Magnetization plateaus of the frustrated Ising Shastry–Sutherland system: Wang–Landau simulation

Lin, Weijie; Yang, Tiankai; Wang, Y.; Qin, Minghui; Liu, J.-M.; Ren, Zhifeng

doi:10.1016/j.physleta.2014.06.047

Cited by 10 publications

(8 citation statements)

References 27 publications

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“…Another remarkable feature of the hysteresis loop in these structured assemblies is the presence of plateaus at a given level of magnetisation. As also stated in the introduction, a sequence of magnetisation plateaus at fractional values M/M s of the saturated magnetisation M s are experimentally observed in tetraborides and some other disordered antiferromagnetic materials with a strong Ising anisotropy and complex morphology lattices [39][40][41]. Our simulations show that the number and position of these M/M s levels correlate well with the composition of the assemblies regarding the dominant building simplexes.…”

Section: Spin Dynamics and Hysteresis Loops In Different Assembliessupporting

confidence: 78%

“…In purely ferromagnetic samples, on the other hand, the reversal starts and spreads in a diffusive manner from the least connected vertices. As mentioned in the Introduction, the occurrence of plateaus of fractional magnetisation in anti-ferromagnetic materials on complex lattices is related to the geometric frustration [39][40][41][42]. In our model systems, a sequence of plateaus appears to vary with the size of building simplexes n and the actual structure of the anti-ferromagnetic bonds.…”

Section: Discussionmentioning

confidence: 73%

“…A typical example is the case of Ising spins s = ±1 on a triangular lattice when the combination of ferromagnetic/antiferromagnetic interactions J ij = ±1 gives the product J ij J jk J ki < 0 along the triangle edges. In a more complex lattice geometry, different patterns of antiferromagnetic ordering take part, leading to the residual entropy [38] and a sequence of fractional magnetisation plateaus on the hysteresis loop in Ising-type [39][40][41] and XY-antiferromagnetic [42] systems.…”

Section: Introductionmentioning

confidence: 99%

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Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Tadić

Andjelković²,

Šuvakov³

et al. 2020

Entropy

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Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n − 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.

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Section: Spin Dynamics and Hysteresis Loops In Different Assembliessupporting

confidence: 78%

Section: Discussionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Tadić

Andjelković²,

Šuvakov³

et al. 2020

Entropy

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“…The geometric frustration effects have been shown to enable an unusual magnetic order and new dynamical phenomena in condensed matter physics [41][42][43][44] as well as in the Ising model applications [45,46]. For example, one of the prominent features of spin frustration is the appearance of the fractional magnetisation plateaus in the hysteresis loop [38,47,48]. In [34], the nanonetworks of self-assembled mono-disperse cliques were studied.…”

Section: Introductionmentioning

confidence: 99%

Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions

Tadić¹,

Gupte²

2020

Preprint

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Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, and higher cliques). Current research aims at quantifying these hidden geometries by the algebraic topology methods and deep graph theory and understanding the dynamic processes on simplicial complexes. Here, we use the recently introduced model for geometrical self-assembly of cliques to grow nano-networks of triangles and study the filed-driven spin reversal processes on them. With the antiferromagnetic interactions between the Ising spins attached to the nodes, this assembly ideally supports the geometric frustration, which is recognized as the origin of some new phenomena in condensed matter physics. In the dynamical model, a gradual switching from the pairwise to triangle-based interactions is controlled by a parameter. Thus, the spin frustration effects on each triangle give way to the mesoscopic ordering conditioned by a complex arrangement of triangles. We show how the balance between these interactions changes the shape of the hysteresis loop. Meanwhile, the fluctuations in the accompanying Barkhausen noise exhibit robust indicators of self-organized criticality, which is induced by the network geometry alone without any magnetic disorder.

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“…The existence of many local minima in frustrated magnets is one of the main reasons of the under-performance of the usual Monte Carlo techniques. Recently, the WLA has been successfully applied to specific problems in frustrated systems and dimer models, such as the formation of magnetisation plateaus in the Ising Shastry-Sutherland model 6 or to determine the order of a transition in the Heisenberg stacked triangular antiferromagnet 7 and in dimer models with nextnearest-neighbor interactions 8 . In the present work we explore thoroughly a simple classical frustrated model, the nearest-neighbour spin-ice model (nnSP), by means of the WLA.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

et al. 2016

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In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features of the spin-ice materials. Despite its simplicity it exhibits a remarkably rich behaviour. The model has been studied using a variety of techniques, thus it serves as an ideal benchmark to test the capabilities of the Wang Landau algorithm in magnetically frustrated systems. We study in detail the residual entropy of the nnSI and, by introducing an applied magnetic field in two different crystallographic directions ([111] and [100],) we explore the physics of the kagome-ice phase, the transition to full polarisation, and the three dimensional Kasteleyn transition. In the latter case, we discuss how additional constraints can be added to the Hamiltonian, by taking into account a selective choice of states in the partition function and, then, show how this choice leads to the realization of the ideal Kasteleyn transition in the system.

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Magnetization plateaus of the frustrated Ising Shastry–Sutherland system: Wang–Landau simulation

Cited by 10 publications

References 27 publications

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions

Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

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