Classical ground states of spin lattices

Schmidt, Heinz‐Jürgen; Richter, Johannes

doi:10.1088/1751-8121/aca36d

Cited by 7 publications

(3 citation statements)

References 33 publications

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“…, n analytically and thus obtain explicit or parametric expressions for the magnetization curve. Alternatively, we used a generalized Luttinger-Tisza method [43] to obtain analytical results for the latter case. This method provides rigorous results and it can be used to confirm the semi-analytical results.…”

Section: Methodsmentioning

confidence: 99%

“…When the magnetic field H reaches or exceeds a certain saturation value H sat , all spins align parallel to the direction of the magnetic field. In calculating H sat for the systems considered in this work we have followed the approach presented in [43][44][45], which will be briefly recapitulated here. This approach is limited to finite spin systems but it turns out that the results for H sat are independent of the system size (provided N is not too small) and hence also hold for the infinite square-kagomé spin lattice.…”

Section: Data Availability Statementmentioning

confidence: 99%

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Exotic magnetization curves in classical square-kagomé spin lattices

Schmidt,

Richter

2024

J. Phys. A: Math. Theor.

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Classical spin systems with non-coplanar ground states typically exhibit nonlinear magnetization curves characterized by kinks and jumps. Our article briefly summarizes the most important related analytical results. In a comprehensive case study, we then address AF-square kagom'{e} and AF/FM-square kagom'{e} spin lattices equipped with additional cross-plaquette interactions. It is known that these systems have non-coplanar ground states that assume a cuboctahedral structure in the absence of a magnetic field. When a magnetic field $H$ is switched on, a rich variety of different phases develops from the cuboctahedral ground state, which are studied in their dependence on $H$ and a cross-plaquette coupling constant $J_3>0$.For the AF square-kagom'{e} spin lattice, we carefully identify and describe seven phases that appear in a phase diagram with five triple points. The transitions between these phases are predominantly discontinuous, although two cases exhibit continuous transitions. In contrast, the phase diagram of the AF/FM square-kagom'{e}model shows only four phases with a single triple point,but these also lead to exotic magnetization curves.Here, too, there are two types of phase boundaries belonging to continuous and discontinuous transitions.

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Section: Methodsmentioning

confidence: 99%

Section: Data Availability Statementmentioning

confidence: 99%

Exotic magnetization curves in classical square-kagomé spin lattices

Schmidt,

Richter

2024

J. Phys. A: Math. Theor.

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“…5 with J × < 0 and J + ≥ 0, which can be derived by applying the generalized Luttinger-Tisza method of Ref. [40], see also the Mathematica files in the Supplement [41]. In this cuboc-d phase, the antipodal squares of the cuboctahedron are deformed into non-coplanar closed polygon chains with equal edges, while the square in the equatorial plane is deformed into a coplanar rectangle.…”

Section: Cuboc Ordermentioning

confidence: 99%

Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets

Gembé¹,

Schmidt²,

Hickey³

et al. 2023

Preprint

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Motivated by the recent synthesis of a number of Mott insulating square-kagome materials, we explore the rich phenomenology of frustrated magnetism induced by this lattice geometry, also referred to as the squagome or shuriken lattice. On the classical level, square-kagome antiferromagnets are found to exhibit extensive degeneracies, order-by-disorder, and non-coplanar ordering tendencies, which we discuss for an elementary, classical Heisenberg model with nearest-neighbor and cross-plaquette interactions. Having in mind that upon introducing quantum fluctuations non-coplanar order can melt into chiral quantum spin liquids, we provide detailed information on the multitude of non-coplanar orders, including some which break rotational symmetry (possibly leading to nematic quantum orders), as well as a number of (incommensurate) spin spiral phases. Using extensive numerical simulations, we also discuss the thermodynamic signatures of these phases, which often show multi-step thermal ordering. Our comprehensive discussion of the classical square-kagome Heisenberg model, often drawing comparisons to the conventional kagome antiferromagnet, sets the stage for future explorations of quantum analogs of the various phases, either conceptually such as in quantum spin-1/2 generalizations of our model or experimentally such as in the Cu-based candidate materials.

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The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states

Richter,

Schmidt,

Schnack

2024

J. Phys.: Condens. Matter

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We consider a classical Heisenberg model onthe kagom'{e} and the square kagom'{e} lattice, where at zero magnetic fieldnon-coplanar cuboctahedral ground states with twelve sublatticesexist if suitable exchange couplings are introduced between the other neighbors.Such 'cuboc ground states' are remarkable because they allow for chiral ordering.For these models, we discuss the magnetization processin an applied magnetic field $H$ by both numerical and analytical methods.We find some universal properties that are present in all models.The magnetization curve $M(H)$ usually contains only non-linear componentsand there is at least one magnetic field driven phase transition.Details of the $M(H)$ curve such as the number and characteristics(continuous or discontinuous) of the phase transitions depend on the latticeand the details of the exchange between the further neighbors.Typical features of these magnetization processes can alreadybe derived for a paradigmatic 12-spin model that we define in this work.

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Classical ground states of spin lattices

Cited by 7 publications

References 33 publications

Exotic magnetization curves in classical square-kagomé spin lattices

Exotic magnetization curves in classical square-kagomé spin lattices

Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets

The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states

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