Accounting for quantum effects in stopping site DFT calculations for muon spectroscopy

Abstract

The technique of μ+SR is one of the most accurate methods of probing the local magnetism of materials, but to fully utilise its potential, knowledge of the location of the muon sites is required. A popular method is to use density functional theory (DFT) to determine the classical sites from first principles. In this thesis, we present the results of multiple μ+SR experiments on crystalline materials, where in each case analysis was aided by knowledge of the sites, with a focus on accounting for the quantum behaviour of the muon.

The ground state of the molecular honeycomb lattice Cu(pym)1.5(H2O)(BF4)2 is determined using ZF μ+SR with a transition at T_N = 4.02 ± 0.01 K from a low-temperature phase with an incommensurate magnetic structure, an unusual feature for a coordination polymer. Above the transition interactions with fluorine atoms dominate the signal,consistent with the class of candidate muon sites found through DFT calculations. We also present results on a pair of very different systems where a combination of ZF μ+SR experiments and DFT calculations suggest that different muon sites are realised on the two sides of a structural transition. In the first case we look at magnetic switching in the molecular crystal 4-(2-benzimidazolyl)-1,2,3,5-dithiadiazolyl with temperature, finding hysteretic behaviour centred at 274 ± 11 K and caused by a structural phase transition. We also report the results of applying an external current to the Mott insulator material Sr2IrO4, finding that our experimental measurements can be explained by a change in the class of muon sites realised as calculated by DFT and an additional FM component to the magnetic structure with mz ≤ 0.0214 μB.

The results of an analysis of a pair of analogous chiral spin chain compounds [Ni(pym) (H2O)4] SO4 (S = 1) and [Cu(pym) (H2O)4] SiF6 ⋅ H2O (S = 1/2) are also presented. Using ZF μ+SR measurements on the nickel chain we confirm a phase transition at T_N = 1.82 ± 0.02 K to an ordered magnetic ground state and use the magnetic dipole field iii each DFT site to determine the most likely pair of realised sites and confirm that our calculations are consistent with a proposed canted AFM magnetic structure, which we determine to have 1.27 μB and make an angle of 34° with the c-axis. Similarly, TF μ+SR measurements are used to confirm that the application of an external field stabilises an ordered magnetic ground state with a phase transition at B = 3 T. By calculating the muon sites and using the information to directly simulate the measured polarisation spectra we also find that our results can be explained with an increasing field-dependent copper magnetic moment up to 0.4 μ_B.

Finally, the results of a series of quantum tunnelling calculations in a set of methylated benzene crystals at low temperatures are presented. A potential energy barrier is constructed for transitions between all possible pairs of sites using DFT calculations and the transition rate is estimated using the WKB approximation. We then simulate the avoided level crossing (ALC) μ+SR spectra expected in each case for different degrees of tunnelling between sites, finding that more tunnelling narrows the resonances and decreases their number. We find the greatest agreement with experimental data for an intermediate amount of tunnelling over the case without tunnelling and with all possible transitions,which is an encouraging result for this novel method of simulating muon quantum behaviour.