The synthesis, structure, and magnetic behavior of the complexes Cu(qnx)Br(2) (1), Cu(2,3-dmpz)Br(2) (2), Cu(qnx)Cl(2) (3), and Cu(2,3-dmpz)Cl(2) (4) (qnx = quinoxaline, dmpz = dimethylpyrazine) are described. Both X-ray structural data and fitting of the magnetic data suggest that the compounds are well-described as strong-rung, two-leg magnetic ladders with J(rung) ranging from -30 K to -37 K, and J(rail) ranging from -14 K to -24 K. An unexpected decrease in the exchange constant for J(rail) (through the diazine ligand) is observed when the halide ion is changed from bromide to chloride, along with a small decrease in the magnetic exchange through the halide ion. Theoretical calculations on 2 and 4 via a first-principles bottom-up approach confirmed the description of the complexes as two-leg magnetic ladders. Furthermore, the calculations provide an explanation for the experimentally observed change in the value of the magnetic exchange through the dmpz ligand when the halide ion is changed from bromide to chloride, and for the very small change observed in the exchange through the different halide ions themselves via a combination of changes in geometry, bond lengths, and anion volume.

We have simulated and analyzed the susceptibility of a series of two-dimensional (2D) spin-1 2 rectangular Heisenberg antiferromagnetic (as well as mixed exchange antiferromagnetic/ferromagnetic) lattices as a function of J,J and temperature, where J is the dominant magnetic exchange interaction and J , the orthogonal interaction, is related to J by J = αJ , where α can vary from 0 to 1. Previous studies of the compounds pyrazineformatocopper(II) nitrate [Cu(pz)(HCO 2 )](NO 3 ), catena-2-aminopyrimidinedichlorocopper(II) [Cu(2-apm)Cl 2 ], and catena-pyrazinediazidocopper(II) [Cu(pz)(N 3 ) 2 ] indicated that these systems had 2D magnetic spin-spin interactions. However, there were no 2D models that could capture the behavior of any measurable bulk properties of the compounds. The previous authors fit the susceptibility data of the respective compounds to a 1D antiferromagnetic chain with a mean-field correction, or did not fit the data at all. We use the simulations to create this fit function in order to test the 2D model proposed for these spin systems.

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We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing.