Importance of Supersuperexchange Interactions in Determining the Dimensionality of Magnetic Properties. Determination of Strongly Interacting Spin Exchange Paths in A2Cu(PO4)2 (A = Ba, Sr), ACuP2O7 (Ba, Ca, Sr, Pb), CaCuGe2O6, and Cu2UO2(PO4)2 on the Basis of Qualitative Spin Dimer Analysis

Magnetic Orderings in Li2Cu(WO4)2 with Tungstate-Bridged Quasi-1D Spin-1/2 Chains

By both experimental measurements and theoretical calculations, we investigated the magnetic and electronic properties of Li2Cu(WO4)2 as a tungstate-bridged quasi-one-dimensional (1D) copper spin-(1/2) chain system. Interestingly, magnetic susceptibility χ(T) and specific heat measurements show that the system undergoes a three-dimensional antiferromagnetic (AF)-like ordering at TN ≈ 3.7 K, below a broad χ(T) maximum at ∼8.9 K indicating a low-dimensional short-range AF spin correlation. Bonner-Fisher model fitting of χ(T) leads to an AF intrachain exchange constant of J/kB = 15.8 ± 0.1 K, and mean-field theory estimation gives an interchain coupling constant of J⊥/kB = 1.6 K, which supports the quasi-1D nature of this spin system. Theoretical evaluation of exchange coupling constants within the generalized gradient approximation (GGA) plus on-site Coulomb interaction (U) shows that the dominant AF exchange interaction is of ∼13.9 K along the a-axis with weak interchain coupling, in agreement with the experimental result of a quasi-1D spin-(1/2) chain system. The GGA+U calculations also predict that Li2Cu(WO4)2 is a charge transfer-type AF semiconductor with a direct band gap of 1.5 eV.

Electronic structure of Na(2)CuP(2)O(7): a nearly 2D Heisenberg antiferromagnetic system

We have employed first principles calculations to study the electronic structure and the implications for the magnetic properties of Na(2)CuP(2)O(7). Using the self-consistent tight-binding linearized muffin-tin orbital method and the Nth-order muffin-tin orbital downfolding method, we have calculated the various intrachain and interchain hopping parameters between the magnetic Cu(2+) ions. Our calculations for Na(2)CuP(2)O(7) reveal dominant intrachain hopping, but in contrast to the typical quantum spin chains the interchain hoppings are not negligible. The Wannier function plot of the Cu d(x(2)-y(2)) orbitals shows that the exchange interactions are primarily mediated by the oxygens and the distance between the oxygens in Na(2)CuP(2)O(7) is favorable for both intrachain and interchain interactions, suggesting the inapplicability of the one-dimensional Heisenberg model for this system, in agreement with recent experimental results.

Magnetic Properties of Synthetic Libethenite Cu2PO4OH: a New Spin-Gap System

Synthetic mineral libethenite Cu(2)PO(4)OH was prepared by the hydrothermal method, and its structure at 200 K was refined by single-crystal X-ray diffraction. The structure of Cu(2)PO(4)OH is built up from Cu2(2)O(6)(OH)2 dimers of edge-sharing Cu2O(4)(OH) trigonal bipyramids and [Cu1(2)O(6)(OH)(2)] proportional chains of edge-sharing Cu1O(4)(OH)(2) octahedra. Magnetic properties of Cu(2)PO(4)OH were investigated by magnetic susceptibility, magnetization, and specific heat measurements. Cu(2)PO(4)OH is a spin-gap system with a spin gap of about 139 K. It was shown by spin dimer analysis that, to a first approximation, the magnetic structure of Cu(2)PO(4)OH is described by an isolated square-spin cluster model defined by the Cu1-O-Cu2 superexchange J with Cu1...Cu2 = 3.429 A. The fitting analysis of the magnetic susceptibility data with a square-spin cluster model results in J/k(B) = 138 K. Specific heat data show that Cu(2)PO(4)OH does not undergo a long-range magnetic ordering down to 1.8 K. We also report vibrational properties studied with Raman spectroscopy and the thermal stability of Cu(2)PO(4)OH.

A tight-binding method for predicting magnetic ordering in Gd-containing solids: Application to GdB2C2

Herein we present a method to compute d-f mediated exchange coupling in Gd-containing systems with a spin-dependent extended Hückel-tight binding (EHTB) method. EHTB parameters were chosen to exactly reproduce the spin density functional calculation (SDFT) energy gap of the S = 45/2 and 39/2 spin patterns for a model compound, Gd6CoI12(OPH3)6. Comparison between SDFT and EHTB results shows a good match between the spin-pattern energy distribution for the two methods. We applied our EHTB method to the solid-state compound GdB2C2 by considering 6 different variations in the ordering of the 4f7 moments. Calculations indicate that this metallic system should exhibit antiferromagnetic ordering of the 4f7 moments with a magnetic structure consistent with published neutron diffraction results.

Comparison of the crystal structures and magnetic properties of the low- and high-temperature forms of AgCuPO4: crystal structure determination, magnetic susceptibility measurements, and spin dimer analysis

The crystal structure of the low-temperature form of AgCuPO4 (i.e., alpha-AgCuPO4) was determined by powder X-ray diffraction and was compared with that of the high-temperature form of AgCuPO4 (i.e., beta-AgCuPO4). The magnetic properties of the two forms were examined by measuring their magnetic susceptibilities and evaluating the relative strengths of their spin-exchange interactions on the basis of spin-dimer analysis. Both forms of AgCuPO4 have layers of Cu2P2O8 alternating with silver-atom double layers; beta-AgCuPO4 has two Cu2P2O8 layers per unit cell, while alpha-AgCuPO4 has one. The coordinate environment of each Cu2+ ion is close to being a distorted square pyramid in alpha-AgCuPO4, but it is close to being a distorted trigonal bipyramid in beta-AgCuPO4. The magnetic susceptibilities of alpha- and beta-AgCuPO4 are well simulated by an antiferromagnetic alternating-chain model, which leads to J/k(B) = -146.1 K and alphaJ/k(B) = -75.8 K for alpha-AgCuPO4, and J/k(B) = -82.6 K and alphaJ/k(B) = -31.7 K for beta-AgCuPO4 (with the convention in which the spin-exchange parameter between two adjacent spin sites is written as 2J). The spin gaps, delta/k(B), obtained from these parameters are 93.7 K for alpha-AgCuPO4 and 62.3 K for beta-AgCuPO4. The strongest spin exchange in both forms of AgCuPO4 comes from a super-superexchange path, and this interaction is stronger for alpha-AgCuPO4 than for beta-AgCuPO4 by a factor of approximately 2, in good agreement with the experiment. Our analysis supports the use of this model for beta-AgCuPO4 and indicates that the spin lattice of alpha-AgCuPO4 would be better described by a two-dimensional net made up of weakly interacting alternating chains.

Importance of the O−M−O Bridges (M = V5+, Mo6+) for the Spin-Exchange Interactions in the Magnetic Oxides of Cu2+ Ions Bridged by MO4 Tetrahedra: Spin-Lattice Models of Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28

The spin-lattice models relevant for the magnetic oxides Rb2Cu2(MoO4)3, BaCu2V2O8, and KBa3Ca4Cu3V7O28 were determined by evaluating the relative strengths of the spin-exchange interactions between their Cu2+ ions on the basis of spin dimer analysis. Our study shows that the O-M-O bridges (M = V5+, Mo6+) between the magnetic ions Cu2+, provided by the MO4 tetrahedra, are crucial for the spin-exchange interactions and hence for deducing the spin-lattice models needed to interpret the magnetic properties of these oxides. The spin-lattice model of Rb2Cu2(MoO4)3 is not a uniform chain but two interpenetrating spin ladders that interact weakly with geometric spin frustration. The spin-lattice model of BaCu2V2O8 is an alternating chain as expected, but the spin-exchange paths responsible for it differ from those expected. With respect to the strongest spin exchange of BaCu2V2O8, the spin exchange of KBa3Ca4Cu3V7O28 is only slightly weaker, but the strongest spin exchange of Rb2Cu2(MoO4)3 is much weaker. This difference in the spin-exchange strengths is caused by the difference in the bridging modes of the MO4 tetrahedra leading to these spin-exchange interactions.

Investigation of the Crystal Structure and the Structural and Magnetic Properties of SrCu2(PO4)2

SrCu2(PO4)2 was prepared by the solid-state method at 1153 K. Its structure was solved by direct methods in the space group Pccn (No. 56) with Z = 8 from synchrotron X-ray powder diffraction data measured at room temperature. Structure parameters were then refined by the Rietveld method to obtain the lattice parameters, a = 7.94217(8) A, b = 15.36918(14) A, and c = 10.37036(10) A. SrCu2(PO4)2 presents a new structure type and is built up from Sr2O16 and Cu1Cu2O8 units with Cu1...Cu2 = 3.256 A. The magnetic properties of SrCu2(PO4)2 were investigated by magnetic susceptibility, magnetization up to 65 T, Cu nuclear quadrupole resonance (NQR), electron-spin resonance, and specific heat measurements. With spin-dimer analysis, it was shown that the two strongest spin-exchange interactions between Cu sites result from the Cu1-O...O-Cu2 and Cu2-O...O-Cu2 super-superexchange paths with Cu1...Cu2 = 5.861 A and Cu2...Cu2 = 5.251 A, and the superexchange associated with the structural dimer Cu1Cu2O8 is negligible. The magnetic susceptibility data were analyzed in terms of a linear four-spin cluster model, Cu1-Cu2-Cu2-Cu1 with -2J(1)/kB = 82.4 K for Cu1-Cu2 and -2J(2)/k(B) = 59 K for Cu2-Cu2. A spin gap deduced from this model (Delta/kB = 63 K) is in agreement with that obtained from the Cu NQR data (Delta/kB = 65 K). A one-half magnetization plateau was observed between approximately 50 and 63 T at 1.3 K. Specific heat data show that SrCu2(PO4)2 does not undergo a long-range magnetic ordering down to 0.45 K. SrCu2(PO4)2 melts incongruently at 1189 K. We also report its vibrational properties studied with Raman spectroscopy.