Localized Spin Model Research Articles

Ab initio study of spin fluctuations in the itinerant kagome magnet FeSn

Kagome antiferromagnetic metal FeSn has become an attracting platform for the exploration of novel electronic states, such as topological Dirac states and the formation of flat bands by localized electrons. Apart from the electronic properties, Dirac magnons and flat magnon bands have also been proposed by applying simplified Heisenberg models to kagome magnetic systems.Inelastic neutron scattering studies on FeSn found well defined magnon dispersions at low energies,but magnons at high energies are strongly dampled, which can not be explained by localized spin models. In this paper, we utilize both linear spin wave theory and time-dependent density functional perturbation theory to investigate spin fluctuations of FeSn. Through the comparison of calculated spin wave spectra and Stoner continuum, we explicitly show that the damping of magnons at high energies are due to the Landau damping, and the appearance of high energy optical-magnon like branches at the M and K point are resulted by relatively low Stoner excitation intensity at those regions.

Magnetic Structures of Electron Systems on the Extended Spatially Completely Anisotropic Triangular Lattice near Quantum Critical Points

We examine magnetic structures of electron systems on an extended triangular lattice that consists of two types of bond triangles with electron transfer energies t_l and t'_l (l = 1, 2, and 3), respectively. We examine the ground state in the mean-field theory when t_1 = t'_1, focusing on collinear states with two sublattices. It is shown that when the imbalance of the spatial anisotropies of the two triangles is large, up-up-down-down (uudd) phases are stable, and the most likely ground states of the lambda-(BETS)_2FeCl_4 system are the Neel state with the modulation vector (\pi/c,\pi/a) and a uudd state, where c = a_1 = a'_1 and a = (a_2+a'_2)/2, with a_1, a_1', a_2, and a_2' being the lattice constants of the bonds with t_1, t'_1, t_2, and t'_2, respectively. These results are consistent with those from the classical spin system. In addition, this study reveals behaviors near the quantum critical point, which cannot be reproduced in the localized spin model. As the imbalance of the spatial anisotropies increases, the U_c of the Neel state increases, and that of the uudd state decreases. In the phase diagrams containing areas of the paramagnetic state, the Neel state with (\pi/c,\pi/a), and a uudd state, their boundaries terminate at a triple point, near which all the transitions are of the first order. The phase boundary between the antiferromagnetic phases does not depend on U, and the transition is of the first order everywhere on the boundary. By contrast, the transitions from the two antiferromagnetic phases to the paramagnetic phase are of the second order, unless the system is close to the triple point.

Magnetic Switching by Oxygen Adsorption in Metal–Organic Framework Systems

In this letter, we address magnetization switching by oxygen adsorption in porous metal-organic framework systems. To this end, we construct a simple localized spin model combined with a Langmuir-type formula for oxygen adsorption and study its finite-temperature properties using Monte Carlo simulation. We successfully explain the main features of this phenomenon, such as the discontinuous changes in magnetic states, sensitivity of the magnetic transition temperatures to oxygen pressure, and absence of singularities in adsorbed oxygen. Based on this model, we also reproduce the observed magnetic transition temperatures for a typical value of oxygen adsorption energy.

Dual nature of magnetism in MnSi

The temperature dependence of the manganese magnetic moment and the spin-lattice relaxation rate measured by the muon spin relaxation technique in the magnetically ordered phase of the chiral intermetallic cubic MnSi system are both explained in terms of helimagnon excitations of a localized spin model. The two free parameters characterizing the helimagnon dispersion relation are determined. A combined analysis of the two data sets cannot be achieved using the self-consistent renormalization theory of spin fluctuations which assumes the magnetism of MnSi to arise uniquely from electronic bands. As a result of this work, MnSi is proposed to be a dual electronic system composed of localized and itinerant magnetic electrons. Finally we note that the analysis framework can be applied to other helimagnets such as the magnetoelectric compound Cu2OSeO3.

Superconducting Correlations in the One-Dimensional Kondo Lattice Models under Magnetic Fields

We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.

Reconstructing quantum states with generative models

A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an experimentally friendly method for density matrix reconstruction based on deep neural-network generative models. The learning procedure comes with a built-in approximate certificate of the reconstruction and makes no assumptions on the state under scrutiny, making it both reliable and unconditional. It can efficiently handle a broad class of complex systems including prototypical states in quantum information, as well as ground states of local spin models common to condensed matter physics. The key insight is to reduce the state tomography task to an unsupervised learning problem of the statistics of an informationally complete set of quantum measurements. This constitutes a modern machine learning approach to the validation of large quantum devices, which may prove relevant as a neural-network ansatz over mixed states suitable for variational optimization.

Topological magnons in a one-dimensional itinerant flatband ferromagnet

Different from previous scenarios that topological magnons emerge in local spin models, we propose an alternative that itinerant electron magnets can host topological magnons. A one-dimensional Tasaki model with a flat band is considered as the prototype. This model can be viewed as a quarter filled periodic Anderson model with impurities located in between and hybridizing with the nearest-neighbor conducting electrons, together with a Hubbard repulsion for these electrons. By increasing the Hubbard interaction, the gap between the acoustic and optical magnons closes and reopens while the Berry phase of the acoustic band changes from 0 to $\pi$, leading to the occurrence of a topological transition. After this transition, there always exist in-gap edge magnonic modes which is consistent with the bulk-edge correspondence. The Hubbard interaction driven transition reveals a new mechanism to realize non-trivial magnon bands.

Magnetic ground state and magnon-phonon interaction in multiferroic h−YMnO3

Inelastic neutron scattering has been used to study the magneto-elastic excitations in the multiferroic manganite hexagonal YMnO$_3$. An avoided crossing is found between magnon and phonon modes close to the Brillouin zone boundary in the $(a,b)$-plane. Neutron polarization analysis reveals that this mode has mixed magnon-phonon character. An external magnetic field along the $c$-axis is observed to cause a linear field-induced splitting of one of the spin wave branches. A theoretical description is performed, using a Heisenberg model of localized spins, acoustic phonon modes and a magneto-elastic coupling via the single-ion magnetostriction. The model quantitatively reproduces the dispersion and intensities of all modes in the full Brillouin zone, describes the observed magnon-phonon hybridized modes, and quantifies the magneto-elastic coupling. The combined information, including the field-induced magnon splitting, allows us to exclude several of the earlier proposed models and point to the correct magnetic ground state symmetry, and provides an effective dynamic model relevant for the multiferroic hexagonal manganites.

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Antiferromagnetic Correlations in Two-Dimensional Fermionic Mott-Insulating and Metallic Phases.

We experimentally study the emergence of antiferromagnetic correlations between ultracold fermionic atoms in a two-dimensional optical lattice with decreasing temperature. We determine the uniform magnetic susceptibility of the two-dimensional Hubbard model from simultaneous measurements of the insitu density distribution of both spin components. At half filling and strong interactions our data approach the Heisenberg model of localized spins with antiferromagnetic correlations. Moreover, we observe a fast decay of magnetic correlations when doping the system away from half filling.

Continuous local model for two-dimensional spin ice

We propose a classical continuous model Hamiltonian with a ground state presenting a spin ice structure. We analyze the introduction of metastable excitations on this ground state, showing the emergence of pairs of magnetic monopoles. The interaction between monopoles and dipoles in the system is studied. As a consequence, we obtain an effective nonlocal interaction between monopoles and dipoles from a local classical spin model.

More on the rainbow chain: entanglement, space-time geometry and thermal states

The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = −h2 (h is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature TR and the physical temperature T.

Spin excitations in the quasi-two-dimensional charge-ordered insulatorα−(BEDT−TTF)2I3probed viaC13NMR

The spin excitations from the nonmagnetic charge-ordered insulating state of $\alpha$-(BEDT-TTF)$_2$I$_3$ at ambient pressure have been investigated by probing the static and low-frequency dynamic spin susceptibilities via site-selective nuclear magnetic resonance at $^{13}$C sites. The site-dependent values of the shift and the spin-lattice relaxation rate $1/T_1$ below the charge-ordering transition temperature ($T_{CO} \approx$ 135 K) demonstrate a spin density imbalance in the unit cell, in accord with the charge-density ratio reported earlier. The shift and $1/T_1$ show activated temperature dependence with a static (shift) gap $\Delta_S \approx$ 47-52 meV and a dynamic ($1/T_1$) gap $\Delta_R \approx$ 40 meV. The sizes of the gaps are well described in terms of a localized spin model, where spin one-half antiferromagnetic dimer chains are weakly coupled with each other.

Application of orthorhombic standardization in magnetic susceptibility studies of localized spin models with S=1, 3/2, 2, 5/2

The standardization idea is nowadays tacitly accepted in EMR area, however, its usefulness in magnetism studies has not been fully recognized as yet. This idea arises due to intrinsic features of orthorhombic Hamiltonians of any physical nature, including the crystal (ligand) field (CF/LF) Hamiltonians or the zero-field splitting (ZFS) ones. Standardization limits the ratio of the orthorhombic parameter to the axial one to a fixed range between 0 and a specific value that depends on the notation used. For the ZFS parameters expressed in the conventional spin Hamiltonian (SH) notation the ratio λ=E/D can always be limited to the range (0, ±1/3) by appropriate choice of coordinate system. Implications of standardization of orthorhombic spin Hamiltonians for interpretation of experimental magnetic susceptibility data are considered. Using a numerical example, we show the existence of alternative solutions for ZFS parameters potentially obtainable from fitting experimental magnetic data and discuss their importance. For the first time algebraic applications of the standardization to the expressions for magnetic susceptibility tensor derived earlier for localized spin models with S=1, 3/2, 2, 5/2 and with rhombic anisotropy are explored. The numerical and algebraic results allow us to formulate an 'invariance principle'. These considerations facilitate interpretation of experimental magnetic data and provide an additional check of correctness of analytical magnetic susceptibility expressions.

Asymmetric Magnon Excitation by Spontaneous Toroidal Ordering

Effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin-orbit coupling and the multi-orbital correlation effect. We show that the model exhibits a Neel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order on the zigzag chain leads to a band-bottom shift, while a toroidal octupole order on the honeycomb lattice gives rise to a valley splitting. These asymmetric magnon excitations could be a source of unusual magnetic responses, such as nonreciprocal magnon transport. A variety of modulations are discussed while changing the lattice and magnetic symmetries. Implications of candidate materials for asymmetric magnon excitations are presented.

Classical mutual information in mean-field spin glass models

We investigate the classical Renyi entropy S_n and the associated mutual information I_n in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model on the n-sheets booklet. This is obtained by gluing together n independent copies of the model, and it is the main ingredient to construct the Renyi entanglement-related quantities. We find a glassy phase at low temperature, whereas at high temperature the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends non-trivially on the geometry of the booklet. At high-temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for S_n and I_n, and for standard thermodynamic quantities. Both S_n and I_n exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities S_n/N, I_n/N, in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.

Spin glass reflection of the decoding transition for quantum error correcting codes

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette $\Z2$ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of ``post-topological'' extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with finite rates the number of distinct classes of such extended defects is exponentially large, corresponding to extensive ground state entropy of these codes. Here, the transition can be driven by the entropy of the extended defects, a mechanism distinct from that in the local spin models where the number of defect types (domain walls) is always finite.

Magnetic excitations of perovskite rare-earth nickelates: RNiO3

To gain insight into the ground state of perovskite nickelates RNiO3 (R: rare-earth), in particular charge disproportionation of the Ni ions and the magnetic configuration, we studied the magnetic excitations of the collinear, orthogonal and intermediate phases proposed for these materials. We used a localized spin model, including two kinds of Ni-spin magnitudes to describe an eventual charge disproportionation. For the magnetic couplings, we considered Heisenberg-like interactions up to next-nearest-neighbors, for the ferromagnetic and antiferromagnetic couplings present in the collinear phases. To describe the non-collinear phases, as proposed for other multiferroics, we considered Dzyaloshinskii–Moriya-type couplings to allow for the possibility of a relative angle θ, between nearest-neighbor spins in the two different magnetic sublattices. Using a simplified spin chain model for these compounds, we first analysed the stability of the collinear, orthogonal, and intermediate phases in the classical case. We then explored the quantum ground state indirectly, calculating the spin excitations obtained for each phase, using the Holstein–Primakoff transformation and the linear spin-wave approximation. For the collinear and orthogonal (θ=π/2) phases we predict differences in the magnon spectra, concretely in the number of magnon branches or the magnitude of the magnon gap, which would allow to distinguish between these phases, and in particular probe the charge disproportionation, in future experiments such as inelastic neutron scattering or resonant inelastic X-ray scattering.

Renormalization of electron self-energies via their interaction with spin excitations: A first-principles investigation

Access to magnetic excitation spectra of single atoms deposited on surfaces is nowadays possible by means of low-temperature inelastic scanning tunneling spectroscopy. We present a first-principles method for the calculation of inelastic tunneling spectra utilizing the Korringa-Kohn-Rostoker Green function method combined with time-dependent density functional theory and many-body perturbation theory. The key quantity is the electron self-energy describing the coupling of the electrons to the spin excitation within the adsorbate. By investigating Cr, Mn, Fe, and Co adatoms on a Cu(111) substrate, we spin-characterize the spectra and demonstrate that their shapes are altered by the magnetization of the adatoms, of the tip and the orbital decay into vacuum. Our method also predicts spectral features more complex than the steps obtained by simpler models for the adsorbate (e.g., localized spin models).

Magnetic susceptibility and short-range order in iron pnictides: Anisotropic J1-J2 Heisenberg model

A spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the anisotropic non-frustrated J 1-J 2 model for the iron pnictides AFe2As2 (A = Ca, Sr, Ba) is presented. The two-spin correlation functions, the spin-excitation spectrum, and the staggered magnetization are calculated self-consistently as functions of temperature and spin. The temperature dependence of the magnetic (uniform static) susceptibility, in particular the linear increase with T in a wide temperature region that is in good quantitative agreement with experiments, is ascribed to a strong in-plane antiferromagnetic short-range order. The values of the Neel temperature resulting from the localized spin model with realistic out-of-plane couplings are found to be much higher than the measured values. From this an extension of the model by including itinerant degrees of freedom is suggested.