Heisenberg Exchange Interaction Research Articles

Rotationally Invariant Circuits: Universality with the Exchange Interaction and Two Ancilla Qubits.

Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has recently been shown that this universality does not hold in the presence of continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even approximately, using local symmetric unitaries on the subsystems. In this Letter, we show that, despite these constraints, any SU(2) rotationally invariant unitary can be realized with the Heisenberg exchange interaction, which is 2-local and rotationally invariant, provided that the system interacts with a pair of ancilla qubits. We also show that a single ancilla is not enough to achieve universality. Furthermore, we study qubit circuits formed from k-local rotationally invariant unitaries and fully characterize the constraints imposed by locality on the realizable unitaries. We also find an interpretation of these constraints in terms of the average energy of states with a fixed angular momentum.

Observation of Topological Hall Effect in a Chemically Complex Alloy.

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Estimation of Heisenberg exchange interaction in rigid photoexcited chromophore-radical compound by transient EPR.

The magnetic field dependence of the spin polarization in a photoexcited rigid chromophore-radical conjugate is theoretically investigated. The excitation of the chromophore-radical conjugate often populates the metastable doublet and quartet states formed by the interactions of the unpaired electrons of the triplet chromophore and the radical. The intensities of the +1/2 ↔ - 1/2 transitions of the doublet and quartet manifolds are sensitive to the ratio jω = 3J/ω0 between the triplet-doublet exchange interaction J and the Zeeman energy ω0. It is shown that the analytical expressions of these intensities previously found for the triplet mechanism of the initial spin polarization can be expanded and applied to a broader class of compounds that may have other intersystem crossing pathways of the depopulation of the excited singlet state of the chromophore. It is also shown that the exchange interaction can be evaluated not only by comparing the electron paramagnetic resonance spectra obtained in different microwave frequency bands but also by comparing the data obtained in the same microwave band but with a shift of the frequency of the resonator. The results obtained broaden the potential applications of the previously proposed approach for analyzing the correlation between the exchange coupling and the distance separating the radical and the chromophore spins, as well as the structure of the bridge connecting their fragments.

The magnetic susceptibility of Mn<sub>3</sub>Sn single crystal is enhanced under GPa-level uniaxial stress

At room temperature, controlling the spin of noncollinear antiferromagnetic Mn<sub>3</sub>Sn presents a challenge. In this study, we modulate the magnetic structure by subjecting Mn<sub>3</sub>Sn single crystals to GPa-level uniaxial stress using a high-pressure binding deformation approach. Initially, the single crystal is sliced into regular cuboids, then embedded in a stainless steel sleeve, and finally, uniaxial stress is applied along the [01<span style="text-decoration:overline">2</span>0] and [01<span style="text-decoration:overline">1</span>0] directions of the Mn<sub>3</sub>Sn single crystal. Under high stress, the single crystal undergoes plastic deformation. Our observations reveal lattice distortion in the deformed single crystal, with the lattice parameter gradually decreasing as the stress level increases. In addition, the magnetic susceptibility of Mn<sub>3</sub>Sn under GPa uniaxial stress (<i>χ</i>) is different from that under MPa uniaxial stress, and its value is no longer fixed but increases with the increase of stress. When 1.12 GPa stress is applied in [01<span style="text-decoration:overline">2</span>0] direction, <i>χ</i> reaches 0.0203 <i>μ</i><sub>B</sub> f.u.<sup>-1</sup>T<sup>-1</sup>, which is 1.42 times that of the undeformed sample. In the case of stress applied along the [01<span style="text-decoration:overline">1</span>0] direction, <i>χ </i>≈ 0.0332 <i>μ</i><sub>B</sub> f.u.<sup>-1</sup>T<sup>-1</sup> when the stress is 1.11 GPa. This result is also 2.66 times greater than the reported results. We further calculate the trimerization parameter (<i>ξ</i>), isotropic Heisenberg exchange interaction (<i>J</i>), and anisotropic energy (<i>δ</i>) of the system under different stresses. Our results show that <i>ξ</i> gradually increases, <i>J</i> gradually decreases, and <i>δ</i> gradually increases with the increase of stress. These results show that the GPa uniaxial stress introduces anisotropic strain energy into the single crystal, breaking the symmetry of the in-plane hexagon of the kagome lattice, which causes the bond length of the two equilateral triangles composed of Mn atoms to change. Thus, the exchange coupling between Mn atoms in the system is affected, the anisotropy of the system is enhanced, and the antiferromagnetic coupling of the system is enhanced. Therefore, the system <i>χ </i>is no longer a constant value and gradually increases with the increase of stress. This discovery will provide new ideas for anti-ferromagnetic spin regulation.

Electronic Structure of Above-Room-Temperature van der Waals Ferromagnet Fe3GaTe2.

Fe3GaTe2, a recently discovered van der Waals ferromagnet, demonstrates intrinsic ferromagnetism above room temperature, necessitating a comprehensive investigation of the microscopic origins of its high Curie temperature (TC). In this study, we reveal the electronic structure of Fe3GaTe2 in its ferromagnetic ground state using angle-resolved photoemission spectroscopy and density functional theory calculations. Our results establish a consistent correspondence between the measured band structure and theoretical calculations, underscoring the significant contributions of the Heisenberg exchange interaction (Jex) and magnetic anisotropy energy to the development of the high-TC ferromagnetic ordering in Fe3GaTe2. Intriguingly, we observe substantial modifications to these crucial driving factors through doping, which we attribute to alterations in multiple spin-splitting bands near the Fermi level. These findings provide valuable insights into the underlying electronic structure and its correlation with the emergence of high-TC ferromagnetic ordering in Fe3GaTe2.

A comparative study of structural, electronic, magnetic, and pressure-dependent properties of Full-Heusler Fe2XSi (X=Mn and Co): first-principles calculation and Monte Carlo Simulation

This study investigates the structural, electronic, magnetic, and pressure-dependent properties of Fe2XSi (X=Mn and Co) full-Heusler alloy through a comprehensive computational approach. The structural stability of these alloys confirmed L21 and XA prototypes as favorable structures for Fe2MnSi and Fe2CoSi, respectively. In addition, Fe2MnSi exhibits 100% spin polarization suggesting its potential suitability for spintronics applications. Conversely, Fe2CoSi does not exhibit similar behavior. The calculated magnetic moments of these alloys revealed an increase due to Coulomb interaction (U). The magnetic moments satisfy the Slater-Pauling relation, with calculated values of 3 for Fe2MnSi and 5 for Fe2CoSi. Heisenberg exchange interaction parameters are calculated to illustrate distinct magnetic interactions within the alloys. The study further explores thermomagnetic properties through Monte Carlo simulations, including thermal magnetization, thermal magnetic susceptibility, and Curie temperature The calculated were found to be 294 K for Fe2MnSi and 1029 K for Fe2CoSi, showing close agreement with experimental data. We additionally investigate the pressure-dependent properties of these alloys, revealing a non-linear dependence of the band gap on pressure for Fe2MnSi, with values decreasing from 0.668 eV to 0.259 eV as pressure increased from −15.917 to 23.712 GPa. For Fe2CoSi, the band gap remained zero across varying pressure conditions, indicating its metallic conducting behavior.

Polarons and bipolarons in one-dimensional systems (arbitrary coupling)

The properties of a one-dimensional (1D) polaron and a bipolaron in the region of strong and intermediate coupling are investigated. The Buimistrov–Pekar (BP) method was chosen for the calculation of the energy of self-trapped states. Calculations were carried out by the variational method using wave functions of various types. The lowest polaron and bipolaron energies were obtained using the Gaussian system of functions. In the limit of weak electron-phonon coupling, both the BP and the Feynman methods lead to a linear dependence of the polaron energy where is the Fröhlich constant of electron-phonon coupling. Such dependence can be interpreted as a transition from an autolocalized (in the strong coupling region) to a delocalized polaron state. At where, and are the high-frequency and static dielectric constants, the critical value of the electron-phonon coupling constant, at which the bipolaron states become unstable, is in the range where the upper limit was calculated with respect to the double energy of the Feynman polaron, and the lower bound was obtained using the Buimistrov–Pekar method. The triplet states of a bipolaron do not form a bound state. The Heisenberg exchange interaction of polarons has an antiferromagnetic character.

Oxygen on-site Coulomb energy in Pr1.3−xLa0.7CexCuO4 and Bi2Sr2CaCu2O8+δ and its relation with Heisenberg exchange

We study the electronic structure of electron-doped Pr$_{1.3-x}$La$_{0.7}$Ce$_{x}$CuO$_{4}$ (PLCCO ; $T_{c}$ = 27 K, x = 0.1) and hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212 ; $T_{c}$ = 90 K) cuprate superconductors using x-ray absorption spectroscopy (XAS) and resonant photoemission spectroscopy (Res-PES). From Res-PES across the O K-edge and Cu L-edge, we identify the O 2p and Cu 3d partial density of states (PDOS) and their correlation satellites which originate in two-hole Auger final states. Using the Cini-Sawatzky method, analysis of the experimental O 2p PDOS shows an oxygen on-site Coulomb energy for PLCCO to be $U_{p}$ = 3.3$\pm$0.5 eV and for Bi2212, $U_{p}$ = 5.6$\pm$0.5 eV, while the copper on-site Coulomb correlation energy, $U_{d}$ = 6.5$\pm$0.5 eV for Bi2212. The expression for the Heisenberg exchange interaction $J$ in terms of the electronic parameters $U_{d}$, $U_{p}$, charge-transfer energy $\Delta$ and Cu-O hopping $t_{pd}$ obtained from a simple Cu$_2$O cluster model is used to carry out an optimization analysis consistent with $J$ known from scattering experiments. The analysis also provides the effective one band on-site Coulomb correlation energy $\tilde{U}$ and the effective hopping $\tilde{t}$. PLCCO and Bi2212 are shown to exhibit very similar values of $\tilde{U}$/$\tilde{t}$ $\sim$9-10, confirming the strongly correlated nature of the singlet ground state in the effective one-band model for both the materials.

A spin model for intrinsic antiferromagnetic skyrmions on a triangular lattice

Skyrmions are prospected as the potential future of data storage due to their topologically protected spin structures. However, traditional ferromagnetic (FM) skyrmions experience deflection when driven with an electric current, hindering their usage in spintronics. Antiferromagnetic (AFM) skyrmions, consisting of two FM solitons coupled antiferromagnetically, are predicted to have zero Magnus force, making them promising candidates for spintronic racetrack memories. Currently, they have been stabilized in synthetic AFM structures, i.e., multilayers hosting FM skyrmions, which couple antiferromagnetically through a non-magnetic spacer, while recent first-principle simulations predict their emergence in an intrinsic form, within a row-wise AFM single monolayer of Cr deposited on a PdFe bilayer grown on Ir (111) surfaces. The latter material forms a triangular lattice, where single and interlinked AFM skyrmions can be stabilized. Here, we explore the minimal Heisenberg model, enabling the occurrence of such AFM solitons and the underlying phase diagrams by accounting for the interplay between the Dzyaloshinskii–Moriya and Heisenberg exchange interactions, as well as the magnetic anisotropy and impact of the magnetic field. By providing the fundamental basis to identify and understand the behavior of intrinsic AFM skyrmions, we anticipate our model to become a powerful tool for exploring and designing new topological magnetic materials to conceptualize devices for AFM spintronics.

Ab initio description of magnetic and critical properties of spin-glass pyrochlore NaSrMn2F7

In this study, I have investigated the magnetic and critical properties of manganese pyrochlore fluoride NaSrMn2F7, which exhibits a glass transition at Tf = 2.5 (K) due to charge disorder. A DFT + U + SOC framework is used in this paper to derive spin-Hamiltonian terms, including isotropic and anisotropic exchange interactions. An optimized geometry reveals a local distortion of the F–Mn–F angle along the ⟨111⟩ direction (95.48° and 84.51°), which is considered a weak bond disorder (δJ). Despite the complex structure of this material, first principle calculations show that its magnetic properties are only controlled by the nearest neighbor’s Heisenberg exchange interaction, and other interactions do not affect spin arrangements in the ground state. Thus, this material is considered a suitable candidate for studying electron correlation in spin glasses. Using a replica-exchange framework, Monte Carlo simulations indicate that with δJ=0, no phase transition is observed when magnetic susceptibility changes with temperature. The results demonstrate that the presence of local bond disorder serves as a perturbation, and the degeneracy of the energy manifold of the system persists if its effect is not taken into consideration. Based on δJ=0.13(meV) and the derived spin Hamiltonian, 2.6 (K) is obtained as the phase transition temperature.

A deep investigation of NiO and MnO through the first principle calculations and Monte Carlo simulations

In this study, we use Hubbard-corrected density functional theory (DFT+U) to derive spin model Hamiltonians consisting of Heisenberg exchange interactions up to the fourth nearest neighbors and bi-quadratic interactions. We map the DFT+U results of several magnetic configurations to the Heisenberg spin model Hamiltonian to estimate Heisenberg exchanges. We demonstrate that the number of magnetic configurations should be at least twice the number of exchange parameters to estimate exchange parameters correctly. To calculate biquadratic interaction, we propose specific non-collinear magnetic configurations that do not change the energy of the Heisenberg spin model. We use classical Monte Carlo (MC) simulations to evaluate DFT+U results. We obtain the temperature dependence of magnetic susceptibility and specific heat to determine the Curie–Weiss and Néel temperatures. The MC simulations reveal that although the biquadratic interaction can not change the Néel temperature, it modifies the order parameter. We indicate that for a fair comparison between classical MC simulations and experiments, we need to consider the quantum effect by applying correction in classical MC simulations.

Spin-based quantum Otto engines and majorization

The concept of majorisation is explored as a tool to characterize the performance of a quantum Otto engine in the quasi-static regime. For a working substance in the form of a spin of arbitrary magnitude, majorisation yields a necessary and sufficient condition for the operation of the Otto engine, provided the canonical distribution of the working medium at the hot reservoir is majorised by its canonical distribution at the cold reservoir. For the case of a spin-1/2 interacting with an arbitrary spin via isotropic Heisenberg exchange interaction, we derive sufficient criteria for positive work extraction using the majorisation relation. Finally, local thermodynamics of spins as well as an upper bound on the quantum Otto efficiency is analyzed using the majorisation relation.

Measuring interfacial Dzyaloshinskii-Moriya interaction in ultrathin magnetic films

In magnetically ordered systems the Heisenberg exchange interaction between neighboring spins favors collinear alignment such as that seen in ferromagnets and antiferromagnets. The inclusion of antisymmetric exchange, also known as the Dzyaloshinskii--Moriya interaction (DMI), promotes an orthogonal arrangement between spins and is the subject of this review. The DMI interaction is responsible for chiral magnetism, spin-textured skyrmions, and magnetoelectric effects in multiferroic materials. The review, organized by measurement method, is focused on experiments that determine the DMI associated with thin film interfaces occurring in a variety of samples.

Quantifying symmetric exchange in ultrathin ferromagnetic films with chirality

The symmetric (Heisenberg) exchange interaction is fundamental to magnetism and assumes critical importance in designing magnetic materials for novel emergent phenomena and device applications. However, quantifying exchange is extremely challenging for ultrathin magnetic films, as techniques and approximations reliably used for bulk materials are largely inapplicable in the two-dimensional limit. Here we present and contrast the measurement of exchange stiffness $A$ by several methods on a series of five Co/Pt-based ultrathin ($1--2$ nm) films. We compare results from (a) spin-wave spectroscopy by Brillouin light scattering, (b) three analytical models describing the temperature dependence of magnetization obtained by magnetometry, (c) microscopic domain periodicity measurements and simulations, and (d) ab initio density functional theory calculations. While different methods present some qualitatively consistent trends across samples, we note, for any given sample, considerable differences (up to $5\ifmmode\times\else\texttimes\fi{})$ in the absolute values of $A$ across the techniques, consistent with discrepancies of $A$ reported in literature for nominally similar samples. We analyze possible sources of the discrepancies across various methods, notably including their relationship to the spin-wave dispersion, and the wave-vector ranges probed. We compare the strengths and limitations of the techniques, and outline directions for their future use in characterizing exchange interactions in ultrathin films.

The exact solution of the edge-modified graphene nanoribbon-like structure Ising-Heisenberg spin (1,1/2) system

A two-fold rotational symmetry ferromagnetic Ising-Heisenberg model modified by edge spin ( S = 1 / 2 ) with antiferromagnetic Heisenberg exchange interaction, whose shape is graphene nanoribbon-like has been constructed, and the host Ising spin ( S = 1 ). By use of the star-triangle transformation and the transfer matrix method, the edge states, thermodynamics and magnetization behavior of the system display various properties. The results perform that the unique edge-spin states and the host-spin states of the system are influenced with each other. And there are eleven different ground state phases, which are presented as the values of magnetic susceptibility multiplied by temperature at ultra-low temperature in the parameter space of single-ion anisotropy and antiferromagnetic Heisenberg interaction. Because of a large number of excited states close to the ground state, the specific heat curve shows multi-peak phenomena, which are analyzed by corresponding to the entropy of the system. The magnetization process of the system is complex, due to the direct correlation of the edge-spin states and the host-spin states of system, in which many different magnetization plateaus appear. The rigorous results of the number and width of magnetization plateaus and the saturation of the magnetization are written. This study offers unique opportunities for future technological applications such as proposed designs of graphene-based quantum spintronic devices as well as magnetic ordering.

Reciprocal space study of Heisenberg exchange interactions in ferromagnetic metals

The modern quantum theory of magnetism in solids is getting commonly derived using Green's functions formalism. The popularity draws itself from remarkable opportunities to capture the microscopic landscape of exchange interactions, starting from a tight-binding representation of the electronic structure. Indeed, the conventional method of infinitesimal spin rotations, considered in terms of local force theorem, opens vast prospects of investigations regarding the magnetic environment, as well as pairwise atomic couplings. However, this theoretical concept practically does not devoid of intrinsic inconsistencies. In particular, naturally expected correspondence between single and pairwise infinitesimal spin rotations is being numerically revealed to diverge. In this work, we elaborate this question on the model example and canonical case of bcc iron. Our analytical derivations discovered the principal preference of on-site magnetic precursors if the compositions of individual atomic interactions are in focus. The problem of extremely slow or even absent spatial convergence while considering metallic compounds was solved by suggesting the original technique, based on reciprocal space framework. Using fundamental Fourier transform-inspired interconnection between suggested technique and traditional spatial representation, we shed light on symmetry breaking in bcc Fe on the level of orbitally decomposed total exchange surrounding.

Inelastic neutron studies and diffraction in magnetic fields of TbFeO3 and YbFeO3

Investigations of the orthoferrites TbFeO3 and YbFeO3 were performed by neutron inelastic scattering and neutron single crystal diffraction in magnetic fields. The low temperature evolution of energy gaps was explored for both compounds and considered from the point of view of changes of rare earth ion anisotropy. Exchange parameters between nearest neighbors for Fe3+ in TbFeO3 were obtained. The magnetic phase diagram for YbFeO3 was obtained and discussed as a result of the energy balance between Heisenberg exchange interactions, Dzyaloshinsky-Moriya interaction, anisotropy and external magnetic field.

Negative sign free formulations of generalized Kitaev models with higher symmetries

We provide a negative-sign-free formulation of the auxiliary field quantum Monte Carlo algorithm for generalized Kitaev models with higher symmetries. Our formulation is based on the Abrikosov fermion representation of the spin-1/2 degree of freedom and the phase pinning approach [Phys. Rev. B 104, L081106 (2021)]. Enhancing the number of fermion flavors or orbitals from one to $N$ allows one to generalize the inherent $Z_2$ global symmetry to Z$_2$$\times$SU($N$)$_o$. Using this general approach, we study the Z$_2$$\times$SU(2)$_o$ Kitaev-Heisenberg model reflecting the competition between the isotropic Heisenberg exchange and Kitaev-type bond-directional exchange interactions. We show that the symmetry enhancement provides a path to escape frustration and that the spin liquid phases in the original Z$_2$ symmetric model are not present in this model. Nevertheless, the ground-state phase diagram is extremely rich and has points with higher global and local continuous symmetries as well as de-confined quantum critical points.

The exact solution of the edge-modified kekulene-like nanostructure Ising-Heisenberg spin system

A ferromagnetic model of kekulene-like nanostructure is established, in which the Ising ring (S = 1) decorated by the edge-spin (S = 3/2) through antiferromagnetic Heisenberg exchange interaction. The thermodynamic properties and magnetization behavior of the system were investigated by use of the exact diagonalization and transfer matrix method . It was found that there are six different phases with different values of magnetic susceptibility multiplied by temperature at low temperature in the parameter space of single-ion anisotropy, but it gets only one value taken in the high-temperature limit. The multi-peak phenomena of the specific heat curve at ultra-low temperature are corresponding to the entropy of the system, which the abundant and dense excited states are near the ground state. It shows many different magnetization plateaus in the magnetization process of the system, but no spontaneous magnetization appears. The number and width of magnetization plateaus and the saturation of the magnetization are affected by the single-ion anisotropy. • The edge-modified kekulene-like nanostructure Ising-Heisenberg spin-(1,3/2) system has been exactly determined. • There are six different phases with different values of the magnetic susceptibility multiplied by temperature at low temperature in the parameter space of single-ion anisotropy, but it gets only one value taken in the high-temperature limit. • The multi-peak phenomena of the specific heat curve at ultra-low temperature are corresponding to the entropy of the system, which the abundant and dense excited states near the ground state. • The magnetization of the system shows many different jumps (magnetic plateaus) with the external magnetic field increasing.

Incommensurate magnetic ordering in CrB2

Incommensurate magnetism in CrB2 is studied in terms of a spin model based on density functional theory calculations. Heisenberg exchange interactions derived from the paramagnetic phase using the disordered local moment (DLM) theory show significant differences compared with those resulting from the treatment of the material as a ferromagnet; of these two methods, the DLM theory is found to give a significantly more realistic description. We calculate strongly ferromagnetic interactions between Cr planes but largely frustrated interactions within Cr planes. Although we find that the ground state ordering vector is sensitive to exchange interactions over a large number of neighbour shells, the q-vector of the incommensurate spin spiral state is satisfactorily reproduced by the theory (0.213 compared with the known ordering vector along Γ–). The strong geometric frustration of the exchange interactions causes a rather low Néel temperature (about 97 K), also in good agreement with experiment.