Category: 未分類

Ground state phase diagrams of the S=1 Kitaev model with bilinear-biquadratic interactions, shown for different degrees of freedom in spin space: CP², CP¹, and a discrete eight-color model.

Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom.
In this study, with a specific emphasis on S = 1 magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle et al., Phys. Rev. B 107, L140403 (2023)], we investigate the S = 1 Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple-q phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom—from CP² to CP¹ and ultimately to a discrete eight-color model—we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by Z₂ flux order, and a gapped continuum of excitations. This work contributes not only to the specific exploration of S = 1 Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets.

This work is published as “Eight-color chiral spin liquid in the S=1 bilinear-biquadratic model with Kitaev interactions“, Rico Pohle, Nic Shannon, and Yukitoshi Motome, Phys. Rev. Research 6, 033077 (2024)

Phase Diagram of the Shuriken Ising model as a function of the exchange ratio x = J_AB / J_AA. The phase diagram supports 2 ordered phases [ferromagnetic (FM) and staggered ferromagnetic phase (SFM)]; 2 classical spin liquid phases (SL_1,2) and a binary paramagnetic phase (BPM).

Competing interactions are a prerequisite for geometrical frustration. One well-known example of frustration are Ising spins on triangular corner-sharing plaquettes as for example on the Kagome lattice in 2 dimensions, leading to an extensive ground state degeneracy.  But what happens when different disordered phases co-exist and compete between each other?  By using the same triangular building blocks as for Kagome, we consider the so-called Shuriken lattice (also known as Square-Kagome lattice), which shows, contrary to Kagome, inequivalent sites belonging to loops of different sizes, namely 4 and 8. The presence of these two types of loops together with a large unit-cell offers a natural setting to tune the anisotropy in order to explore a variety of phases.
In order to shed light on this question,we investigated thermodynamic properties of the Ising model of the anisotropic Shuriken lattice using classical Monte Carlo simulations, analytical Husimi tree calculations and exact decoration-iteration transformation. By tuning the anisotropy of the lattice, it was possible to observe a reentrant behavior between disordered regimes from a high-temperature paramagnet to a classical spin liquid into a low-temperature binary paramagnet (BPM in the Fig.). The term ”binary paramagnet” illustrates the fact that the corresponding highly-degenerate ground state is made of two different types of uncorrelated (super-) spins. We round off our studies with an analytical method mapping the Shuriken lattice onto a checkerboard lattice with temperature dependent coupling parameters, giving insights into dominant competing interactions within the ordered and disordered regimes.

This work was published as “Reentrance of disorder in the anisotropic shuriken Ising model”, Rico Pohle, Owen Benton, and L.D.C. Jaubert, Phys. Rev. B 94, 0144290 (2016)

Phase diagram of the bilayer-breathing-kagome model of Ca₁₀Cr₇O₂₈, together with related ground-state degeneracies, and “ring”-like features associated with a spiral spin liquid.

Quantum spin liquids form an exotic class of quantum phases of matter, accompanied by emergent gauge fields, topological order and fractionalized excitations, with strong interaction effects and long-range entanglement.  The recently discovered material Ca₁₀Cr₇O₂₈ shows strong indications of hosting such a novel phase of matter, but with properties that sets it apart from any previously studied quantum spin liquid.
In this work, we make a crucial step towards understanding the nature and origin of the spin liquid behaviour in Ca₁₀Cr₇O₂₈. Using a combination of Monte Carlo and molecular dynamics simulation, and spin-wave calculations, we carry out a comprehensive study of a bilayer breathing kagome model derived from experiment. We identify the low-energy physics as being that of a spiral spin liquid, characterised by a “ring”-like feature in the spin structure factor. Meanwhile, at higher energies, we can trace the dynamical properties to a dynamical Columb spin liquid, found when the material is saturated in magnetic field. Hence we establish that Ca₁₀Cr₇O₂₈ is a rare case of a many-body system where two types of spin liquid coexist at different time scales.

This work was published as “Theory of Ca₁₀Cr₇O₂₈ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics” Rico Pohle, Han Yan and Nic Shannon, Phys. Rev. B 104, 024426 (2021)

Low frequency part of the optical conductivity σ(ω) for (a) Triangular zigzag, (b) triangular armchair, (c) hexagonal zigzag, (d) hexagonal armchair, (e)–(f) rectangular graphene quantum dot for both x- and y- polarized light.

The discovery of Graphene, has sparked a renaissance in the study of two-dimensional materials and their potential technological applications. Graphene quantum dots (GQD’s) bring another new opportunity with potential applications in fields ranging from quantum computation to solar energy. However, in order to tailor the properties of a GQD to a specific purpose it is vital to understand the relationship between the size and shape of the dot and its physical properties.
On this work we explore the role that size, shape, edge-type and atomic vacancies play in the optical response of GQD’s. Using group theory, we reveal optical selection rules which follow from the symmetry of a regular shaped GQD, identifying the different roles played by linear and circularly-polarised light in different GQD’s with different shape. The study of the optical conductivity σ(ω) of GQD’s within a simple tight-binding model showed that for GQD’s of intermediate size (≈ 10nm), σ(ω) is sensitive to the edge-type of the dot, with the presence of zigzag edges heralded by a new peak in σ(ω) at the UV end of the visible spectrum (see Fig.). States causing this peak were identified to be 1-dimensional, providing a natural explanation for large binding energies of the associated excitons in bulk graphene. Shape-asymmetry and atomic vacancies in the optical response of GQD’s can be used to even enhance the number of these states. Since GQD’s with both regular and irregular shapes are now available we hope that this article will stimulate further experimental work on this topic.

This work was published as “Symmetry and optical selection rules in graphene quantum dots”, R. Pohle, E. G. Kavousanaki, K. M. Dani, and N. Shannon.  Phys. Rev. B 97, 115404 (2018)

Curie-law crossover of the Ising antiferromagnet on the kagome lattice.

The Curie-Weiss law is widely used to estimate the strength of frustration in spin liquid materials. However, the Curie-Weiss law was originally derived as an estimate of magnetic correlations close to a mean-field phase transition, which – by definition – is absent in spin liquids. Consequently, certain materials were reported to exhibit deviations from the Curie-Weiss law, making a conclusive determination of their Curie-Weiss temperature challenging, especially when the high-temperature regime becomes inaccessible in experiments.
In this work, we show that the concept of a ”Curie-law crossover” (see Fig.1) provides an accurate description of the thermodynamic properties in spin liquids. We study the generic aspect of the Curie-law crossover by comparing a variety of frustrated spin models in two and three dimensions, using both classical Monte Carlo simulations and analytical Husimi tree calculations. While the Husimi tree approximation is quantitatively accurate for all temperatures, we find that the crossover is influenced by the structure of the frustrated unit cell, rather than its lattice dimension. As a complement to traditional methods, we propose an “easy-to-use” fitting Ansatz of the reduced susceptibility, χT, which can be used to estimate the Curie-Weiss temperature, even when the high-temperature regime is not accessible in experiment. Applications to spin liquid candidate materials such as the S=1 pyrochlore magnet NaCaNi2F7, the square-kagome material KCu6AlBiO4(SO4)5Cl, and the spiral-spin liquid FeCl3 are discussed.

This work was published as “Curie-law crossover in spin liquids“, Rico Pohle and Ludovic D. C. Jaubert,
Phys. Rev. B 108, 024411 (2023).

Ground state phase diagram of the S=1 Kitaev model under the influence of bilinear-biquadratic interactions.

New discoveries are often made on the border between different disciplines. One major discipline in solid state physics is dedicated to quantum spin liquids, an unconventional state of matter accompanied by emergent gauge fields, topological order, and fractionalized excitations. Another concept is that of spin nematics, a magnetically ordered state dominated by quadrupole moments, which breaks spin-rotation symmetry by selecting an axis, while not choosing a particular direction. Usually seen as two separate areas of study, we are interested in combining those two disciplines, by asking the question: “What happens, when a spin nematic and a spin liquid meet?”
To answer this question, we showed that the S=1 Kitaev model under the influence of bilinear-biquadratic interactions hosts many unconventional ordered and disordered phases. We obtain a comprehensive phase diagram including chiral ordered and quadrupolar ordered phases, in addition to already known ferro, antiferro, zigzag and stripy phases. Intriguingly, we find that the competition between Kitaev and positive biquadratic interactions also promotes a noncoplanar finite-temperature spin liquid state, with macroscopic degeneracy and finite scalar chirality.
Our results show that the competition between spin liquid and spin nematic phases is a promising way to explore new magnetic states of matter.

This work was published as “Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions”, R. Pohle, N. Shannon, Y. Motome, Phys. Rev. B 107, L140403 (2023).

Dynamical structure factors for spin quadrupoles (left) and spin dipoles (right).

Spin-1 magnets allow for dipolar and quadrupolar moments on a single site, leading to rich physical properties as seen in spin nematic phases, Fe-based superconductors and cold atom systems. However, experimental probing of these unconventional phases remains challenging, and therefore requires new theoretical tools to describe and interpret their ground state and excitation properties.
In this work, we introduce a new Monte Carlo and Molecular Dynamics method designed to study thermodynamic and dynamic properties of spin-1 magnets. We benchmark our numerical implementation by on the ferroquadrupolar phase of the spin-1 bilinear-biquadratic (BBQ) Hamiltonian on the triangular lattice, and show excellent agreement with analytical flavour-wave theory and low-temperature expansion results.
These results open the door to efficiently study realistic spin-1 magnets, and spin-1 models in the context of cold atoms, and Fe-based superconductors.

This work was published as “Semi-classical simulation of spin-1 magnets”, Kimberly Remund, Rico Pohle, Yutaka Akagi, Judit Romhànyi and Nic Shannon, Phys. Rev. Research 4, 033106 (2022)

Illustration of connection between pinch points and half moons. 

Magnetic frustration leads to the emergence of diverse exotic behaviors, and the study of their theories and phenomenology is crucial. For example, sophisticated understanding has been established for models with underlying U(1) symmetry and the associated pinch-point features in their spin-spin correlations.
However, this turned out to be only half the story. Attached to the pinch points, there exists another highly universal feature in the shape of two “half moons” in a wide range of frustrated magnetic models and recent experiments on Nd₂Zr₂O₇.
In this work we establish its theoretical interpretation, which turned out to be a hidden side of the pinch-points. It is a result of decomposition and decoupling of the emergent magnetic field in the system, which leads to an extra pinch point on the dispersive band. The half moons are essentially the pinch points seen on a constant energy cross-section.

This work was published as “Half moons are pinch points with dispersion”, Han Yan, Rico Pohle and Nic Shannon, Phys. Rev. B, 98 140402(R) (2018). It was also singled out as an Editor’s Suggestion, and for inclusion in Kalaidascope.