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Materials composed of spin-1 antiferromagnetic (AFM) chains are known to adopt complex ground states that are sensitive to the single-ion-anisotropy (SIA) energy ( $D$), and intrachain ( $J_0$) and interchain ( $J_{1,2}^{\prime }$) exchange energy scales. While theoretical and experimental studies have extended this model to include various other energy scales, the effect of the lack of a common SIA axis is not well explored. Here we investigate the magnetic properties of $\mathrm{Ni}\left(\mathrm{pyrimidine}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_2{\left({\mathrm{NO}}_3\right)}_2$, a chain compound where the tilting of Ni octahedra leads to a twofold alternation of the easy-axis directions along the chain. Muon-spin relaxation measurements indicate a transition to long-range order at $T_{\text{N}}=2.3\mathrm{K}$and the magnetic structure is initially determined to be antiferromagnetic and collinear using elastic neutron diffraction experiments. Inelastic neutron scattering measurements were used to find $J_0=5.107\left(7\right)\mathrm{K}, D=2.79\left(1\right)\mathrm{K},J_1^{\prime }=0.00\left(5\right)\mathrm{K}, J_2^{\prime }=0.18\left(3\right)\mathrm{K}$, and a rhombic anisotropy energy $E=0.19\left(9\right)\mathrm{K}$. Mean-field modeling reveals that the ground state structure hosts spin canting of $\varphi \approx 6.5^{\circ }$, which is not detectable above the noise floor of the elastic neutron diffraction data. Monte Carlo simulation of the powder-averaged magnetization, $M\left(H\right)$, is then used to confirm these Hamiltonian parameters, while single-crystal $M\left(H\right)$simulations provide insight into features observed in the data. Published by the American Physical Society2025 

We investigate the magnetic properties of $S=1$antiferromagnetic diamond-lattice, $\mathrm{Ni}{X}_2{\left(\mathrm{pyrimidine}\right)}_2$ $(X=\mathrm{Cl}, \mathrm{Br})$, hosting a single-ion anisotropy (SIA) orientation which alternates between neighboring sites. Through neutron diffraction measurements of the $X=\mathrm{Cl}$compound, the ordered state spins are found to align collinearly along a pseudo-easy axis, a unique direction created by the intersection of two easy planes. Similarities in the magnetization, exhibiting spin-flop transitions, and the magnetic susceptibility in the two compounds imply that the same magnetic structure and a pseudo-easy axis is also present for $X=\mathrm{Br}$. We estimate the Hamiltonian parameters by combining analytical calculations and Monte Carlo (MC) simulations of the spin-flop and saturation field. The MC simulations also reveal that the spin-flop transition occurs when the applied field is parallel to the pseudo-easy axis. Contrary to conventional easy-axis systems, there exist field directions perpendicular to the pseudo-easy axis for which the magnetic saturation is approached asymptotically and no symmetry-breaking phase transition is observed at finite fields. Published by the American Physical Society2024 

Abstract The observables associated with a quantum system S form a non-commutative algebra A S . It is assumed that a density matrix ρ can be determined from the expectation values of observables. But A S admits inner automorphisms a ↦ u a u − 1 , a , u ∈ A S , u * u = u u * = 1 , so that its individual elements can be identified only up to unitary transformations. So since Tr  ρ ( uau *) = Tr( u * ρu ) a , only the spectrum of ρ , or its characteristic polynomial, can be determined in quantum mechanics. In local quantum field theory, ρ cannot be determined at all, as we shall explain. However, abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables in abelian algebras A M ⊂ A S ( M for measurement, S for system). We study the uncertainties in extending ρ | A M to ρ | A S (the determination of which means measurement of A S ) and devise a protocol to determine ρ | A S ≡ ρ by determining ρ | A M for different choices of A M . The problem we formulate and study is a generalization of the Kadison–Singer theorem. We give an example where the system S is a particle on a circle and the experiment measures the abelian algebra of a magnetic field B coupled to S . The measurement of B gives information about the state ρ of the system S due to operator mixing. Associated uncertainty principles for von Neumann entropy are discussed in the appendix, adapting the earlier work by Białynicki-Birula and Mycielski (1975 Commun. Math. Phys. 44 129) to the present case. 

Beta-lactam antibiotics, which are used extensively in human and veterinary applications, are commonly detected in surface waters. To examine how the distinct structures of different generations of beta-lactam antibiotics can influence their persistence or degradation in environmental aqueous media, we examined the fate of two penams (amoxicillin and cloxacillin) and two cephems (cephalexin and ceftriaxone) at pH 5.0 and pH 7.0. By contrast to the lack of hydrolysis of the penam antibiotics at both pHs, we observed hydrolysis of cephalexin at pH 7.0 (t1/2 = 12 d) and ceftriaxone at pH 5.0 (t1/2 = 2.8 d). Using high-performance liquid chromatography coupled with a diode array detector or a high-resolution mass spectrometer, we were able to confirm thiotriazinone and 3-desacetyl cefotaxime as major hydrolysis products of ceftriaxone, and propose the hydrolytic cleavage of the benzene and cephem moieties from cephalexin. In addition, we studied the effects of smectite clay particles suspended in solutions without or with dissolved organic matter. The adsorption capacity of the clay was 4- to 9-fold higher at pH 7.0 than at pH 5.0. Subsequent X-ray diffraction analysis revealed that the antibiotic adsorption was not within the clay interlayer nanopores but occurred primarily on the external clay surfaces. The addition of dissolved organic matter interfered with the adsorption of a cephem antibiotic (ceftriaxone) on the clay, but the adsorption of a penam antibiotic (amoxicillin) remained unaffected. We employed molecular modeling simulations to probe the mechanisms of adsorption on the mineral surface. Our findings offer new insights on how the compound structures can dictate different fates of the beta-lactam class of antibiotics in environmental media.