Magnetic correlations of the quasi-one-dimensional half-integer spin-chain antiferromagnets SrM2M_2V2_2O8_8 (MM = Co, Mn)

Magnetic correlations of two iso-structural quasi-one-dimensional (1D) antiferromagnetic spin-chain compounds Sr$M_2$V$_2$O$_8$ ($M$ = Co, Mn) have been investigated by magnetization and powder neutron diffraction. Two different collinear antiferromagnetic (AFM) structures, characterized by the propagation vectors, $k$ = (0 0 1) and $k$ = (0 0 0), have been found below $\sim$ 5.2 K and $\sim$ 42.2 K for the Co- and Mn-compounds, respectively. For the Mn-compound, AFM chains (along the $c$ axis) order ferromagnetically within the $ab$ plane, whereas, for the Co-compound, AFM chains order ferro-/antiferromagnetically along the $a/b$ direction. The critical exponent study confirms that the Co- and Mn-compounds belong to the Ising and Heisenberg universality classes, respectively. For both compounds, short-range spin-spin correlations are present over a wide temperature range above $T_N$. The reduced ordered moments at base temperature (1.5 K) indicate the presence of quantum fluctuations in both compounds due to the quasi-1D magnetic interactions.Comment: 14 pages, 10 figures, 9 table

A study on analysis of yield gap in pulses of Nadia district of West Bengal, India

The study on yield gap in pulses (Lentil) of West Bengal revealed that the technology gap is accounted to be 346.23 kg/ha and technology index and the index of realised potential yield are estimated to 22.56 and 77.44 %, respectively. The extension gap and the index of realized potential farm yield are 215.12 kg/ha and 81.9 %, respectively. Lentil cultivation generates a net return of ` 47083.07/ha from an investment of ` 29640.30/ha in experimental field whereas an expenditure accounting ` 23240.76 and ` 18559.71/ha are made in demonstration and actual farmer`s field to realize a net return of ` 36171.44 and ` 30096.79/ha. Although, the most viable alternative crop, rape and mustard has marginal advantage over lentil economically, considering the long term beneficial effects of pulses soil fertility, programmes need to be taken to motivate farmers to allocate more area to pulses. Low productivity and non-availability of quality occupy the first and second position with 82.73 and 71.25 % Garrett`s score constructed based on the perception of sample farmers. Development of improved seeds responsive to modern crop production technology is the most vital for long term solution of the present crisis in pulses, but for the time being, programmes for technology dissemination and adoption through various extension methods is necessary in bridging the extension gap to improve the pulses situation of West Bengal

Effect of Pruning on Productivity in Sweet Orange

To sustainable production of quality fruits in eight year old sweet orange plants of cv. Mosambi budded onto Citrus jambheri rootstock, and grown in laterite soil at Jhargram, Paschim Medinipur, a canopy management trial was conducted for two consecutive years. The treatments included T1: No pruning; T2: Removal of dead and dry shoots and branches; T3: T2 + Removal of thin shoots and water-sprouts arising from the leaders at 90° angle; T4: T3 + Removal of selected laterals; T5: T4 + Removal of selected leaders for formation of open-centre-canopy. Randomized Block Design with five replications was set up. Results indicated that fruit production improved with regular pruning. Significantly high fruit retention (68%) with maximum number of fruits (250) was recorded in plants where open-canopy was maintained by judicious removal of the leaders, laterals, thin shoots and dead wood. Trees with open-canopy not only resulted in 71.4% increase in fruit number, but also enhanced fruit weight by 17.9% over Control. Significantly good fruit quality in terms of TSS, total sugars and Vitamin C content was recorded in fruits from the open canopy treatment. Dry weight of shoots / branch was lowest (1.50kg) in open-canopy treatment and highest in the unpruned Control (3.0kg). Foliar N, P and K status did not vary significantly with different pruning practices

Field Induced Magnetic Ordering and Single-ion Anisotropy in the Quasi-1D Haldane Chain Compound SrNi2V2O8: A Single Crystal investigation

Field-induced magnetic ordering in the Haldane chain compound SrNi$_{2}$V$_{2}$O$_{8}$ and effect of anisotropy have been investigated using single crystals. Static susceptibility, inelastic neutron scattering, high-field magnetization, and low temperature heat-capacity studies confirm a non-magnetic spin-singlet ground state and a gap between the singlet ground state and triplet excited states. The intra-chain exchange interaction is estimated to be $J \sim 8.9{\pm}$0.1 meV. Splitting of the dispersions into two modes with minimum energies 1.57 and 2.58 meV confirms the existence of single-ion anisotropy $D(S^z){^2}$. The value of {\it D} is estimated to be $-0.51{\pm}0.01$ meV and the easy axis is found to be along the crystallographic {\it c}-axis. Field-induced magnetic ordering has been found with two critical fields [$\mu_0H_c^{\perp c} = 12.0{\pm}$0.2 T and $\mu_0H_c^{\parallel c} = 20.8{\pm}$0.5 T at 4.2 K]. Field-induced three-dimensional magnetic ordering above the critical fields is evident from the heat-capacity, susceptibility, and high-field magnetization study. The Phase diagram in the {\it H-T} plane has been obtained from the high-field magnetization. The observed results are discussed in the light of theoretical predictions as well as earlier experimental reports on Haldane chain compounds

Observation of long range magnetic ordering in pyrohafnate Nd2Hf2O7: A neutron diffraction study

We have investigated the physical properties of a pyrochlore hafnate Nd2Hf2O7 using ac magnetic susceptibility \chi_ac(T), dc magnetic susceptibility \chi(T), isothermal magnetization M(H) and heat capacity C_p(T) measurements, and determined the magnetic ground state by neutron powder diffraction study. An upturn is observed below 6 K in C_p(T)/T, however both C_p(T) and \chi(T) do not show any clear anomaly down to 2 K. The \chi_ac(T) shows a well pronounced anomaly indicating an antiferromagnetic transition at T_N = 0.55 K. The long range antiferromagnetic ordering is confirmed by neutron diffraction. The refinement of neutron diffraction pattern reveals an all-in/all-out antiferromagnetic structure, where for successive tetrahedra, the four Nd3+ magnetic moments point alternatively all-into or all-out-of the tetrahedron, with an ordering wavevector k = (0, 0, 0) and an ordered state magnetic moment of m = 0.62(1) \mu_B/Nd at 0.1 K. The ordered moment is strongly reduced reflecting strong quantum fluctuations in ordered state.Comment: 10 pages, 9 figures and 2 tables; to appear in Phys. Rev.

AlgRel.wl\texttt{AlgRel.wl}: Algebraic Relations for the Product of Propagators in Feynman integrals

Motivated by the foundational work of Tarasov, who pointed out that the algebraic relations of the type considered here can lead to functional reduction of Feynman integrals. We have suitably modified the method to be able to implement and automatize it and present a $\textit{Mathematica}$ package $\texttt{AlgRel.wl}$. The purpose of this package is to help derive the algebraic relations with arbitrary kinematic quantities, for the product of propagators. Under specific choices of the arbitrary parameters that appear in these relations, we can write the original integral with all massive propagators in general, as a sum of integrals which have fewer massive propagators. The resulting integrals are of reduced complexity for computational purposes. For the one-loop case, this would result in integrals with just one massive propagator. The method can also be applied to higher-loop integral using the loop-by-loop approach. We demonstrate the procedure and the results obtained using various one-loop and higher-loop examples. Due to the fact that the Feynman integrals are intimately related to the hypergeometric functions, a useful consequence of these algebraic relations is in deriving the sets of non-trivial reduction formulae. We present various such reduction formulae and further discuss how, many more such formulae can be obtained than described here. The $\texttt{AlgRel.wl}$ package and an example notebook $\texttt{Examples.nb}$ can be found at https://github.com/TanayPathak-17/Algebraic-relation-for-the-product-of-propagatorsComment: 23 pages, 9 figure