Surface spin dynamics of antiferromagnetically coupled frustrated triangular films

Abstract

Results are presented for spin-wave dispersions in geometrically frustrated stacked triangular antiferromagnets with a thin film or semi-infinite geometry having either zero, easy-plane, or easyaxis anisotropy. Surface effects on the equilibrium spin configurations and excitation spectrum are investigated for the case of antiferromagnetically coupled films, serving to extend previous results on ferromagnetically coupled layers [E. Meloche et al., Phys. Rev. B 74, 094424 (2006)]. An operator equation of motion formalism is applied to systems which are quasi-one and quasi-two dimensional in character. In contrast to the case of ferromagnetically coupled films the new results show surface modes that are well separated in frequency from bulk excitations. Magnetic excitations in thin films with an even or an odd number of layers show qualitatively different behavior. These results are relevant for a wide variety of stacked triangular antiferromagnetics materials. PACS numbers: 75.30.Ds, 75.70.-i I. INTRODUCTION The significant amount of research effort devoted to the discovery and understanding of new aspects of geometrically frustrated magnetic systems in recent decades has been almost exclusively focused on the study of bulk properties. 1 Among such systems, a large number of materials have been identified which are realizations of the prototype frustrated triangular antiferromagnet (AF). In addition to the AF near-neighbor in-plane coupling, the vast majority of these systems are also characterized by AF coupling between stacked triangular layers, such as in most of the ABX 3 compounds. 2 Theoretical and experimental studies of magnetic excitations in these model materials have revealed important information on the nature of the fundamental interactions and exposed new types of spin-wave modes in the bulk systems. 3,4,5,6 Interest in surface effects on frustrated magnetic systems has been enhanced recently with where J i,j > 0 represents the intralayer nearest-neighbor AF exchange coupling and J ′ i,i ′ > 0 represents the interlayer AF exchange coupling. The effects of anisotropic exchange coupling are included through the parameters σ and σ ′ , and D i represents the strength of the single-ion anisotropy at a magnetic site labelled i. The Hamiltonian in Eq. (1) can used to describe systems characterized with easy-plane (D i > 0) and easy-axis (D i < 0) single-ion anisotropy.where the position vector ρ = (x, y) and the amplitudes S ± A1,n (k ) depend on the z coordinate through the layer index n. Similar expressions are defined for sites on sublattices B 1 , C 1 , A 2 , B 2 and C 2 . For a semi-infinite system the set of finite difference equations connecting the Fourier amplitudes may be expressed in supermatrix form as Mb = 0, where M is an ∞ × ∞ block-tridiagonal matrix defined as are considered. For simplicity, we outline the calculation of Q A (k , n). This quantity can be written in terms of the transverse spin-correlation functions S − A,n (t)S + A,n (t ′ ) k and S + A,n (t)S − A,n (t ′ ) k evaluated at equa...

Absence of long-range order in a general spin-S kagome lattice Ising antiferromagnet

“…Similar ordering was also confirmed in the actively studied 3D stacked IATL (SIATL) model [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] due to additional unfrustrated interactions in the stacking direction along the z axis. In particular, the system has been found to undergo the phase transition from the paramagnetic to the PD phase, which belongs to the 3D XY universality class [8,12,15,16,22], albeit the tricritical behavior has also been suggested [9]. However, the PD phase does not persist to very low temperatures.…”

“…For example, the increased magnitude of the spin S in the 2D IATL model was found to lead to a so-called partial-disordered (PD) structure (M, 0, −M) with two sublattices ordered antiferromagnetically and the third one disordered [4][5][6][7]. Similar ordering was also confirmed in the actively studied 3D stacked IATL (SIATL) model [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] due to additional unfrustrated interactions in the stacking direction along the z axis. In particular, the system has been found to undergo the phase transition from the paramagnetic to the PD phase, which belongs to the 3D XY universality class [8,12,15,16,22], albeit the tricritical behavior has also been suggested [9].…”

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

“…In zero field, the system has been found to undergo a second-order phase transition from the paramagnetic (P) to a partially disordered (PD) phase (M, −M, 0), with two sublattices ordered antiferromagnetically and the third one disordered. There is a wide consensus that the transition belongs to the 3D XY universality class [1,2,10,13,18] albeit the tricritical behavior has also been suggested [4]. Another phase transition at lower temperatures to a ferrimagnetic (FR) phase (M, −M/2, −M/2), with one sublattice fully ordered and two partially disordered has been proposed [2,6,17] but questioned by several other studies [3,4,20,22], which argued that the low-temperature phase is a 3D analog of the 2D Wannier phase.…”

Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

“…The possible size of simulation has been restricted to the system with |J c /J ab | = 10, 36 × 36 × 360 spins, and 2 × 10 6 MC steps. [11] Considering that the ratio |J c /J ab | in real compounds is in the order of 100, we need to develop another algorithm that improves the simulation efficiency.We notice that the similar slow-dynamic situation occurs in the quantum Monte Carlo (QMC) simulation.[12] The d-dimensional quantum system is mapped to the (d + 1)-dimensional classical system, on which the simulation is performed. The additional dimension is called the Trotter direction, and its length is called the Trotter number.…”

“…The possible size of simulation has been restricted to the system with |J c /J ab | = 10, 36 × 36 × 360 spins, and 2 × 10 6 MC steps. [11] Considering that the ratio |J c /J ab | in real compounds is in the order of 100, we need to develop another algorithm that improves the simulation efficiency.…”