| In low-dimensional quantum spin systems, there will be magnetic ordering, magnetic disordering and a variety of critical state. In these systems, quantum effect is notable. Strong quantum fluctuations often makes the systems exhibit complex properties, such as spin quasi-long-range ordering, the spin gap, spin-liquid phase ,the transition of quantum ordering to disordering and so on. While in frustrated quantum spin systems, magnetic frustration and quantum fluctuations coexist, which makes the systems exhibit more complex thermodynamic properties. In recent years, people found the coexistence of magnetic frustration and quantum fluctuations, in the quasi one-dimensional and two-dimensional edge sharing copper oxides. They have done a lot of relevant theoretical and experimental studies on these compounds. But, how to explain the complex ground state, excited state and calculate the size of the internal magnetic interactions is still a challenge to the people.In this paper, Li1-xNaxCu2O2 (x =0,0.05,0.1,0.2) single crystals were grown using self-flux method. To research and explore the low temperature thermodynamic properties of these crystals, we measured the magnetic susceptibility along c axis. We found the phenomena of competition from magnetic frustration and quantum fluctuations. Na doping introduced disordering in the system, which makes its ground state more complicated; Basing on Heisenberg exchange interaction theory, we gave the interpretation of the magnetic properties of Li1-xNaxCu2O2 qualitative, and we fitted the susceptibility results using a fitting formula. From the fitting results we got the exact interaction parameters. So we can find the relation between thermodynamic properties and doping effects.In chapter 1, we introduced the basic theory of magnetic, the history of quantum spin system and Heisenberg exchange interaction theory. Then we introduced the source of frustration in quantum spin systems and the source of magnetic frustration in edge sharing copper oxides. Finally, we introduced several typical frustrated Heisenberg quantum models. In chapter 2, we introduced the magnetic susceptibility and ESR measurement, gave the magnetic susceptibility of several typical magnets. Then we detailedly described the phase diagram of frustrated quantum spin system. Finally we introduced a formula,with which we can fit the magnetic susceptibility of S=1/2 frustrated quantum spin system.In chapter 3, we introduced a classic method of crystal growth: self-flux method in detail. Then we described the details of the growth of Li1-xNaxCu2O2 (x=0,0.05,0.1,0.2 ), and how to estimate the quantity of the crystals. In chapter 4, we studied the change in the magnetic susceptibility and the lattice parameters of Na doped LiCu2O2 single crystals. Basing on Heisenberg exchange interaction theory, we described properties of its ground state. We fitted the magnetic susceptibility, using a fitting formula and calculated the lattice parameters a, b, c of the crystals with different Na doping level. The main purpose is to study the change of magnetic transition temperature, magnetic interaction parameters, frustration factor and lattice parameters along with the doping level. Susceptibility results revealed that due to the coexistence of quantum fluctuations and frustration, the ground state of the crystal is not traditional spiral spin magnetic ordering, but incommensurate quantum magnetic ordering, spin gap not fully formed; Na doping introduced disorder in the systems, and the increase of doping level significantly enhanced the degree of disorder. From the fitting results, we found nearest-neighbor interactions J1, next-nearest-neighbor interaction J2 significantly decreased with the increase of Na doping level. The lattice parameters a, b, c of the crystals increased. The increase of the distance of magnetic ions may be the main reason for the decrease of magnetic interaction parameters. What's more, frustration factorαremained unchanged, corresponding to the unchanging of magnetic transition temperature. This phenomena confirmed that frustration factorαis the main character of frustrated quantum spin system.
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