Researches On Transport Properties And Thermal Phase Transitions In Frustrated Magnets

Magnetism and magnetic materials not only play critical roles in our daily lives and industries,but have also attract widespread interests from theoretical and experimental physicists due to their novel phenomena.The competing interactions make frustrated magnets possess curious ground state and elementary excitations.And definitely,they will affect its transport properties.In addition,various perturbations in real materials make the magnetic structures and phase transitions of such materials more complicated and interesting.Therefore,starting from the basic properties of a classical spin liquid model,we study its energy and spin transports.Next,based on the investigations of frustrated magnets in experiments,we theoretically realize the tune of the melting processes in dipolar kagome spin ice by quantum fluctuations.Classical spin liquids have a substantive ground-state degeneracy,and some of them have no coherent elementary excitations.Conserved quantities,such as energy and spin,can not propagate in these systems by coherent quasiparticles.It inevitably leads to the low-temperature transport properties of classical spin liquids very different from those of pure and ordering metals,insulators,and magnets,which possess divergent conductivities and diffusion coefficients.The kinetic theory based on carriers is invalid in this kind of systems.Therefore,as an example,we use the classical Heisenberg pyrochlore spin liquid model,based on molecular dynamic simulations,and investigate transport properties of conserved quantities quantitatively in the limit of zero temperature.We choose the transports of energy and spin,and obtain finite zero-temperature thermal and spin conductivities.Then we calculate their diffusion coefficients due to Einsteinian relationship.In our results,we offer the relationship between transport conductivities and temperature as well as external magnetic field.At the same time,due to the time-scale separation of different degrees of freedom,we view the slow modes as static at low temperatures fields,then map the model into an effective disorder model in which fast modes carrying conserved quantities propagate in a disordered static background.The thermal and spin conductivities obtained from semi-analytical calculations not only validate our numerical results,but also explain that the limited conductivities and diffusion coefficients result from the finite mean free path of the conductive modes propagating in a quasistatic disordered background.In real materials,perturbations,such as anisotropy caused by crystal field splitting,chemical composition and structural disorders,further exchange interactions,and long-range dipolar interactions,come in.Frustrated magnets thus deviate from the classical spin-liquid model,and show more complex magnetic orders and phase transitions.Based on the richness of theoretical researches on different kagome spin ices,as well as the experimental explorations of phase transitions and quantum fluctuations in A₂R₃Sb₃O₁₄systems,we consider whether it is possible to control different melting processes in kagome spin ice by quantum regulations.Therefore,we use the transversefield kagome Ising model with dipolar interaction.We find at small magnetic fields,the system orders with a3^1/2×3^1/2 unit cell.During heating,it will undergo a three-state Potts phase transition and then a two-dimensional Ising phase transition,which is consistent with the classical dipolar kagome spin ice.While as the transverse field is large enough,it goes through a floating Kosterlitz-Thouless(KT)phase,which sandwiched by two KT phase transitions before entering paramagnetic phase.This is very similar to the six-state clock model.The two completely different melting pathways is connected through a short line of first-order phase transition or a multicritical point of second-order transition.In addition,detailed introductions of numerical methods we adapted in this the-sis will be offered in the chapter 2.It includes classical Monte Carlo(CMC)simula-tion based on heat bath and overrelaxation method,and quantum Monte Carlo(QMC)method using Suzuki-Trotter decomposition and Metropolis algorithm.In QMC,we discuss different Metropolis update schemes according to specific spin configurations.Finally,we introduce the molecular dynamical simulation used for classical spin systems.