In this paper, we used a theoretical measure known as distance between the states, E(ρe), to determine the bipartite entanglement of a one dimensional magnetic dimer system. The calculation was compared with the well-known entanglement measure, concurrence, and found to be the same. E(ρe) was, then, expressed in terms of two thermodynamic quantities, namely, magnetic susceptibility and specific heat. Experimental verification of temperature variation of the bipartite entanglement measure in terms of magnetic susceptibility and specific heat was done on single crystals of copper acetate-an excellent one dimensional dimer system. The results showed the existence of bipartite entanglement till temperatures as high as room temperature! Large sized single crystals of copper acetate were grown by a new evaporation technique and characterised by TGA, IR and Raman spectroscopy measurements. Density functional theory calculations were done to calculate the delocalisation index which showed much lower values of δ(Cu, Cu) than other bonds, implying that the probability of direct Cu-Cu exchange in copper acetate is very small. Band structure calculations revealed the presence of flat bands at the Fermi level implying very weak intermolecular interactions in copper acetate. 

This work reports the synthesis, structure and magnetic properties of a facile spin 1/2 one dimensional Heisenberg antiferromagnet bis(4-aminopyridinium) bis(oxalato)cuprate(II) dihydrate, (C5H7N2)2ijCuIJC2O4)2] ·2H2O. Single crystals of large sizes of the title compound were obtained using the technique liquid– liquid diffusion or layer diffusion with 100% yield. Single crystal X-ray diffraction measurements revealed the very good quality of the grown single crystals with a small value of goodness of fit R obtained (1.058). Powder X-ray diffraction showed the presence of peaks of the main phase with no impurity peaks, confirming the good quality of the crystals. The structure comprises corner sharing CuO6 octahedra resulting in Cu–Cu chains in the a-direction that are very well isolated in the b and c directions. Density functional theory (DFT) calculations with three different basis sets (B3LYP/6-311++G(d, p); B3LYP/LanL2DZ and B3LYP/6-311++G(d,p), B3LYP/LanL2DZ) generated the optimized geometry of a monomeric unit as well as its vibrational spectra. A vibrational frequency corresponding to the CuO6 octahedron was found in the experimentally obtained FTIR spectrum that matched very well with the theoretically obtained IR spectra incorporating the mixed basis. Temperature dependent dc magnetic susceptibility measurements revealed a low temperature peak, suggesting the presence of low dimensional magnetism in the system. Bonner–Fisher fit confirmed the one dimensional nature of the magnetic interaction with an exchange coupling constant of 1.23 K. Magnetisation measurements along with quantum Monte Carlo simulations confirm this metal–organic crystal to be a very good spin-1/2 Heisenberg antiferromagnet with a low saturation field Hs of 1.75 T. 

We present high resolution thermal expansion measurement data obtained with high relative sensitivity of ΔL/L = 10−9 and accuracy of ± 2 % using closed cycle refrigerators employing two different dilatometers. Experimental details of the set-up utilizing the multi-function probe integrated with the cold head of two kinds of closed cycle refrigerators, namely, pulse tube and GiffordMcMahon cryocoolers, has been described in detail. The design consists of decoupling the bottom sample puck and taking connections from the top of the multi-function probe to mitigate the vibrational noise arising from the cold heads, using which smooth and high quality thermal expansion data could be obtained. It was found that dilatometer#2 performs a better noise mitigation than dilatometer#1 due to the constrained movement of the spring in dilatometer#2. This was confirmed by finite element method simulations that were performed for understanding the spring movement in each dilatometer using which the effect of different forces/pressures and vibrations on the displacement of the spring was studied. Linear thermal expansion coefficient α obtained using both dilatometers was evaluated using derivative of a polynomial fit. The resultant α obtained using dilatometer#2 and either of the closed cycle cryostats on standard metals silver and aluminium showed excellent match with published values obtained using wet cryostats. Finally, thermal expansion measurements is reported on single crystals of two high temperature superconductors YBa2Cu3−xAlxO6+δ and Bi2Sr2CaCu2O8+x along the c-axis with very good match found with published data obtained earlier using wet liquid helium based cryostats.