Relation between microscopic interactions and macroscopic properties in ferroics

Lehmann, Jannis; Bortis, Amadé; Derlet, P. M.; Donnelly, Claire; Leo, Naëmi; Heyderman, Laura J.; Fiebig, Manfred

doi:10.1038/s41565-020-0763-9

Cited by 18 publications

(21 citation statements)

References 35 publications

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“…These findings were supported with Monte-Carlo simulations by Amadé Bortis (see also Appendix C.5) and published most recently, see Ref. [467]. The chapter closes with a brief presentation of toroidal domain patterns in vortex-based nanomagnetic arrays.…”

Section: Chapter 5 Domains In Artificial Magneto-toroidal Crystalssupporting

confidence: 79%

Toroidal Order in Magnetic Metamaterials

Lehmann¹

2022

Springer Theses

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Section: Chapter 5 Domains In Artificial Magneto-toroidal Crystalssupporting

confidence: 79%

Toroidal Order in Magnetic Metamaterials

Lehmann¹

2022

Springer Theses

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“…These findings were supported with Monte-Carlo simulations by Amadé Bortis (see also Appendix C.5) and published most recently, see Ref. [6]. The chapter closes with a brief presentation of toroidal domain patterns in vortex-based nanomagnetic arrays.…”

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confidence: 79%

Domains in Artificial Magneto-Toroidal Crystals

Lehmann

2021

Toroidal Order in Magnetic Metamaterials

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One of the two key requirements of n-dimensional ferroic systems is the spontaneous formation of homogeneously ordered areas, called domains, separated one from another by distinct (n − 1)-dimensional entities, called domain walls, see Sect. 2.1.4 on page 16. These walls constitute natural interfaces within the system between two or more energetically degenerate realisations of a particular order. For the artificial nanomagnetic arrays investigated throughout this work, the spontaneous formation of long-range order connected to an order parameter is a hallmark for their classification as primary ferroic order [1]. Suitable symmetry groups allowing for toroidal order have already been identified a few decades ago and are listed in Sect. 2.1.6 on page 19. The nanomagnetic arrays that have been investigated here, see Fig. 4.1 on page 83, fall in one of these groups, setting the basis for their further scrutiny not only on the macroscopic but also on the microscopic scale. Since ferrotoroidicity has been explored as a macroscopic phenomenon so far, microscopic origins of the ordering remain largely unexplored. In conventional materials, spins in a toroidally ordered crystal do not couple directly but via a fragile and wellbalanced competition of different inter-and intra-exchange paths [2,3]. These are typically variants of superexchange-or super-superexchange interaction via nonmagnetic ligands, e.g., oxoanions (such as phosphates, silicates, germanates) [4]. For the present work, a substitution of microscopic exchange interactions with magnetic dipole-dipole interaction provides a direct geometric access to inherent coupling mechanisms, see for instance Fig. 2.13. Note that toroidal moments and toroidal crystals with a significant contribution from the magnetic-dipole interaction [5] have also been found and studied in systems with a ring-like arrangement of high-magneticmoment rare-earth ions in molecular metal-organic frameworks [4], see Section 2.1.6. At this point, it is worth to recapitulate that ferroic order constitutes a macroscopic phenomenon without any constraints on the microscopic level. This allows for the engineering of a particular ferroic state using 'unconventional' constituents and arbitrary underlying interactions.

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“…In this case we still have = 8(J 2 − J 1 ) while 31 / ≈ −J 1 /[2(J 2 − J 1 )] and 40 / = −2J 1 /(J 2 − J 1 ), so that the energy cost of introducing ice-rule defects increases in proportion to (1 − J 2 /J 1 ) −1 until J 1 = J 2 where the ice model is recovered. The latter case has already been achieved experimentally in impressive work by Perrin et al [62] that introduced a height offset between the vertical and horizontal sublattices of square ice to equalize J 1 and J 2 , a result recently replicated by Farhan et al [82] and explored in a different system by Lehmann et al [83]. If the interactions were tuned to J 2 /J 1 = 0.99, then the energy cost of introducing defects would be 31 ≈ 50 and 40 = 200 , so that we can expect a substantial temperature window in which the number of defects is small and the pure F-model is a good approximation.…”

Section: Appendix: Exactly Solvable Limits For Artificial Square Icementioning

confidence: 79%

Experimental measures of topological sector fluctuations in the F-model

Arroo

Bramwell

2020

Phys. Rev. B

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The two-dimensional F-model is an ice-rule-obeying model, with a low-temperature antiferroelectric state and high-temperature critical Coulomb phase. Polarization in the system is associated with topological defects in the form of system-spanning windings which makes it an ideal system on which to observe topological sector fluctuations, as have been discussed in the context of spin ice and Berezinskii-Kosterlitz-Thouless (BKT) systems. In particular, the F-model offers a useful counterpoint to the BKT transition in that winding defects are energetically suppressed in the ordered state, rather than dynamically suppressed in the critical phase. In this paper we develop Lieb and Baxter's historic solutions of the F-model to exactly calculate relevant properties, several apparently for the first time. We further calculate properties not amenable to exact solution by an approximate cavity method and by referring to established scaling results. Of particular relevance to topological sector fluctuations are the exact results for the applied field polarization and the "energetic susceptibility." The latter is a both a measure of topological sector fluctuations and, surprisingly, in this case, a measure of the order parameter correlation exponent. In the high-temperature phase, the temperature tunes the density of topological defects and algebraic correlations, with the energetic susceptibility undergoing a jump to zero at the antiferroelectric ordering temperature, analogous to the "universal jump" in BKT systems. We discuss how these results are relevant to experimental systems, including to spin-ice thin films, and, unexpectedly, to three-dimensional dipolar spin ice and water ice, where we find that an analogous "universal jump" has previously been established in numerical studies. This unexpected result suggests a universal limit on the stability of perturbed Coulomb phases that is independent of dimension and of the order of the transition. Experimental results on water ice Ih are not inconsistent with this proposition. We complete the paper by relating our new results to experimental studies of artificial spin-ice arrays.

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Relation between microscopic interactions and macroscopic properties in ferroics

Cited by 18 publications

References 35 publications

Toroidal Order in Magnetic Metamaterials

Toroidal Order in Magnetic Metamaterials

Domains in Artificial Magneto-Toroidal Crystals

Experimental measures of topological sector fluctuations in the F-model

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