Effects Of Geometrical Frustration Research Articles

Excellent Barocaloric Effect by Modulating Geometrical Frustrations in Mn3Pt.

Barocaloric materials hold great promise for next-generation solid-state cooling devices because of their green and efficient cooling performance. The insights into low-pressure-driven barocaloric materials are expected to pave the way for the widespread application of barocaloric refrigeration technology. Here, we reveal the low-pressure-driven large barocaloric effect (BCE) modulated by geometrical frustrations in Mn3Pt. The highest sensitivity to pressure of Mn3Pt in metal BCE materials results in an excellent temperature-change strength of 9.77 K 100-1 MPa-1. Neutron powder diffraction and first-principles calculations point out the dual effect of geometrical frustration on modulating the unusual BCE, which not only induces giant volume expansion by inspiring strong spin fluctuation and magnetic moment but also enhances the sensitivity of magnetic phase transition. The model of the dual effect of geometrical frustration in magnets with geometrical frustration is established, which will promote the research progress of barocaloric refrigeration devices.

Spontaneous resolution of two chiral metal–organic frameworks through local geometric and lattice frustration effects

Two chiral metal–organic frameworks that are differentiated by their Cd-centred helical twists are prepared by spontaneous chiral resolution from rigid, aliphatic, and achiral precursors.

Magnetic interactions in AB-stacked kagome lattices: Magnetic structure, symmetry, and duality

We present the results of an extensive study of the phase diagram and spin wave excitations for a general spin model on a hexagonal AB-stacked kagome system. The boundaries of the magnetic phases are determined via a combination of numerical (Monte Carlo) and analytical (Luttinger-Tisza) methods. We also determine the phase coexistence regions by considering the instabilities in the spin wave spectra. Depending on the strength of the spin-orbit coupling (SOC), some spin and lattice rotations become decoupled, leading to considerably larger symmetry groups than typical magnetic groups. Thus, we provide a detailed symmetry description of the magnetic Hamiltonian with negligible, weak, and intermediate strength of SOC. The spin symmetry in these three cases has a strong effect on the splittings observed in the spin excitation spectra. We further identify a number of self-duality transformations that map the Hamiltonian onto itself. These transformations describe the symmetry of the parameter space and provide an exact mapping between the properties of different magnetic orders and lead to accidental degeneracies. Finally, we discuss the physical relevance of our findings in the context of $\mathrm{Mn}_3X$ compounds.

Effects of Electron Correlation and Geometrical Frustration on Magnetism of Icosahedral Quasicrystals and Approximants — An Attempt to Bridge the Gap between Quasicrystals and Heavy Fermions

Effects of Electron Correlation and Geometrical Frustration on Magnetism of Icosahedral Quasicrystals and Approximants — An Attempt to Bridge the Gap between Quasicrystals and Heavy Fermions

Intermediate valence state in YbB4 revealed by resonant x-ray emission spectroscopy

We report the temperature dependence of the Yb valence in the geometrically frustrated compound from 12 to 300 K using resonant x-ray emission spectroscopy at the Yb transition. We find that the Yb valence, v, is hybridized between the v = 2 and v = 3 valence states, increasing from at 12 K to at 300 K, confirming that is a Kondo system in the intermediate valence regime. This result indicates that the Kondo interaction in is substantial, and is likely to be the reason why does not order magnetically at low temperature, rather than this being an effect of geometric frustration. Furthermore, the zero-point valence of the system is extracted from our data and compared with other Kondo lattice systems. The zero-point valence seems to be weakly dependent on the Kondo temperature scale, but not on the valence change temperature scale T v .

Elastic study of electric quadrupolar correlation in the paramagnetic state of the frustrated quantum magnet Tb2+δTi2−δO7

The electric quadrupolar state in the frustrated quantum magnet ${\mathrm{Tb}}_{2+\ensuremath{\delta}}{\mathrm{Ti}}_{2\ensuremath{-}\ensuremath{\delta}}{\mathrm{O}}_{7}$ has been studied by means of ultrasonic and magnetostriction measurements. A single crystal showed an elastic anomaly around 0.4 K, manifesting a long-range quadrupole ordering. By investigating the anisotropy of the magnetoelastic responses, we found a crossover temperature for the strongly correlated quadrupole state, below which the experimental data of the elastic constant and magnetostriction become qualitatively different from their calculations based on a single-ion model. We suppose that relatively high onset temperature of the quadrupole correlation compared with the transition temperature is ascribed to the geometrical frustration effect, and this correlated state seems to be responsible for the unusual properties in the paramagnetic state of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$.

The use of vector formalism in the analysis of hydrophobic and electric driving forces in biological assemblies.

Abstract Hydrophobic forces are known to have a crucial part not only in the conformation of the three-dimensional structure of proteins, but also in the build-up of DNA–protein complexes. Electric forces also play an important role both in the tertiary as well in the quaternary structure of macromolecular associations. Sometimes both hydrophobic and electric interactions add up their strengths to accomplish these structures but in most cases they act in opposite directions. This fact, together with being overall interactions with different ranges, provides a nuanced equilibrium also modulated by the need to comply with steric hindrances and geometric frustration effects. This review focuses on the utility of using the hydrophobic and electrical dipole moment vectors to describe the interactions that give rise to the structures of biological macromolecules. Although different definitions of both electric dipole and hydrophobic moments have been described in the literature, results obtained in biological assemblies demonstrate the principle of the biological membrane model. According to this model, postulated by our group, biological macromolecules tend to associate by aligning their hydrophobic moments in a similar manner to phospholipids in a membrane. Examples of both closed and open structures are used to assess the predictability of our model. We seek agreement between our results with those described in the current literature. The review ends with possible future projections using this formalism.

Dynamics of magnetic collective modes in square- and triangular-lattice Mott insulators at finite temperature

We study the equilibrium dynamics of magnetic moments in the Mott insulating phase of the Hubbard model on the square and triangular lattice. We rewrite the Hubbard interaction in terms of an auxiliary vector field and use a recently developed Langevin scheme to study its dynamics. A thermal noise, derivable approximately from the Keldysh formalism, allows us to study the effect of finite temperature. At strong coupling, $U\ensuremath{\gg}t$, where $U$ is the local repulsion and $t$ the nearest-neighbor hopping, our results reproduce the well known dynamics of the nearest-neighbor Heisenberg model with exchange $J\ensuremath{\sim}\mathcal{O}({t}^{2}/U)$. These include crossover from weakly damped dispersive modes at temperature $T\ensuremath{\ll}J$ to strong damping at $T\ensuremath{\sim}\mathcal{O}(J)$, and diffusive dynamics at $T\ensuremath{\gg}J$. The crossover temperatures are naturally proportional to $J$. To highlight the progressive deviation from Heisenberg physics as $U/t$ reduces we compute an effective exchange scale ${J}_{\mathrm{eff}}(U)$ from the low-temperature spin-wave velocity. We discover two features in the dynamical behavior with decreasing $U/t$: (i) the low-temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii) the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/{J}_{\mathrm{eff}}$. We relate this to enhanced mode coupling, in particular to thermal amplitude fluctuations, at weaker $U/t$. A comparison of the square and triangular lattice reveals the additional effect of geometric frustration on damping.

Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets.

Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.

Effects of geometric frustration in Kitaev chains

We study the topological phase transitions of a Kitaev chain frustrated by the addition of a single long-range hopping. In order to study the topological properties of the resulting legged-ring geometry (Kitaev tie model), we generalize the transfer matrix approach through which the emergence of Majorana edge modes is analyzed. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the hopping and the chemical potential. Robustness to disorder of non-trivial phases is also proven. Moreover, geometric frustration effects persist when translational invariance is restored by considering a multiple-tie system. These findings shed light on an entire class of experimentally realizable topological systems with long-range couplings.

Uniaxial-Pressure-Induced Release of Magnetic Frustration in a Triangular Lattice Antiferromagnet YbCuGe

We have studied the effect of geometrical frustration on the antiferromagnetic order in the Yb-based triangular lattice compound YbCuGe below TN = 4.2 K by the measurements of magnetization and specific heat under hydrostatic and uniaxial pressures. By applying hydrostatic pressure P up to 1.34 GPa, TN hardly changes. By contrast, TN increases as P is applied along the hexagonal a axis, while TN decreases by the application of P along the c axis. The increase of TN only for P‖a suggests the release of the frustration inherent in the triangular lattice of Yb ions of this compound.

Morphology selection kinetics of crystallization in a sphere

Crystallization under geometrical confinement is of fundamental importance in condensed matter physics, biophysics and material science. Even the influence of the simplest geometry, a sphere, on crystallization remains far from well understood, thereby making morphology control of the final superstructures challenging. Here, we employ charged colloids encapsulated in an emulsion droplet as a model system to access the crystallization kinetics at the single-particle level. We find rapid formation of ‘skin’ layers with an icosahedral arrangement of defects under the geometrical frustration effect, followed by interior ordering and slow ripening. The final morphologies are determined by dynamical interplay between the system-independent skin layer formation and the system-dependent structural transformation towards the most stable solid far from the surface. We reveal the crucial role of kinetics in morphological selection under a geometrical constraint, besides the thermodynamics, which may shed new light on the structural design of nanoscale crystals. The authors investigate the role of spherical confinement and curvature-induced topological defects on the crystallization of charged colloids. They conclude that crystallization in spherical confinement is due to a combination of thermodynamics and kinetic pathways.

Jahn-Teller and geometric frustration effects on the structural and magnetic ground states of substituted spinels (Ni,A)Cr2O4 (A = Mn/Cu)

Comparative study of the effects of substitution (25%) of Jahn-Teller (JT) active Cu2+ and non JT active Mn2+ cations, at the Ni2+ site, on the geometric frustration (GF) and cooperative JT distortion (CJTD) in multiferroic NiCr2O4 has been carried out with the help of low-temperature magnetization, x-ray diffraction and time of flight (TOF) neutron powder diffraction (NPD) measurements. On Mn2+ substitution the CJTD, which causes elongation of the NiO4 tetrahedra in I41/amd phase of NiCr2O4, gets suppressed at room-temperature (RT) and stabilizes the Fd-3m phase in (Ni0.75Mn0.25)Cr2O4. On the contrary the Cu2+ substitution inverts the effect of CJTD and the tetrahedra get flattened at RT, which in turn oppositely distorts the I41/amd lattice in Ni0.75Cu0.25Cr2O4. The frustration index decreases on substitution. Intriguingly, the tetragonal to orthorhombic phase transition and the antiferromagnetic ordering, which are clearly evident in the pristine NiCr2O4 and the Cu2+ substituted sample respectively at 30 K and 70 K, have not been observed for the Mn2+ substituted sample. This has been attributed to the change in Cr3+- Cr3+ direct magnetic-interaction on structural transition. However, the long-range ferrimagnetic order remains intact for all the three compositions i.e. NiCr2O4, Ni0.75Mn0.25Cr2O4 and Ni0.75Cu0.25Cr2O4 occurring at 75 K, 70 K and 95 K, respectively. The Mn2+ substituted compound shows short-range magnetic correlation at low-temperatures, as evident from the diffuse and broad hump in the intensity-vs-d spacing plot of TOF NPD data. This short-range magnetic order has been attributed to the known spiral magnetic order.

Naked-eye visualization of geometric frustration effects in macroscopic spin ices

We study planar rectangular-like arrays composed by macroscopic dipoles (magnetic bars with size around a few centimeters) separated by lattice spacings a and b along each direction. Physical behavior of such macroscopic artificial spin ice (MASI) systems are shown to agree much better with theoretical prediction than their micro- or nano-scaled counterparts, making MASI “almost ideal prototypes” for readily naked-eye visualization of geometrical frustration effects.

Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring

On a ring, a single Jordan-Wigner transformation between the Kitaev model and the spin model suffers redundant degrees of freedom. However, we can establish an exact quaternary Jordan-Wigner mapping involving two Kitaev rings and two spin rings with periodic or antiperiodic boundary conditions. This mapping facilitates us to demonstrate exactly how a topological extended-kink (TEK) phase develops in the interacting Kitaev ring with odd number of lattice sites. The emergence of this new phase is attributed to the effect of geometrical ring frustration. Unlike the usual topological phases protected by energy gap in noninteracting systems, the TEK phase is gapless. And because the spectra of low energy excitations are quadratic, the specific heat per site approaches a half of Boltzmann constant near absolute zero temperature. More interestingly, the ground state is unique, immune to spontaneous symmetry breaking. It exhibits a long-range correlation function with a nonlocal factor, but no local order parameter can be defined. As a concomitant effect, a special kind of localized kink zero mode (KZM) takes place if we introduce a type of bond defect. We also show that the KZM is robust against moderate disorders.

Physical properties of CeIrSi with trillium-lattice frustrated magnetism

Magnetic ($\chi$), transport ($\rho$) and heat capacity ($C_m$)properties of CeIrSi are investigated to elucidate the effect of geometric frustration in this compound with trillium type structure because, notwithstanding its robust effective moment, $\mu_{\rm eff}\approx 2.46\mu_B$, this Ce-lattice compound does not undergo a magnetic transition. In spite of that it shows broad $C_m(T)/T$ and $\chi(T)$ maxima centered at $T_{max}\approx 1.5$\,K, while a $\rho \propto T^2$ thermal dependence, characteristic of electronic spin coherent fluctuations, is observed below $T_{coh} \approx 2.5$\,K. Magnetic field does not affect significantly the position of the mentioned maxima up to $\approx 1$\,T, though $\chi(T)$ shows an incipient structure that completely vanishes at $\mu_0 H \approx 1$\,T. Concerning the $\rho \propto T^2$ dependence, it is practically not affected by magnetic field up to $\mu_0 H = 9$\,T, with the residual resistivity $\rho_0(H)$ slightly decreasing and $T_{coh}(H)$ increasing. These results are compared with the physical properties observed in other frustrated intermetallic compounds

Phase Diagram of a Generalized XY Model with Geometrical Frustration

In the present study we investigate the effects of geometrical frustration on the XY model with antiferromagnetic (AFM) coupling on a triangular lattice, generalized by the inclusion of a third-order antinematic term (AN3). We demonstrate that at non-zero temperatures such a generalization leads to a phase diagram consisting of three different quasi-long-range ordered (QLRO) phases. Compared to the model with the second-order AN coupling (AN2), it includes besides the AFM and AN3 phases which appear in the limits of relatively strong AFM and AN3 interactions, respectively, an additional complex noncollinear QLRO phase at lower temperatures wedged between the AFM and AN3 phases. This new phase originates from the competition between the AFM and AN3 couplings, which is absent in the model with the AN2 coupling.

Site-specific C13 NMR study on the locally distorted triangular lattice of the organic conductor κ−(BEDT−TTF)2Cu2(CN)3

To verify the effect of geometrical frustration, we artificially distort the triangular lattice of quasi-two-dimensional organic conductor $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ [BEDT-TTF: bis(ethylenedithio)terathiofulvalene] by analogous-molecular substitution and apply $^{13}$C NMR of bulk and substituted sites, electric conductivity, and static magnetic susceptibility measurements. The results indicate that the magnetic characteristics of the substituted sample are quantitatively similar to those of the pure sample. Moreover the magnetic characteristics at the substituted sites are also the same as in the bulk. These results suggest that the observed magnetic properties may not be due to the geometrical frustration but the importance of disorder.

Rhombi-chain Bose-Hubbard model: Geometric frustration and interactions

We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid phase is very sensitive to changes away from perfect frustration (half-flux). We provide some proposals to make the model more resilient to variants away from perfect frustration. We also study the bipartite entanglement properties of the chain. We discover that, while the scaling of the block entropy pair-superfluid and of the single-particle superfluid leads to the same central charge, the properties of the low-lying entanglement spectrum levels reveal their fundamental difference.

Two-dimensional triangular-lattice Cu(OH)Cl, belloite, as a magnetodielectric system

Quantum spins on a triangular lattice may bring out intriguing and exotic quantum ground states. Here we report a magnetodielectric system of CuOHCl wherein $S=1/2\mathrm{C}{\mathrm{u}}^{2+}$ spins constitute a two-dimensional triangular lattice with the layers weakly coupled via Cl-H-O bonding. Despite strong magnetic interactions, as expected from the relatively high value of ${\ensuremath{\theta}}_{\mathrm{CW}}=\ensuremath{-}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, antiferromagnetic transition occurred at ${T}_{N}=11\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, followed by an uprising turn of the magnetic susceptibility below \ensuremath{\sim}7 K. Neutron-diffraction experiment revealed a coplanar spin structure on the triangular lattice below the ${T}_{N}$, with each spin pointing toward the center of a triangle. Of the three spins on a triangle, two are antiparallel and the third one is angled ${120}^{\ensuremath{\circ}}$ to the antiparallel spins. A concerted effect of geometric frustration in the triangular lattice and superexchange interactions through a zig-zag path via double Cu-O-Cu and double Cu-Cl-Cu bridges counted for this spin arrangement. Further investigation using dielectric constant and heat capacity measurements, as well as a microscopic probe of muon spin rotation, revealed a magnetodielectric effect and the possibility of multiferroic transition at ${T}^{*}\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which is suspected to be in close relation to geometric frustration in this triangular lattice. The present paper presents a magnetodielectric system on a two-dimensional triangular lattice with chemical stoichiometry. It can also serve as a rare reference to the hotly debated quantum spin-orbital liquid compound $\mathrm{LiNi}{\mathrm{O}}_{2}$.