Antiferromagnetic spin correlations in the Zn-Mg-Ho icosahedral quasicrystal

Sato, Taku; Takakura, Hiroyuki; Tsai, A.‐P.; Shibata, Kaoru; Ohoyama, Kenji; Andersen, Ken H.

doi:10.1103/physrevb.61.476

Cited by 78 publications

(64 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, the real space magnetic ordering of local moments in systems with quasiperiodic long range order remains to be elucidated, and should present novel and complex features, different from properties of crystalline or disordered systems. The archetypal nonfrustrated two-dimensional antiferromagnetic system is that of spins on the square lattice, an old and until recently controversial problem, while the problem we consider now , with its fundamentally different symmetry properties, aims to understand a new class of unfrustrated systems.Experimental work providing motivation for the study of such systems comes from neutron scattering studies of the magnetic phase in a Zn-Mg-Ho quasicrystal [1]. The magnetic diffuse scattering of the low temperature phase shows an icosahedral symmetry, reflecting the underlying quasiperiodicity of this compound.…”

mentioning

confidence: 99%

“…Experimental work providing motivation for the study of such systems comes from neutron scattering studies of the magnetic phase in a Zn-Mg-Ho quasicrystal [1]. The magnetic diffuse scattering of the low temperature phase shows an icosahedral symmetry, reflecting the underlying quasiperiodicity of this compound.…”

mentioning

confidence: 99%

“…We are therefore interested in the cluster energies, E i , as a function of z. In the zeroth approximation the cluster energies are just the HS ǫ A is therefore the sum of the Heisenberg star energy for A sites having a first-order coupling  (1) A , plus a zeroth order A block energy term, plus half the zeroth order block energies of its neighbors as follows: (6) and similar expressions are written for the other six types of site. At each stage of RG, the cluster energies E (n) are used to find the corresponding values of the local order parameters.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Quantum Spins and Quasiperiodicity: A Real Space Renormalization Group Approach

Jagannathan

2004

Phys. Rev. Lett.

View full text Add to dashboard Cite

We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling -the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated, and compared with the results of a recent Quantum Monte Carlo calculation for the tiling. It is conjectured that the ground state energy is exactly equal to that of the quantum antiferromagnet on the square lattice.PACS numbers: 75.10. Jm, 71.23.Ft, 71.27.+a In this paper a renormalization group transformation is used to study the ground state of Heisenberg spins with antiferromagnetic couplings on a two-dimensional quasiperiodic tiling. This system poses a novel theoretical problem, namely, the nature of quantum fluctuations in a structure possessing a number of exact symmetries but no translational invariance. While periodic systems and disordered variants thereof have received much attention, little is known about aperiodic quantum models in two or more dimensions. In particular, the real space magnetic ordering of local moments in systems with quasiperiodic long range order remains to be elucidated, and should present novel and complex features, different from properties of crystalline or disordered systems. The archetypal nonfrustrated two-dimensional antiferromagnetic system is that of spins on the square lattice, an old and until recently controversial problem, while the problem we consider now , with its fundamentally different symmetry properties, aims to understand a new class of unfrustrated systems.Experimental work providing motivation for the study of such systems comes from neutron scattering studies of the magnetic phase in a Zn-Mg-Ho quasicrystal [1]. The magnetic diffuse scattering of the low temperature phase shows an icosahedral symmetry, reflecting the underlying quasiperiodicity of this compound. The nature of the ground state in such a quasicrystalline medium was recently discussed in [2] where Quantum Monte Carlo (QMC) calculations were carried out for an antiferromagnetic Heisenberg model on one of the simplest twodimensional quasiperiodic tilings available, the octagonal tiling. This tiling has been frequently used for numerical investigations of the effects of quasiperiodic modulations in two dimensions. More detailed, analytic and numerical results are available for one dimensional quasiperiodic models, where quantum spins have been considered using real space renormalization transformation [3], and using density matrix renormalization or by using mappings to fermionic models (see [4] and references therein). However, the techniques used are particular to one dimension and not readily generalisable to the two-dimensional structure considered here.The model considered in [2] has a Hamiltonian H = J i,j S i . S j where the spins are located on vertices of the octagonal tiling, and J is coupling along each edge. Spin...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Quantum Spins and Quasiperiodicity: A Real Space Renormalization Group Approach

Jagannathan

2004

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…The non-metallic spin exchange mechanism implicit in those studies has been evidenced in recently synthesized rare earth (R) ZnMg-R quasi-crystals (see e.g. [6]) whose R elements have well localized 4f magnetic moments.…”

mentioning

confidence: 99%

Quasiperiodic spin chains in a magnetic field

2001

View full text Add to dashboard Cite

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin- The magnetic properties of quasi-crystals have become a fundamental issue of study since their discovery in 1984 [1]. A variety of theoretical efforts, ranging from renormalization group (RG) analysis of Ising models in Penrose lattices [2] to exact solutions of both Ising and XY Fibonacci spin chains [3][4][5] have revealed fairly intricate magnetic orderings associated to the quasi-periodicity of these structures. The non-metallic spin exchange mechanism implicit in those studies has been evidenced in recently synthesized rare earth (R) ZnMg-R quasi-crystals (see e.g. [6]) whose R elements have well localized 4f magnetic moments.Bolstered by these latter findings and as a further step within the line of the local moment descriptions referred to above, here we consider the ordering of quasi-periodic spin-1 2 XXZ chains in a magnetic field to elucidate the quantization conditions of massive spin excitations or magnetization plateaux. In periodic systems, this issue has received systematic attention in the last few years from both experimental and theoretical points of view (see e.g. [7]). In this letter, we are specifically interested in studying the antiferromagnetic systemwhere S x , S y , S z denote the spin-1 2 matrices involved in the standard XXZ Hamiltonian (ǫ n = 0 ) in a magnetic field h applied along the anisotropy direction ( |∆| ≤ 1 ). Here, the coupling modulation is introduced via the ǫ n parameters defined as ǫ n = ν δ ν cos (2π ω ν n ) , so quasi-periodicity arises upon choosing an irrational subset of frequencies ω ν with amplitudes δ ν .The interest of (1) stems partly from the widespread applications of 1d Hamiltonians in the description of artificially grown quasi-periodic heterostructures [8], quantum dot crystals [9] and magnetic multilayers [10]. Also, recent investigations of quasi-periodicity involving either the couplings [11] or the magnetic field [12], have been addressed using Abelian bosonization along with RG and numerical techniques. Here we focus on the combined effect of a quasi-periodic exchange modulation under a uniform magnetic field.Of particular importance are the rational frequencies of (1), not only as a way to approach the quasi-periodic limit, but also because they allow for a thorough numerical verification of a novel situation (see [13][14][15] for related work). As we shall see, although the allowed fractional plateaux predicted in the present case fall into the classification provided by the generalized Lieb-Schultz-Mattis theorem [16], a bosonization approach to (1) yields an alternative scenario not envisaged in previous studies [17,18]. This will be reflected in the appearance of magnetization plateaux associated to each of the frequencies present in (1). To strengthen the potential interest of our results, we show how a simple two frequency model exhibits a magnetization curve with two wide plateaux at

show abstract

“…Amongst various physical properties of quasicrystals, the magnetic properties of quasicrystals containing 4f rare earth elements have caught much attention. Magnetic measurements on the Cd(Zn)-Mg-RE (RE= rare earth elements) quasicrystals have been performed systematically, which has shown spin glass-like behaviors of localized RE 3+ spins at low temperature in all the cases, however, no long-range magnetic states has been reported [5,6,7] .…”

Section: Introductionmentioning

confidence: 99%

Magnetic Orders in Compounds Made of Icosahedral Rare-Earth Clusters

Hiroto

Sato

Muro

et al. 2011

Trans. Mat. Res. Soc. Japan

View full text Add to dashboard Cite

We report magnetic properties of Cd 6 RE (RE= Tb, Sm) single-grained crystalline approximants. Magnetic susceptibilities show that various long-range magnetic orders occur at low temperatures for the compounds made of RE icosahedra: Cd 6 Tb shows three types of antiferromagnetic orders with temperature and Cd 6 Sm exhibits also three types of magnetic orders with temperature, i.e., one antiferromagnetic and two types of ferrimagnetic orders.

show abstract

Antiferromagnetic spin correlations in the Zn-Mg-Ho icosahedral quasicrystal

Cited by 78 publications

References 44 publications

Quantum Spins and Quasiperiodicity: A Real Space Renormalization Group Approach

Quantum Spins and Quasiperiodicity: A Real Space Renormalization Group Approach

Quasiperiodic spin chains in a magnetic field

Magnetic Orders in Compounds Made of Icosahedral Rare-Earth Clusters

Contact Info

Product

Resources

About