Field-driven Phase Research Articles

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.

Superconductivity can occur under conditions approaching broken-symmetry parent states1. In bilayer graphene, the twisting of one layer with respect to the other at 'magic' twist angles of around 1 degree leads to the emergence of ultra-flatmoiré superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics2-5, notably superconductivity, which emerges close to interaction-induced insulating states6,7. Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin-valley degenerate flat conduction and valence bands-that is, at moiré band filling factors ν=0,±1,±2,±3. At ν≈-2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν=0 and ν=±1 insulating states. Notably, at ν=±1 we find states with non-zero Chern numbers. For ν=-1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moiré flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties.

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

ABSTRACTThe fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.

Ising versus Potts criticality in low-temperature magnetothermodynamics of a frustrated spin- 12 Heisenberg triangular bilayer

Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. A description based on the effective Ising model implies that the frustrated Heisenberg triangular bilayer with the ferromagnetic interdimer coupling displays in a zero-temperature magnetization curve discontinuous magnetization jump, which is reduced upon increasing of temperature until a continuous field-driven phase transition from the Ising universality class is reached at a certain critical temperature. The frustrated Heisenberg triangular bilayer with the antiferromagnetic interdimer coupling contrarily exhibits multistep magnetization curve with intermediate plateaus at one-third and two-thirds of the saturation magnetization, whereas discontinuous magnetization jumps observable at zero temperature change to continuous field-driven phase transitions from the universality class of three-state Potts model at sufficiently low temperatures. Exact results and Monte Carlo simulations of the effective Ising model are confronted with full exact diagonalization data for the Heisenberg triangular bilayer in order to corroborate these findings.

Decoupling Mesoscale Functional Response in PLZT across the Ferroelectric-Relaxor Phase Transition with Contact Kelvin Probe Force Microscopy and Machine Learning.

Relaxor ferroelectrics exhibit a range of interesting material behavior, including high electromechanical response, polarization rotations, as well as temperature and electric field-driven phase transitions. The origin of this unusual functional behavior remains elusive due to limited knowledge on polarization dynamics at the nanoscale. Piezoresponse force microscopy and associated switching spectroscopy provide access to local electromechanical properties on the micro- and nanoscale, which can help to address some of these gaps in our knowledge. However, these techniques are inherently prone to artefacts caused by signal contributions emanating from electrostatic interactions between tip and sample. Understanding functional behavior of complex, disordered systems like relaxor materials with unknown electromechanical properties therefore requires a technique that allows distinguishing between electromechanical and electrostatic response. Here,contact Kelvin probe force microscopy (cKPFM) is used to gain insight into the evolution of local electromechanical and capacitive properties of a representative relaxor material lead lanthanum zirconate across the phase transition from a ferroelectric to relaxor state. The obtained multidimensional data set was processed using an unsupervised machine learning algorithm to detect variations in functional response across the probed area and temperature range. Further analysis showed the formation of two separate cKPFM response bands below 50 °C, providing evidence for polarization switching. At higher temperatures only one band is observed, indicating an electrostatic origin of the measured response. In addition, the junction potential difference,which was extracted from the cKPFM data,becomes independent of the temperature in the relaxor state. The combination of this multidimensional voltage spectroscopy technique and machine learning allows to identify the origin of the measured functional response and to decouple ferroelectric from electrostatic phenomena necessary to understand the functional behavior of complex, disordered systems like relaxor materials.

Signatures of low-energy fractionalized excitations in α−RuCl3 from field-dependent microwave absorption

Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $\alpha$-RuCl$_3$ over a wide range of frequencies, magnetic fields, and temperatures, covering in particular the vicinity of the field-driven quantum phase transition where long-range magnetic order disappears. In addition to conventional gapped magnon modes we find a highly unusual broad continuum characteristic of fractionalization which -- most remarkably -- extends to energies below the lowest sharp mode and to temperatures significantly higher than the ordering temperature, and develops a gap of a nontrivial origin in strong magnetic fields. Our results unravel the signatures of fractionalized excitations in $\alpha$-RuCl$_3$ and pave the way to a more complete understanding of the Kitaev spin liquid and its instabilities.

Magnetization processes and quantum entanglement in a spin-1/2 Ising-Heisenberg chain model of a heterotrimetallic Fe-Mn-Cu coordination polymer

Abstract We introduce and exactly solve a spin-1/2 Ising-Heisenberg chain that captures some relevant aspects of the heterotrimetallic coordination compound [ Cu II Mn II ( L 1 )] [ Fe III (bpb)(CN)2] · ClO 4 · H 2 O to be further abbreviated as Fe-Mn-Cu. The magnetic backbone of the coordination polymer Fe-Mn-Cu forms a regular alternation of Fe3+ and Mn2+ ions, whereas Cu 2 + ions are laterally attached to Mn2+ ions. The exchange coupling between Fe3+and Mn2+ ions is assumed to be Ising-like, while the exchange coupling between Cu 2 + and Mn2+ ions is assumed to be an anisotropic XXZ Heisenberg interaction. The gyromagnetic factors of all three metal ions are adjusted so as to obtain proper magnetic moment of individual metal ions when they are treated as spin-1/2 carriers. The ground-state phase diagram exhibits four distinct phases, whereas two of them display a quantum entanglement between spin states of Cu 2 + and Mn2+ ions. It is shown that the magnetization continuously varies with the magnetic field within two quantum ground states due to the mismatch between the magnetic moments and it also exhibits interesting field-driven phase transitions. The degree of quantum entanglement between the spin states of Cu 2 + and Mn2+ ions is quantified by the concurrence, which unveils that the entanglement becomes optimal at finite magnetic fields within one of the quantum ground states. The concurrence may exhibit non-monotonous dependences on the magnetic field and temperature.

Continuous field-driven phase transition from the Ising universality class of a frustrated spin-1/2 Heisenberg FM/AF square bilayer

Low-temperature magnetothermodynamics of a highly frustrated spin-1/2 Heisenberg square bilayer with the antiferromagnetic intra-dimer interaction and ferromagnetic inter-dimer interaction is governed by localized many-magnon eigenstates, which can be described by the effective ferromagnetic spin-1/2 Ising model on a square lattice. The mapping correspondence implies that the spin-1/2 Heisenberg FM/AF square bilayer displays in a zero-temperature magnetization curve discontinuous magnetization jump, which diminishes upon increasing of temperature until a continuous field-driven phase transition from the Ising universality class is reached at a certain critical temperature. The exact results and Monte Carlo simulations of the effective Ising model are confronted with full exact diagonalization data of the frustrated Heisenberg square bilayer in order to corroborate these findings.

Magnetoentropic signatures of skyrmionic phase behavior in FeGe

We demonstrate that magnetocaloric measurements can rapidly reveal details of the phase diagrams of high-temperature skyrmion hosts, concurrently yielding quantitative latent heats of the field-driven magnetic phase transitions. Our approach addresses an outstanding issue in the phase diagram of the skyrmion host FeGe by showing that dc magnetic anomalies can be explained in terms of entropic signatures consistent with a phase diagram containing a single pocket of skyrmionic order and a Brazovskii transition.

Role of Reversible Phase Transformation for Strong Piezoelectric Performance at the Morphotropic Phase Boundary.

A functional material with coexisting energetically equivalent phases often exhibits extraordinary properties such as piezoelectricity, ferromagnetism, and ferroelasticity, which is simultaneously accompanied by field-driven reversible phase transformation. The study on the interplay between such phase transformation and the performance is of great importance. Here, we have experimentally revealed the important role of field-driven reversible phase transformation in achieving enhanced electromechanical properties using insitu high-energy synchrotron x-ray diffraction combined with 2D geometry scattering technology, which can establish a comprehensive picture of piezoelectric-related microstructural evolution. High-throughput experiments on various Pb/Bi-based perovskite piezoelectric systems suggest that reversible phase transformation can be triggered by an electric field at the morphotropic phase boundary and the piezoelectric performance is highly related to the tendency of electric-field-driven phase transformation. A strong tendency of phase transformation driven by an electric field generates peak piezoelectric response. Further, phase-field modeling reveals that the polarization alignment and the piezoelectric response can be much enhanced by the electric-field-driven phase transformation. The proposed mechanism will be helpful to design and optimize the new piezoelectrics, ferromagnetics, or other related functional materials.

Distinct domain switching in Nd0.05Ce0.95CoIn5 at low and high fields

Nd0.05Ce0.95CoIn5 features a magnetic field-driven quantum phase transition that separates two antiferromagnetic phases with an identical magnetic structure inside the superconducting condensate. Using neutron diffraction we demonstrate that the population of the two magnetic domains in the two phases is affected differently by the rotation of the magnetic field in the tetragonal basal plane. In the low-field SDW-phase the domain population is only weakly affected while in the high-field Q-phase they undergo a sharp switch for fields around the a-axis. Our results provide evidence that the anisotropic spin susceptibility in both phases arises ultimately from spin-orbit interactions but are qualitatively different in the two phases. This provides evidence that the electronic structure is changed at the quantum phase transition, which yields a modified coupling between magnetism and superconductivity in the Q-phase.

Thermodynamic properties of Ba2CoSi2O6Cl2 in a strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet

The search for flat-band solid-state realizations is a crucial issue to verify or to challenge theoretical predictions for quantum many-body flat-band systems. For frustrated quantum magnets flat bands lead to various unconventional properties related to the existence of localized many-magnon states. The recently synthesized magnetic compound Ba$_2$CoSi$_2$O$_6$Cl$_2$ seems to be an almost perfect candidate to observe these features in experiments. We develop a theory for Ba$_2$CoSi$_2$O$_6$Cl$_2$ by adapting the localized-magnon concept to this compound. We first show that our theory describes the known experimental facts and then we propose new experimental studies to detect a field-driven phase transition related to a Wigner-crystal-like ordering of localized magnons at low temperatures.

Thermodynamic behavior and enhanced magnetocaloric effect in a frustrated spin-[formula omitted] Ising-Heisenberg triangular tube

The thermodynamic behavior of an Ising-Heisenberg triangular tube with Heisenberg intra-rung and Ising inter-rung interactions is exactly obtained in an external magnetic field within the framework of the transfer-matrix method. We report rigorous results for the temperature dependence of the magnetization, entropy, pair correlations and specific heat, as well as typical iso-entropic curves. The discontinuous field-driven ground-state phase transitions are reflected in some anomalous thermodynamic behavior as for instance a striking low-temperature peak of the specific heat and an enhanced magnetocaloric effect. It is demonstrated that the intermediate magnetization plateaus shrink in and the relevant sharp edges associated with the magnetization jump round off upon increasing temperature.

The influence of further-neighbor spin-spin interaction on a ground state of 2D coupled spin-electron model in a magnetic field

An exhaustive ground-state analysis of extended two-dimensional (2D) correlated spin-electron model consisting of the Ising spins localized on nodal lattice sites and mobile electrons delocalized over pairs of decorating sites is performed within the framework of rigorous analytical calculations. The investigated model, defined on an arbitrary 2D doubly decorated lattice, takes into account the kinetic energy of mobile electrons, the nearest-neighbor Ising coupling between the localized spins and mobile electrons, the further-neighbor Ising coupling between the localized spins and the Zeeman energy. The ground-state phase diagrams are examined for a wide range of model parameters for both ferromagnetic as well as antiferromagnetic interaction between the nodal Ising spins and non-zero value of external magnetic field. It is found that non-zero values of further-neighbor interaction leads to a formation of new quantum states as a consequence of competition between all considered interaction terms. Moreover, the new quantum states are accompanied with different magnetic features and thus, several kinds of field-driven phase transitions are observed.

Vortex-core order and field-driven supersolidity

Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov-deGennes mean field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a CDW region whose size is determined by the energy cost of the competing phase. The vortices form a lattice whose lattice parameter shrinks with increasing flux. Eventually, their charge-ordered vortex cores overlap, leading to a field-driven coexistence phase exhibiting both macroscopic charge order and superconductivity -- a `supersolid'. Ultimately, superconductivity disappears via a first-order phase transition into a purely charge ordered state. We construct a phase diagram containing these multiple ordered states, using $t'$, the next-nearest neighbour hopping, to tune the competition between phases.

Relaxation dynamics of modulated magnetic phases in the skyrmion host GaV4S8 : An ac magnetic susceptibility study

We report on the slow magnetization dynamics observed upon the magnetic phase transitions of GaV4S8, a multiferroic compound featuring a long-ranged cycloidal magnetic order and a N\'eel-type skyrmion lattice in a relatively broad temperature range below its Curie temperature. The fundamental difference between GaV4S8 and the chiral helimagnets, wherein the skyrmion phase was first discovered, lies within the polar symmetry of GaV4S8, promoting a cycloidal instead of a helical magnetic order and rendering the magnetic phase diagram essentially different from that in the cubic helimagnets. Our ac magnetic susceptibility study reveals slow relaxation dynamics at the field-driven phase transitions between the cycloidal, skyrmion lattice and field-polarized states. At each phase boundary, the characteristic relaxation times were found to exhibit a strong temperature dependence, starting from the minute range at low temperatures, decreasing to the micro- to millisecond range at higher temperatures.

Magnetic field-driven 3D-Heisenberg-like phase transition in single crystalline helimagnet FeGe

Significant microscopic information about fundamental magnetic interactions of magnetic materials is probed via the critical behavior of paramagnetic-ferromagnetic phase transition. In this work, we demonstrate that the critical behavior of cubic single crystalline FeGe belongs to the isotropic 3D-Heisenberg universality class by measuring the field dependence of magnetic entropy change. The above transition is one of the magnetic field-driven phase transitions but has a feature of the crossover from first- to second-order phase transition. A phenomenological model based on the evolution of magnetic skyrmions was proposed to qualitatively understand the phase transition.

Diversity of quantum ground states and quantum phase transitions of a spin- 12 Heisenberg octahedral chain

The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The model belongs to the class of flat-band systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase and two different spin-liquid phases. If the intra-plaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides an exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifth and three-fifth of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in a vicinity of discontinuous quantum phase transitions.

Magnetic phase transitions and magnetoelastic coupling in S=12 Heisenberg antiferromagnets

We combined magneto-infrared spectroscopy and first-principles calculations to unravel the role of spin-phonon coupling in the vicinity of the magnetic field-driven phase transitions in two chemically similar $S=1/2$ Heisenberg antiferromagnets, ${\mathrm{CuF}}_{2}({\mathrm{H}}_{2}\mathrm{O}){}_{2}$(3-Clpy) and $[\mathrm{Cu}{(\mathrm{pyz})}_{2}({\mathrm{HF}}_{2})]{\mathrm{PF}}_{6}$. This comparison resolves questions about the conditions under which the lattice participates in magnetic-field-driven transitions and, at the same time, provides a way to predict how the lattice is likely to support microscopic spin rearrangements.

Lower Electric Field-Driven Magnetic Phase Transition and Perfect Spin Filtering in Graphene Nanoribbons by Edge Functionalization.

Perfect spin filtering is an important issue in spintronics. Although such spin filtering showing giant magnetoresistance was suggested using graphene nanoribbons (GNRs) on both ends of which strong magnetic fields were applied, electric field controlled spin filtering is more interesting due to much easier precise control with much less energy consumption. Here we study the magnetic/nonmagnetic behaviors of zigzag GNRs (zGNRs) under a transverse electric field and by edge functionalization. Employing density functional theory (DFT), we show that the threshold electric field to attain either a half-metallic or nonmagnetic feature is drastically reduced by introducing proper functional groups to the edges of the zGNR. From the current-voltage characteristics of the edge-modified zGNR under an in-plane transverse electric field, we find a remarkable perfect spin filtering feature, which can be utilized for a molecular spintronic device. Alteration of magnetic properties by tuning the transverse electric field would be a promising way to construct magnetic/nonmagnetic switches.

Ferroelectric domain patterns and domain boundary imprint in the relaxor ferroelectric Pb(Zn1/3Nb2/3)O3-9%PbTiO3 as observed by using piezoresponse force microscopy

Piezoresponse force microscopy is used to observe the ferroelectric domain structures of a typical relaxor ferroelectric Pb(Zn1/3Nb2/3)O3-9%PbTiO3. Detailed structural phases are identified by analyzing the domain patterns from the viewpoint of symmetry. Sequential phase transitions, starting from a rhombohedral phase at room temperature to a tetragonal phase via an intermediate monoclinic one and then to a cubic phase, are observed as the temperature is raised to 500 K. The system also undergoes the same phase sequence, from rhombohedral to monoclinic to tetragonal, as a function of the applied electric field. The domain boundaries are found to be spatially fixed and unchanged despite the multiple phase transition sequence that the system undergoes as the temperature is raised. Contrastingly, this imprint effect is missing in the field-driven phase transition sequence. The imprint effect is presumably caused by electric charges on the domain boundaries, possibly arising from local charge imbalances in the relaxor ferroelectric.