Three-dimensional Long-range Order Research Articles

Magnetic order in theS=1∕2two-dimensional molecular antiferromagnet copper pyrazine perchlorateCu(Pz)2(ClO4)2

We present an investigation of magnetic ordering in the two-dimensional $S=1∕2$ quantum magnet $\mathrm{Cu}{(\mathrm{Pz})}_{2}{(\mathrm{Cl}{\mathrm{O}}_{4})}_{2}$ using specific heat and zero-field muon-spin relaxation $({\ensuremath{\mu}}^{+}\mathrm{SR})$. The magnetic contribution to the specific heat is consistent with an exchange strength of $17.7(3)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We find unambiguous evidence for a transition to a state of three-dimensional long-range order below a critical temperature ${T}_{N}=4.21(1)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using ${\ensuremath{\mu}}^{+}\mathrm{SR}$ even though there is no feature in the specific heat at that temperature. The absence of a specific heat anomaly at ${T}_{N}$ is consistent with recent theoretical predictions. The ratio of ${T}_{N}∕J=0.24$ corresponds to a ratio of intralayer to interlayer exchange constants of $\ensuremath{\mid}{J}^{\ensuremath{'}}∕J\ensuremath{\mid}=6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, indicative of excellent two-dimensional isolation. The scaled magnetic specific heat of $[\mathrm{Cu}{(\mathrm{Pz})}_{2}(\mathrm{H}{\mathrm{F}}_{2})]\mathrm{B}{\mathrm{F}}_{4}$, a compound with an analogous structure, is very similar to that of $\mathrm{Cu}{(\mathrm{Pz})}_{2}{(\mathrm{Cl}{\mathrm{O}}_{4})}_{2}$ although both differ slightly from the predicted value for an ideal 2D $S=1∕2$ Heisenberg antiferromagnet.

In-planeI−Vcharacteristics of interlayer Josephson vortices in cuprate high-Tcsuperconductors: Dynamical simulations

Computer simulations on Josephson vortex systems driven by in-plane currents in cuprate high-${T}_{c}$ superconductors have been performed. For high anisotropy and magnetic field, we find power-law $I\text{\ensuremath{-}}V$ characteristics with the index jumping from 1 (i.e., Ohmic) at high temperatures to $\ensuremath{\geqslant}3$ (i.e., non-Ohmic) at intermediate temperatures, which can be attributed to a Kosterlitz-Thouless (KT) transition. In the KT phase, simulations reveal a resistivity independent of the angle between the current and the magnetic field, i.e., orientation-independent dissipation, due to the intralayer quasi-long-range order and interlayer short-range order of Josephson vortices. For low anisotropy and magnetic field, an orientation-dependent non-Ohmic dissipation is observed where the three-dimensional long-range order exists. The present approach provides a unified explanation to previous experimental observations in the non-Ohmic regime.

Crystals and Crystallinity in Polymeric Materials

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Crystals and Crystallinity in Polymeric Materials

A new view of the concepts of crystallinity and crystals in synthetic macromolecules is discussed. In polymeric materials, crystallinity may be present with the concomitant occurrence of large amounts of structural disorder and in the absence of true three-dimensional long-range order. The structures of semicrystalline polymeric materials are discussed in terms of idealized limit models of crystals, where long-range order may be achieved for structural features that are not necessarily coincident with single atoms and are not necessarily point-centered. Typical examples of non-point-centered structural features are the straight lines corresponding to the chain axes of polymer molecules. This view explains the unusual ability of polymers to crystallize even in the presence of a high degree of structural disorder.

Observation of Three-Dimensional Long-Range Order in Small Ion Coulomb Crystals in an rf Trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of (40)Ca(+) ions confined in a linear rf Paul trap have been observed when the number of ions exceeds approximately 1,000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of approximately 50,000 ions or more.

Honeycombs of triangles and magnetic frustration inSrL2O4(L=Gd, Dy, Ho, Er, Tm, and Yb)

The crystal structures, magnetic order, and susceptibility have been investigated for magnetically frustrated ${\mathrm{SrDy}}_{2}{\mathrm{O}}_{4}$, ${\mathrm{SrHo}}_{2}{\mathrm{O}}_{4}$, ${\mathrm{SrEr}}_{2}{\mathrm{O}}_{4}$, ${\mathrm{SrTm}}_{2}{\mathrm{O}}_{4}$, and ${\mathrm{SrYb}}_{2}{\mathrm{O}}_{4}$. Powder neutron-diffraction structural refinements reveal columns of $L{\mathrm{O}}_{6}$ octahedra that run along one crystallographic direction, with Sr-O polyhedra in the interstices. The lanthanide sublattice displays multiple triangular interconnections: one-dimensional strings form the backbones of four types of chains of lanthanide triangles sharing edges arranged in a honeycomb pattern. This crystal structure produces strong geometric frustration for the magnetic system that is evidenced in both magnetic susceptibility and neutron-scattering data at low temperatures. The susceptibility measurements for the series, including ${\mathrm{SrGd}}_{2}{\mathrm{O}}_{4}$ for which data are also reported, lack the sharp features characteristic of three-dimensional long-range magnetic ordering. Metamagnetic behavior is observed in the magnetization vs applied field data at 1.8 K for the cases of $L=\mathrm{Dy}$, Er, and Ho. Magnetic neutron-scattering studies for the Dy and Er materials show only very broad magnetic scattering at low temperatures, while the Ho system exhibits long-range two-dimensional order. Any magnetic scattering in the Tm and Yb compounds, if present, was too weak to be detected in these measurements.

Neutron diffraction study of the magnetic ordering of jamesonite (FePb4Sb6S14)

Jamesonite, Fe2+Pb4Sb6S14, is a natural sulfide in which Fe octahedra form single chains, that would favor a quasi-one-dimensional magnetism. The susceptibility shows an antiferromagnetic behavior with a broad maximum at 30K and an irregularity at 5K. A neutron powder diffraction study has been undertaken between 1.4 and 44K. In the diffractograms, below 5K, supplementary peaks of magnetic origin and characteristic of a three-dimensional long-range magnetic ordering appear. The magnetic structure corresponds to a canted antiferromagnet with a propagation wave-vector k=[0.5,0,0] and a magnetic ordered magnetic moment on Fe atoms of 3.3(1)μB at 1.4K. Below 30K one-dimensional magnetic ordering or correlations are visible in the diagrams and persist down to 1.4K.

The synthesis, magnetic properties and crystal structure of a Cu(II) methylenediphosphonate, [Cu 2(O 3PCH 2PO 3)

The hydrothermal reaction of Cu(SO 4)·5H 2O, methylenediphosphonate and water in the mole ratio 1.0:1.5:4100 at 150 °C for 48 h yielded clear colorless crystals of [Cu 2(O 3PCH 2PO 3)] ( 1). The structure of 1 is a three-dimensional framework constructed from chains of edge-sharing {CuO 5} trigonal bipyramids linked through the {O 3PCH 2PO 3} 4− subunits. The magnetic data from 35 to 300 K were fit to the Heisenberg linear antiferromagnetic chain model, giving g=1.98 and J/ k B=−35.9 K. At lower temperatures, a Néel transition suggests three-dimensional long-range ordering. Crystal data: CH 2Cu 2O 6P 2, orthorhombic, Pnma, a=13.698(1), b=8.0094(6), c=4.8950(4) Å, V=537.04(7) Å 3, Z=4, D calc=3.699 g cm −3.

SPIN CORRELATIONS IN MAGNETIZED HALDANE CHAINS

Neutron scattering experiments have been carried out in high magnetic fields to understand the magnetized state of the uniform spin-1 antiferromagnetic chain. In zero field this system has a cooperative singlet ground state with a gap to a propagating triplet excitation. The quasi-one-dimensional uniform spin-1 antiferromagnets NENP (Ni(C2D8N2)2NO2CIO4) and NDMAP (Ni(C5D14N2)2N3PF6) were examined. NENP has an alternating g-tensor such that staggered magnetization is induced for arbitrarily small fields and there is no finite field phase transition. In the high field phase the lowest energy mode has a field dependent gap and an unusually small effective spin wave velocity. NDMAP has only one spin per unit cell and hence a uniform g-tensor. This system has a critical transition at a finite field. Surprisingly the high field phase has quasi-two-dimensional or three-dimensional long-range order depending on the direction of the applied field. In the paramagnetic high field phase immediately above the ordering transition of NDMAP, there are gapless magnetic excitations that are broader in Q than the higher energy gap mode. The data is compared to theoretical predictions of a gapless incommensurate phase above the critical field.

Three-dimensional antiferromagnetism in triamminodiperoxychromate, Cr(NH 3) 3(O 2) 2: a precursor to a new class of Cr(IV) magnets

This study presents the first observation of long-range antiferromagnetic order in a simple Cr(IV)-peroxo, S=1 complex. Magnetic susceptibility, χ, and heat capacity, C p, results are presented for both powders and single crystals of triamminodiperoxychromate, Cr(NH 3) 3(O 2) 2. For the investigated compound, the spin state of S=1 was determined by analysis of χ from 2 to 200 K, and correlated with the entropy expected for such a system as determined by C p measurements from 2.5 to 20 K. Sharp λ-like transitions were observed in both χ and C p, with maxima at 8.80 and 8.46 K, respectively; characteristic of three-dimensional long-range antiferromagnetic ordering. The χ and C p results correlated well using the Fisher heat capacity relationship. Further analysis of C p determined that the majority of the spin entropy is engaged at temperatures below 8.46 K. This class of compounds might serve as precursors for CrO 2 related materials.

Spiral magnetic structure of Fe in Van der Waals gapped FeOCl and polyaniline-intercalated FeOCl

High-resolution and magnetic neutron-diffraction measurements were performed to investigate the crystal and magnetic structures of bilayered FeOCl and polyaniline-intercalated FeOCl. A quasi-two-dimensional crystallographic structure, where charge neutral $({\mathrm{Fe}}_{2}{\mathrm{O}}_{2}{\mathrm{Cl}}_{2}{)}_{n}$ lamellas are weakly linked via Van der Waals interactions, has made FeOCl a good host for accommodating guest molecules. A three-dimensional long-range ordering of the Fe spins in FeOCl develops below 80 K, with a magnetic unit cell 28 times the size of the nuclear one. A spiral magnetic structure was obtained, reflecting the competition between antiferromagnetic superexchange coupling and ferromagnetic direct exchange coupling. Polyaniline intercalation interrupts the magnetic correlations between the neighboring bilayers, rendering a coupled-bilayer quasi-two-dimensional magnetic order for the Fe spins in $({\mathrm{C}}_{6}{\mathrm{D}}_{4}\mathrm{ND}{)}_{0.16}\mathrm{FeOCl}.$ No significant change on the ordering temperature of the Fe spins by the intercalation reaction was observed.

Lattice variation, reentrant electric properties, and magnetic order in bilayered La 1.02Sr 1.98Mn 2O 7

Neutron diffraction, dc electric resistivity, and ac magnetic susceptibility measurements were performed to study the structural, electric, and magnetic properties of naturally bilayered La 1.02Sr 1.98Mn 2O 7. An insulator to metal transition was clearly seen at ∼170 K. Below 60 K, the system reentered the insulating state. Three-dimensional (3D) long-range order of the Mn spins was found, with an ordering temperature of T m≈180 K and a saturated moment of 〈 μ Z〉=2.70(2) μ B. The in-plane couplings were ferromagnetic. Within each bilayer, simple antiferromagnetic couplings between the ferromagnetic sheets were found, whereas the neighboring bilayers were coupled ferromagnetically. A structural change that results in a reduction of the thermal contraction rate occurs at ∼250 K as well.

Short-range and long-range magnetic ordering in α-CuV 2O 6

Magnetic properties of α-CuV 2O 6 with linear chains of edge-sharing CuO 6 octahedra were studied by magnetic susceptibility and electron spin resonance measurements. The broad maximum of magnetic susceptibility at T M =44 K , corresponding to the intrachain exchange interaction J 1 =34 K , indicates one-dimensional short-range magnetic ordering within the chains. Three-dimensional long-range antiferromagnetic ordering takes place at T N =24 K suggesting a rather big value for the interchain exchange interaction J 2 ∼13 K . The 76 GHz energy gap, found in the antiferromagnetic resonance spectrum, agrees with the spin-flop magnetic field value of about 2.7 T.

Competing frustration and dilution effects on the antiferromagnetism inLa2−xSrxCu1−zZnzO4

The combined effects of hole doping and magnetic dilution on a lamellar Heisenberg antiferromagnet are studied in the framework of the frustration model. Magnetic vacancies are argued to remove some of the frustrating bonds generated by the holes, thus explaining the increase in the temperature and concentration ranges exhibiting three-dimensional long-range order. The dependence of the N\'eel temperature on both hole and vacancy concentrations is derived quantitatively from earlier renormalization-group calculations for the nondilute case, and the results reproduce experimental data with no new adjustable parameters.

Magnetic neutron scattering study of SrV 3O 7

Neutron powder diffraction experiments were performed for SrV 3O 7, which is characterized by the 1/4 depleted V 4+( S=1/2) square lattice model. An antiferromagnetic three-dimensional (3D) long-range order was observed below T N=34.3 K. The ‘Stripe Order’ spin structure, which is not expected from a classical Heisenberg model, is realized. This spin structure is the same as found in CaV 3O 7, but the spin direction here is parallel to the a(stacking)-axis, instead of the c-axis for CaV 3O 7.

Short-range and long-range magnetic ordering inα−CuV2O6

Magnetic properties of the triclinic copper vanadate $\ensuremath{\alpha}\ensuremath{-}{\mathrm{CuV}}_{2}{\mathrm{O}}_{6}$ with linear chains of edge-sharing ${\mathrm{CuO}}_{6}$ octahedra were studied by magnetic susceptibility and electron-spin-resonance measurements. The broad maximum of a magnetic susceptibility at ${T}_{M}=44\mathrm{K}$ corresponding to the intrachain exchange interaction $J=34\mathrm{K}$ indicates one-dimensional short-range magnetic ordering within the chains. Three-dimensional long-range antiferromagnetic ordering takes place at ${T}_{N}=24\mathrm{K},$ suggesting a rather large value for the interchain exchange interaction ${J}_{\ensuremath{\perp}}\ensuremath{\sim}16.5\mathrm{K}.$ The energy gap found in the antiferromagnetic resonance spectrum 76 GHz agrees with the spin-flop magnetic-field value of about 2.7 T.

Field-induced 3D-LRO of Haldane-gap antiferromagnet NDMAZ

The heat capacity and magnetization measurements of the single crystal of Haldane-gap antiferromagnet NDMAZ were carried out at low temperatures down to 0.1 K and under magnetic fields up to 14 T. We have observed three-dimensional long-range ordering of NDMAZ at around T ⋍ 0.3 K above H ⋍ 13 T ( H| c), which is ascribed to both the field-induced gap quenching and the existence of finite interchain interaction. Applying the higher external field, the transition temperature reaches up to 0.6 K at H = 14 T, showing a negative curvature with respect to the external field.

Field-Induced Magnetic Long-Range Order in the Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain System (CH 3) 2CHNH 3CuCl 3 Observed by Specific Heat Measurements

The compound (CH 3 ) 2 CHNH 3 CuCl 3 has recently been found to be an ideal ferromagnetic-antiferromagnetic alternating Heisenberg chain with the energy gap Δ/ k =17∼18 K [H. Manaka et al. : J. Phys. Soc. Jpn. 66 (1997) 564]. When an external field H is applied to this compound, the energy gap should vanish at the critical field H c1 = Δ/ g µ B . Just above H c1 , the three-dimensional magnetic long-range order is expected, if the interchain coupling exists. Motivated by this expectation, we performed specific heat measurements over a temperature range from 0.5 to 5 K applying H up to 12 T. As a result, we found a λ-type anomaly of specific heat over 10∼12 T, which indicates a transition to the three-dimensional long range order. The temperature at which the λ-type anomaly appears increases with increasing H . The critical field obtained by extrapolating the curve of the λ peak position versus H is 9.0 T, which is close to that obtained from a magnetization measurement.

Sr1.8Nd1.2Mn2O7: Synthesis, Crystal Structure, and Physical Properties

A detailed investigation into the preparation of powder samples of the n = 2 Ruddlesden−Popper (RP) oxide Sr1.8Nd1.2Mn2O7 is presented. This material is of interest as it displays colossal magntoresistance (CMR) without three-dimensional ferromagnetic long-range order. It is shown that Rietveld refinement of high-resolution powder X-ray and neutron diffraction data is essential to assess the outcomes of syntheses because of the potential coexistence of two very similar Ruddlesden−Popper phases. Phase coexistence or significant temperature-dependent anisotropic strain can be indicated by the broadening of the {0 0 10} reflection at 5 K. This suggests that a more subtle form of the previously reported phase separation at x = 0 is also difficult to avoid at the x = 0.2 composition. Precise attention to reaction temperature and time is required to prepare samples containing only one n = 2 Ruddlesden−Popper phase, and contamination by small quantities of the n = ∞ perovskite is a pervasive problem. Neutron powder diffraction structural analysis of the highest quality sample allows a comparison with the three-dimensional ferromagnet Sr1.8La1.2Mn2O7. The structure suggests that only slight changes in the Mn−O bond lengths are required to radically alter the electronic structure of n = 2 Ruddlesden−Popper phases.

Effect of cobalt doping on the magnetic properties of the spin-Peierls cuprateCuGeO3

The magnetization of single crystals in the system $({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}){\mathrm{GeO}}_{3}$ has been measured for compositions in the range $0.000<~x<~0.0547.$ These crystals exhibit paramagnetic behavior, which has been fit with a Curie-Weiss expression to determine the effective moment $({\ensuremath{\mu}}_{\mathrm{eff}})$ along the three principle crystal directions. For $x<~0.0225,$ the spin-Peierls transition is apparent in the magnetization data, with the transition temperature ${(T}_{\mathrm{sp}})$ decreasing with increased cobalt doping. For $x>~0.0204,$ an anisotropic magnetic transition occurs below 6 K, and is attributed to three-dimensional long-range antiferromagnetic ordering. When the field is directed along the $c$ axis, spin-flop behavior is observed at a critical field $[{H}_{c}(x,T)]$ for temperatures less than the N\'eel temperature ${(T}_{N}).$ Due to the strong paramagnetism in this system, ${T}_{N}$ and ${T}_{\mathrm{sp}}$ as a function of cobalt concentration were measured with single-crystal microcalorimetry. The effects of cobalt doping are discussed with respect to recent reports of Zn, Si, and Ni doping.