2D XY Research Articles

MXene Fe2C as a promising candidate for the 2D XY ferromagnet

Monolayer Fe2C is expected to possess strong electronic correlations, which can significantly contribute to electronic and magnetic properties. In this study we consider electronic and magnetic properties of MXene Fe2C within the DFT+DMFT approach. We establish the existence of local magnetic moments in this compound, characterized by sufficiently long lifetime of fs. We also calculate exchange interaction parameters accounting for electronic correlations using the recently developed approach for paramagnetic phase. At low temperatures, we obtain the strongest exchange interaction 11 meV between next nearest neighboring Fe atoms, located above (or below) the carbon plane, and the subleading interaction 6 meV between the next to next nearest neighboring atoms, located across the carbon plane. The resulting dependence of the Berzinskii–Kosterlitz–Thouless (BKT) and Curie temperatures on magnetic anisotropy is obtained. The BKT temperature for the pristine Fe2C is K, which makes this compound a good candidate for the two-dimensional ferromagnet with XY anisotropy.

Rational design of a two-dimensional high-temperature ferromagnet from HCP cobalt.

Cobalt has the highest Curie temperature (Tc) among the elemental ferromagnetic metals and has a hexagonal close-packed (HCP) structure at room temperature. In this study, HCP Co was thinned to the thickness of several (n) unit cells along the c-axis and then passivated by halogen atoms, thus being named Co2nX2 (X = F, Cl, Br and I). For Co2X2 and Co3X2, all of them are not only kinetically but also thermodynamically stable from the viewpoint of the phonon spectra and molecular dynamics. Similar to HCP Co, two-dimensional (2D) Co2F2, Co2Cl2 and Co3X2 (X = Cl, Br and I) are still ferromagnetic metals within the Stoner model but Co2X2 (X = Br and I) is a ferromagnetic half-metal with the coexistence of the metallic behavior for one spin and the insulating behavior for the other spin. Taking into account the spin-orbital coupling (SOC), the easy-magnetization axis is within the plane where the magnetization is isotropic, making it look like a 2D XY magnet. Applying a critical biaxial strain could lead to an easy-magnetization axis changing from the in-plane to the out-of-plane direction. Finally, we use classical Monte Carlo simulations to estimate the Curie temperature (Tc) which is as high as 957 and 510 K for Co2F2 and Co2Cl2, respectively, because of the strong direct exchange interaction. Different from being obtained by mechanical or liquid exfoliation from van der Waals layered structures, our study opens up new possibilities to search for novel 2D ferromagnets from the elemental ferromagnets and provides opportunities for realizing realistic ultra-thin spintronic devices.

Exploitable magnetic anisotropy and half-metallicity controls in multiferroic van der Waals heterostructure

Two-dimensional (2D) XY ferromagnets have drawn pronounced interest in recent years, but the characteristic of easy-plane magnetization restricts their application in spintronics to some extent. Here, we propose a general strategy for constructing multiferroic van der Waals heterostructures, aiming to achieve electrical control over the magnetic anisotropy in 2D XY ferromagnets. The validity of this strategy is verified by the heterostructure composed of ferromagnetic VBi2Te4 and ferroelectric In2Se3 monolayers. By manipulating the polarized states of In2Se3, the VBi2Te4 can be reversibly transformed between 2D XY and Heisenberg ferromagnets, characterized by the switching of easy magnetization axis between in-plane and out-of-plane directions. More interestingly, accompanied by the changes in magnetic anisotropy, the VBi2Te4 also demonstrates a phase transition from a semiconductor to a half-metal state, which can be ascribed to the band alignment and interfacial charge transfer. The switchable magnetic and electronic properties enable the heterostructure to be utilized in nonvolatile memory and logic devices. Additionally, the half-metallicity and magnetocrystalline anisotropy energy of the heterostructure can be effectively tuned by biaxial strain. These findings not only pave the way for electrically nonvolatile control of 2D XY ferromagnet, but also facilitate the development of interfacial magnetoelectric physics and applications.

Moving from continuous to discrete symmetry in the 2D XY model

Moving from continuous to discrete symmetry in the 2D XY model

Widening of working temperature range in Mn5-xCuxGe3 (x = 0.1 and 0.3) magnetocaloric compounds by compositional tuning

This study presents the effect of Cu doping on the fundamental properties, magnetocaloric effect, and critical behavior of Mn5Ge3 system. Mn5-xCuxGe3 compounds with x = 0.1 and 0.3 conform D88-hexagonal structure. The unit cell volume decreases, and MnI-MnI distance increases with Cu content. This modifies the exchange interaction and impacts Curie temperature and saturation magnetization accordingly. The critical exponents β and γ of x = 0.1 compound are of 3D Ising class, while the x = 0.3 compound shows non-conventional behavior with its γ lying within the 3D Ising framework and β lying between 3D XY and Heisenberg classes. Both the compounds have extended-type spin interactions, and the decay of the exchange integrals has been calculated. Mn5-xCuxGe3 compounds clearly outperform most materials of Mn5Ge3 class in terms of the magnetocaloric effect. They show an appreciable reversible isothermal entropy change across a wide temperature span with a large relative cooling power near the room temperature effect. These compounds can be combined with other suitable Mn5Ge3 materials and used in ‘active magnetic regenerative (AMR)’ systems as layered refrigerants for more efficient magnetocaloric cooling.

Vortex Glass-Vortex Liquid Transition in BaFe2(As1-xPx)2 and CaKFe4As4 Superconductors from Multi-Harmonic AC Magnetic Susceptibility Studies.

For practical applications of superconductors, understanding the vortex matter and dynamics is of paramount importance. An important issue in this context is the transition of the vortex glass, which is a true superconducting phase, into a vortex liquid phase having a linear dissipation. By using multi-harmonic susceptibility studies, we have investigated the vortex glass-vortex liquid phase transitions in CaKFe4As4 and BaFe2(As0.68P0.32)2 single crystals. The principle of our method relates the on-set of the third-harmonic susceptibility response with the appearance of a vortex-glass phase in which the dissipation is non-linear. Similar to the high-critical temperature cuprate superconductors, we have shown that even in these iron-based superconductors with significant lower critical temperatures, such phase transition can be treated as a melting in the sense of Lindemann's approach, considering an anisotropic Ginzburg-Landau model. The experimental data are consistent with a temperature-dependent London penetration depth given by a 3D XY fluctuations model. The fitting parameters allowed us to extrapolate the vortex melting lines down to the temperature of liquid hydrogen, and such extrapolation showed that CaKFe4As4 is a very promising superconducting material for high field applications in liquid hydrogen, with a melting field at 20 K of the order of 100 T.

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition.

We investigate the critical phenomena emerging from a statistical mechanics model of musical harmony on a three-dimensional (3D) lattice, and the resulting structure of the ordered phase. In this model, each lattice site represents a tone, with nearest neighbors interacting via the perception of dissonance between them. With dissonance assumed to be an octave-wise periodic function of pitch difference, this model is a 3D XY system with the same symmetry and dimensionality as superfluid helium and models of the cosmological axion field. We use numerical simulation to observe a phase transition from disordered sound to ordered arrangements of musical pitches as a parameter analogous to the temperature is quenched towards zero. We observe the divergence of correlation length and relaxation time at the phase boundary, consistent with the critical exponents in similar systems. Furthermore, the quenched low-temperature phase of these systems displays topological defects in the form of vortex strings that thread throughout the system volume. We observe the formation of these vortex strings in accordance with the Kibble-Zurek mechanism, and discuss the structure of these vortex strings in the context of the theory of musical harmony, finding both similarities to established music theory, and uncovering new avenues to explore.

Dynamics of topological defects in the noisy Kuramoto model in two dimensions

We consider the two-dimensional (2D) noisy Kuramoto model of synchronization with short-range coupling and a Gaussian distribution of intrinsic frequencies, and investigate its ordering dynamics following a quench. We consider both underdamped (inertial) and over-damped dynamics, and show that the long-term properties of this intrinsically out-of-equilibrium system do not depend on the inertia of individual oscillators. The model does not exhibit any phase transition as its correlation length remains finite, scaling as the inverse of the standard deviation of the distribution of intrinsic frequencies. The quench dynamics proceeds via domain growth, with a characteristic length that initially follows the growth law of the 2D XY model, although is not given by the mean separation between defects. Topological defects are generically free, breaking the Berezinskii-Kosterlitz-Thouless scenario of the 2D XY model. Vortices perform a random walk reminiscent of the self-avoiding random walk, advected by the dynamic network of boundaries between synchronised domains; featuring long-time super-diffusion, with the anomalous exponentα= 3/2.

Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition

The Berezinski˘ı-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex–anti-vortex (V–AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model

Phase Transition in the 2D XY Model with 3-Fold Nematic Interactions

In this work the results of the study on a generalization of the XY model with an additional q-fold nematic-like term through Monte Carlo simulations in two dimensions (2D) have been presented. While the conventional 2D XY model has only integer vortexes, the generalized 2D XY model has both integer and non-integer 1/q vortexes, making the phase diagram of the generalized 2D XY model is much richer than that of the conventional 2D XY model. Here, we located the phase transition between the disordered phase (P), the quasi-long-range order phase (F), and the nematic phase (N) for the case of q = 3. We provided the numerical evidence to clarify the N−F phase transition of either the first-ordered or second-ordered phase transition. The results showed that the N−F phase transition is the second-ordered, not the first-order phase transition.

Phase Coherence of Pairs of Cooper Pairs as Quasi-Long-Range Order of Half-Vortex Pairs in a Two-Dimensional Bilayer System.

It is known that the loss of phase coherence of Cooper pairs in two-dimensional superconductivity corresponds to the unbinding of vortex-antivortex pairs with the quasi-long-range order in the order-parameter phase field, described by the Berezinskii-Kosterlizt-Thouless (BKT) transition of a 2D XY model. Here we show that the second-order Josephson coupling can induce an exotic superconducting phase in a bilayer system. By using tensor-network methods, the partition function of the 2D classical model is expressed as a product of 1D quantum transfer operator, whose eigenequation can be solved by an algorithm of matrix product states rigorously. From the singularity shown by the entanglement entropy of the 1D quantum analog, various phase transitions can be accurately determined. Below the BKT phase transition, an interlayer Ising long-range order is established at T_{Ising}, and the phase coherence of both intralayers and interlayers is locked together. For two identical layers, the Ising transition coincides with the BKT transition at a multicritical point. For two inequivalent layers, however, there emerges an intermediate quasi-long-range order phase (T_{Ising}<T<T_{BKT}), where the vortex-antivortex bindings occur in the layer with the larger intralayer coupling, but only half-vortex pairs with topological strings exist in the other layer, corresponding to the phase coherence of pairs of Cooper pairs. So our study provides a promising way to realize the charge-4e superconductivity in a bilayer system.

4D-XY Superfluid Transition and Dissipation in 4He Confined in Nanoporous Media

4He confined in nanoporous Gelsil glass is a unique, strongly correlated Bose system exhibiting quantum phase transition (QPT) by controlling pressure. Previous studies revealed that the QPT occurs with four-dimensional (4D) XY criticality, which appears in the zero-temperature limit of the superfluid density. However, the P–T phase diagram also suggested that the 4D XY nature appears at finite temperatures. Here, we have determined the critical exponent of the superfluid density ρs of 4He in two Gelsil samples that have pore diameter to be about 3 nm, using a newly developed mechanical resonator technique. The critical exponent ζ in the powerlaw fitting ρs ∝ |1 − T/Tc|ζ, where Tc is the superfluid transition temperature, was found to be 1.0 ± 0.1 for all pressures realized in this experiment, 0.1 < P < 2.4 MPa. This value of ζ gives decisive evidence that the finite-temperature superfluid transition belongs to the 4D XY universality class. The emergence of the 4D XY criticality is explained by the existence of many nanoscale superfluid droplets, the so-called localized Bose–Einstein condensates (LBECs), above Tc. Due to the large energy cost for 4He atoms to move between the LBECs, the phase of the LBEC order parameters fluctuates not only in spatial (3D) but imaginary time (+1D) dimensions, resulting in the 4D XY criticality by a temperature near Tc. Since the finite size of the system in the imaginary time dimension Lτ is larger than the pore size, the 4D XY critical phenomenon is observed. In the very vicinity of Tc at which the correlation length exceeds Lτ, there may be a crossover from 4D to 3D XY criticality. Below Tc, macroscopic superfluidity grows in the nanopores of Gelsil by the alignment of the phases of the LBEC order parameters. An excess dissipation peak observed below Tc is well explained by this phase-matching process.

Magnetic transitions with magnetocaloric effects near room temperature related to structural transitions in Y0.9Pr0.1Fe2D3.5 deuteride

The structural and magnetic properties of Y0.9Pr0.1Fe2D3.5 deuteride have been investigated by synchrotron and neutron diffraction, magnetic measurements, and differential scanning calorimetry. Deuterium insertion induces a 23.5% cell volume increase and a lowering of crystal symmetry compared to the cubic C15 Y0.9Pr0.1Fe2 parent compound (Fd-3m SG). The deuteride is monoclinic (P21/c SG) below 330 K and undergoes a first-order transition between 330 and 350 K toward a pseudo-cubic structure (R-3 m SG) with TO–D = 342(2) K. In both structures, the D atoms are located in 96% R2Fe2 and 4% RFe3 tetrahedral interstitial sites (R = Y0.9Pr0.1). The compound is ferromagnetic, accompanied by a magnetostrictive effect below TC = 274 K. The analysis of the critical exponents indicates a second-order type transition with a deviation from the isotropic 3D Heisenberg model toward the 3D XY model. This implies an easy plane of magnetization in agreement with cell parameter variation showing planar magnetic orientation. A weak magnetic peak is even observed at the order–disorder transition with a maximum at 343 K. Magnetic entropy variations are characteristic of direct and inverse magnetocaloric effects at TC and TO–D, respectively.

Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, II: K2CuF4 Phase Transition

AbstractIn Part I of this diptych, we outlined the theory and an analysis methodology for quantitative phase recovery from real-space distortions of Fresnel images acquired in the parallel mode of transmission electron microscopy (TEM). In that work, the properties of the method, termed TEM-differential phase contrast (TEM-DPC), were highlighted through the use of simulated data. In this work, we explore the use of the TEM-DPC technique with experimental cryo-TEM images of a thin lamella of a low-temperature two-dimensional (2D) ferromagnetic material, K2CuF4, to perform two tasks. First, using images recorded below the ordering temperature, we compare the TEM-DPC method with the transport of intensity one for phase recovery and discuss the relative advantages the former has for experimental data. Second, by tracking the induction of the sample as it is driven through a phase transition by heating, we extract estimates for the critical temperature and critical exponent of the order parameter. The value of the latter is consistent with the 2D XY class, raising the prospect that a Kosterlitz–Thoules transition may have occurred.

Defect Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors.

We consider a nonequilibrium extension of the 2D XY model, equivalent to the noisy Kuramoto model of synchronization with short-range coupling, where rotors sitting on a square lattice are self-driven by random intrinsic frequencies. We study the static and dynamic properties of topological defects (vortices) and establish how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition scenario. The nonequilibrium drive breaks the quasi-long-range ordered phase of the 2D XY model into a mosaic of ordered domains of controllable size and results in self-propelled vortices that generically unbind at any temperature, featuring superdiffusion ⟨r^{2}(t)⟩∼t^{3/2} with a Gaussian distribution of displacements. Our work provides a simple framework to investigate topological defects in nonequilibrium matter and sheds new light on the problem of synchronization of locally coupled oscillators.

Signatures for Berezinskii-Kosterlitz-Thouless critical behavior in the planar antiferromagnet BaNi2V2O8

We investigate the critical properties of the spin-$1$ honeycomb antiferromagnet BaNi$_2$V$_2$O$_8$, both below and above the ordering temperature $T_N$ using neutron diffraction and muon spin rotation measurements. Our results characterize BaNi$_2$V$_2$O$_8$ as a two-dimensional (2D) antiferromagnet across the entire temperature range, displaying a series of crossovers from 2D Ising-like to 2D XY and then to 2D Heisenberg behavior with increasing temperature. In particular, the extracted critical exponent of the order parameter reveals a narrow temperature regime close to $T_N$, in which the system behaves as a 2D XY antiferromagnet. Above $T_N$, evidence for Berezinsky-Kosterlitz-Thouless behavior driven by vortex excitations is obtained from the scaling of the correlation length. Our experimental results are in accord with classical and quantum Monte Carlo simulations performed for microscopic magnetic model Hamiltonians for BaNi$_2$V$_2$O$_8$.

Engineering of the XY Magnetic Layered System with Adeninium Cations: Monocrystalline Angle-Resolved Studies of Nonlinear Magnetic Susceptibility.

An original example of modular crystal engineering involving molecular magnetic {CuII[WV(CN)8]}− bilayers and adeninium cations (AdeH+) toward the new layered molecular magnet (AdeH){CuII[WV(CN)8]}·2H2O (1) is presented. 1 crystallizes within the monoclinic C2 space group (a = 41.3174(12), b = 7.0727(3), c = 7.3180(2) Å, β = 93.119(3)°, and V = 2135 Å3). The bilayer topology is based on a stereochemical matching between the square pyramidal shape of CuII moiety and the bicapped trigonal prismatic shape of [WV(μ-CN)5(CN)3], and the separation between bilayers is significantly increased (by ∼50%; from ca. 9.5 to ca. 14.5 Å) compared to several former analogues in this family. This was achieved via a unique combination of (i) a 1D ribbonlike hydrogen bond system {AdeH+···H2O···AdeH+···}∞ exploiting planar water-assisted Hoogsteen···Sugar synthons with (ii) parallel 1D π–π stacks {AdeH+···AdeH+}∞. In-plane 2D XY magnetism is characterized by a Tc close to 33 K, Hc,in-plane = 60 Oe, and Hc,out-of-plane = 750 Oe, high values of in-plane γ critical exponents (γb = 2.34(6) for H||b and γc = 2.16(5) for H||c), and a Berezinskii–Kosterlitz–Thouless (BKT) topological phase transition, deduced from crystal-orientation-dependent scaling analysis. The obtained values of in-plane ν critical exponents, νb = 0.48(5) for H||b and νc = 0.49(3) for H||c, confirm the BKT transition (νBKT = 0.5). Full-range angle-resolved monocrystalline magnetic measurements supported by dedicated calculations indicated the occurrence of nonlinear susceptibility performance within the easy plane in a magnetically ordered state. We refer the occurrence of this phenomenon to spontaneous resolution in the C2 space group, a tandem not observed in studies on previous analogues and rarely reported in the field of molecular materials. The above magneto-supramolecular strategy may provide a novel means for the design of 2D molecular magnetic networks and help to uncover the inherent phenomena.

Studying the low-entropy Mott transition of bosons in a three-dimensional optical lattice by measuring the full momentum-space density

We report on a combined experimental and theoretical study of the low-entropy Mott transition for interacting bosons trapped in a three-dimensional (3D) cubic lattice -- namely, the interaction-induced superfluid-to-normal phase transition in the vicinity of the zero-temperature Mott transition. Our analysis relies on the measurement of the 3D momentum distribution, which allows us to extract the momentum-space density $\rho({\bf k}={\bf 0})$ at the center of the Brillouin zone. Upon varying the ratio between the interaction $U$ and the tunnelling energy $J$ across the superfluid transition, we observe that $\rho({\bf k}={\bf 0})$ exhibits a sharp transition at a value of $U/J$ consistent with the bulk prediction from quantum Monte Carlo. In addition, the variation of $\rho({\bf k}={\bf 0})$ with $U/J$ exhibits a critical behavior consistent with the expected 3D XY universality class. Our results show that the tomographic reconstruction of the momentum distribution of ultracold bosons can reveal traits of the critical behavior of the superfluid transition even in an inhomogeneous trapped system.

Phase-pure two-dimensional FexGeTe2 magnets with near-room-temperature TC

Two-dimensional (2D) ferromagnets with out-of-plane (OOP) magnetic anisotropy are potential candidates for realizing the next-generation memory devices with ultra-low power consumption and high storage density. However, a scalable approach to synthesize 2D magnets with OOP anisotropy directly on the complimentary metal-oxide semiconductor (CMOS) compatible substrates has not yet been mainly explored, which hinders the practical application of 2D magnets. This work demonstrates a cascaded space confined chemical vapor deposition (CS-CVD) technique to synthesize 2D FexGeTe2 ferromagnets. The weight fraction of iron (Fe) in the precursor controls the phase purity of the as-grown FexGeTe2. As a result, high-quality Fe3GeTe2 and Fe5GeTe2 flakes have been grown selectively using the CS-CVD technique. Curie temperature (TC) of the as-grown FexGeTe2 can be up to ∼ 280 K, nearly room temperature. The thickness and temperature-dependent magnetic studies on the Fe5GeTe2 reveal a 2D Ising to 3D XY behavior. Also, Terahertz spectroscopy experiments on Fe5GeTe2 display the highest conductivity among other FexGeTe2 2D magnets. The results of this work indicate a scalable pathway for the direct growth and integration of 2D ternary magnets on CMOS-based substrates to develop spintronic memory devices.

Breathing kagome XY quantum magnet with four-site ring exchange

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.