Magnetism in rare-earth quasicrystals: RKKY interactions and ordering

Abstract

We study magnetism in simple models for rare earth quasicrystals, by considering Ising spins on a quasiperiodic tiling, coupled via RKKY interactions. Computing these interactions from a tight-binding model on the tiling, we find that they are frustrated and strongly dependent on the local environment. Although such features are often associated with spin glass behaviour, we show using Monte Carlo simulations that the spin system has a phase transition to a low-temperature state with long-range quasiperiodic magnetic order.PACS numbers: 75.50. Kj, Understanding how the magnetic properties of complex materials arise from their atomic structure represents one of the fundamental challenges of condensed matter physics. In the context of quasicrystals [1] this leads to the question of how their magnetism [2,3] is influenced by their unusual electronic properties, which include a pseudogap at the Fermi energy [4,5], multifractal wave functions [6] and anomalous electronic transport [7,8]. Magnetic rare earth (R) quasicrystals in particular serve to motivate simple models, as they contain welldefined local moments at concentrations of 5-10% interacting via long-range RKKY interactions [9,10]. Examples of these quasicrystals In this paper we take a two-step theoretical approach to studying such systems. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling. Second, we examine the statistical mechanics of Ising spins with these interactions, using extensive Monte Carlo simulations. While there has been much previous work studying spin models for magnetic quasicrystals [13][14][15][16][17][18][19][20], it has been based on choices of interaction (nearest neighbour exchange [13,14], dipolar and further neighbour exchange [15][16][17], or RKKY interactions with a form taken from periodic systems [18][19][20]) that do not incorporate the unique coupling of electronic to magnetic properties that is to be expected in quasicrystals. Our model is designed to address this aspect of the physics in a simple way.We find substantial differences between RKKY interactions on a quasiperiodic tiling and those in simple metals [21]. While both ferromagnetic and antiferromagnetic interactions arise in the tiling, they have no well-defined spatial period since there is no Fermi wavevector. And as there is no translational invariance, the RKKY coupling between pairs of sites is a function not only of their separation, but is also strongly dependent on the local environment. One might expect that the combination of frustration and aperiodicity would lead to spin freezing [22], and in other settings quasiperiodic systems are known to behave like random ones [23]. Our results, however, exclude canonical spin glass behaviour, via the scaling of domain wall energy with length. We demonstrate that instead there is quasiperiodic spin order at low temperature, by examining the Fourier transform of spin configurations.We model conduction electrons by a pure hopping Hamiltonian H el = l,...

Crystal electric field excitations in the quasicrystal approximantTbCd6studied by inelastic neutron scattering

“…9,10 The origin of the differences in magnetic behavior between the periodic approximants and quasicrystalline phases remain an open and intriguing issue, especially in light of the fact that numerous theoretical studies have established that longrange magnetic order on a quasilattice is quite possible. [11][12][13][14][15][16][17] Nevertheless, there are differences between the local environments surrounding the R ions in the approximant and quasicrystalline structures. The 1/1-RCd 6 approximants may be described, at ambient temperature, as a body-centered cubic packing of interpenetrating rhombic triacontahedron (RTH) Tsai-type clusters, 2,18 featuring an icosahedron of 12 R ions comprising the third shell of each cluster.…”

Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism

“…[11][12][13][14][15][16][17] Most magnetic quasicrystals studied to date are ternary compounds, such as i-R-Mg-Zn, 9,18,19 i-R-Mg-Cd, 9,20 and i-R-Ag-In 21,22 (R = rare earth), where chemical disorder in the local environment of the magnetic R-ion is a complicating factor.…”

Long-range magnetic order in models for rare-earth quasicrystals

“…Our method is more accurate than the continued fraction expansion, which has been employed previously for quasiperiodic tilings. 23,24,28 The method can be applied to general tight-binding systems. For a particular model we need to specify three features: (i) the tiling; (ii) the positions of the spins on the tiling; and (iii) the value of the Fermi energy E F .…”

“…In our previous work (Ref. 23) we studied the distribution of χ l,m in detail for the Ammann Beenker tiling. We observe the same qualitative behaviour also for the Penrose tiling and we briefly summarize the main findings here before focussing on results from Monte Carlo simulations.…”

“…In previous work (Ref. 23) we have studied the structure of the RKKY interactions for a limited number of systems. Here we present a much more thorough analysis and classification of quasiperiodic spin systems.…”