Green's function approach to the magnetic properties of the kagome antiferromagnet

The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions are obtained and characterize this system as a two-dimensional quantum spin liquid. Spin-spin correlation functions decay exponentially with distance down to low temperature and the calculated missing entropy at T=0 is found to be $0.46\ln{2}$. Within the present scheme, the specific heat exhibits a single peak structure and a $T^2$ dependence at low temperature.Comment: 6 (two-column revtex4) pages, 5 ps figures. Submitted to Phys. Rev.

Orbital liquid in three dimensional Mott insulator: LaTiO3LaTiO_3

We present a theory of spin and orbital states in Mott insulator $LaTiO_3$. The spin-orbital superexchange interaction between $d^1(t_{2g})$ ions in cubic crystal suffers from a pathological degeneracy of orbital states at classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of $t_{2g}$ level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of $LaTiO_3$.Comment: 5 pages, 3 figure

Accounting for nutrition-related health impacts in food life cycle assessment: insights from an expert workshop

\ua9 The Author(s) 2024.Sub-optimal dietary patterns make major contributions to the Global Burden of Disease and are among the most pressing issues affecting human health. Consequently, they are key to consider when assessing the human health and other environmental impacts of foods and diets within life cycle assessments. The UN Environment Life Cycle Initiative convened a task force on nutrition-related human health impacts as part of the Global Life Cycle Impact Assessment Method (GLAM) project. The health impacts of dietary patterns can be expressed in disability-adjusted life years (DALYs), in line with reporting human health impacts of other impact categories within the life cycle impact assessment (LCIA) framework. The task force held a workshop with nutrition experts to receive guidance in its process to develop a consensus-based impact assessment framework for addressing nutrition-related health impacts in LCIA. The workshop aimed to (1) evaluate the general assessment framework, (2) discuss scientific questions for quantifying human health impacts from nutrition for food items and diets, and (3) provide initial guidance for further development. The proposed framework based on the Global Burden of Disease (GBD) risk ratios was regarded as a good starting point to assess the relative health risks of the general population, provided that the dietary context is considered and several limitations, such as incomplete disease coverage, are acknowledged. The experts advised against a potentially misleading use of adult-derived dietary risk factors for children. To improve global coverage of the GLAM framework, it is important to consider a wider range of dietary patterns. The experts also recommended using a metric complementary to DALYs, such as nutrient adequacy, also considering, e.g., vitamin A and iron, to complement the assessment

Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin-1/2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T^2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low temperature magneto-thermal effect is associated to the existence of low-lying fluctuating singlets, but also that the whole picture (T^2 behavior of Cv and thermally activated spin susceptibility) implies contribution of both non magnetic and magnetic excitations. Comparison with experiments is made.Comment: 4 pages, LaTeX 2.09 and RevTeX with 3 figures embedded in the text. Version to appear in Phys. Rev. Let

Magnetization of coupled spin clusters in Ladder Geometry

In this paper, we construct a class of spin-1/2 antiferromagnetic (AFM) two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For n=4 and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site (m) versus magenetic field (h) plot exhibits well-defined magnetization plateaus.Comment: 9 pages, latex, 6 figures, To be published in Phys. Rev.

Transition to Long Range Magnetic Order in the Highly Frustrated Insulating Pyrochlore Antiferromagnet Gd_2Ti_2O_7

Experimental evidence from measurements of the a.c. and d.c. susceptibility, and heat capacity data show that the pyrochlore structure oxide, Gd_2Ti_2O_7, exhibits short range order that starts developing at 30K, as well as long range magnetic order at $T\sim 1$K. The Curie-Weiss temperature, $\theta_{CW}$ = -9.6K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below $\sim$10K while magnetic heat capacity contributions are found at temperatures above 20K. A sharp maximum in the heat capacity at $T_c=0.97$K signals a transition to a long range ordered state, with the magnetic specific accounting for only $\sim$ 50% of the magnetic entropy. The heat capacity above the phase transition can be modeled by assuming that a distribution of random fields acts on the $^8S_{7/2}$ ground state for Gd$^{3+}$. There is no frequency dependence to the a.c. susceptibility in either the short range or long range ordered regimes, hence suggesting the absence of any spin-glassy behavior. Mean field theoretical calculations show that no long range ordered ground state exists for the conditions of nearest-neighbor antiferromagnetic exchange and long range dipolar couplings. At the mean-field level, long range order at various commensurate or incommensurate wave vectors is found only upon inclusion of exchange interactions beyond nearest-neighbor exchange and dipolar coupling. The properties of Gd$_2Ti_2O_7 are compared with other geometrically frustrated antiferromagnets such as the Gd_3Ga_5O_{12} gadolinium gallium garnet, RE_2Ti_2O_7 pyrochlores where RE = Tb, Ho and Tm, and Heisenberg-type pyrochlore such as Y_2Mo_2O_7, Tb_2Mo_2O_7, and spinels such as ZnFe_2O_4Comment: Letter, 6 POSTSCRIPT figures included. (NOTE: Figure 5 is not included --) To appear in Physical Review B. Contact: [email protected]

Susceptibility and dilution effects of the kagome bi-layer geometrically frustrated network. A Ga-NMR study of SrCr_(9p)Ga_(12-9p)O_(19)

We present an extensive gallium NMR study of the geometrically frustrated kagome bi-layer compound SrCr_(9p)Ga_(12-9p)O_(19) (Cr^3+, S=3/2) over a broad Cr-concentration range (.72<p<.95). This allows us to probe locally the kagome bi-layer susceptibility and separate the intrinsic properties due to the geometric frustration from those related to the site dilution. Our major findings are: 1) The intrinsic kagome bi-layer susceptibility exhibits a maximum in temperature at 40-50 K and is robust to a dilution as high as ~20%. The maximum reveals the development of short range antiferromagnetic correlations; 2) At low-T, a highly dynamical state induces a strong wipe-out of the NMR intensity, regardless of dilution; 3) The low-T upturn observed in the macroscopic susceptibility is associated to paramagnetic defects which stem from the dilution of the kagome bi-layer. The low-T analysis of the NMR lineshape suggests that the defect can be associated with a staggered spin-response to the vacancies on the kagome bi-layer. This, altogether with the maximum in the kagome bi-layer susceptibility, is very similar to what is observed in most low-dimensional antiferromagnetic correlated systems; 4) The spin glass-like freezing observed at T_g=2-4 K is not driven by the dilution-induced defects.Comment: 19 pages, 19 figures, revised version resubmitted to PRB Minor modifications: Fig.11 and discussion in Sec.V on the NMR shif

Area of Concern: A new paradigm in life cycle assessment for the development of footprint indicators

Purpose As a class of environmental metrics, footprints have been poorly defined, have shared an unclear relationship to Life Cycle Assessment (LCA), and the variety of approaches to quantification have sometimes resulted in confusing and contradictory messages in the marketplace. In response, a task force operating under the auspices of the UNEP/SETAC Life Cycle Initiative project on environmental Life Cycle Impact Assessment (LCIA) has been working to develop generic guidance for developers of footprint metrics. The purpose of this paper is to introduce a universal footprint definition and related terminology as well as to discuss modelling implications. Methods The task force has worked from the perspective that footprints should be underpinned by the same data systems and models as used in LCA. However, there are important differences in purpose and orientation relative to LCA impact category indicators. Footprints have a primary orientation toward society and nontechnical stakeholders. They are also typically of narrow scope, having the purpose of reporting only in relation to specific topics. In comparison, LCA has a primary orientation toward stakeholders interested in comprehensive evaluation of overall environmental performance and trade-offs among impact categories. These differences create tension between footprints, the existing LCIA framework based on the Area of Protection paradigm, and the core LCA standards ISO14040/44. Results In parallel to Area of Protection, we introduce Area of Concern as the basis for a universal footprint definition. In the same way that LCA uses impact category indicators to assess impacts that follow a common cause-effect pathway toward Areas of Protection, footprint metrics address Areas of Concern. The critical difference is that Areas of Concern are defined by the interests of stakeholders in society rather than the LCA community. In addition, Areas of Concern are stand-alone and not necessarily part of a framework intended for comprehensive environmental performance assessment. The Area of Concern paradigm is needed to support the development of footprints in a way that fulfils their distinctly different purpose. It is also needed as a mechanism to extricate footprints from some of the provisions of ISO 14040/44 which are not considered relevant. Specific issues are identified in relation to double counting, aggregation, and the selection of relevant indicators. Conclusions The universal footprint definition and related terminology introduced in this paper create a foundation that will support the development of footprint metrics in parallel with LCA