On the nature of the spin frustration in the CuO2 ribbon chains of LiCuVO4: crystal structure determination at 1.6 K, magnetic susceptibility analysis, and density functional evaluation of the spin exchange constants

The spin-1/2 Cu(2+) ions of LiCuVO(4) form one-dimensional chains along the b direction, and the spin frustration in LiCuVO(4) is described in terms of the nearest-neighbor ferromagnetic exchange J(1) and the next-nearest-neighbor antiferromagnetic exchange J(2) in these chains. Recently, it has become controversial whether or not J(1) is stronger in magnitude than J(2). To resolve this controversy, we determined the crystal structure of LiCuVO(4) at 1.6 K by neutron diffraction, analyzed the magnetic susceptibility of LiCuVO(4) to deduce the Curie-Weiss temperature θ and the J(2)/J(1) ratio, and finally extracted the spin exchange constants of LiCuVO(4) on the basis of density functional calculations. Our work shows unambiguously that the Curie-Weiss temperature θ of LiCuVO(4) is negative in the range of -20 K, so that J(2) is substantially stronger in magnitude than J(1).     

Investigation of the spin exchange interactions and magnetic Structures of the CrVO4-type transition metal phosphates,sulfates, and vanadates by spin dimer analysis

The CrVO(4)-type magnetic oxides MM'O(4) consist of edge-sharing MO(4) octahedral chains condensed with M'O(4) tetrahedra and exhibit a wide variety of magnetic structures. The magnetic properties of these oxides were examined by studying their spin exchange interactions on the basis of spin dimer analysis. The nature and magnitudes of the intra- and interchain spin exchange interactions depend on the square-to-rectangle distortion in the basal planes of the MO(4) chain and on the difference between the M 3d and O 2p orbital energies. The spiral magnetic structures of beta-CrPO(4) and MnSO(4) originate from the pseudohexagonal arrangement of the MO(4) chains and the frustrated interchain antiferromagnetic interactions.     

Spin dimer analysis of the spin exchange interactions in paramelaconite Cu(4)O(3) and its analogue Ag(2)Cu(2)O(3) and the spin ordering of the Cu(2)O(3) spin lattice leading to their magnetic phase transitions

The magnetic structures of the Cu(2)O(3) spin lattices present in Cu(4)O(3) and Ag(2)Cu(2)O(3) were analyzed by studying their spin exchange interactions on the basis of spin dimer analysis. Calculations of spin exchange parameters were calibrated by studying LiCuVO(4) whose intrachain and interchain antiferromagnetic spin exchange parameters are known experimentally. The magnetic phase transition of Cu(4)O(3) at 42.3 K doubles the unit cell along each crystallographic direction. The spin arrangements of the Cu(2)O(3) lattice consistent with this experimental observation are different from conventional antiferromagnetic ordering. Our analysis indicates that spin fluctuation should occur in Cu(4)O(3), low-dimensional magnetism should be more important than magnetic frustration in Cu(4)O(3), and Ag(2)Cu(2)O(3) and Cu(4)O(3) should have similar structural and magnetic properties.     

Spin dimer analysis of the anisotropic spin exchange interactions in the distorted wolframite-type oxides CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4

The distorted wolframite-type oxides CuWO4 and CuMoO4-III have a structure in which CuO4 zigzag chains, made up of cis-edge-sharing CuO6 octahedra, run along the c-direction and hence exhibit low-dimensional magnetic properties. We examined the magnetic structures of these compounds and their isostructural analogue Cu(Mo(0.25)W0.75)O4 on the basis of the spin-orbital interaction energies calculated for their spin dimers. Our study shows that these compounds consist of two-dimensional (2D) magnetic sheets defined by one superexchange (intrachain Cu-O-Cu) and three super-superexchange (interchain Cu-O.O-Cu) paths, the strongly interacting spin units of these 2D magnetic sheets are the two-leg antiferromagnetic (AFM) ladder chains running along the (a + c)-direction, and the spin arrangement between adjacent AFM ladder chains leads to spin frustration. The similarities and differences in the magnetic structures of CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4 were discussed by examining how adjacent AFM ladder chains are coupled via the superexchange paths in the 2D magnetic sheets and how adjacent 2D magnetic sheets are coupled via another superexchange paths along the c-direction. Our study reproduces the experimental finding that the magnetic unit cell is doubled along the a-axis in CuWO(4) and along the c-axis in CuMoO4-III and predicts that the magnetic unit cell should be doubled along the a- and b-axes in Cu(Mo(0.25)W0.75)O4. In the understanding of the strength of a super-superexchange interaction, the importance of the geometrical factors controlling the overlap between the tails of magnetic orbitals was pointed out.     

Analysis of the spin exchange interactions in the three phases of vanadium pyrophosphate, (VO)2P2O7, in terms of spin-orbital interaction energy

The spin exchange interactions in the ambient-pressure orthorhombic (APO), high-pressure orthorhombic (HPO), and ambient-pressure monoclinic (APM) phases of the vanadium pyrophosphate, (VO)2P2O7, were analyzed by calculating the spin-orbital interaction energies delta e-delta e0 of their spin dimers. The anisotropy of the spin exchange interactions in the HPO phase is well explained by the delta e-delta e0 values. For the APO phase, the reported crystal structure does not provide accurate enough delta e-delta e0 values to conclude unambiguously which of the V1-V2 and V3-V4 chains has a larger spin gap and which of the bridged and edge-sharing spin dimers has a stronger spin exchange interaction in the V1-V2 and V3-V4 chains. The APM phase is predicted to exhibit essentially two spin gaps, with a large spin gap for the V8-V5-V7-V6 chain and a very small one for the V4-V2-V3-V1 chain.     

Magnetic superstructures of cupric oxide CuO as ordered arrangements of one-dimensional antiferromagnetic chains

In cupric oxide CuO, each Cu(2+) ion has 12 nearest-neighbor Cu(2+) ions grouped into six pairs related by inversion symmetry. The relative strengths of the Cu-O-Cu superexchange interactions in cupric oxide CuO were estimated by spin dimer analysis to confirm that the strongest superexchange interactions form one-dimensional antiferromagnetic chains along the [101] direction, and the remaining interactions are weak. We analyzed ordered arrangements of these one-dimensional antiferromagnetic chains to examine why the antiferromagnetic phase transition of CuO below 212.5 K adopts a (2a, b, 2c) superstructure. The local spin arrangement around each Cu(2+) ion is more balanced in the ordered spin structures leading to a (2a, b, 2c) supercell than in any other ordered spin structures.     

Spin dimer and classical spin analyses of the ordered magnetic structures of alkali iron pyrophosphates NaFeP(2)O(7) and LiFeP(2)O(7)

The magnetic oxides NaFeP(2)O(7) and LiFeP(2)O(7), made up of FeO(6) octahedra containing high-spin Fe(3+)(d(5)) ions, undergo a three-dimensional antiferromagnetic ordering at low temperatures. The strengths of various Fe-O...O-Fe super-superexchange interactions of NaFeP(2)O(7) and LiFeP(2)O(7) were estimated on the basis of spin dimer analysis to probe the nature of their ordered magnetic structures. It is found that the critical factor governing the strength of a Fe-O...O-Fe super-superexchange interaction is not the Fe...Fe distance but the O...O distance. Using the spin exchange parameters thus obtained, the total spin exchange interaction energies were calculated for various ordered spin arrangements of NaFeP(2)O(7) and LiFeP(2)O(7) on the basis of classical spin analysis to confirm that the observed magnetic structures are the magnetic ground states.     

Time evolution of a single spin inhomogeneously coupled to an interacting spin environment

We study the time evolution of a single spin coupled by exchange interaction to an environment of interacting spin bath modeled by the XY Hamiltonian. By evaluating the spin correlator of the single spin, we observed that the decay rate of the spin oscillations strongly depends on the relative magnitude of the exchange coupling between the single spin and its nearest neighbor J(') and coupling among the spins in the environment J. The decoherence time varies significantly based on the relative coupling magnitudes of J and J('). The decay rate law has a Gaussian profile when the two exchange couplings are of the same order J(') approximately J but converts to exponential and then a power law as we move to the regimes of J(')>J and J(')相似文献   

Extension of the LAP functional to include parallel spin correlation

The kinetic energy density-dependent correlation functional LAP1 is extended to include parallel-spin correlation beyond the exchange level. Two exchange–correlation schemes are considered, combining the new correlation functional (LAP3) with the GGA exchange of Becke and the GGA exchange of Perdew. Extensive tests on molecules and hydrogen-bonded systems are presented and discussed elucidating the role of parallel–spin correlation in different cases. Its inclusion in the LAP functional leads, on average, to a slight improvement of the calculated binding energies and equilibrium geometries of molecules. Particularly high sensitivity of the energy results on the relative share of parallel-spin correlation is observed for aromatic molecules and for systems involving weak hydrogen bonds. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 427–446, 1997     

Analysis of the spin exchange interactions and the ordered magnetic structures of lithium transition metal phosphates LiMPO4 (M = Mn, Fe, Co, Ni) with the olivine structure

The olivine-type compounds LiMPO4 (M = Mn, Fe, Co, Ni) consist of MO4 layers made up of corner-sharing MO6 octahedra of high-spin M2+ ions. To gain insight into the magnetic properties of these phosphates, their spin exchange interactions were estimated by spin dimer analysis using tight binding calculations and by electronic band structure analysis using first principles density functional theory calculations. Three spin exchange interactions were found to be important for LiMPO4, namely, the intralayer superexchange J1, the intralayer super-superexchange Jb along the b-direction, and the interlayer super-superexchange J2 along the b-direction. The magnetic ground state of LiMPO4 was determined in terms of these spin exchange interactions by calculating the total spin exchange interaction energy under the classical spin approximation. In the spin lattice of LiMPO4, the two-dimensional antiferromagnetic planes defined by the spin exchange J1 are antiferromagnetically coupled by the spin exchange J2, in agreement with available experimental data.     

On the high magnetic-ordering temperature of the 5d magnetic oxide Ca3LiOsO6 crystallizing in a trigonal crystal structure: density functional analysis

The 5d magnetic oxide Ca(3)LiOsO(6) has a trigonal arrangement of its LiOsO(6) chains parallel to the c-direction and hence has triangular arrangements of high-spin Os(5+) (d(3)) ions but exhibits no spin frustration and undergoes a long-range antiferromagnetic ordering at a high temperature. The origin of this apparently puzzling observation was examined by evaluating the nearest-neighbor Os-O···O-Os spin exchange interactions of Ca(3)LiOsO(6) on the basis of density functional calculations. Our study shows that, of the two nearest-neighbor interchain spin exchanges, one dominates over the other and that the intrachain spin exchange and the dominating interchain spin exchange are strong and form a three-dimensional antiferromagnetic spin lattice with no spin frustration, which is responsible for the long-range antiferromagnetic ordering of Ca(3)LiOsO(6) at high temperature. In determining the strengths of the Os-O···O-Os exchange interactions of Ca(3)LiOsO(6), the Li(+) and Ca(2+) ions of the O···Li(+)···O and O···Ca(2+)···O linkages are found to play only a minor role.     

Importance of supersuperexchange interactions in determining the dimensionality of magnetic properties. Determination of strongly interacting spin exchange paths in A(2)Cu(PO(4))(2) (A = Ba, Sr), ACuP(2)O(7) (Ba, Ca, Sr, Pb), CaCuGe(2)O(6), and Cu(2)UO(2)(PO(4))(2) on the basis of qualitative spin dimer analysis

The patterns of the Cu(2+) ion arrangements in the magnetic oxides A(2)Cu(PO(4))(2) (A = Ba, Sr), ACuP(2)O(7) (Ba, Ca, Sr, Pb), CaCuGe(2)O(6), and Cu(2)UO(2)(PO(4))(2) are quite different from the patterns of the strongly interacting spin exchange paths deduced from their magnetic properties. This apparently puzzling observation was explained by evaluating the strengths of the Cu-O-Cu superexchange and Cu-O...O-Cu supersuperexchange interactions of these oxides on the basis of qualitative spin dimer analysis. Supersuperexchange interactions are found to be crucial in determining the dimensionality of magnetic properties of these magnetic oxides.     

Altering the spin state of transition metal centers in metal-organic frameworks by molecular hydrogen adsorption: a first-principles study

Our first-principles calculation shows that molecular hydrogen (H(2)) adsorption at an exposed Fe(II) site in metal-organic frameworks could induce a spin flip in the Fe(II) center resulting in a spin-state transition from a triplet high-spin (HS) to a singlet low-spin (LS) state. The Kubas-type Fe-H(2) interaction, where H(2) coordinates onto the Fe(II) center as a σ-ligand, is found commensurate in strength with the exchange interaction of Fe 3d electrons, which is responsible for the occurrence of the spin-state transition in this system. The H(2) binding energies are 0.08 and 0.35 eV per H(2) at the HS and LS states, respectively. This effect is expected to find applications in spin-control in molecular magnets, hydrogen sensing and storage.     

Spin dimer analysis of the magnetic structures of Ba3Cr2O8, Ba3Mn2O8, Na4FeO4, and Ba2CoO4 with a three-dimensional network of isolated MO4 (M = Cr, Mn, Fe, Co) tetrahedra

The spin exchange interactions of the magnetic oxides Ba3Cr2O8, Ba3Mn2O8, Na4FeO4, and Ba2CoO4 with a three-dimensional network of isolated MO4 (M = Cr, Mn, Fe, Co) tetrahedra were examined by performing spin dimer analysis on the basis of tight-binding electronic structure calculations. Although the shortest O...O distances between adjacent MO4 tetrahedra are longer than the van der Waals distance, our analysis shows that the super-superexchange interactions between adjacent MO4 tetrahedra are substantial and determine the magnetic structures of these oxides. In agreement with experiment, our analysis predicts a weakly interacting isolated AFM dimer model for both Ba3Cr2O8 and Ba3Mn2O8, the (0.0, 0.5, 0.0) magnetic superstructure for Na4FeO4, the (0.5, 0.0, 0.5) magnetic superstructure for Ba2CoO4, and the presence of magnetic frustration in Ba2CoO4. The comparison of the intra- and interdimer spin exchange interactions of Ba3Cr2O8 and Ba3Mn2O8 indicates that orbital ordering should be present in Ba3Cr2O8.     

Two-dimensional superstructures and softened C-H stretching vibrations of cyclohexane on Rh(111): effects of preadsorbed hydrogen

Adsorption structures and interaction of cyclohexane molecules on the clean and hydrogen-preadsorbed Rh(111) surfaces were investigated using scanning tunneling microscopy, spot-profile-analysis low-energy electron diffraction, temperature-programmed desorption, and infrared reflection absorption spectroscopy (IRAS). Various ordered structures of adsorbed cyclohexane were observed as a function of hydrogen and cyclohexane coverages. When the fractional coverage (θ(H)) of preadsorbed hydrogen was below 0.8, four different commensurate or higher-order commensurate superstructures were found as a function of θ(H); whereas more densely packed incommensurate overlayers became dominant at higher θ(H). IRAS measurements showed sharp softened C-H vibrational peaks at 20 K, which originate from the electronic interaction between adsorbed cyclohexane and the Rh surface. The multiple softened C-H stretching peaks in each phase are due to the variation in the adsorption distance from the substrate. At high hydrogen coverages they became attenuated in intensity and eventually diminished at θ(H) = 1. The gradual disappearance of the soft mode correlates well with the structural phase transition from commensurate structures to incommensurate structures with increasing hydrogen coverage. The superstructure of adsorbed cyclohexane is controlled by the delicate balance between adsorbate-adsorbate and adsorbate-substrate interactions which are affected by preadsorbed hydrogen.     

Pulsed electron spin nutation spectroscopy of weakly exchange-coupled biradicals: a general theoretical approach and determination of the spin dipolar interaction

Weakly exchange-coupled biradicals have attracted much attention in terms of their DNP application in NMR spectroscopy for biological systems or the use of synthetic electron-spin qubits. Pulse-ESR based electron spin nutation (ESN) spectroscopy applied to biradicals is generally treated as transition moment spectroscopy from the theoretical side, illustrating that it is a powerful and facile tool to determine relatively short distances between weakly exchange-coupled electron spins. The nutation frequency as a function of the microwave irradiation strength ω(1) (angular frequency) for any cases of weakly exchange-coupled systems can be classified into three categories; D(12) (spin dipolar interaction)-driven, Δg-driven and ω(1)-driven nutation behaviour with the increasing strength of ω(1). For hetero-spin biradicals, Δg effects can be a dominating characteristic in the biradical nutation spectroscopy. Two-dimensional pulse-based electron spin nutation (2D-ESN) spectroscopy operating at the X-band can afford to determine small values of D(12) in weakly exchange-coupled biradicals in rigid glasses. The analytical expressions derived here for ω(1)-dependent nutation frequencies are based on only four electronic spin states relevant to the biradicals, while real biradical systems often have sizable hyperfine interactions. Thus, we have evaluated nuclear hyperfine effects on the nutation frequencies to check the validity of the present theoretical treatment. The experimental spin dipolar coupling of a typical TEMPO-based biradical 1, (2,2,6,6-tetra[((2)H(3))methyl]-[3,3-(2)H(2),4-(2)H(1),5,5-(2)H(2)]piperidin-N-oxyl-4-yl)(2,2,6,6-tetra[((2)H(3))methyl]-[3,3-(2)H(2),4-(2)H(1),5,5-(2)H(2),(15)N]piperidin-(15)N-oxyl-4-yl) terephthalate in a toluene glass, with a distance of 1.69 nm between the two spin sites is D(12) = -32 MHz (the effect of the exchange coupling J(12) is vanishing due to the homo-spin sites of 1, i.e.Δg = 0), while 0 < |J(12)|≦ 1.0 MHz as determined by simulating the random-orientation CW ESR spectra of 1. In addition, we have carried out Q-band pulsed ELDOR (ELectron-electron DOuble Resonance) experiments to confirm whether the obtained values for D(12) and J(12) are accurate. The distance is in a fuzzy region for the distance-measurements capability of the conventional, powerful ELDOR spectroscopy. The strong and weak points of the ESN spectroscopy with a single microwave frequency applicable to weakly exchange-coupled multi-electron systems are discussed in comparison with conventional ELDOR spectroscopy. The theoretical spin dipolar tensor and exchange interaction of the TEMPO biradical, as obtained by sophisticated quantum chemical calculations, agree with the experimental ones.     

BIRD-J-resolved HMBC and BIRD-high-resolution HMBC pulse sequences for measuring heteronuclear long-range coupling constants and proton-proton spin coupling constants in complicated spin systems

Efficient pulse sequences for measuring long-range C-H coupling constants (J(C-H)) and proton-proton spin coupling constants (J(H-H)), named BIRD-J-resolved HMBC and BIRD-high-resolution HMBC, respectively, have been developed. In spin systems possessing a secondary methyl group positioned between protonated carbons (e.g. -CH(2)-CH(CH(3))-CH(2)-), the methine proton splits in a complicated fashion, resulting in difficulty in the determination of its spin coupling constants. For easy and accurate measurements of the long-range J(C-H) and J(H-H) in such a spin system, the BIRD pulse [90°x(H)-180°x (H/C)- 90° (-x)(H)] or [90°x(H)-180°x(H/C)-90° (-x)(H)180°x(C)] is incorporated into the J-resolved portion of the pulse sequence. As a result, the above secondary methyl group can be selectively decoupled, providing simplified cross-peak patterns, which are suitable for the accurate measurements of the long-range J(C-H) and J(H-H).     

Structure and magnetism of a spin ladder system: (C5H9NH3)2CuBr4

The crystal structure of bis(cyclopentylammonium)tetrabromocuprate(II) has been determined at room temperature and at -70 degrees C. The room temperature structure is orthorhombic, space group Pn2(1)a, with a = 12.092(6) A, b = 8.134(4) A, and c = 18.698(10) A. The low temperature structure is also orthorhombic, space group Pna2(1), with a = 24.111(5) A, b = 8.089(2) A, and c = 18.448(4) A. DSC studies reveal the presence of a weak endotherm at -13 degrees C. The structures of the two phases are very similar, differing only in the relative orientations of the cyclopentyl rings of the organic cations and slight displacements of the anionic tetrahedra. The CuBr(4)(2)(-) anions in the low temperature phase are arranged to define a spin ladder system through Cu-Br.Br-Cu two-halide exchange pathways. Magnetic susceptibility data have been analyzed and yield antiferromagnetic exchange strengths 2J(rail)/k = -11.6 K and 2J(rung)/k = -5.5 K with a singlet-triplet gap energy Delta/k(B) = 2.3 K. This is the first report of a spin ladder with a stronger interaction along the axis of the ladder than along the rungs.     

Determination of the spin-lattice relevant for the quaternary magnetic oxide Bi4Cu3V2O14 on the basis of tight-binding and density functional calculations

The quaternary magnetic oxide Bi4Cu3V2O14 consists of Cu4O8 triple chains made up of corner-sharing CuO4 square planes. To determine its spin-lattice, the spin exchange interactions of Bi4Cu3V2O14 were evaluated by performing a spin dimer analysis based on tight-binding calculations and a mapping analysis based on first principles density functional theory calculations. Both calculations show that the spin-lattice of Bi4Cu3V2O14 is not an antiferromagnetically coupled diamond chain, which results from an idealized view of the structure of the Cu4O8 triple chain and a neglect of super-superexchange interactions. The correct spin-lattice is an antiferromagnetic chain made up of antiferromagnetic linear trimers coupled through their midpoints via super-superexchange interaction, which predicts that Bi4Cu3V2O14 has an antiferromagnetic spin ground state and has no spin frustration, both in agreement with experiment.     

Analysis of the spin lattice model for the spin-gapped layered compounds Na(3)Cu(2)SbO(6) and Na(2)Cu(2)TeO(6) on the basis of electronic structure calculations

The spin lattice model for the spin-gapped layered magnetic solids Na3Cu2SbO6 and Na2Cu2TeO6 was examined by evaluating the three spin exchange interactions of their Cu2MO6 (M = Sb, Te) layers in terms of spin dimer analysis based on extended Hückel tight binding calculations and mapping analysis based on first principles density functional theory electronic band structure calculations. For both compounds, our calculations show that the two strongest spin exchange interactions, that is, the Cu-O...O-Cu super-superexchange (J2) and the Cu-O-Cu superexchange (J1) interactions, form alternating chains that interact weakly through the Cu-O-Cu superexchange (J3) interactions. The dominant one of the three spin exchange interactions is J2, and it is antiferromagnetic in agreement with the fact that both of the compounds are spin gapped. For Na3Cu2SbO6 and Na2Cu2TeO6, the superexchange J1 is calculated to be ferromagnetic, hence, leading to the alternating chain model in which antiferromagnetic and ferromagnetic spin exchange interactions alternate. This picture does not agree with the recent experimental analysis, which showed that the temperature-dependent magnetic susceptibilities of both compounds should be described by the alternating chain model in which two antiferromagnetic spin exchange interactions of different strengths alternate.