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Low-dimensional quantum magnets, due to the existence of abundant exotic quantum phases therein and experimental feasibilities in laboratories, continues intriguing people in condensed matter physics. In this work, a comprehensive study of Cu(NO$_3$)$_2$ $\cdot$ 2.5H$_2$O (copper nitrate hemipentahydrate, CN), a spin chain material, is performed with multi-technique approach including thermal tensor network (TTN) simulations, first-principles calculations, as well as magnetization measurements in experiments. Employing a cutting-edge TTN method developed in the present work, we determine the couplings $J=5.13$ K, $\alpha=0.23(1)$ and Land\'e factors $g_{\parallel}=2.31$, $g_{\perp}=2.14$ in an alternating Heisenberg antiferromagnetic chain model, with which one can fit strikingly well the magnetothermodynamic properties. Part of the fitted experimental data are measured on the single-crystal CN specimens synthesized by us. Based on first-principles calculations, we reveal explicitly the spin chain scenario in CN by displaying the calculated electron density distributions, from which the distinct superexchange paths are visualized. On top of that, we investigated the magnetocaloric effect (MCE) in CN by calculating its isentropes and magnetic Gr\"ueisen parameter (GP). Prominent quantum-criticality-enhanced MCE was uncovered, the TTN simulations are in good agreements with measured isentropic lines in the sub-Kelvin region. We propose that CN is potentially a very promising quantum critical coolant, due to the remarkably enhanced MCE near both critical fields of moderate strengths as 2.87 and 4.08 T, respectively., Comment: 14 pages, 9 + 4 figures

We report the effects of the electric field on the magnetic coercive field (H c) and uniaxial magnetic anisotropy (UMA) orientation of polycrystalline Ni film grown on an unpoled (0 1 1) [Pb(Mg1/3Nb2/3)O3](1−x)–[PbTiO3] x (PMN-PT) single crystal substrate. Under various electric fields, normalized magnetic hysteresis loops of Ni films change in width; this represents the change of coercive field (ΔH c). Loop shapes are found to depend on the angle between the magnetic field and the sample, where changes in the shape reveal a small rotation of UMA. All these changes show that the magnetic properties vary periodically with a periodic electric field, by strain-mediated magnetoelectric coupling in the Ni/Ag/PMN-PT/Ag heterostructure. The poled PMN-PT produces strains under electric fields in the range of −4.2 kV cm−1 ≤ E ≤ 4.2 kV cm−1, then transfers it to Ni films resulting in changes to its H c and UMA. The curves of the in-plane H c and strain, at two mutually orthogonal directions, represent butterfly patterns versus the applied electric field. In addition, the changes observed in both the H c and strain show asymmetric features in two orthogonal directions, which results in a small rotation angle of the UMA of Ni as the electric field decreases. The effective manipulation of magnitude and orientation of magnetic anisotropy via electric fields in ferromagnetic/ferroelectric (FM/FE) heterostructures is an important step towards controlling the magnetic tunnel junctions.