin of the magnetoelectric response.

Recently, charge density wave (CDW) order in the CuO(2) planes of underdoped YBa(2)Cu(3)O(6+δ) was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of YBa(2)Cu(3)O(6.75) with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice reflection at Q=[0.33 0 L] whose energy and polarization dependence agrees with expectations for oxygen ordering and a spatial modulation of the Cu valence in the chains. Incommensurate peaks at [0.30 0 L] and [0 0.30 L] from the CDW order in the planes are shown to be distinct in Q as well as their temperature, energy, and polarization dependence, and are thus unrelated to the structure of the chain layer. Moreover, the energy dependence of the CDW order in the planes is shown to result from a spatial modulation of energies of the Cu 2p to 3d(x(2)-y(2)) transition, similar to stripe-ordered 214 cuprates.

Using powder neutron diffraction, we have discovered an unusual magnetic order-order transition in the Ising spin chain compound Ca(3)Co(2)O(6). On lowering the temperature, an antiferromagnetic phase with a propagation vector k = (0.5, -0.5, 1) emerges from a higher temperature spin density wave structure with k = (0, 0, 1.01). This transition occurs over an unprecedented time scale of several hours and is never complete.

Using powder neutron diffraction, we have discovered an unusual magnetic order-order transition in the Ising spin chain compound Ca3Co2O6. On lowering the temperature, an antiferromagnetic phase with a propagation vector k=(0.5,-0.5,1) emerges from a higher temperature spin density wave structure with k=(0,0,1.01). This transition occurs over an unprecedented time scale of several hours and is never complete.

Geometrical frustration of the Fe ions in LuFe 2 O 4 leads to intricate charge and magnetic order and a strong magnetoelectric coupling. Using resonant x-ray diffraction at the Fe K edge, the anomalous scattering factors of both Fe sites are deduced from the (h/3 k/3 l/2) reflections. The chemical shift between the two types of Fe ions equals 4.0(1) eV corresponding to full charge separation into Fe2 + and Fe 3+ . The polarization and azimuthal angle dependence of the superlattice reflections demonstrate the absence of differences in anisotropic scattering revealing random orientations of the Fe 2+ orbitals characteristic of an orbital glass state.

We have studied the temperature dependences of the so-called charge and orbital ordering reflections in the neighborhood of the Verwey transition by means of resonant x-ray scattering at the Fe K and L edges on a high purity single crystal of magnetite. Contrary to recently published results [J. E. Lorenzo, Phys. Rev. Lett. 101, 226401 (2008)10.1103/PhysRevLett.101.226401], we show that all the reflections studied disappear simultaneously at the Verwey transition for both edges, on and off resonance. This means that there is no correlation between the Verwey (123.5 K) and the spin-reorientation (130 K) transitions and that the resonant reflections are driven by the lattice distortions.

Geometrical frustration of the Fe ions in LuFe2O4 leads to intricate charge and magnetic order and a strong magnetoelectric coupling. Using resonant x-ray diffraction at the Fe K edge, the anomalous scattering factors of both Fe sites are deduced from the (h/3 k/3 l/2) reflections. The chemical shift between the two types of Fe ions equals 4.0(1) eV corresponding to full charge separation into Fe2+ and Fe3+. The polarization and azimuthal angle dependence of the superlattice reflections demonstrate the absence of differences in anisotropic scattering revealing random orientations of the Fe2+ orbitals characteristic of an orbital glass state.

We present a detailed powder and single-crystal neutron diffraction study of the spin chain compound ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{2}{\mathrm{O}}_{6}$. Below 25 K, the system orders magnetically with a modulated partially disordered antiferromagnetic structure. We give a description of the magnetic interactions in the system which is consistent with this magnetic structure. Our study also reveals that the long-range magnetic order coexists with a shorter-range order with a correlation length scale of $\ensuremath{\sim}180\text{ }\text{ }\AA{}$ in the $ab$ plane. Remarkably, on cooling, the volume of material exhibiting short-range order increases at the expense of the long-range order.

We present a detailed powder and single-crystal neutron diffraction study of the spin chain compound Ca3Co2O6. Below 25 K, the system orders magnetically with a modulated partially disordered antiferromagnetic structure. We give a description of the magnetic interactions in the system which is consistent with this magnetic structure. Our study also reveals that the long-range magnetic order coexists with a shorter-range order with a correlation length scale of approximately 180 angstroms in the ab plane. Remarkably, on cooling, the volume of material exhibiting short-range order increases at the expense of the long-range order.