91̽��

Abstract:

We report muon-spin relaxation (μ+SR) measurements of copper acetate [Cu(CH3CO2)2·H2O], a model spin-1/2 Heisenberg antiferromagnetic dimer chain with an alternation parameter α = 0.001. Zero-field μ+SR data collected from 2 to 200 K revealed an oscillatory asymmetry that was analyzed using a model based on the muon-stopping site determined by density-functional theory +μ calculations. Below 50 K, the fitted parameters capture spin dynamics characteristic of the singlet ground state, while at higher temperatures, an additional relaxation was observed due to the thermally populated triplet state, affecting the local magnetic field around the muon-stopping site. The temperature dependence of the fitting parameters was found to exhibit characteristics similar to those of a bipartite entanglement measure, “distance between the states,” obtained from the magnetic susceptibility data. Longitudinal-field μ+SR measurements reveal field-dependent relaxation at field values much lower than the field values required to close the spin singlet-triplet gap, emphasizing the importance of quantum fluctuations in the spin dynamics of the dimerized copper acetate.

Abstract:

We present single-crystal neutron diffraction, powder muon spin rotation, and pulsed-field magnetometry measurements on the Heisenberg quantum chiral chain $\left[\mathrm{Cu}\left(\mathrm{pym}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]{\mathrm{SiF}}_6·{\mathrm{H}}_2\mathrm{O}$ (pym = pyrimidine), which displays a fourfold-periodic rotation of the local environment around the Cu() $S=1/2$ ions from site to site along the chain. Previous measurements on this material have shown the absence of magnetic order down to surprisingly low temperatures $\ge 20$  mK, as well as the presence of an energy gap for magnetic excitations that grows linearly with magnetic field. Here we find evidence at dilution refrigerator temperatures for a field-induced transition to long-range magnetic order above an applied magnetic field of 3 T. From the polarization of magnetic moments observed with magnetic fields applied in the $[-1,2,0]$ direction, we can identify the static magnetic structure that best accounts for the data. The proposed model is 91̽��ed microscopically by the presence of an alternating component of the $g$ tensor, which produces an internal twofold staggered field that dictates both the direction of the ordered moments and the effective coupling between adjacent chains. The observed magnetic structure is contrary to previous proposals for the departure of the magnitude and field dependence of the energy gap from the predictions of the sine-Gordon model.