Commensurate State Research Articles

Magnetic structures of PrMn7O12 : Intersublattice magnetoelastic coupling and incommensurate spin canting

We report on the magnetic structures of PrMn7O12, resolving both a high-temperature structure in common with the other R3+Mn7O12 systems and an additional low-temperature phase characterized by a superposed incommensurate (ICM) spin canting. A phenomenological model is developed to account for large magnetoelastic coupling immediately below the Curie temperature, demonstrating that A′B exchange is primarily responsible for the ferrimagnetic structures observed across the R3+Mn7O12 family. Finally, an analytical mean-field minimal model is presented that successfully accounts for all magnetic structures observed in this family of materials, including the canted commensurate and ICM ground states. Published by the American Physical Society 2024

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8

We report the experimental determination of the magnetic exchange parameter ( J/kB = 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8 using the temperature dependence of dc-magnetic susceptibility χ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strength Jex−NN∼ 2.45 K. Five different magnetic phase transitions (6.2–11.2 K) and spin-flip transitions (9.6–7.7 kOe) have been probed using the ∂ ( χT )/ ∂T vs. T, heat capacity (CP -T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the CP -T near TN (11.2 K) has been analyzed using the power-law expression CM = A|T — TN|−α resulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < TN (T > TN ), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8 and was evident from the Kohlrausch–Williams–Watts analysis of complex modulus and impedance spectra (0 ⩽β⩽ 1). Mott’s variable-range hopping of charge carriers process is evident through the resistivity analysis ( ρac -T −1/4 ) in the temperature range 275 ∘C–350 ∘C. Moreover, the frequency-dependent analysis of σac (ω) follows Jonscher’s power law yielding two distinct activation energies ( Ea∼ 0.37 and 2.29 eV) between the temperature range 39 ∘C–99 ∘C and 240 ∘C–321 ∘C.

Incommensurate charge density wave order in U2Ti

Density functional theory predicted that the ground state of U2Ti should undergo a Peierls-like doubling of its unit cell along the c axis on cooling from high temperature [G. Kaur , ]. We report x-ray diffraction, heat capacity, and resistivity measurements showing that with decreasing temperature the transition from the parent hexagonal structure occurs in two steps, via an incommensurate state below TICDW=71(1) K which then undergoes a lock-in transition to the predicted commensurate Peierls-like state at TCCDW=46(3) K. The signatures of the upper transition in thermodynamic and transport measurements are weak, meaning that similar incommensurate charge density waves (ICDWs) preceding CDWs might occur more widely in other systems but elude detection. The collinear nature of both the ICDW and Peierls-like states we report is much simpler than more complex incommensurate states seen in α−U, which may in time provide greater insight into the mechanism for ICDW formation. Published by the American Physical Society 2024

Accurate determination of stability characteristics of spatially modulated shear layers

We present a method for accurately determining the stability characteristics of spatially modulated shear layers. The algorithm can handle arbitrary commensurate states, which are not accessible to classical direct-numerical-simulation-based approaches. It uses spectral discretization of the field equations to handle field modulations and the spectrally accurate immersed boundary conditions method to handle the geometry modulations. The algorithm can deal with pattern interaction effects driven by modulations of different physical origins. Various tests demonstrate that the algorithm delivers spectral accuracy for eigenvalues and eigenfunctions. The algorithm can be easily extended to analyse many sources and patterns of modulation with minimal commitment to the user's time.

Friction resonance in commensurate and incommensurate states

This paper studies excitation-dependent energy dissipation in friction process under both commensurate and incommensurate states between graphene layers. The results show that when excitation frequency of tip is equal to its natural frequency, friction resonance and its accompanying broken phenomena occur in both contact states, which even leads to breakdown of system. The origin of friction resonance is disclosed systematically through fast Fourier transform of instantaneous friction force. Moreover, the influence of rising temperature on frictional energy dissipation is opposite between commensurate and incommensurate cases, which can be ascribed to net effect between thermal lubrication and thermal collision. Finally, we quantitatively detect phononic mechanism of frictional energy dissipation via calculating phonon number in different contact states.

Molecular dynamics simulation of frictional properties of Pt cluster on graphite under load

Structural lubricity, characterized by nearly frictionless behavior at solid incommensurate interfaces with weak interactions, holds significant technological importance. However, various factors can lead to the breakdown of structural lubricity, such as spontaneous reorientation to a commensurate state, applied load, edge effects, deformations, and wear. To overcome these challenges, clusters can be employed at interfaces. With their high Young’s modulus and stiffness, clusters can withstand high loads and tolerate elastic deformations. Therefore, Pt cluster, which inherently possess incommensurate contact with graphite surface, are expected to exhibit structural superlubric behavior, even under high loads, as long as they can sustain incommensurate contact. Our molecular dynamics (MD) simulations, however, have revealed that a Pt cluster on graphite can undergo metastable transitions from the incommensurate state to a commensurate state, resulting in subsequent stick-slip behavior. In the absence of any external load, the Pt cluster has demonstrated the ability to maintain incommensurate contact with almost zero friction force, primarily attributed to its weak interaction with graphite. However, the presence of an applied load force leads to the loss of the initial incommensurate contact between the Pt cluster and graphite, resulting in the emergence of high friction forces and the breakdown of structural lubricity with a similar stick-slip behavior to that observed in the comparative simulations conducted for the commensurate state. It becomes evident that the maintenance of incommensurate contact is crucial for achieving superlubric behavior in Pt cluster-graphite systems, while the presence of an applied load force can disrupt this behavior and lead to higher friction forces.

Multi- k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe

The magnetic structure, magnetoresistance (MR), and Hall effect of the noncentrosymmetric magnetic semimetal NdAlGe are investigated, revealing an unusual magnetic state and anomalous transport properties that are associated with the electronic structure of this compound. The magnetization and MR measurements are both highly anisotropic and indicate an Ising-like magnetic system. The magnetic structure is complex in that it involves two magnetic ordering vectors, including an incommensurate spin density wave and commensurate ferrimagnetic state in zero field. We have discovered a large anomalous Hall conductivity that reaches $\ensuremath{\approx}430\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, implying that it originates from an intrinsic Berry curvature effect stemming from Weyl nodes found in the electronic structure. These electronic structure calculations indicate the presence of nested Fermi surface pockets with nesting wave vectors like the measured magnetic ordering wave vector and the presence of Weyl nodes in proximity to the Fermi surface. We associate the incommensurate magnetic structure with the large anomalous Hall response to be the result of the combination of Fermi surface nesting and the Berry curvature associated with Weyl nodes.

Manipulate the interfacial friction of χ3-borophene on graphene heterojunction via rotation

Manipulating friction between two-dimensional (2D) material heterojunctions is crucial for their application in microscale functional devices. In this study, we have systematically investigated the frictional properties of χ3-Borophene(Bo)/Bo, Bo/Graphene(Gr), and Bo/Gr(30°) by first-principles calculations. The results indicate that the formation of Bo/Gr heterojunctions indeed reduces interfacial sliding potential energy corrugation of Borophene. Interestingly, friction anisotropy appears when commensurate state forms between Gr and Bo along armchair direction of Bo/Gr heterojunction. In addition, this anisotropy vanishes after rotating the heterojunction with an angle of 30°. The Fourier transformation method is applied to illustrate the commensurability of heterojunctions along specific directions. Finally, the interfacial friction behavior is further confirmed to be consistent with the fluctuation of interfacial charge transfer, which emphasizes the atomic stacking and chemical property of heterojunctions.

Electronic states of domain walls in commensurate charge density wave ground state and mosaic phase in 1T -TaS2

Domain walls (DWs) in the charge-density-wave (CDW) Mott insulator 1T-TaS2 have unique localized states, which play an important role in exploring the electronic properties of the material. However, the electronic states in DWs in 1T-TaS2 have not been clearly understood, mostly due to the complex structures, phases, and interlayer stacking orders in the DW areas. Here, we explored the electronic states of DWs in the large-area CDW phase and mosaic phase of 1T-TaS2 by scanning tunneling spectroscopy. Due to the different densities of DWs, the electronic states of DWs show distinct features in these phases. In the large area CDW phase, both the domain and the DWs (DW1, DW2, DW4) have zero conductance at the Fermi level; while in the mosaic phase, they can be metallic or insulating depending on their environments. In areas with a high density of DWs, some electronic states were observed both on the DWs and within the domains, indicating delocalized states over the whole region. Our work contributes to further understanding of the interplay between CDW and electron correlations in 1T-TaS2.

Stripe helical magnetism and two regimes of anomalous Hall effect in NdAlGe

We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state below $T_{\text{com}}=5.1$ K. Using small-angle neutron scattering, we showed that the zero-field cooled ferrimagnetic domains form stripes in real space with characteristic length scales of 18 nm and 72 nm parallel and perpendicular to the [110] direction, respectively. Interestingly, for the transport properties, NdAlSi does not exhibit an anomalous Hall effect (AHE) that is commonly observed in magnetic Weyl semimetals. In contrast to NdAlSi, we identify two different AHE regimes in NdAlGe that are respectively governed by intrinsic Berry curvature and extrinsic disorders/spin fluctuations. Our study suggests that Weyl-mediated magnetism prevails in this group of noncentrosymmetric magnetic Weyl semimetals NdAl$X$, but transport properties including AHE are affected by material-specific extrinsic effects such as disorders, despite the presence of prominent Berry curvature.

Velocity-dependent phononic friction in commensurate and incommensurate states

We investigate that multiple friction peaks occur with an increase in velocity in commensurate and incommensurate states between graphene layers. Fast Fourier transform analysis of instantaneous friction force confirms that frictional spectrum mainly distributes at washboard frequency of tip and its harmonics. When washboard frequency approaches natural frequency of tip and its fractional frequencies, resonance will occur in both contact cases, resulting in friction peaks. Further observations indicate that phonon spectra of tip and substrate match in commensurate state, thereby establishing effective energy dissipation channels; however, phonon spectra do not match in incommensurate state. Finally, we deduce a theoretical model for calculating number of excited phonons and quantitatively explain friction discrepancy in different contact states and velocities.

Static and dynamic magnetic properties of the spin- triangle lattice antiferromagnet Na3Fe(PO4)2 studied by 31P NMR

31P nuclear magnetic resonance (NMR) measurements have been carried out to investigate the magnetic properties and spin dynamics of Fe3+ (S = 5/2) spins in the two-dimensional triangular lattice (TL) compound Na3Fe(PO4)2. The temperature (T) dependence of nuclear spin-lattice relaxation rates () shows a clear peak around Néel temperature, K, corresponding to an antiferromagnetic (AFM) transition. From the temperature dependence of NMR shift (K) above , an exchange coupling between Fe3+ spins was estimated to be K using the spin-5/2 Heisenberg isotropic-TL model. The temperature dependence of divided by the magnetic susceptibility (χ), , above proves the AFM nature of spin fluctuations below in the paramagnetic state. In the magnetically ordered state below , the characteristic rectangular shape of the NMR spectra is observed, indicative of a commensurate AFM state in its ground state. The strong temperature dependence of 1/T 1 in the AFM state is well explained by the two-magnon (Raman) process of the spin waves in a 3D antiferromagnet with a spin-anisotropy energy gap of 5.7 K. The temperature dependence of sublattice magnetization is also well reproduced by the spin waves. Those results indicate that the magnetically ordered state of Na3Fe(PO4)2 is a conventional 3D AFM state, and no obvious spin frustration effects were detected in its ground state.

Anomalous strain-dependent charge density in honeycomb borophene

The electronic properties of honeycomb borophene under strain were investigated using first principles. The biaxial tensile strain was found to alter the interlayer interaction between the substrate layer and the sample layer, manifested as controlled by strain in a commensurate contact state intralayer and interlayer coupling strength. In addition, honeycomb borophene was found to have an anomalous strain-dependent charge density. We explain that this charge density fluctuation is determined by the electron-deficient nature of borophene itself and the change in the amount of electron injection into the borophene layer under strain. This study provides new insights into the changes in the interaction between two-dimensional materials and substrate layers under strain.

Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates

We examine the dynamics of an individually driven skyrmion moving through a background lattice of skyrmions coupled to a 2D periodic substrate as we vary the ratio of the number of skyrmions to the number of pinning sites across commensurate and incommensurate conditions. As the skyrmion density increases, the skyrmion Hall angle is nonmonotonic, dropping to low or zero values in commensurate states and rising to an enhanced value in incommensurate states. Under commensuration, the driven skyrmion is channeled by a symmetry direction of the pinning array and exhibits an increased velocity. At fillings for which the skyrmion Hall angle is zero, the velocity has a narrow band noise signature, while for incommensurate fillings, the skyrmion motion is disordered and the velocity noise is broad band. Under commensurate conditions, multi-step depinning transitions appear and the skyrmion Hall angle is zero at low drives but becomes finite at higher drives, while at incommensurate fillings there is only a single depinning transition. As the gyrotropic component of the skyrmion dynamics, called the Magnus force, increases, peaks in the velocity that appear in commensurate regimes cross over to dips, and new types of directional locking effects can arise in which the skyrmion travels along other symmetry directions of the background lattice. At large Magnus forces, and particularly at commensurate fillings, the driven skyrmion can experience a velocity boost in which the skyrmion moves faster than the applied drive due to the alignment of the Magnus-induced velocity with the driving direction. In some cases, an increase of the Magnus force can produce regimes of enhanced pinning when the skyrmion is forced to move along a nonsymmetry direction of the periodic pinning array. This is in contrast to systems with random pinning, where increasing the Magnus force generally reduces the pinning effect. We demonstrate these dynamics for both square and triangular substrates and map out the different regimes as a function of filling fraction, pinning force, and the strength of the Magnus force in a series of dynamic phase diagrams.

Financing official statistics: Some reflections

Government control over the financing of official statistics has long been seen as threat to their integrity. This paper reviews the personal experience of the author over 40 years working in and around official statistics in the United Kingdom. It notes that as a state function, official statistics must be funded by the state and respect the accountability arrangements necessary for state funding to be seen as legitimate. It considers that the critical element is strong protection from partisan manipulation for political ends. The paper concludes that the COVID pandemic has accelerated a trend for recognition of the value of official statistics and the consequent need for commensurate state funding.

Active rheology and anticommensuration effects for driven probe particles on two-dimensional periodic pinning substrates

For an assembly of particles interacting with a two-dimensional periodic substrate, a series of commensuration effects can arise when the number of particles is an integer multiple of the number of substrate minima. Such commensuration effects can appear for vortices in type-II superconductors with periodic pinning or for colloidal particles on optical landscapes. Under bulk external driving, the pinning or drag on the particles is strongly enhanced at commensuration. Here we consider the active rheology of a single particle driven through an assembly of particles coupled to a periodic substrate at different commensurate conditions. For increasing density at fixed driving force, we observe nonmonotonic drag along with what we call an anticommensuration effect where the drag or pinning effectiveness is reduced in commensurate states, opposite from the behavior typically observed under bulk driving. The velocity enhancement or drag reduction appears when the background particles form a crystalline state that is coupled more strongly to the substrate than to the driven particle, while under incommensurate conditions, the background particles are disordered and produce enhanced drag on the probe particle. The velocity noise of the driven particle has a narrow band signature at commensuration and a broad band signature away from commensuration. We map out the regions in which viscous flow, periodic flow, and a pinned phase appear. We show that the effects we observe are robust on both square and triangular substrate arrays and for both vortices in type-II superconductors and colloidal particles on optical landscapes.

Effect of N-doping on tribological properties of graphene by molecular dynamics simulation

Graphene has attracted a lot of attention due to its excellent electrical properties, however, the gapless nature of graphene limits its further applications. Doping is an effective way to open the bandgap, in which nitrogen-doped (N-doped) graphene has potential applications, but the study of its tribological properties is still lacking. In this work, the effects of nitrogen doping on the tribological properties of graphene under different interfacial structures are investigated by molecular dynamics simulation. The simulation models include a hexagonal graphene sheet, graphene or N-doped graphene substrate. The results show that the nitrogen doping has different effects on friction when interface structure is in a commensurate state and an incommensurate state. In a commensurate state, N-doping reduces the friction between interfaces in all cases, but the friction first goes up and then decreases with the increase of doping ratio of nitrogen. The local maximum value of friction occurs at a doping ratio of 7.5%. This phenomenon results from the interface structure and the change of van de Waals force between interfaces. The introduction of nitrogen atoms causes the lattice of graphene to distort, which results in the formation of local incommensurate state, thus reducing the interfacial potential barrier and friction. However, the van der Waals force between nitrogen atom and carbon atom between layers is stronger than that between carbon atoms and carbon atoms, which causes the friction to increase. When the doping ratio is low or high, lattice distortion plays more important role. The friction of N-doped graphene shows much smaller increase with load than that of ideal graphene, which indicates that the N-doped graphene possesses a better performance under high load. When the interface structure is in an incommensurate state, the introduction of nitrogen atoms shows slight influence on lattice mismatch, therefore, the change of atomic type plays a dominant role in determining the friction between interfaces, which goes up with the increase of N-doping ratio. When the substrate is graphene with vacancy defects, the value of friction between interfaces is larger than the ideal graphene substrate or N-doped graphene substrate, which indicates that the doping of nitrogen atoms has positive effect on reducing the friction of graphene with defects.

Comment on ‘Out-of-equilibrium Frenkel–Kontorova model’ (Imparato A 2021 J. Stat. Mech. 013214)

We explain the ‘phases’ of a Frenkel–Kontorova chain of atoms in a different way to the commented article. We reject the decision of states of the chain into commensurate and incommensurate states introduced by Aubry.

Tri-hexagonal charge order in kagome metal CsV3Sb5 revealed by 121Sb nuclear quadrupole resonance

We report 121Sb nuclear quadrupole resonance (NQR) measurements on kagome superconductor CsV3Sb5 with T c = 2.5 K. 121Sb NQR spectra split after a charge density wave (CDW) transition at 94 K, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between 91 K and 94 K manifests that it is a first order phase transition. The CDW order exhibits tri-hexagonal deformation with a lateral shift between the adjacent kagome layers, which is consistent with 2 × 2 × 2 superlattice modulation. The superconducting state coexists with CDW order and shows a conventional s-wave behavior in the bulk state.

Orbitally selective Mott phase in electron-doped twisted transition metal-dichalcogenides: A possible realization of the Kondo lattice model

Moir\'e superpotentials in two-dimensional materials allow unprecedented control of the ratio between kinetic and interaction energy. By this they pave the way to study a wide variety of strongly correlated physics under a new light. In particular, the transition-metal dichalcogenides (TMDs) are promising candidate ``quantum simulators'' of the Hubbard model on a triangular lattice. Indeed, Mott and generalized Wigner crystals have been observed in such devices. Here we theoretically propose to extend this model into the multiorbital regime by focusing on electron-doped systems at filling higher than 2. As opposed to hole bands, the electronic bands in TMD materials include two, nearly degenerate species, which can be viewed as two orbitals with different effective mass and binding energy. Using realistic band-structure parameters and a slave-rotor mean-field theory, we find that an orbitally selective Mott (OSM) phase can be stabilized over a wide range of fillings, where one band is locked in a commensurate Mott state, while the other remains itinerant with variable density. This scenario thus realizes the basic ingredients in the Kondo lattice model: a periodic lattice of localized magnetic moments interacting with metallic states. We also discuss possible experimental signatures of the OSM state.