Spin Correlation Length Research Articles

The interplay of topology and antiferromagnetic order in two-dimensional van der Waals crystals of (Ni x Fe1−x )2P2S6

The Mermin–Wagner theorem forbids spontaneous symmetry breaking of spins in one/two-dimensional (2D) systems at a finite temperature and rules out the stabilization of this ordered state. However, it does not apply to all types of phase transitions in low dimensions, such as the topologically ordered phase rigorously shown by Berezinskii–Kosterlitz–Thouless (BKT) and experimentally realized in very limited systems such as superfluids and superconducting thin films. Quasi-2D van der Waals magnets provide an ideal platform to investigate the fundamentals of low-dimensional magnetism. We explored the quasi-2D honeycomb antiferromagnetic single crystals of (Ni x Fe1−x )2P2S6 (x = 1, 0.7, 0.5, 0.3, and 0) using in-depth temperature-dependent Raman measurements supported by first-principles calculations of the phonon frequencies. Quite surprisingly, we observed renormalization of the phonon modes much below the long-range magnetic ordered temperature attributed to the topological ordered state, namely the BKT phase, which is also found to change as a function of doping. The extracted critical exponent of the order-parameter (spin–spin correlation length, ξ(T) ) evinces the signature of a topologically active state driven by vortex–antivortex excitations. As a function of doping, a tunable transition from paramagnetic to antiferromagnetic ordering is shown via phonons reflected in the strong renormalization of the self-energy parameters of the Raman active phonon modes. The extracted exchange parameter (J) is found to vary by ∼100% by increasing the value of doping, ranging from ∼6 meV (for x = 0.3) to 13 meV (for x = 1).

Anomalous finite-size effect on the magnetostructural transition in CrN

We report a systematic investigation of the finite-size effect on magnetostructural transition in CrN based on a series of nanoparticle samples with various sizes prepared by a high-pressure method, leading to the discovery of anomalous critical behaviors near transition, especially for spin correlation length. Such critical anomalies are presumably attributed to the strong spin-lattice coupling in this nitride, because the spin correlation of fluctuation can be greatly affected by the concurrent structural distortion. Using the conventional Gibbs-Thomson theorem and size-dependent effect, the scaling relationship between transition temperature and spin correlation length is deduced by involving a term of the transition-induced volume change that rationalizes the role that the lattice degree of freedom played during magnetic ordering. A phenomenological model is also established for understanding the kinetics and dynamics of magnetic fluctuation at transition in a finite-size system. In addition, our results also show that CrN nanoparticles possess a compressed surface shell, which can be described by Laplace pressure, obeying a unique $\frac{1}{{d}^{1.8}}$ finite-size scaling law.

DMRG analysis of magnetic order in the zigzag edges of hexagonal CrN nanoribbons

We investigate the finite-temperature magnetic order at the edges of hexagonal CrN nanoribbons by using density functional theory combined with the density matrix renormalization group (DMRG) method. Moreover, the spin-dependent transport in nanoribbons is calculated within the semiclassical Boltzmann transport theory. We find that the zigzag edges have lower energy with respect to armchair edges. The zigzag edges of CrN nanoribbon show half-metallic electronic character, which is the same as for the two-dimensional (2D) monolayer. The localized electronic states on the zigzag edges reduce the electronic band gap energy for spin-down electrons. The ab initio electronic results are mapped into an effective 1D Heisenberg spin model up to the next-nearest-neighbor exchange interaction term. For zigzag ribbons, the nearest-neighbor and next-nearest-neighbor magnetic exchange are around 10--12 and $\ensuremath{-}2$ to 0 $\text{meV}/\text{Cr}\phantom{\rule{4.pt}{0ex}}\text{atom}$, respectively. The finite spin correlation length in 1D nanoribbons drops sharply to zero with temperature. The absence of long-range spin correlations at the edges is a practical drawback for future room temperature 2D spintronic devices. The maximally localized Wannier functions are used for band interpolation and spin-dependent transport calculations by using the semiclassical Boltzmann equation. We show that the zigzag edges of CrN are a perfect spin filter under both electron and hole doping.

Classical triangular lattice antiferromagnetic Ising model as a free-fermion/superconductor system

We present a treatment of the triangular lattice antiferromagnetic Ising model (TAFIM) based on a small number of elementary ideas common to statistical and solid-state physics. The TAFIM is represented as a reduced BCS model in one space, one (imaginary) time dimension. The representation is approximate for nonzero temperature, but allows quick derivation of asymptotically exact thermodynamic functions, and the divergence of the spin–spin correlation length. The fermionic representation is exact at zero temperature. We demonstrate the existence of a two-dimensional continuum of zero-temperature equilibrium macrostates characterized by satisfied bond fractions of the three different orientations, and calculate their entropy densities.

Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet.

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2}. At zero field, a transition to long-range order occurs at 1.38K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J^{'}/k_{B}≈1 mK. Because of the moderate intralayer exchange coupling of J/k_{B}=6.8 K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J^{'} only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum MonteCarlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

Long-lived solitons and their signatures in the classical Heisenberg chain.

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with ln(1+S_{i}·S_{j}) interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

Magnetic structure and spin fluctuations in the colossal magnetoresistance ferrimagnet Mn3Si2Te6

The ferrimagnetic insulator Mn3Si2Te6, which features a Curie temperature Tc at 78 K and a delicate yet consequential magnetic frustration, exhibits colossal magnetoresistance (CMR) when the magnetic field is applied along the magnetic hard axis, surprisingly inconsistent with existing precedents [Y. Ni, H. Zhao, Y. Zhang et al. Phys. Rev. B 103, L161105 (2021)]. This discovery motivates a thorough single-crystal neutron diffraction study in order to gain insights into the magnetic structure and its hidden correlation with the new type of CMR. Here we report a noncollinear magnetic structure below the Tc where the moments lie predominantly within the basal plane but tilt toward the c axis by ~10o at ambient conditions. A substantial magnetic diffuse scattering decays slowly and persists well above the Tc. The evolution of the spin correlation lengths agrees well with the electrical resistivity, underscoring the role of spin fluctuation contributing to the magnetoresistivity near the transition. Application of magnetic field along the c axis, renders a swift occurrence of CMR but only a slow tilting of the magnetic moments toward the c axis. The unparalleled changes indicate a non-consequential role of magnetic polarization.

Disorder effects on hot spots in electron-doped cuprates

Antiferromagnetic fluctuations in two dimensions cause a decrease in spectral weight at so-called hot spots associated with the pseudogap in electron-doped cuprates. In the $2\text{D}$ Hubbard model, these hot spots occur when the Vilk criterion is satisfied, namely, when the spin correlation length exceeds the thermal de Broglie wavelength. Using the two-particle self-consistent approach, here we show that this criterion may be violated near the antiferromagnetic quantum critical point when sufficient disorder is added to the model. Static disorder decreases inelastic scattering, in contradiction with Matthiessen's rule, leading to a shift in the position of the quantum critical point and a modification of the conditions for the appearance of hot spots. This opens the road to a study of the interplay between disorder, antiferromagnetic fluctuations, and superconductivity in electron-doped cuprates.

Phonon, magnon and magnetic properties of Cu‐doped NiO nanostructures

AbstractWe have extensively studied the phonon, magnon and magnetic properties of copper (Cu)‐doped nanocrystalline nickel(II) oxide (NiO) using room‐temperature Raman spectroscopy. The required nanomaterials were synthesized using a simple sol–gel method. The phonon modes of NiO nanoparticles have been observed in a large background of magnon excitations, and the wavenumbers of phonon modes were deviated from the theoretical predictions due to the phonon–magnon interaction. The variations of magnon excitations with the Cu doping concentrations were investigated based on reduced spin correlation length and superexchange interaction. The two‐magnon (2M) excitations were suppressed and blue shifted with Cu doping concentration indicating the variations in the magnetic behaviour. The modification of antiferromagnetic nature and the formation of multiphase magnetic properties of NiO nanoparticles were investigated using a vibrating sample magnetometer (VSM) and discussed in detail. The variations in the phonon and magnon excitations can be used to probe the magnetic nature and spintronic applications of NiO nanoparticles.

Dissipationless spin current generation in a Kitaev chiral spin liquid

$\alpha$-RuCl$_3$ is a promising candidate material for the Kitaev spin liquid state where the half quantization of the thermal Hall effect, suggesting a topological character, has been observed. However, its relation to the existence of chiral Majorana fermions, which is predicted from the theory of the Kitaev model, is still under debate. Here we propose a more direct signature of a chiral Majorana edge mode which emerges in a universal scaling of the Drude weight of the edge spin Seebeck effect in the Kitaev model. Moreover, the absence of backscatterings in the chiral edge mode results in the generation of a dissipationless spin current in spite of an extremely short spin correlation length close to a lattice constant in the bulk. This result is not only experimentally observable, but also opens a way towards spintronics application of Kitaev materials. In contrast to magnetically ordered systems, a Kitaev spin liquid state is stable even in the atomic scale and makes it possible to fabricate a highly integrated device with substantial efficiency to generate a spin current. This proposal for using $\alpha$-RuCl$_3$ as a nano-scale device will pioneer Kitaev spintronics.

Probing the magnetic polaron state in the ferromagnetic semiconductor HgCr2Se4 with muon-spin spectroscopy and resistance-fluctuation measurements

Combined resistance noise and muon-spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements of the ferromagnetic semiconductor ${\mathrm{HgCr}}_{2}{\mathrm{Se}}_{4}$ suggest a degree of magnetoelectric coupling and provide evidence for the existence of isolated magnetic polarons. These form at elevated temperatures and undergo a percolation transition with a drastic enhancement of the low-frequency $1/f$-type charge fluctuations at the insulator-to-metal transition at $\ensuremath{\sim}95--98\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in the vicinity of the magnetic ordering temperature ${T}_{\mathrm{C}}\ensuremath{\sim}105--107\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Upon approaching the percolation threshold from above, the strikingly unusual dynamics of a distinct two-level fluctuator superimposed on the $1/f$ noise can be described by a slowing down of the dynamics of a nanoscale magnetic cluster, a magnetic polaron, when taking into account an effective radius of the polaron depending on the spin correlation length. Coinciding temperature scales found in $\ensuremath{\mu}\mathrm{SR}$ and noise measurements suggest changes in the magnetic dynamics over a wide range of frequencies and are consistent with the existence of large polarized and domain-wall-like regions at low temperatures, that result from the freezing of spin dynamics at the magnetic polaron percolation transition.

Structure and Magnetism of Few-Layer Nanographene Clusters in Carbon Microspheres

The solid-phase pyrolysis method was used to synthesize carbon microspheres, consisting of clusters of few-layer nanographene and amorphous carbon. Powders of metal-free phthalocyanine and polyethylene served as precursors of the synthesized carbon microspheres. The pyrolysis products of metal-free phthalocyanine samples SPc(700) and SPc(900) contained 4 and 1 atom % nitrogen, respectively, replacing carbon in the graphene lattice in pyrrolic and pyridinic coordination. There are no impurity nitrogen atoms in the products of the pyrolysis of polyethylene. The SPc(700) sample showed strong paramagnetism with a concentration of paramagnetic centers of ∼5 × 1019 spin g–1 and a temperature-independent diamagnetism susceptibility of χDia = −1 × 10–6 emu g–1 Oe–1. In a temperature range of 5–300 K, ferromagnetism was also revealed with a temperature dependence similar to that of ferromagnetic cluster spin glasses, with maximum saturation magnetization, MSFM = 3 × 10–2 emu g–1, and coercive force, Hc = 400 Oe, at Tsg = 25 K. It was shown that the ferromagnetism in the SPc(700) sample is due to π(p)-electrons of zigzag-type edge states as well as nitrogen impurity atoms. The experimental results are interpreted based on the temperature dependence of the spin correlation length. It was revealed that the temperature dependence of the integral of the magnetic resonance absorption intensity closely resembles the temperature behavior of the saturation magnetization of the ferromagnetic component.

Spin susceptibilities in magnetic type-I and type-II Weyl semimetals

We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation (RPA) method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $\gamma$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to type-II. The lower temperature, the sharper is the drop in $U_c$ at the critical point between them. The variation of $U_c$ with a slight doping near half-filling is also studied. It is generally found that these Weyl systems show a strongly anisotropic spin response with an enhanced doubly degenerate transverse susceptibility perpendicular to tilt direction, inherited from $\mathcal{C}_{4z}$ rational symmetry of bare Hamiltonian, but with the longitudinal response suppressed with respect to that. For small tilts $\gamma$ and strong enough interaction, we find two degenerate ordering patterns with spin order orthogonal to the tilt direction but much shorter spin correlation length parallel to the spin direction. With increasing the tilt, the system develops instabilities with respect to in-plane magnetic orders with wavevector $(0,\pi, q_z)$ and $(\pi,0, q_z)$, with $q_z$ increasing from 0 to $\pi$ before the transition to a type-II Weyl semimetal is reached. These results indicate a greater richness of magnetic phases in correlated Weyl semimetals that also pose challenges for precise theoretical descriptions.

Classical many-body chaos with and without quasiparticles

We study correlations, transport and chaos in a Heisenberg magnet as a classical model many-body system. By varying temperature and dimensionality, we can tune between settings with and without symmetry breaking and accompanying collective modes or quasiparticles. We analyse both conventional and out-of-time-ordered spin correlators (`decorrelators') to track the spreading of a spatiotemporally localised perturbation -- the wingbeat of the butterfly -- as well as transport coefficients and Lyapunov exponents. We identify a number of qualitatively different regimes. Trivially, at $T=0$, there is no dynamics at all. In the limit of low temperature, $T=0^+$, integrability emerges, with infinitely long-lived magnons; here the wavepacket created by the perturbation propagates ballistically, yielding a lightcone at the spin wave velocity which thus subsumes the butterfly velocity; inside the lightcone, a pattern characteristic of the free spin wave spectrum is visible at short times. On top of this, residual interactionslead to spin wave lifetimes which, while divergent in this limit, remain finite at any nonzero $T$. At the longest times, this leads to a `standard' chaotic regime; for this regime, we show that the Lyapunov exponent is simply proportional to the inverse spin-wave lifetime. Visibly strikingly, between this and the `short-time' integrable regimes, a scarred regime emerges: here, the decorrelator is spatiotemporally highly non-uniform, being dominated by rare and random scattering events seeding secondary lightcones. As the spin correlation length decreases with increasing $T$, the distinction between these regimes disappears and at high temperature the previously studied chaotic paramagnetic regime emerges. For this, we elucidate how, somewhat counterintuitively, the ballistic butterfly velocity arises from a diffusive spin dynamics.

Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice

Within the tensor network framework, the (positive) thermal density operator can be approximated by a double layer of infinite Projected Entangled Pair Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the thermal properties of the spin-1/2 Heisenberg model on the square lattice, we introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based Trotter-Suzuki decomposition of the imaginary-time evolution operator. A variational optimization is performed on the plaquettes, using a full (for $D=4$) or simple (for $D=7$) environment obtained from the single-site Corner Transfer Matrix Renormalization Group fixed point. The method is benchmarked by a comparison to quantum Monte Carlo in the thermodynamic limit. Although the iPEPO spin correlation length starts to deviate from the exact exponential growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various observables turns out to be quite accurate once plotted w.r.t the inverse correlation length. We also find that a direct $T=0$ variational energy optimization provides results in full agreement with the $\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the imaginary-time evolution procedure. Extension of the method to frustrated models is described and preliminary results are shown.

Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks

In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigenequation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meet at a multicritical point from which a deconfinement crossover line extends into the disordered phase.

Local distributions of the 1D dilute Ising model

The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

Defect induced ferromagnetism in NiO nanocrystals: Insight from experimental and DFT+U study

We investigate the defects induced magnetic properties of NiO nanocrystals prepared by mechanical alloying ball milling process. The average crystallite size reduces to ∼12nm after 40 hours of milling but the face centered cubic structure is stable both in pure and milled NiO powders. The unmilled pure NiO is anti-ferromagnetic in nature, whereas the as-milled nanoparticles are ferromagnetic at room temperature with saturation magnetization reaching a maximum of 0.85 emu/g. X-ray photoelectrons spectroscopy (XPS) shows two distinct peaks at 854.2 and 856.1 eV specifically related to the typical Ni-O bonds from Ni2+ and Ni3+ respectively. This is clearly supports the presence of non-stoichiometry in the milled samples due to decrease in Ni2+-O2−-Ni2+ spin correlation length caused by defects. These defects and crystallinity are characterized by Raman spectra which shows that the two-magnon band disappears, one-phonon (1P) longitudinal optical (LO) band broadens, two-phonon (2P) LO band exhibits red-shift and disappears eventually with decreasing of particle size. Magnetic hysteresis (M-H) loops reveals the ferro-magnetic nature of NiO nanocrystals. Considering these defects, we have also investigated the electronic and magnetic properties systematically within the framework of density functional theory. Our results suggest that the vacancies created by only oxygen as well as both nickel and oxygen are largely responsible for ferro-magnetism in nanoscale NiO powders.

Hubbard model on the honeycomb lattice: From static and dynamical mean-field theories to lattice quantum Monte Carlo simulations

We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- \textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.

Emergence of pseudogap from short-range spin-correlations in electron-doped cuprates

Complex electron interactions underlie the electronic structure of several families of quantum materials. In particular, the strong electron Coulomb repulsion is considered the key ingredient to describing the emergence of exotic and/or ordered phases of quantum matter, from high-temperature superconductivity to charge- and magnetic-order. However, a comprehensive understanding of fundamental electronic properties of quantum materials is often complicated by the appearance of an enigmatic partial suppression of low-energy electronic states, known as the pseudogap. Here we take advantage of ultrafast angle-resolved photoemission spectroscopy to unveil the temperature evolution of the low-energy density of states in the electron-doped cuprate Nd2-xCexCuO4, an emblematic system where the pseudogap intertwines with magnetic degrees of freedom. Using an optical excitation we drive the electronic system across the pseudogap onset temperature T*, and we report the direct relation between the momentum-resolved pseudogap spectral features and the spin-correlation length with a remarkable sensitivity. This transient approach, corroborated by mean-field model calculations, allows us to establish the pseudogap in electron-doped cuprates as a precursor to the incipient antiferromagnetic order even when long-range antiferromagnetic correlations are not established, as in the case of optimal doping.