Quantum Spin Liquid States In Triangular And Kagome Antiferromagnets

In the 1980s,theoretical scientists proposed a new state of matter called quantum spin liquid to reveal the mechanism of high-temperature superconductivity.Due to the unique magnetic excitation of quantum spin liquids,which may reveal the mechanism of high-temperature superconductivity and be applied to topological quantum calculations,many experimental researchers have sought and studied materials exhibiting quantum spin liquid behavior.Although various candidate materials for quantum spin liquid have emerged within decades,each material has its own defects,such as the most representative material in this field,ZnCu₃（OH）₆Cl₂,which has severe Cu²⁺and Zn²⁺substitution defects.These defects seriously affect the measurement process and results of the material,so until today,there is still no consensus on whether the ground state of Zn Cu3（OH）6Cl2material is a quantum spin liquid or whether there is a band gap in quantum spin liquid.Both the two-dimensional triangular lattice Cu₂（OH）₃NO₃material and the kagome lattice material YCu₃（OH）_6.5Br_2.5do not exhibit magnetic ion substitution defects,making them ideal experimental objects for studying quantum spin liquids.This thesis investigates the magnetic properties of materials Cu₂（OH）₃NO₃and YCu₃（OH）_6.5Br_2.5,and the main research contents are as follows:First,We synthesized Cu₂（OH）₃NO₃large-size single crystal samples using hydrother-mal method,which were confirmed to be of high quality by powder X-ray diffractometer and single X-ray diffractometer.Steady state field magnetic susceptibility,pulsed strong mag-netic field magnetization,specific heat and elastic powder neutron diffraction were carried out on Cu₂（OH）₃NO₃high-quality large-size single crystal samples.Cu₂（OH）₃NO₃shows two field-induced quantum phase transitions in a strong magnetic field,and the critical mag-netic fields of the phase transitions are 14～19 T and 46～52 T,respectively.Although the steady field magnetic susceptibility and specific heat experiment results of the material show that Cu₂（OH）₃NO₃undergoes a magnetic ordered phase transition at low temperature,the elastic powder neutron diffraction experiment does not observe the signal of the long-range magnetic order.We have combined multiple measurement methods to draw the T-H phase diagram of the material.The steady state filed magnetic susceptibility,pulsed strong magnetic field magnetization and specific heat data of Cu₂（OH）₃NO₃are fitted by Lanczos diagonalization multi-body calculation method.The S=1/2 spatial anisotropic triangular lattice Heisenberg model used in the calculation is semi-quantitatively consistent with the modulation behavior of the singular phase in the material under the magnetic field.The conclusion drawn from the magnetic study of Cu₂（OH）₃NO₃is that the ground state of the material is a coexistence state of weak magnetic long-rang order and short-rang resonate-valence-bond correlation.Second,We explored the complete deuterization process of YCu₃（OH）_6.5Br_2.5material and conducted first-principles and multi-body model calculations.The results of the first principles calculations show that long-range interactions within the material can be ignored;there is almost no quasi-free spin inside the material.The model of multi-body computation considers the introduction of perturbations such as Dzyaloshinsky-Moriya interaction,next nearest neighbor interaction and magnetic anisotropy interaction,and discusses the Heisen-berg model including random distribution disorder.The results of multibody calculation show that the Heisenberg model,which takes into account the spatial disorder of exchange interaction with local symmetry,is in the best agreement with the specific heat and magnetic susceptibility data of material,and the magnetic specific heat data did not conform to the behavior of random singlet frustrated magnets.The conclusion drawn from the calculation and analysis of YCu₃（OH）_6.5Br_2.5material is that there are bond randomness defects in the material,which affect the ground state magnetic properties of the material.Third,We used nuclear magnetic resonance technology to study the dynamic proper-ties of YCu₃（OH）_6.5Br_2.5material.The nuclear magnetic resonance peak of the material did not undergo splitting at low temperatures,ruling out the possibility of magnetic ordered phase transition.The spin lattice relaxation time T1of YCu₃（OH）_6.5Br_2.5exhibits the sim-ilar behavior as other quantum spin liquid candidate materials.The broadening and fre-quency shift of the nuclear magnetic resonance peak of the material were well explained through Lanczos diagonalization calculations.The nuclear magnetic resonance experiment of YCu₃（OH）_6.5Br_2.5material concludes that most spins in YCu₃（OH）_6.5Br_2.5material are not frozen at low temperature,and the quantum fluctuation of the material are still strong.Fourth,We measured the extremely low temperature thermal conductivity of YCu₃（OH）_6.5Br_2.5single crystal and did not observe a linear change in thermal conductivity with temperature.The experimental conclusion of extremely low temperature thermal conductivity is that there are no freely movable Fermi excitons in YCu₃（OH）_6.5Br_2.5material.Due to the quenching of Cu²⁺3d electron orbitals,it is the spin S=1/2 magnetic ion with the weakest spin-orbit coupling.And there is only one chemical position of Cu²⁺in the triangular lattice Cu₂（OH）₃NO₃and kagome lattice YCu₃（OH）_6.5Br_2.5materials.So the magnetic properties of the above materials should conform to the spin S=1/2 isotropic Quantum Heisenberg model.But the theoretical calculation in the article shows that the magnetic properties of both materials deviate from the ideal spin S=1/2 isotropic Heisen-berg model:magnetic properties of triangular lattice Cu₂（OH）₃NO₃are consistent with spin S=1/2 spatial anisotropic Quantum Heisenberg model;magnetic properties of kagome lattice YCu₃（OH）_6.5Br_2.5needs to consider bond randomness in spin S=1/2 isotropic Quantum Heisenberg model.The main reason for the deviation from theory is that both materials have their own defects.Cu₂（OH）₃NO₃material exhibits perturbations such as Dzyaloshinsky-Moriya interactions due to its own symmetry.The YCu₃（OH）_6.5Br_2.5mate-rial exhibits bond randomness defects due to the substitution of non-magnetic ions.These deficiencies constrain the research of this thesis.In the future,we will search for more per-fect quantum spin liquid candidate materials.