Study Of Quantum Muons In μSR Depolarization Spectra Of Fluorides Using Two-Component Density Functional Theory

Muon spin rotation/relaxation/resonance(μSR)spectroscopy has been widely used in condensed matter physics,materials science,chemistry,and biological macromolecules.Nearly 100%of spin-polarized muons generated by accelerator will lose energy once injected into materials and eventually stay in local positions between crystal lattices,causing local relaxation of the crystal structure.A local magnetic field will lead to the spin depolarization of muons until they decay into positrons and neutrinos with a lifetime of 2.2 μs.By detecting the asymmetry of the outgoing positrons,the direction of muon spins at the time of decay can be obtained.Finally,millions of outgoing positrons can be recorded and the spin polarization function P_μ(t)of muons can be deduced.The information of the local magnetic field can be obtained by fitting P_μ(t)with certain mathematical models.Therefore,the spin states of electrons and nuclei can then be studied.The μSR spectroscopy has been widely used in the research of superconducting materials and magnetic materials.Recently,the use of Density Functional Theory(DFT)to study the muon stopping site and the muon-crystal interaction as a universal method has developed rapidly.However,the calculating P_μ(t)of fluorides using common DFT method show significant differences from experimental results.In this thesis,Two-Component Density Functional Theory(TCDFT),which can naturally includes the quantum effect of the muon and the electrons,was used to study the muon-crystal interaction.We extended the current TCDFT method by considering the muon-atom interaction and using three muon-electron correlation forms to enable TCDFT to be used for lattice relaxation calculations.Using this method in fluorides,we obtained the lattice relaxation result of the nearest theoretical calculation without considering the muon-electron correlation.Accordingly,we obtained the length of the nearest neighbor F-muon bond in calcium fluoride,which is l.165 ?,very close to the experimental result of 1.172(1)A.Our result is also better than the best international DFT result of 1.134 A.The F-muon bond length of the nearest and second nearest neighbors are 1.1704 and 1.2204 ? respectively for lead fluoride,which are also closer to the experimental results of 1.1419(4)and 1.2601(7)? compared with 1.0967 and 1.2057 ? of the best DFT results in the world.Then,two existing muon-electron correlation forms,eμc-1 and Quantum Monte Carlo(QMC)fitted correlation form,were used in our TCDFT calculation.The ranks for the reliability of abovementioned muon-electron correlation form forms are:no muon-electron correlation form>muon-electron correlation form obtained by QMC>the best DFT result in the world>eμc-1.Currently,specific muon-electron correlation forms have only been proposed very recently and their correctness has not been widely verified.Thus,we propose that fluorides can provide a platform for testing the validity of muon-electron correlation forms.We calculated the spin polarization function P_μ(t)of muon under the local magnetic field by using the relaxation crystal structures and the muon wave functions,which are obtained by TCDFT.By comparing the P_μ(t)results directly with the experimental data,we further verified the reliability of TCDFT.The reliability ranks are also:no muon-electron correlation form>muon-electron correlation form obtained by QMC>the best DFT result in the world>eμc-1.In addition,the spatial distribution of muon wave functions have a certain influence on P_μ(t).For example,the muon wave functions obtained using no correlation form and the muon-electron correlation form obtained by QMC are similar,which will make P_μ(t)closer to the experimental data.In contrast,the muon wave function obtained using eμc-1 will make P_μ(t)deviate further from the experimental data.Thus we further confirmed the validity of the muon-electron correlation obtained by QMC and no correlation form.