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Atomic Alignment in PbS Nanocrystal Superlattices with Compact Inorganic Ligands via Reversible Oriented Attachment of Nanocrystals
Authors:
Ahhyun Jeong,
Aditya N. Singh,
Josh Portner,
Xiaoben Zhang,
Saghar Rezaie,
Justin C. Ondry,
Zirui Zhou,
Junhong Chen,
Ye Ji Kim,
Richard D. Schaller,
Youssef Tazoui,
Zehan Mi,
Sadegh Yazdi,
David T. Limmer,
Dmitri V. Talapin
Abstract:
Nanocrystals (NCs) serve as versatile building blocks for the creation of functional materials, with NC self-assembly offering opportunities to enable novel material properties. Here, we demonstrate that PbS NCs functionalized with strongly negatively charged metal chalcogenide complex (MCC) ligands, such as $Sn_2S_6^{4-}$ and $AsS_4^{3-}$, can self-assemble into all-inorganic superlattices with b…
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Nanocrystals (NCs) serve as versatile building blocks for the creation of functional materials, with NC self-assembly offering opportunities to enable novel material properties. Here, we demonstrate that PbS NCs functionalized with strongly negatively charged metal chalcogenide complex (MCC) ligands, such as $Sn_2S_6^{4-}$ and $AsS_4^{3-}$, can self-assemble into all-inorganic superlattices with both long-range superlattice translational and atomic-lattice orientational order. Structural characterizations reveal that the NCs adopt unexpected edge-to-edge alignment, and numerical simulation clarifies that orientational order is thermodynamically stabilized by many-body ion correlations originating from the dense electrolyte. Furthermore, we show that the superlattices of $Sn_2S_6^{4-}$-functionalized PbS NCs can be fully disassembled back into the colloidal state, which is highly unusual for orientationally attached superlattices with atomic-lattice alignment. The reversible oriented attachment of NCs, enabling their dynamic assembly and disassembly into effectively single-crystalline superstructures, offers a pathway toward designing reconfigurable materials with adaptive and controllable electronic and optoelectronic properties.
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Submitted 17 January, 2026;
originally announced January 2026.
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Exploring the magnetic properties of individual barcode nanowires using wide-field diamond microscopy
Authors:
Jungbae Yoon,
Jun Hwan Moon,
Jugyeong Jeong,
Yu Jin Kim,
Kihwan Kim,
Hee Seong Kang,
Yoo Sang Jeon,
Eunsoo Oh,
Sun Hwa Lee,
Kihoon Han,
Dongmin Lee,
Chul-Ho Lee,
Young Keun Kim,
Donghun Lee
Abstract:
Barcode magnetic nanowires typically comprise a multilayer magnetic structure in a single body with more than one segment type. Interestingly, owing to selective functionalization and novel interactions between the layers, barcode magnetic nanowires have attracted significant attention, particularly in the field of bioengineering. However, an analysis of their magnetic properties at the individual…
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Barcode magnetic nanowires typically comprise a multilayer magnetic structure in a single body with more than one segment type. Interestingly, owing to selective functionalization and novel interactions between the layers, barcode magnetic nanowires have attracted significant attention, particularly in the field of bioengineering. However, an analysis of their magnetic properties at the individual nanowire level remains challenging. With this background, herein, we investigated the characterization of magnetic nanowires at room temperature under ambient conditions based on magnetic images obtained via wide-field quantum microscopy with nitrogen-vacancy centers in diamond. Consequently, we could extract critical magnetic properties, such as the saturation magnetization and coercivity, of single nanowires by comparing the experimental results with those of micromagnetic simulations. This study opens up the possibility for a versatile characterization method suited to individual magnetic nanowires.
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Submitted 21 February, 2023;
originally announced February 2023.
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Proposal for the search for new spin interactions at the micrometer scale using diamond quantum sensors
Authors:
P. -H. Chu,
N. Ristoff,
J. Smits,
N. Jackson,
Y. J. Kim,
I. Savukov,
V. M. Acosta
Abstract:
For decades, searches for exotic spin interactions have used increasingly-precise laboratory measurements to test various theoretical models of particle physics. However, most searches have focused on interaction length scales greater than 1 mm, corresponding to hypothetical boson masses less than 0.2 meV. Recently, quantum sensors based on Nitrogen-Vacancy (NV) centers in diamond have emerged as…
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For decades, searches for exotic spin interactions have used increasingly-precise laboratory measurements to test various theoretical models of particle physics. However, most searches have focused on interaction length scales greater than 1 mm, corresponding to hypothetical boson masses less than 0.2 meV. Recently, quantum sensors based on Nitrogen-Vacancy (NV) centers in diamond have emerged as a promising platform to probe spin interactions at the micrometer scale, opening the door to explore new physics at this length scale. Here, we propose experiments to search for several hypothetical interactions between NV electron spins and moving masses. We focus on potential interactions involving the coupling of NV spin ensembles to both spin-polarized and unpolarized masses attached to vibrating mechanical oscillators. For each interaction, we estimate the sensitivity, identify optimal experimental conditions, and analyze potential systematic errors. Using multi-pulse quantum sensing protocols with NV spin ensembles to improve sensitivity, we project new constraints that are ~5 orders-of-magnitude improvement over previous constraints at the micrometer scale. We also identify a spin-polarized test mass, based on hyperpolarized 13C nuclear spins in a thin diamond membrane, which offers a favorable combination of high spin density and low stray magnetic fields. Our analysis is timely in light of a recent preprint (arXiv:2010.15667) reporting a surprising non-zero result of micrometer-scale spin-velocity interactions.
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Submitted 29 December, 2021;
originally announced December 2021.
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Spin-Orbit Torque Engineering in β-W/CoFeB Heterostructures via Ta and V Alloying at Interfaces
Authors:
Gyu Won Kim,
Do Duc Cuong,
Yong Jin Kim,
In Ho Cha,
Taehyun Kim,
Min Hyeok Lee,
OukJae Lee,
Hionsuck Baik,
Soon Cheol Hong,
Sonny H. Rhim,
Young Keun Kim
Abstract:
Spin-orbit torque manifested as an accumulated spin-polarized moment at nonmagnetic normal metal, and ferromagnet interfaces is a promising magnetization switching mechanism for spintronic devices. To fully exploit this in practice, materials with a high spin Hall angle, i.e., a charge-to-spin conversion efficiency, are indispensable. To date, very few approaches have been made to devise new nonma…
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Spin-orbit torque manifested as an accumulated spin-polarized moment at nonmagnetic normal metal, and ferromagnet interfaces is a promising magnetization switching mechanism for spintronic devices. To fully exploit this in practice, materials with a high spin Hall angle, i.e., a charge-to-spin conversion efficiency, are indispensable. To date, very few approaches have been made to devise new nonmagnetic metal alloys. Moreover, new materials need to be compatible with semiconductor processing. Here we introduce W-Ta and W-V alloys and deploy them at the interface between $β$-W/CoFeB layers. First, spin Hall conductivities of W-Ta and W-V structures with various compositions are carried out by first-principles band calculations, which predict the spin Hall conductivity of the W-V alloy is improved from $-0.82 \times 10^3$ S/cm that of W to $-1.98 \times 10^3$ S/cm. Subsequently, heterostructure fabrication and spin-orbit torque properties are characterized experimentally. By alloying $β$-W with V at a concentration of 20 at%, we observe a large enhancement of the absolute value of spin Hall conductivity of up to $-(2.77 \pm 0.31) \times 10^3$ S/cm. By employing X-ray diffraction and scanning transmission electron microscopy, we further explain the enhancement of spin-orbit torque efficiency is stemmed from W-V alloy between W and CoFeB.
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Submitted 9 June, 2021;
originally announced June 2021.
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Enhancement of perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction in thin ferromagnetic films by atomic-scale modulation of interfaces
Authors:
A. S. Samardak,
A. V. Davydenko,
A. G. Kolesnikov,
A. Yu. Samardak,
A. G. Kozlov,
Bappaditya Pal,
A. V. Ognev,
A. V. Sadovnikov,
S. A. Nikitov,
A. V. Gerasimenko,
In Ho Cha,
Yong Jin Kim,
Gyu Won Kim,
Oleg A. Tretiakov,
Young Keun Kim
Abstract:
To stabilize the non-trivial spin textures, e.g., skyrmions or chiral domain walls in ultrathin magnetic films, an additional degree of freedom such as the interfacial Dzyaloshinskii-Moriya interaction (IDMI) must be induced by the strong spin-orbit coupling (SOC) of a stacked heavy metal layer. However, advanced approaches to simultaneously control IDMI and perpendicular magnetic anisotropy (PMA)…
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To stabilize the non-trivial spin textures, e.g., skyrmions or chiral domain walls in ultrathin magnetic films, an additional degree of freedom such as the interfacial Dzyaloshinskii-Moriya interaction (IDMI) must be induced by the strong spin-orbit coupling (SOC) of a stacked heavy metal layer. However, advanced approaches to simultaneously control IDMI and perpendicular magnetic anisotropy (PMA) are needed for future spin-orbitronic device implementations. Here, we show an effect of atomic-scale surface modulation on the magnetic properties and IDMI in ultrathin films composed of 5d heavy metal/ferromagnet/4d(5d) heavy metal or oxide interfaces, such as Pt/CoFeSiB/Ru, Pt/CoFeSiB/Ta, and Pt/CoFeSiB/MgO. The maximum IDMI value corresponds to the correlated roughness of the bottom and top interfaces of the ferromagnetic layer. The proposed approach for significant enhancement of PMA and IDMI through the interface roughness engineering at the atomic scale offers a powerful tool for the development of the spin-orbitronic devices with the precise and reliable controllability of their functionality.
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Submitted 21 May, 2020;
originally announced May 2020.
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Neutron Scattering Studies of Spin-Phonon Hybridization and Superconducting Spin-Gaps in High Temperature Superconductor $La_{2-x}(Sr,Ba)_{x}CuO_{4}$
Authors:
J. J. Wagman,
J. P. Carlo,
J. Gaudet,
G. Van Gastel,
D. L. Abernathy,
M. B. Stone,
G. E. Granroth,
A. I. Koleshnikov,
A. T. Savici,
Y. J. Kim,
H. Zhang,
D. Ellis,
Y. Zhao,
L. Clark,
A. B. Kallin,
E. Mazurek,
H. A. Dabkowska,
B. D. Gaulin
Abstract:
We present time-of-fight neutron-scattering measurements on single crystals of $La_{2-x}Ba_{x}CuO_{4}$ (LBCO) with 0 $\leq$ x $\leq$ 0.095 and $La_{2-x}Sr_{x}CuO_{4}$ (LSCO) with x = 0.08 and 0.11. This range of dopings spans much of the phase diagram relevant to high temperature cuprate superconductivity, ranging from insulating, three dimensional (3D) commensurate long range antiferromagnetic or…
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We present time-of-fight neutron-scattering measurements on single crystals of $La_{2-x}Ba_{x}CuO_{4}$ (LBCO) with 0 $\leq$ x $\leq$ 0.095 and $La_{2-x}Sr_{x}CuO_{4}$ (LSCO) with x = 0.08 and 0.11. This range of dopings spans much of the phase diagram relevant to high temperature cuprate superconductivity, ranging from insulating, three dimensional (3D) commensurate long range antiferromagnetic order, for x $\leq$ 0.02, to two dimensional (2D) incommensurate antiferromagnetism co-existing with superconductivity for x $\geq$ 0.05. Previous work on lightly doped LBCO with x = 0.035 showed a clear resonant enhancement of the inelastic scattering coincident with the low energy crossings of the highly dispersive spin excitations and quasi-2D optic phonons. The present work extends these measurements across the phase diagram and shows this enhancement to be a common feature to this family of layered quantum magnets. Furthermore we show that the low temperature, low energy magnetic spectral weight is substantially larger for samples with non-superconducting ground states relative to any of the samples with superconducting ground states. Spin gaps, suppression of low energy magnetic spectral weight as a function of decreasing temperature, are observed in both superconducting LBCO and LSCO samples, consistent with previous observations for superconducting LSCO.
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Submitted 29 September, 2015;
originally announced September 2015.
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Heterostructures produced from nanosheet-based inks
Authors:
F. Withers,
H. Yang,
L. Britnell,
A. P Rooney,
E. Lewis,
A. Felten,
C. R. Woods,
V. Sanchez Romaguera,
T. Georgiou,
A. Eckmann,
Y. J. Kim,
S. G. Yeates,
S. J. Haigh,
A. K. Geim,
K. S. Novoselov,
C. Casiraghi
Abstract:
The new paradigm of heterostructures based on two-dimensional (2D) atomic crystals has already led to the observation of exciting physical phenomena and creation of novel devices. The possibility of combining layers of different 2D materials in one stack allows unprecedented control over the electronic and optical properties of the resulting material. Still, the current method of mechanical transf…
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The new paradigm of heterostructures based on two-dimensional (2D) atomic crystals has already led to the observation of exciting physical phenomena and creation of novel devices. The possibility of combining layers of different 2D materials in one stack allows unprecedented control over the electronic and optical properties of the resulting material. Still, the current method of mechanical transfer of individual 2D crystals, though allowing exceptional control over the quality of such structures and interfaces, is not scalable. Here we show that such heterostructures can be assembled from chemically exfoliated 2D crystals, allowing for low-cost and scalable methods to be used in the device fabrication.
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Submitted 4 September, 2014;
originally announced September 2014.
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Spectroscopic Properties of Nanotube-Chromophore Hybrids
Authors:
Changshui Huang,
Randy K. Wang,
Bryan M. Wong,
David J. McGee,
François Léonard,
Yun Jun Kim,
Kirsten F. Johnson,
Michael S. Arnold,
Mark A. Eriksson,
Padma Gopalan
Abstract:
Recently, individual single-walled carbon nanotubes (SWNTs) functionalized with azo-benzene chromophores were shown to form a new class of hybrid nanomaterials for optoelectronics applications. Here we use a number of experimental techniques and theory to understand the binding, orientation, and nature of coupling between chromophores and the nanotubes, all of which are of relevance to future opti…
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Recently, individual single-walled carbon nanotubes (SWNTs) functionalized with azo-benzene chromophores were shown to form a new class of hybrid nanomaterials for optoelectronics applications. Here we use a number of experimental techniques and theory to understand the binding, orientation, and nature of coupling between chromophores and the nanotubes, all of which are of relevance to future optimization of these hybrid materials. We find that the binding energy between chromophores and nanotubes depends strongly on the type of tether that is used to bind the chromophores to the nanotubes, with pyrene tethers resulting in more than 90% of the bound chromophores during processing. DFT calculations show that the binding energy of the chromophores to the nanotubes is maximized for chromophores parallel to the nanotube sidewall, even with the use of tethers; second harmonic generation shows that there is nonetheless a partial radial orientation of the chromophores on the nanotubes. We find weak electronic coupling between the chromophores and the SWNTs, consistent with non-covalent binding. The chromophore-nanotube coupling, while weak, is sufficient to quench the chromophore fluorescence. Stern-Volmer plots are non-linear, which supports a combination of static and dynamic quenching processes. The chromophore orientation is an important variable for chromophore-nanotube phototransistors, and our experiments suggest the possibility for further optimizing this orientational degree of freedom.
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Submitted 21 December, 2013;
originally announced December 2013.
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Measurement of Filling-Factor-Dependent Magnetophonon Resonances in Graphene Using Raman Spectroscopy
Authors:
Y. Kim,
J. M. Poumirol,
A. Lombardo,
N. G. Kalugin,
T. Georgiou,
Y. J. Kim,
K. S. Novoselov,
A. C. Ferrari,
J. Kono,
O. Kashuba,
V. I. Fal'ko,
D. Smirnov
Abstract:
We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45T. This reveals a filling-factor-dependent, multi-component anticrossing structure of the Raman G peak, resulting from magnetophonon resonances between magnetoexcitons and E$_{2g}$ phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier d…
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We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45T. This reveals a filling-factor-dependent, multi-component anticrossing structure of the Raman G peak, resulting from magnetophonon resonances between magnetoexcitons and E$_{2g}$ phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier densities and strain. Random fluctuations of strain-induced pseudo-magnetic fields lead to increased scattering intensity inside the anti-crossing gap, consistent with the experiment.
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Submitted 19 June, 2013; v1 submitted 26 November, 2012;
originally announced November 2012.
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Ultrafast collinear scattering and carrier multiplication in graphene
Authors:
D. Brida,
A. Tomadin,
C. Manzoni,
Y. J. Kim,
A. Lombardo,
S. Milana,
R. R. Nair,
K. S. Novoselov,
A. C. Ferrari,
G. Cerullo,
M. Polini
Abstract:
Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic, and nanophotonic materials. The interaction of light with carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools via phonon emission. Here we combine pump-probe spectroscopy, featuring extreme temporal resolution an…
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Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic, and nanophotonic materials. The interaction of light with carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools via phonon emission. Here we combine pump-probe spectroscopy, featuring extreme temporal resolution and broad spectral coverage, with a microscopic theory based on the quantum Boltzmann equation, to investigate electron-electron collisions in graphene during the very early stages of relaxation. We identify the fundamental physical mechanisms controlling the ultrafast dynamics in graphene, in particular the significant role of ultrafast collinear scattering, enabling Auger processes, including charge multiplication, key to improving photovoltage generation and photodetectors.
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Submitted 25 September, 2012;
originally announced September 2012.
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New Experimental Limit on the Electric Dipole Moment of the Electron in a Paramagnetic Insulator
Authors:
Y. J. Kim,
C. -Y. Liu,
S. K. Lamoreaux,
G. Visser,
B. Kunkler,
A. N. Matlashov,
J. C. Long,
T. G. Reddy
Abstract:
We report results of an experimental search for the intrinsic Electric Dipole Moment (EDM) of the electron using a solid-state technique. The experiment employs a paramagnetic, insulating gadolinium gallium garnet (GGG) that has a large magnetic response at low temperatures. The presence of the eEDM would lead to a small but non-zero magnetization as the GGG sample is subject to a strong electric…
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We report results of an experimental search for the intrinsic Electric Dipole Moment (EDM) of the electron using a solid-state technique. The experiment employs a paramagnetic, insulating gadolinium gallium garnet (GGG) that has a large magnetic response at low temperatures. The presence of the eEDM would lead to a small but non-zero magnetization as the GGG sample is subject to a strong electric field. We search for the resulting Stark-induced magnetization with a sensitive magnetometer. Recent progress on the suppression of several sources of background allows the experiment to run free of spurious signals at the level of the statistical uncertainties. We report our first limit on the eEDM of $(-5.57 \pm 7.98 \pm 0.12)\times$10$^{-25}$e$\cdot$cm with 5 days of data averaging.
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Submitted 1 June, 2015; v1 submitted 22 April, 2011;
originally announced April 2011.
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Structural and magnetic properties of Ni doped CeO2 nanoparticles
Authors:
Shalendra Kumar,
Young. Joo. Kim,
B. H. Koo,
C. G. Lee
Abstract:
We report room temperature ferromagnetism in Ni doped CeO2 nanoparticles using X-ray diffraction (XRD), high resolution transmission electron microscopy (HR-TEM), and dc magnetization measurements. Nanoparticles of Ce1-xNixO2 (0.0 \leq x \leq 0.10) were prepared by using a co-precipitation method. XRD measurements indicate that all samples exhibit single phase nature with cubic structure and ruled…
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We report room temperature ferromagnetism in Ni doped CeO2 nanoparticles using X-ray diffraction (XRD), high resolution transmission electron microscopy (HR-TEM), and dc magnetization measurements. Nanoparticles of Ce1-xNixO2 (0.0 \leq x \leq 0.10) were prepared by using a co-precipitation method. XRD measurements indicate that all samples exhibit single phase nature with cubic structure and ruled out the presence of any secondary phase. Lattice parameters, strain and particle size calculated from XRD data have been found to decrease with increase in Ni doping. Inter-planner distance measured from HR-TEM images for different Ni doped samples indicate that Ni ions are substituting Ce ions in CeO2 matrix. Magnetization measurements performed at room temperature display weak ferromagnetic behavior of Ce1-xNixO2 (0.0 \leq x \leq 0.10) nanoparticles. Magnetic moment calculated from magnetic hysteresis loop was found to increases with Ni doping up to 7% and then start decreasing with further doping.
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Submitted 27 January, 2011;
originally announced January 2011.
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30 inch Roll-Based Production of High-Quality Graphene Films for Flexible Transparent Electrodes
Authors:
Sukang Bae,
Hyeong Keun Kim,
Youngbin Lee,
Xianfang Xu,
Jae-Sung Park,
Yi Zheng,
Jayakumar Balakrishnan,
Danho Im,
Tian Lei,
Young Il Song,
Young Jin Kim,
Kwang S. Kim,
Barbaros Özyilmaz,
Jong-Hyun Ahn,
Byung Hee Hong,
Sumio Iijima
Abstract:
We report that 30-inch scale multiple roll-to-roll transfer and wet chemical doping considerably enhance the electrical properties of the graphene films grown on roll-type Cu substrates by chemical vapor deposition. The resulting graphene films shows a sheet resistance as low as ~30 Ohm/sq at ~90 % transparency which is superior to commercial transparent electrodes such as indium tin oxides (ITO).…
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We report that 30-inch scale multiple roll-to-roll transfer and wet chemical doping considerably enhance the electrical properties of the graphene films grown on roll-type Cu substrates by chemical vapor deposition. The resulting graphene films shows a sheet resistance as low as ~30 Ohm/sq at ~90 % transparency which is superior to commercial transparent electrodes such as indium tin oxides (ITO). The monolayer of graphene shows sheet resistances as low as ~125 Ohm/sq with 97.4% optical transmittance and half-integer quantum Hall effect, indicating the high-quality of these graphene films. As a practical application, we also fabricated a touch screen panel device based on the graphene transparent electrodes, showing extraordinary mechanical and electrical performances.
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Submitted 16 March, 2010; v1 submitted 30 December, 2009;
originally announced December 2009.
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Room temperature ferromagnetism in chemically synthesized ZnO rods
Authors:
Shalendra Kumar,
Y. J. Kim,
B. H. Koo,
S. Gautam,
K. H. Chae,
Ravi Kumar,
C. G. Lee
Abstract:
We report structural and magnetic properties of pure ZnO rods using X-ray diffraction (XRD), magnetization hysteresis (M-H) loop and near edge x-ray fine structure spectroscopy (NEXAFS) study at O K edge. Sample of ZnO was prepared by co-precipitation method. XRD and selective area electron diffraction measurements infer that ZnO rods exhibit a single phase polycrystalline nature with wurtzite l…
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We report structural and magnetic properties of pure ZnO rods using X-ray diffraction (XRD), magnetization hysteresis (M-H) loop and near edge x-ray fine structure spectroscopy (NEXAFS) study at O K edge. Sample of ZnO was prepared by co-precipitation method. XRD and selective area electron diffraction measurements infer that ZnO rods exhibit a single phase polycrystalline nature with wurtzite lattice. Field emission transmission electron microscopy, field emission scanning electron microscopy micrographs infers that ZnO have rod type microstructures with dimension 200 nm in diameter and 550 nm in length. M-H loop studies performed at room temperature display room temperature ferromagnetism in ZnO rods. NEXAFS study reflects absence of the oxygen vacancies in pure ZnO rods.
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Submitted 21 November, 2009;
originally announced November 2009.
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Effect of many-body quantum fluctuations on matrix Berry phases of a two-dimensional n-type semiconductor quantum dot
Authors:
S. C. Kim,
Y. J. Kim,
P. S. Park,
N. Y. Hwang,
S. -R. Eric Yang
Abstract:
In the presence of spin-orbit coupling and inversion symmetry of the lateral confinement potential a single electron does not exhibit matrix Berry phases in quasi-two-dimensional semiconductor quantum dots. In such a system we investigate whether many-body correlation effects can lead to finite matrix Berry phases. We find that the transformation properties of many-electron wavefunctions under t…
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In the presence of spin-orbit coupling and inversion symmetry of the lateral confinement potential a single electron does not exhibit matrix Berry phases in quasi-two-dimensional semiconductor quantum dots. In such a system we investigate whether many-body correlation effects can lead to finite matrix Berry phases. We find that the transformation properties of many-electron wavefunctions under two-dimensional inversion operation do not allow finite matrix Berry phases. This effect is exact and is independent of the form of electron-electron interactions. On the other hand, quasi-two-dimensional semiconductor quantum dots with lateral confinement potential without inversion symmetry can have finite matrix Berry phases. We find that many-body quantum fluctuations can change matrix Berry phases significantly in such systems.
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Submitted 1 October, 2008;
originally announced October 2008.
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Charge-Transfer Excitations in the Model Superconductor HgBa$_2$CuO$_{\bf 4+δ}$
Authors:
L. Lu,
X. Zhao,
G. Chabot-Couture,
J. N. Hancock,
N. Kaneko,
O. P. Vajk,
G. Yu,
S. Grenier,
Y. J. Kim,
D. Casa,
T. Gog,
M. Greven
Abstract:
We report a Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of charge-transfer excitations in the 2-8 eV range in the structurally simple compound HgBa$_2$CuO$_{4+δ}$ at optimal doping ($T_{\rm c} = 96.5 $ K). The spectra exhibit a significant dependence on the incident photon energy which we carefully utilize to resolve a multiplet of weakly-dispersive ($ < 0.5$ eV) electron-hole e…
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We report a Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of charge-transfer excitations in the 2-8 eV range in the structurally simple compound HgBa$_2$CuO$_{4+δ}$ at optimal doping ($T_{\rm c} = 96.5 $ K). The spectra exhibit a significant dependence on the incident photon energy which we carefully utilize to resolve a multiplet of weakly-dispersive ($ < 0.5$ eV) electron-hole excitations, including a mode at 2 eV. The observation of this 2 eV excitation suggests the existence of a charge-transfer pseudogap deep in the superconducting phase. Quite generally, our data demonstrate the importance of exploring the incident photon energy dependence of the RIXS cross section.
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Submitted 7 September, 2005; v1 submitted 19 January, 2005;
originally announced January 2005.
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Effect of a magnetic field on the spin- and charge-density wave order in La1.45Nd0.4Sr0.15CuO4
Authors:
S. Wakimoto,
R. J. Birgeneau,
Y. Fujimaki,
N. Ichikawa,
T. Kasuga,
Y. J. Kim,
K. M. Kojima,
S. -H. Lee,
H. Niko,
J. M. Tranquada,
S. Uchida,
M. v. Zimmermann
Abstract:
The spin-density wave (SDW) and charge-density wave (CDW) order in superconducting La1.45Nd0.4Sr0.15CuO4 were studied under an applied magnetic field using neutron and X-ray diffraction techniques. In zero field, incommensurate (IC) SDW order appears below ~ 40 K, which is characterized by neutron diffraction peaks at (1/2 +/- 0.134, 1/2 +/- 0.134, 0). The intensity of these IC peaks increases r…
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The spin-density wave (SDW) and charge-density wave (CDW) order in superconducting La1.45Nd0.4Sr0.15CuO4 were studied under an applied magnetic field using neutron and X-ray diffraction techniques. In zero field, incommensurate (IC) SDW order appears below ~ 40 K, which is characterized by neutron diffraction peaks at (1/2 +/- 0.134, 1/2 +/- 0.134, 0). The intensity of these IC peaks increases rapidly below T_Nd ~ 8 K due to an ordering of the Nd^3+ spins. The application of a 1 T magnetic field parallel to the c-axis markedly diminishes the intensity below T_Nd, while only a slight decrease in intensity is observed at higher temperatures for fields up to 7 T. Our interpretation is that the c-axis field suppresses the parasitic Nd^3+ spin order at the incommensurate wave vector without disturbing the stripe order of Cu^2+ spins. Consistent with this picture, the CDW order, which appears below 60 K, shows no change for magnetic fields up to 4 T. These results stand in contrast to the significant field-induced enhancement of the SDW order observed in superconducting La2-xSrxCuO4 with x ~ 0.12 and stage-4 La2CuO4+y. The differences can be understood in terms of the relative volume fraction exhibiting stripe order in zero field, and the collective results are consistent with the idea that suppression of superconductivity by vortices nucleates local patches of stripe order.
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Submitted 24 January, 2003; v1 submitted 9 September, 2002;
originally announced September 2002.
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Resonant inelastic x-ray scattering study of charge excitations in La2CuO4
Authors:
Y. J. Kim,
J. P. Hill,
C. A. Burns,
S. Wakimoto,
R. J. Birgeneau,
D. Casa,
T. Gog,
C. T. Venkataraman
Abstract:
We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La$_2$CuO$_4$. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of $\sim 2.2$ eV at the zone center, and a dispersion of $\sim 1$ eV. The spectral weight of this mode becomes dramatically small…
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We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La$_2$CuO$_4$. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of $\sim 2.2$ eV at the zone center, and a dispersion of $\sim 1$ eV. The spectral weight of this mode becomes dramatically smaller around ($π$, $π$). The second peak shows a smaller dispersion ($\sim 0.5$ eV) with a zone-center energy of $\sim 3.9$ eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.
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Submitted 27 June, 2002;
originally announced June 2002.
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Common features of nanoscale structural correlations in magnetoresistive manganites with ferromagnetic low-temperature state
Authors:
V. Kiryukhin,
T. Y. Koo,
A. Borissov,
Y. J. Kim,
C. S. Nelson,
J. P. Hill,
D. Gibbs,
S-W. Cheong
Abstract:
We report x-ray scattering studies of nanoscale structural correlations in Nd$_{1-x}$Sr$_x$MnO$_3$ and La$_{1-x}$(Ca,Sr)$_x$MnO$_3$, $x$=0.2--0.5. We find that the correlated regions possess a temperature-independent correlation length of 2-3 lattice constants which is the same in all samples. The period of the lattice modulation of the correlated regions is proportional to the Ca/Sr doping conc…
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We report x-ray scattering studies of nanoscale structural correlations in Nd$_{1-x}$Sr$_x$MnO$_3$ and La$_{1-x}$(Ca,Sr)$_x$MnO$_3$, $x$=0.2--0.5. We find that the correlated regions possess a temperature-independent correlation length of 2-3 lattice constants which is the same in all samples. The period of the lattice modulation of the correlated regions is proportional to the Ca/Sr doping concentration $x$. Remarkably, the lattice modulation periods of these and several other manganites with a ferromagnetic ground state fall on the same curve when plotted as a function of $x$. Thus, the structure of the correlated regions in these materials appears to be determined by a single parameter, $x$. We argue that these observations provide important clues for understanding the Colossal Magnetoresistance phenomenon in manganites.
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Submitted 5 December, 2001;
originally announced December 2001.
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Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets: Sr_2CuO_2Cl_2 and Sr_2Cu_3O_4Cl_2
Authors:
Y. J. Kim,
R. J. Birgeneau,
F. C. Chou,
R. W. Erwin,
M. A. Kastner
Abstract:
We report a neutron scattering study of the long-wavelength dynamic spin correlations in the model two-dimensional $S=1/2$ square lattice Heisenberg antiferromagnets Sr$_2$CuO$_2$Cl$_2$ and Sr$_2$Cu$_3$O$_4$Cl$_2$. The characteristic energy scale, $ω_0 (T/J)$, is determined by measuring the quasielastic peak width in the paramagnetic phase over a wide range of temperature (…
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We report a neutron scattering study of the long-wavelength dynamic spin correlations in the model two-dimensional $S=1/2$ square lattice Heisenberg antiferromagnets Sr$_2$CuO$_2$Cl$_2$ and Sr$_2$Cu$_3$O$_4$Cl$_2$. The characteristic energy scale, $ω_0 (T/J)$, is determined by measuring the quasielastic peak width in the paramagnetic phase over a wide range of temperature ($0.2 \alt T/J \alt 0.7$). The obtained values for $ω_0 (T/J)$ agree {\it quantitatively} between the two compounds and also with values deduced from quantum Monte Carlo simulations. The combined data show scaling behavior, $ω\sim ξ^{-z}$, over the entire temperature range with $z=1.0(1)$, in agreement with dynamic scaling theory.
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Submitted 13 February, 2001; v1 submitted 13 December, 2000;
originally announced December 2000.
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X-ray Scattering and Magnetic Susceptibility Study of doped CuGeO_3
Authors:
Y. J. Wang,
Y. J. Kim,
R. J. Christianson,
S. C. LaMarra,
F. C. Chou,
T. Masuda,
I. Tsukada,
K. Uchinokura,
R. J. Birgeneau
Abstract:
We report comprehensive synchrotron x-ray scattering and magnetic susceptibility studies of the doped spin-Peierls materials Cu_{1-x}Zn_xGeO_3 and CuGe_{1-y}Si_yO_3. Temperature versus dopant concentration phase diagrams are mapped out for both Zn and Si dopants. The phase diagrams of both Cu_{1-x}Zn_xGeO_3 and CuGe_{1-y}Si_yO_3 closely resemble that of Cu_{1-x}Mg_xGeO_3, including the observati…
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We report comprehensive synchrotron x-ray scattering and magnetic susceptibility studies of the doped spin-Peierls materials Cu_{1-x}Zn_xGeO_3 and CuGe_{1-y}Si_yO_3. Temperature versus dopant concentration phase diagrams are mapped out for both Zn and Si dopants. The phase diagrams of both Cu_{1-x}Zn_xGeO_3 and CuGe_{1-y}Si_yO_3 closely resemble that of Cu_{1-x}Mg_xGeO_3, including the observation that the spin gap is established at a much higher temperature than the temperature at which the spin-Peierls dimerization attains long-range order. The spin-Peierls transitions in doped samples exhibit unusual phase transition behavior, characterized by highly rounded phase transitions, Lorentzian squared lineshapes, and very long relaxation times. Phenomenological explanations for these observations are given by considering the effects of competing random bond interactions as well as random fields generated by the dopants. We have also confirmed the reentrance of the spin-Peierls phase when the temperature is lowered through the antiferromagnetic ordering transition. The low temperature re-entrance of the spin-Peierls phase has been explained speculatively using a local phase separation scheme between the spin-Peierls phase and the Neel phase.
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Submitted 1 August, 2002; v1 submitted 30 November, 2000;
originally announced December 2000.
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Quantum Fluctuations in the Frustrated Antiferromagnet Sr_2Cu_3O_4Cl_2
Authors:
A. B. Harris,
A. Aharony,
O. Entin-Wohlman,
I. Ya. Korenblit,
R. J. Birgeneau,
Y. J. Kim
Abstract:
Sr_2Cu_3O_4Cl_2 is an antiferromagnet consisting of weakly coupled CuO planes which comprise two weakly interacting antiferromagnetic subsystems, I and II, which order at respective temperatures T_I \approx 390K and T_{II} \approx 40K. Except asymptotically near the ordering temperature, these systems are good representations of the two-dimensional quantum spin 1/2 Heisenberg model. For T< T_{II…
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Sr_2Cu_3O_4Cl_2 is an antiferromagnet consisting of weakly coupled CuO planes which comprise two weakly interacting antiferromagnetic subsystems, I and II, which order at respective temperatures T_I \approx 390K and T_{II} \approx 40K. Except asymptotically near the ordering temperature, these systems are good representations of the two-dimensional quantum spin 1/2 Heisenberg model. For T< T_{II} there are four low-energy modes at zero wave vector, three of whose energies are dominated by quantum fluctuations. For T_{II} < T < T_I there are two low energy modes. The mode with lower energy is dominated by quantum fluctuations. Our calculations of the energies of these modes (including dispersion for wave vectors perpendicular to the CuO planes) agree extremely well with the experimental results of inelastic neutron scattering (in the accompanying paper) and for modes in the sub meV range observed by electron spin resonance. The parameters needed to describe quantum fluctuations are either calculated here or are taken from the literature. These results show that we have a reasonable qualitative understanding of the band structure of the lamellar cuprates needed to calculate the anisotropic exchange constants used here.
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Submitted 20 September, 2000;
originally announced September 2000.
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Neutron Scattering study of Sr_2Cu_3O_4Cl_2
Authors:
Y. J. Kim,
R. J. Birgeneau,
F. C. Chou,
M. Greven,
M. A. Kastner,
Y. S. Lee,
B. O. Wells,
A. Aharony,
O. Entin-Wohlman,
I. Ya. Korenblit,
A. B. Harris,
R. W. Erwin,
G. Shirane
Abstract:
We report a neutron scattering study on the tetragonal compound Sr_2Cu_3O_4Cl_2, which has two-dimensional (2D) interpenetrating Cu_I and Cu_{II} subsystems, each forming a S=1/2 square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the inter-subsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show tha…
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We report a neutron scattering study on the tetragonal compound Sr_2Cu_3O_4Cl_2, which has two-dimensional (2D) interpenetrating Cu_I and Cu_{II} subsystems, each forming a S=1/2 square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the inter-subsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the Cu_{II} subsystem. Due to quantum fluctuations a dramatic increase of the Cu_I out-of-plane spin-wave gap is also observed. The temperature dependence and the dispersion of the spin-wave energy are quantitatively explained by spin-wave calculations which include quantum fluctuations explicitly. The values for the nearest-neighbor superexchange interactions between the Cu_I and Cu_{II} ions and between the Cu_{II} ions are determined experimentally to be J_{I-II} = -10(2)meV and J_{II}= 10.5(5)meV, respectively. Due to its small exchange interaction, J_{II}, the 2D dispersion of the Cu_{II} SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a novel dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the Cu_{II} SLQHA is obtained up to a very high temperature, T/J_{II}\approx 0.75. This result is compared with several theoretical predictions as well as recent experiments on the S=1/2 SLQHA.
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Submitted 21 September, 2000; v1 submitted 20 September, 2000;
originally announced September 2000.
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Magnetic properties of the S=1/2 quasi-one-dimensional antiferromagnet CaCu2O3
Authors:
V. Kiryukhin,
Y. J. Kim,
K. J. Thomas,
F. C. Chow,
R. W. Erwin,
Q. Huang,
M. A. Kastner,
R. J. Birgeneau
Abstract:
We report single crystal growth and magnetic susceptibility and neutron diffraction studies of the S=1/2 quasi-1D antiferromagnet CaCu2O3. The structure of this material is similar to that of the prototype two-leg spin-ladder compound SrCu2O3. However, the Cu-O-Cu bond angle in the ladder rungs in CaCu2O3 is equal to 123 deg, and therefore the magnetic interaction along the rungs is expected to…
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We report single crystal growth and magnetic susceptibility and neutron diffraction studies of the S=1/2 quasi-1D antiferromagnet CaCu2O3. The structure of this material is similar to that of the prototype two-leg spin-ladder compound SrCu2O3. However, the Cu-O-Cu bond angle in the ladder rungs in CaCu2O3 is equal to 123 deg, and therefore the magnetic interaction along the rungs is expected to be much weaker in this material. At high temperatures, the magnetic susceptibility of CaCu2O3 can be decomposed into a contribution from 1D antiferromagnetic chains of finite-size chain segments together with a weak Curie contribution. The intrachain magnetic exchange constant, determined from the magnetic susceptibility measurements, is 2000 K. CaCu2O3 undergoes a Neel transition at T_N=25 K with ordering wavevector of (0.429(5), 0.5, 0.5). The magnetic structure is incommensurate in the direction of the frustrated interchain interaction. Weak commensurate (0.5, 0.5, 0.5) magnetic peaks are also observed below T_N. Application of a magnetic field induces a metamagnetic transition at which the incommensurability of the magnetic structure is substantially reduced. The material possesses only short-range magnetic order above the transition field.
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Submitted 11 September, 2000;
originally announced September 2000.
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Electronic and Magnetic Properties of Electron-doped Superconductor, Sm_{1.85}Ce_{0.15}CuO_{4-delta}
Authors:
B. K. Cho,
Jae Hoon Kim,
Young Jin Kim,
Beom-hoan O,
J. S. Kim,
G. R. Stewart
Abstract:
Temperature-dependent magnetization (M(T)) and specific heat (C_p(T)) measurements were carried out on single crystal Sm_{1.85}Ce_{0.15}CuO_{4-delta} (T_c = 16.5 K). The magnetic anisotropy in the static susceptibility, chi {equiv} M/H, is apparent not only in its magnitude but also in its temperature dependence, with chi_{perp} for H{perp}c larger than chi_{parallel} for H{parallel}c. For both…
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Temperature-dependent magnetization (M(T)) and specific heat (C_p(T)) measurements were carried out on single crystal Sm_{1.85}Ce_{0.15}CuO_{4-delta} (T_c = 16.5 K). The magnetic anisotropy in the static susceptibility, chi {equiv} M/H, is apparent not only in its magnitude but also in its temperature dependence, with chi_{perp} for H{perp}c larger than chi_{parallel} for H{parallel}c. For both field orientations, chi does not follow the Curie-Weiss behavior due to the small energy gap of the J = 7/2 multiplet above the J = 5/2 ground-state multiplet. However, with increasing temperature, chi_{parallel}(T) exhibits a broad minimum near 100 K and then a slow increase while chi_{perp}(T) shows a monotonic decrease. A sharp peak in C_p(T) at 4.7 K manifests an antiferromagnetic ordering. The electronic contribution, gamma, to C_p(T) is estimated to be gamma = 103.2 (7) mJ/moleSmK^2. The entropy associated with the magnetic ordering is much smaller than Rln2, where R is the gas constant, which is usually expected for the doublet ground state of Sm^{+3}. The unusual magnetic and electronic properties evident in M(T) and C_p(T) are probably due to a strong anisotropic interaction between conduction electrons and localized electrons at Sm^{+3} sites.
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Submitted 13 August, 2000;
originally announced August 2000.
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Direct Observation of the Quantum Energy Gap in S = 1/2 Tetragonal Cuprate Antiferromagnets
Authors:
K. Katsumata,
M. Hagiwara,
Z. Honda,
J. Satooka,
Amnon Aharony,
R. J. Birgeneau,
F. C. Chou,
O. Entin-Wohlman,
A. B. Harris,
M. A. Kastner,
Y. J. Kim,
Y. S. Lee
Abstract:
Using an electron spin resonance spectrometer covering a wide range of frequency and magnetic field, we have measured the low energy excitations of the S=1/2 tetragonal antiferromagnets, Sr_{2}CuO_{2}Cl_{2} and Sr_{2}Cu_{3}O_{4}Cl_{2}. Our observation of in-plane energy gaps of order 0.1 meV at zero external magnetic field are consistent with a spin wave calculation, which includes several kinds…
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Using an electron spin resonance spectrometer covering a wide range of frequency and magnetic field, we have measured the low energy excitations of the S=1/2 tetragonal antiferromagnets, Sr_{2}CuO_{2}Cl_{2} and Sr_{2}Cu_{3}O_{4}Cl_{2}. Our observation of in-plane energy gaps of order 0.1 meV at zero external magnetic field are consistent with a spin wave calculation, which includes several kinds of quantum fluctuations that remove frustration. Results agree with other experiments and with exchange anisotropy parameters determined from a five band Hubbard model.
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Submitted 1 August, 2000;
originally announced August 2000.
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Monte Carlo Study of the S=1/2 and S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Square Lattice
Authors:
Y. J. Kim,
R. J. Birgeneau
Abstract:
We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x-direction ($J_x$) is different from that in the y-direction ($J_y$). By varying the anisotropy $α$ from 0 to 1, we interpolate between the one-dimensional chain and the two-dimensional isotropic square lattice. Both $S=1/2$ and S=1 systems are con…
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We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x-direction ($J_x$) is different from that in the y-direction ($J_y$). By varying the anisotropy $α$ from 0 to 1, we interpolate between the one-dimensional chain and the two-dimensional isotropic square lattice. Both $S=1/2$ and S=1 systems are considered separately in order to facilitate comparison. The temperature dependence of the uniform susceptibility and the spin-spin correlation length are computed down to very low temperatures for various values of $α$. For S=1, the existence of a quantum critical point at $α^{S=1}_c=0.040(5)$ as well as the scaling of the spin gap is confirmed. Universal quantities predicted from the ${\cal O}(3)$ nonlinear $σ$ model agree with our results at $α=0.04$ without any adjustable parameters. On the other hand, the $S=1/2$ results are consistent with $α^{S=1/2}_c=0$, as discussed by a number of previous theoretical studies. Experimental implications for $S=1/2$ compounds such as Sr$_2$CuO$_3$ are also discussed.
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Submitted 30 June, 2000; v1 submitted 18 April, 2000;
originally announced April 2000.
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Quantum Monte Carlo Study of Weakly Coupled Spin Ladders
Authors:
Y. J. Kim,
R. J. Birgeneau,
M. A. Kastner,
Y. S. Lee,
Y. Endoh,
G. Shirane,
K. Yamada
Abstract:
We report a quantum Monte Carlo study of the thermodynamic properties of arrays of spin ladders with various widths ($n$), coupled via a weak inter-ladder exchange coupling $αJ$, where $J$ is the intra-ladder coupling both along and between the chains. This coupled ladder system serves as a simplified model for the magnetism of presumed ordered spin and charge stripes in the two-dimensional CuO…
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We report a quantum Monte Carlo study of the thermodynamic properties of arrays of spin ladders with various widths ($n$), coupled via a weak inter-ladder exchange coupling $αJ$, where $J$ is the intra-ladder coupling both along and between the chains. This coupled ladder system serves as a simplified model for the magnetism of presumed ordered spin and charge stripes in the two-dimensional CuO$_2$ planes of hole-doped copper oxides. Our results for $n=3$ with weak inter-ladder coupling $α=0.05$, estimated from the $t-t'-t''-J$ model, show good agreement with the ordering temperature of the recently observed spin density wave condensation in La$_2$CuO$_{4+y}$. We show that there exists a quantum critical point at $α_c \simeq 0.07$ for $n=4$, and determine the phase diagram. Our data at this quantum critical point agree quantitatively with the universal scaling predicted by the quantum nonlinear $σ$ model. We also report results on random mixtures of $n=2$ and $n=3$ ladders, which correspond to the doping region near but above 1/8. Our study on the magnetic static structure factor reveals a saturation of the incommensurability of the spin correlations around 1/8, while the incommensurability of the charge stripes grows linearly with hole concentration. The implications of this result for the interpretation of neutron scattering experiments on the dynamic spin fluctuations in La$_{2-x}$Sr$_x$CuO$_4$ are discussed.
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Submitted 17 February, 1999;
originally announced February 1999.
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Monte Carlo Study of Correlations in Quantum Spin Chains at Non-Zero Temperature
Authors:
Y. J. Kim,
M. Greven,
U. -J. Wiese,
R. J. Birgeneau
Abstract:
Antiferromagnetic Heisenberg spin chains with various spin values ($S=1/2,1,3/2,2,5/2$) are studied numerically with the quantum Monte Carlo method. Effective spin $S$ chains are realized by ferromagnetically coupling $n=2S$ antiferromagnetic spin chains with $S=1/2$. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak inte…
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Antiferromagnetic Heisenberg spin chains with various spin values ($S=1/2,1,3/2,2,5/2$) are studied numerically with the quantum Monte Carlo method. Effective spin $S$ chains are realized by ferromagnetically coupling $n=2S$ antiferromagnetic spin chains with $S=1/2$. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, $T/J \approx 0.01$. The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of $S$. For $S$=2 chains which have a gap $Δ$, the correlation length and the uniform susceptibility in the temperature range $Δ< T < J$ are well predicted by a semi-classical theory due to Damle and Sachdev.
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Submitted 18 August, 1998; v1 submitted 20 December, 1997;
originally announced December 1997.