Exploring Magnetic Orders And Phase Transitions In Spin Frustrated Systems

Spin frustrated systems,which exhibit a number of emergent physical phenomena,have been under intensive investigations since 1950s.Spin frustration,derived from the presence of competing interactions,is ubiquitous and a source of degeneracy and disorder in condensed matter physics.In disordered magnetic materials,frustration leads to spin glass phenomena,with analogies to the behavior of structural glasses and neural networks.In structurally ordered magnetic materials,spin frustration has also been the topic of extensive theoretical and experimental studies over the past two decades.The geometrical frustration has opened a door to a wide range of fundamentally emergent and exotic behaviors,including spin liquids in which the spins continue to fluctuate down to the lowest temperature,and spin ice systems which may enter fascinating topological Coulomb state and thus retain macroscopic zero-temperature entropy.This thesis mainly focuses on some strongly geometrically frustrated systems,which include the anti-ferromagnetically coupled spins on triangular lattice,dipolar kagome spin ice model,artificial square spin ice model,pyrochlore spin ice model,and so on.Meanwhile,several numerical simulation methods and skills have been employed to explore novel phenomena in these systems.This thesis is organized as follows:In the first chapter,a brief introduction to the spin frustrated systems,including the history,conceptual framework,and some fundamental physical properties,is presented at the beginning.The following section is devoted to the discussion of two typical geometrical frustrated systems,namely the triangular spin model and spin ice,where most of our works are based on.Furthermore,the geometrical structure,the magnetic ground state and charge order,the dynamic of theses systems,and potential research topics are discussed.In the second chapter,some numerical simulation methods,which are mostly employed in our practical simulations,are introduced in the first section.In the second section,we present a modified Wang-Landau sampling(m-WLS)for continuous statistical models by partitioning the energy space into a set of windows with logarithmically shrinking width.To demonstrate its necessity and advantages,we apply this sampling to several continuous models,including the two-dimensional square XY spin model,triangular J1-J2 spin model,and Lennard-Jones cluster model.This m-WLS provides much more accurate boundary density of states(DOS),and thus a precise evaluation of the thermodynamic behaviors of the continuous models at extreme low temperature becomes accessible.The present algorithm also allows efficient computation besides the highly reliable data sampling.In the third chapter,we discuss the role of the long-ranged dipolar interactions in modulating the step-like magnetization of Ca3Co2O6 spin model and the kagome spin ice model.First,we present our simulation results of the Ca3Co2O6 spin model.It is revealed that the longranged dipolar interaction is equivalent to an effective short-ranged interaction term.An inclusion of this term allows a columnar-state platform and a 1/2 platform in addition to the two-step feature in the magnetization in response to magnetic field.The magnetization plateau of the dipolar Kagome spin ice is presented in the second section.It is revealed that the lattice exhibits the fantastic three-step magnetization in response to increasing magnetic field along the[10]and[01]directions,respectively.In the fourth chapter,the magnetic-charge ordering and corresponding magnetic/monopole phase transitions of the artificial square spin ice model are studied using the conserved monopole density algorithm.The dynamics of low monopole density lattices leads to the monopole dimerization.For the high monopole density cases,the lattice undergoes two consecutive phase transitions from high-temperature charge-disordered phase into staggered charge-ordered phase before eventually toward the long-range magnetically-ordered phase.In the fifth chapter,we explore the spin ice model under uniaxial pressure.For the known spin ices,the interaction correction(?)introduced by the uniaxial pressure varies in quite a wide range from positive to negative.When ? is positive,the ground state characterized by the ferromagnetic spin chains is quite unstable,and in real materials it serves as intermediate state connecting the ice state and the long range ordered dipolar spin ice ground state.In the case of negative ?,the system relaxes from the highly degenerate ice state to an ordered ferromagnetic state via a first order phase transition.Furthermore,the domain walls in such ferromagnetic state are the hotbed of the excitations of magnetic monopoles.The sixth chapter is devoted to the conclusion and perspectives.