Magnetic Properties of Quasicrystals and Their Approximants

Stadnik, Z. M.

doi:10.1016/b978-0-444-59593-5.00002-7

Cited by 8 publications

(13 citation statements)

References 136 publications

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“…So far quasiperiodic magnetic order has not been observed in rare earth quasicrystals. 8 Experimental data for many of these materials shows a spin-glass-behaviour with a separation of the field-cooled and zero-field-cooled magnetic susceptibility below a freezing temperature T f . 7,8,10 In most cases the Weiss temperature Θ is negative, indicating predominantly antiferromagnetic interactions.…”

Section: E Comparison To Experimental Resultsmentioning

confidence: 99%

“…An important question in this context is how these electronic properties influence the magnetism in quasicrystals. 7,8 In general, one can distinguish two types of magnetic quasicrystals: those with magnetic moments at (i) transition metal or (ii) rare earth sites. In the first, moment formation is an important aspect of the theoretical problem since they appear only at a small fraction of sites.…”

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

Thiem

Chalker

2015

Phys. Rev. B

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We take a two-step theoretical approach to study magnetism of rare earth quasicrystals by considering Ising spins on quasiperiodic tilings, coupled via RKKY interactions. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on the two-dimensional quasiperiodic tilings. We find that the magnetic interactions are frustrated and strongly dependent on the local environment. This results in the formation of clusters with strong bonds at certain patterns of the tilings that repeat quasiperiodically. Second, we examine the statistical mechanics of Ising spins with these RKKY interactions, using extensive Monte Carlo simulations. Although models that have frustrated interactions and lack translational invariance might be expected to display spin glass behaviour, we show that the spin system has a phase transition to low-temperature states with long-range quasiperiodic magnetic order. Additionally, we find that in some of the systems spin clusters can fluctuate much below the ordering temperature.PACS numbers: 75.50. Kj, Quasicrystals with their unusual atomic structure characterized by long-range order without a threedimensional translational periodicity 1 are known to have rather exotic physical properties, and so far we lack a good theoretical understanding for many of them. For instance, the electronic properties of this material class include a pseudogap at the Fermi energy 2,3 and multifractal (critical) wave functions 4 resulting in anomalous electronic transport 5,6 . An important question in this context is how these electronic properties influence the magnetism in quasicrystals. 7,8In general, one can distinguish two types of magnetic quasicrystals: those with magnetic moments at (i) transition metal or (ii) rare earth sites. In the first, moment formation is an important aspect of the theoretical problem since they appear only at a small fraction of sites.7 By contrast, the second class suggests a simpler description, with well-defined local moments at concentrations of 5-10% interacting via long-range RKKY interactions which are mediated by the conduction electrons.9,10 Examples of the latter class include the icosahedral i-ZnMgR and i-AgInR materials 9,11 , as well as decagonal d-ZnMgR materials 12 and the recently discovered binary phasesHere we use tight-binding models and Ising models to address this theoretical problem. We examine the form of the RKKY interactions based on a tight-binding Hamiltonian defined on two-dimensional quasiperiodic tilings (see Section I). We find that the coupling between pairs of sites depends not only on their distance but also varies strongly with the local environment on the tiling. Although we find ferromagnetic and antiferromagnetic bonds as in periodic systems, the magnetic interactions do not show a well-defined spatial period with a Fermi wave vector because quasicrystals do not have a Brillouin zone. Second, we study the consequences of these interactions (see Section II), by taking them as exchange constants between Ising spins located at a fr...

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Section: E Comparison To Experimental Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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

Thiem

Chalker

2015

Phys. Rev. B

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“…In the case of quasicrystals this resulted in a controversial debate about the mechanisms of the formation and the alignment of magnetic moments in quasiperiodic atomic structures [1,2]. Regarding the second issue, several theoretical models predicted the occurrence of long-range magnetic order, but experimental results revealed a spin-glass-like behaviour at low temperatures [1].…”

Section: Introductionmentioning

confidence: 99%

RKKY Interactions and Low-Temperature Behaviour of Spins in Quasiperiodic Tilings

Thiem¹

2014

Acta Phys. Pol. A

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We study the structure of the RudermanKittelKasuyaYosida interactions for selected quasiperiodic tilings. The interaction energies between the magnetic impurities in these systems are computed by a continued fraction expansion for the Green function of the conduction electrons. Based on these results we study the alignment of the magnetic moments in the AmmannBeenker tiling by Monte Carlo simulations. In particular, we are interested in the structure of the magnetic ground state and the low-temperature behaviour for the Ising model.

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“…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].…”

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confidence: 99%

“…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 [3] include the icosahedral i-ZnMgR [9] and i-AgInR [11] materials, as well as some decagonal d-ZnMgR materials [12] and the recently discovered binary phases i-RCd [10].…”

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Magnetism in rare-earth quasicrystals: RKKY interactions and ordering

Thiem

Chalker

2015

EPL

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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,...

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Magnetic Properties of Quasicrystals and Their Approximants

Cited by 8 publications

References 136 publications

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

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

RKKY Interactions and Low-Temperature Behaviour of Spins in Quasiperiodic Tilings

Magnetism in rare-earth quasicrystals: RKKY interactions and ordering

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