Spin Order Research Articles

Two-Dimensional Multiferroics with Intrinsic Magnetoelectric Coupling in A-Site Ordered Perovskite Monolayers

The magnetoelectric coupling effect in multiferroics provides a route to realize the control of magnetism by electric field. Here, we demonstrate the coexistence and coupling of ferroelectricity and ferromagnetism in designed A-site ordered perovskite oxide monolayers by combining symmetry analysis and first-principles calculation. These monolayers all exhibit a layered ordering and tilt distortion, and some of them exhibit rotation or Jahn-Teller distortion simultaneously, leading to the emergence of in-plane ferroelectricity. The Mn-based monolayers exhibit robust ferromagnetism, while some monolayers tend to form E-type spin order due to the splitting of the nearest-neighbor exchange interactions. Whether polarization reversal can lead to magnetization reversal depends on the mode of ferroelectric switching, that is, only the ferroelectric switching that reversing the tilt distortion can lead to magnetization reversal. This work demonstrates the feasibility of controlling the direction of magnetization by electric field in the monolayer limit of perovskites.

Evolution of magnetic properties in iron-based superconductor Eu-doped CaFe2As2

This work presents the evolution of magnetic properties of EuxCa1−xFe2As2 (0 ≤ x ≤ 1, ECFA) samples. Unlike the resistivity data, that for magnetic susceptibility χ (T) does not show any clear evidence of the spin density wave (SDW) transition. When the Curie-Weiss contribution is subtracted, a weak anomaly appears at a temperature close to the SDW transition temperature (TSDW) determined from the resistivity data. To understand the magnetic orders arising from Fe-moments and Eu2+ spins order, we have studied the doping dependence of TSDW and Eu2+ antiferromagnetic order TN. It is found that TSDW increases almost linearly with increasing x and remains nearly unchanged above x ∼ 0.4, whereas TN first appears at x ∼ 0.4 and varies almost linearly with further increasing x. These observations suggest that magnetic orders due to two sublattices are coupled to each other. The results discussed here are helpful for understanding the magnetic properties of ECFA and other iron-based superconductors.

Gravitational Faraday effect from on-shell amplitudes

Effects of massive object’s spin on massive-massless 2 → 2 classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter λ/b, where λ is the massless particle’s wavelength and b is the impact parameter. Corrections in λ/b start to appear from mathcal{O} (G2), with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to mathcal{O} (G2) and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin [1] is reproduced by λ/b correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed [2–8], along with the associated shift symmetry [7], and argue that it holds to arbitrary spin order at mathcal{O} (G2) in the massless probe limit.

Display of converse and direct magnetoelectric effect in double perovskite LaYFe2O6

This work reports the simultaneous observation of converse magnetoelectric (CME) and direct magnetoelectric (DME) effects in LaYFe2O6. The structural, magnetic, and magnetoelectric properties of LaYFe2O6, prepared by the sol-gel auto-combustion method and sintered at various temperatures, have been studied. The x-ray powder diffraction study suggests the double perovskite structure with symmetries P21nm (∼90%) and Pbnm (∼10%). The alternate ordering of La and Y ions is confirmed by the neutron powder diffraction (ND) study, which also suggests the antiferromagnetic (AFM) ordering of spins. AFM behavior is also manifested by the magnetic field-dependent magnetization (M) measurement. A higher P21nm phase content is desirable in the context of magnetoelectricity. Magnetic transition (∼700 K) is asserted in the temperature-dependent M measurement. The isothermal magnetization study shows weak ferromagnetism probably due to gradually increasing spin canting with temperature until the transition temperature. The highest CME coefficient (∼2.26 mOe cm/V) as well as DME coefficient (∼0.45 mV/cm Oe) in this material are recorded. True magnetoelectricity for temperature as high as 400 K opens up a new avenue on the playground of magnetoelectric (ME)-based applications.

Elemental excitations in MoI3 one-dimensional van der Waals nanowires

We report the polarization-dependent Raman spectra of exfoliated MoI3, a van der Waals material with a “true one-dimensional” crystal structure that can be exfoliated to individual atomic chains. The temperature evolution of several Raman features reveals an anomalous behavior suggesting a phase transition of magnetic origin. Theoretical considerations indicate that MoI3 is an easy-plane antiferromagnet with alternating spins along the dimerized chains and with inter-chain helical spin ordering. The calculated frequencies of phonons and magnons are consistent with the interpretation of the experimental Raman data. The obtained results shed light on the specifics of the phononic and magnonic states in MoI3 and provide a strong motivation for further study of this unique material with potential for future spintronic applications.

Effect of cobalt substitution on the structural, ferroelectric, and magnetic properties of bismuth ferrite thin films

Epitaxial films of multiferroic BiFe1−xCoxO3 (BFCO) with 0≤x≤0.35 are grown on (001)-oriented SrTiO3 and SrRuO3 buffered SrTiO3 substrates using the pulsed laser deposition technique. The effect of structural transformation from rhombohedral to tetragonal phase with increasing cobalt substitution on the magnetic, electrical, and piezo-/ferroelectric properties is investigated. Piezoresponse force microscopy is used to quantify the coercive voltage from the phase hysteresis loops for different thickness films to investigate the semi-empirical Kay–Dunn scaling law with varying cobalt concentrations. For the rhombohedral structure, a reduction of the coercive voltage is observed with increasing substitution of Fe by Co. The coercive voltage of a 10 nm BFCO (x=0.35) film is found to be 0.63 V, which is 67% lower than that of a pure BiFeO3 (BFO) (1.9 V) film of the same thickness. Cobalt substitution also leads to changes in the magnetic and electrical properties due to modification of spin ordering and reduction of the bandgap, respectively. Further, to validate the experimental results, we have performed theoretical calculations using density functional theory. The theoretical results indicate a reduction in unit cell volume and enhancement in net magnetization can be achieved with cobalt substitution, in agreement with experimental results. Partial Co substitution can, thus, provide a pathway to realize BFO-based nonvolatile magnetoelectric devices with reduced operating voltage.

Parahydrogen-induced polarization and spin order transfer in ethyl pyruvate at high magnetic fields

Nuclear magnetic resonance has experienced great advances in developing and translating hyperpolarization methods into procedures for fundamental and clinical studies. Here, we propose the use of a wide-bore NMR for large-scale (volume- and concentration-wise) production of hyperpolarized media using parahydrogen-induced polarization. We discuss the benefits of radio frequency-induced parahydrogen spin order transfer, we show that 100% polarization is theoretically expected for homogeneous B0 and B1 magnetic fields for a three-spin system. Moreover, we estimated that the efficiency of spin order transfer is not significantly reduced when the B1 inhomogeneity is below ± 5%; recommendations for the sample size and RF coils are also given. With the latest breakthrough in the high-yield synthesis of 1-13C-vinyl pyruvate and its deuterated isotopologues, the high-field PHIP-SAH will gain increased attention. Some remaining challenges will be addressed shortly.

Formation of spin and charge ordering in the extended Hubbard model during a finite-time quantum quench

We investigate the formation of charge and spin ordering by starting from a non-interacting state and studying how it evolves in time under a Hamiltonian with finite electronic interactions. We consider the one-dimensional, half-filled extended Hubbard model, which we solve within time-dependent density matrix renormalization group. By employing linear finite-time quenches in the onsite and nearest-neighbor interactions, we find the existence of impulse, intermediate, and adiabatic regimes of time evolution. For the quenches we analyze, we observe that the adiabatic regime is reached with distinct ramping time scales depending on whether the charge density wave (CDW) or the spin density wave (SDW) is formed. The former needs to be slower than the latter to prevent entangled excited states from being accessed during the quench. More interestingly, in the intermediate regime, we observe an enhancement of the entanglement entropy with respect to its initial value, which precedes the formation of the CDW ordering; a similar enhancement is not seen in the quench towards SDW. Our findings also show that the breaking of the system integrability, by turning on the nearest-neighbor interactions, does not give rise to significant changes in the non-equilibrium behavior within the adiabatic approximation.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.

Adiabatic Passage through Level Anticrossings in Systems of Chemically Inequivalent Protons Incorporating Parahydrogen: Theory, Experiment, and Prospective Applications.

Level anticrossings (LACs) are ubiquitous in quantum systems and have been exploited for spin-order transfer in hyperpolarized nuclear magnetic resonance spectroscopy. This paper examines the manifestations of adiabatic passage through a specific type of LAC found in homonuclear systems of chemically inequivalent coupled protons incorporating parahydrogen (pH2). Adiabatic passage through such a LAC is shown to elicit translation of the pH2 spin order. As an example, with prospective applications in biomedicine, proton spin polarizations of at least 19.8 ± 2.6% on the methylene protons and 68.7 ± 0.5% on the vinylic protons of selectively deuterated allyl pyruvate ester are demonstrated experimentally. After ultrasonic spray injection of a precursor solution containing propargyl pyruvate and a dissolved Rh catalyst into a chamber pressurized with 99% para-enriched H2, the products are collected and transported to a high magnetic field for NMR detection. The LAC-mediated hyperpolarization of the methylene protons is significant because of the stronger spin coupling to the pyruvate carbonyl 13C, setting up an ideal initial condition for subsequent coherence transfer by selective INEPT. Furthermore, the selective deuteration of the propargyl side arm increases the efficiency and polarization level. LAC-mediated translation of parahydrogen spin order completes the first step toward a new and highly efficient route for the 13C NMR signal enhancement of pyruvate via side-arm hydrogenation with parahydrogen.

Evidence for charge and spin density waves in single crystals of La3Ni2O7 and La3Ni2O6

Charge and spin order is intimately related to superconductivity in copper oxide superconductors. To elucidate the competing orders in various nickel oxide compounds are crucial given the fact that superconductivity has been discovered in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ films. Herein, we report structural, electronic transport, magnetic, and thermodynamic characterizations on single crystals of La$_3$Ni$_2$O$_7$ and La$_3$Ni$_2$O$_6$. La$_3$Ni$_2$O$_7$ is metallic with mixed Ni$^{2+}$ and Ni$^{3+}$ valent states. Resistivity measurements yield two transition-like kinks at $\sim$110 and 153 K, respectively. The kink at 153 K is further revealed from magnetization and specific heat measurements, indicative of the formation of charge and spin order. La$_3$Ni$_2$O$_6$ single crystals obtained from topochemical reduction of La$_3$Ni$_2$O$_7$ are insulating and show an anomaly at $\sim$176 K on magnetic susceptibility. The transition-like behaviors of La$_3$Ni$_2$O$_7$ and La$_3$Ni$_2$O$_6$ are analogous to the charge and spin order observed in La$_4$Ni$_3$O$_{10}$ and La$_4$Ni$_3$O$_8$, suggesting charge and spin order is a common feature in the ternary La-Ni-O system with mixed-valent states of nickel.

Solitons in low-dimensional magnets: Elementary excitations with a nontrivial dispersion law

Solitons are known to play the role of elementary excitations for one-dimensional ordered systems, like atomic chains with charge or spin ordering. The main characteristic of solitons is their dispersion relation, dependence of soliton energy on the linear momentum. Topological kink-type solitons are the simplest and most important for the description of many physical properties of one-dimensional magnets. Here we provide a detailed analysis of solitons in some general class of magnets, ferrimagnets with the spin compensation point. The nonlinear spin dynamics of ferrimagnets are examined using a nonlinear sigma-model for the antiferromagnetic vector, which is a generalization of the Landau-Lifshitz equation for ferromagnets and sigma-model for the antiferromagnets. The characteristic features of this equation are governed by the value of the compensation parameter, describing the rate of compensation of spins of sublattices. The dispersion relation for kink-type solitons appears to be quite nontrivial, including periodic dispersion law for continuum model of magnet or the presence of ending point for kink spectrum.

Polarizing insensitive nuclei at ultralow magnetic fields using parahydrogen: A facile route to optimize adiabatic magnetic field sweeps.

Parahydrogen induced polarization (PHIP) provides a powerful tool to enhance inherently weak nuclear magnetic resonance signals, particularly in biologically relevant compounds. The initial source of PHIP is the non-equilibrium spin order of parahydrogen, i.e., dihydrogen, where the two protons make up a singlet spin state. Conversion of this spin order into net magnetization of magnetic heteronuclei, e.g., 13C, provides one of the most efficient ways to exploit PHIP. We propose a facile route to increase the performance of PHIP transfer in experiments with adiabatic sweeps of the ultralow magnetic field. To date, this technique yields the highest efficiency of PHIP transfer, yet, it has been mostly utilized with linear field sweeps, which does not consider the underlying spin dynamics, resulting in sub-optimal polarization. This issue was previously addressed by using the "constant" adiabaticity method, which, however, requires extensive calculations for large spin systems. In this work, the field sweep is optimized by utilizing the field dependence of the average 13C polarization. Both the experimental detection and the numerical simulation of this dependence are straightforward, even for complex multi-spin systems. This work provides a comprehensive survey of PHIP transfer dynamics at ultralow fields for two molecular systems that are relevant for PHIP, namely, maleic acid and allyl pyruvate. The proposed optimization allowed us to increase the resulting 13C polarization in 13C-allyl pyruvate from 6.8% with a linear profile to 8.7% with an "optimal" profile. Such facile optimization routines are valuable for adiabatic experiments in complex spin systems undergoing rapid relaxation or chemical exchange.

Tunable stripe order and weak superconductivity in the Moiré Hubbard model

The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we study the superconducting correlation function and point out the possibility of weak superconductivity.

Enhanced magnetoelectric effect by spin-orbit coupling in M-type hexaferrite

Magnetoelectric (ME) effect triggered by spiral spin orders in various hexaferrites develops both the theory and application of ME coupling. However, the strength of such ME effect is restricted by the small spin-orbit coupling (SOC) of $3d$ electrons in M-type hexaferrite. Here, we introduce the $5d$ element Ir with large SOC into $\mathrm{Sr}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}$. It is found that a low ${\mathrm{Ir}}^{4+}\text{\ensuremath{-}}\mathrm{doping}$ level (about 4.2% of total ${\mathrm{Fe}}^{3+}$ ions) can induce conical spin order in $\mathrm{Sr}{\mathrm{Mg}}_{x}{\mathrm{Ir}}_{x}{\mathrm{Fe}}_{12\ensuremath{-}2x}{\mathrm{O}}_{19}$ ceramics, mainly because ${\mathrm{Ir}}^{4+}$ ions prefer to enter a crucial $4{f}_{2}$ magnetic-interacted site and thus strengthen the local Dzyaloshinskii-Moriya interaction. Spin-order-induced polarization $({P}_{\mathrm{spin}})$ is achieved and displays a synchronous temperature-dependent behavior with the displacive polarization $({P}_{\mathrm{disp}})$. This interesting ME effect is discussed via $d\text{\ensuremath{-}}p$ hybridization emerging at $\mathrm{Fe}{\mathrm{O}}_{5}$ trigonal bipyramids. Moreover, ${P}_{\mathrm{spin}}$ response decreases step by step during the periodical ME test, reflecting the controllable helicity and the possible multilevel states. These results demonstrate the impact of the $5d$ element with strong SOC on the formation of conical spin order and the enhancement of ME effect in M-type hexaferrite, and also reveal the interconnectedness between ${P}_{\mathrm{spin}}$ and ${P}_{\mathrm{disp}}$.

NLO deflections for spinning particles and Kerr black holes

We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.

Generating two-dimensional ferromagnetic charge density waves via external fields

Two-dimensional (2D) ferromagnetic charge density wave (CDW), an exotic quantum state for exploring the intertwining effect between correlated charge and spin orders in 2D limit, has not been discovered in the experiments yet. Here, we propose a feasible strategy to realize 2D ferromagnetic CDWs under external fields, which is demonstrated in monolayer VSe$_2$ using first-principles calculations. Under external tensile strain, two novel ferromagnetic CDWs ($\sqrt{3}$$\times$$\sqrt{3}$ and 2$\times2\sqrt{3}$ CDWs) can be generated, accompanied by distinguishable lattice reconstructions of magnetic V atoms. Remarkably, because the driving forces for generating these two ferromagnetic CDWs are strongly spin-dependent, fundamentally different from that in conventional CDWs, the $\sqrt{3}$$\times$$\sqrt{3}$ and 2$\times2\sqrt{3}$ CDWs can exhibit two dramatically different half-metallic phases under a large strain range, along with either a flat band or a Dirac cone around Fermi level. Our proposed strategy and material demonstration may open a door to generate and manipulate correlation effect between collective charge and spin orders via external fields.

Magnetic Ordering in a High-Spin Donor-Acceptor Conjugated Polymer.

The development of open-shell organic molecules that magnetically order at room temperature,which can be practically applied, remains a grand challenge in chemistry, physics, and materials science. Despite the exploration of vast chemical space, design paradigms for organic paramagnetic centers generally result in unpaired electron spins that are unstable or isotropic. Here, a high-spin conjugated polymer is demonstrated, which is composed of alternating cyclopentadithiophene and benzo[1,2-c;4,5-c']bis[1,2,5]thiadiazole heterocycles, in which macromolecular structure and topology coalesce to promote the spin center generation and intermolecular exchange coupling. Electron paramagnetic resonance (EPR) spectroscopy is consistent with spatially localized spins, while magnetic susceptibility measurements show clear anisotropic spin ordering and exchange interactions that persist at room temperature. The application of long-range π-correlations for spin center generation promotes remarkable stability. This work offers a fundamentally new approach to the implementation of this long-sought-after physical phenomenon within organic materials and the integration of manifold properties within emerging technologies.

Tuning the topological state of a helical atom chain via a Josephson phase

By solving the Bogoliubov-de Gennes equations, we study the quasiparticle spectrum of a magnetic atom chain placed inside a short constriction-type Josephson junction. A helical magnetic order of the atomic spins is assumed, so that a topologically nontrivial state with Majorana edge modes at the ends of the chain can appear. It is found that in the presence of a nonzero Josephson phase the subgap spectrum of an infinite chain consists of four branches (Shiba bands). This spectrum is almost certainly gapped if the atomic spins form a coplanar spiral. The Majorana number of the given system is calculated analytically. It is demonstrated that a Josephson phase shift can be used to drive the system into a topologically nontrivial state and to tune the size of the topological gap. The spatial structure of Majorana edge modes is studied as well. We generalize the effective model based on discrete Bogoliubov-de Gennes equations developed by Pientka et al. for a bulk superconductor to the case of a Josephson junction. Using these discrete equations, the wave functions of Majorana zero modes are calculated analytically for a coplanar atomic spin spiral with arbitrary pitch. The wave functions exhibit an intermediate asymptotic behavior with a nonexponential fall-off with distance from the edge of the atomic chain.

Classical Gravitational Spinning-Spinless Scattering at O(G^{2}S^{∞}).

Making use of the recently derived, all-spin, opposite-helicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at O(G^{2}) and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with considerations of the ultrarelativistic limit we can uniquely assign values to the parameters remaining in the even-in-spin sector. Once these parameters are determined, much of the spin dependence of the amplitude resums into hypergeometric functions. Finally, we derive the eikonal phase for aligned-angular-momentum scattering.