Heisenberg Spin Exchange Interactions Research Articles

Monte Carlo simulation of a model cuprate

We develop a classical Monte Carlo algorithm based on a quasi-classical approximation for a pseudospin S = 1 Hamiltonian in real space to construct a phase diagram of a model cuprate with a high Tc. A model description takes into account both local and nonlocal correlations, Heisenberg spin-exchange interaction, correlated single-particle, and two-particle transport. We formulate a state selection algorithm for a given parameterization of the wave function in order to ensure a uniform distribution of states in the phase space. The simulation results show a qualitative agreement with the experimental phase diagrams.

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value pc of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc and a metallic spin glass with carrier density p for p<pc. Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.6 MoreReceived 24 December 2019Revised 18 February 2020Accepted 23 March 2020DOI:https://doi.org/10.1103/PhysRevX.10.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum criticalityQuantum phase transitionsPhysical SystemsCupratesTechniquesSachdev-Ye-Kitaev modelCondensed Matter, Materials & Applied Physics

Measuring radical diffusion in viscous liquids by electron paramagnetic resonance

Relative diffusion of free radicals in solution modulates the Heisenberg spin exchange and dipole-dipole interactions among them, which affects their electron paramagnetic resonance (EPR) spectra. The radical concentration dependence of EPR parameters can, in turn, give information about radical diffusivity in a liquid. We studied the diffusivities of the 14N- and 15N-labeled perdeuterated TEMPONE radicals at various temperatures in three viscous liquids: 1‑ethyl‑3‑methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquid, propylene carbonate, and ethylene glycol. By fitting EPR spectra at various radical concentrations, we obtained the concentration coefficients of EPR parameters. The concentration coefficients were related to the radical diffusivity by solving the kinetic equations for the spin evolution of a radical pair, considering the radicals as continuously diffusing spherical objects in the hard-core pair potential. We tested the method by comparing the calculated radical diffusivities of isotopically substituted TEMPONE radicals. Temperature dependences of radical diffusivities were discussed in terms of the Stokes-Einstein relation. Additionally, the radical diffusivities were compared to the self-diffusivities of the studied liquids. At lower temperatures, the radical diffusivities follow the self-diffusivities, while at the higher temperatures, the radical diffusivities start deviating from the self-diffusivities.

Geometrically frustrated Ising-Heisenberg spin model on expanded Kagomé lattice

Here we consider the Ising-Heisenberg model in the expanded Kagom\'e lattice, also known as triangle-dodecagon (3-12) or star lattice. This model can still be understood as a decorated honeycomb lattice. Assuming that the Heisenberg spins are at the vertices of the triangle while other spins are of the Ising type. Thus, this model is equivalent to an effective Kagom\'e Ising lattice, through the decoration transformation technique. Thus this means that the model is exactly solvable so we can study the most relevant properties of this model. Like the phase diagram at zero temperature, exhibiting a frustrated phase, a ferromagnetic phase, a classical ferrimagnetic phase and a quantum ferrimagnetic phase. We observed that Heisenberg spin exchange interaction influences the frustrated phase, but we rigorously verify that the magnitude and origin of the frustration emerge in a similar way to antiferromagnetic Ising Kagom\'e lattice. Likewise, the thermodynamic properties of the model can also be obtained, such as the critical temperature as a dependence of the Hamiltonian parameters and the spontaneous magnetization of the model. Besides, we investigated the entropy of the model, identifying its residual entropy in the frustrated region. Even we analyze the specific heat behavior as a temperature dependence, to deal with the phase transition.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin–orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii–Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain , where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for and for . The associated anomalous thermal Hall conductivity develops an abrupt change at , due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water.

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting to find the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14N- and 15N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Tunneling spectroscopy and Majorana modes emergent from topological gapless phases in high-Tccuprate superconductors

We explore possible signatures for observing Majorana Fermions in the tunneling spectroscopy of high-Tc cuprate superconductors. We find that as long as the Rashba spin orbit interaction is in presence either through proximity effect due to an electrode made by heavy metal or by the intrinsic nature of cuprates, in addition to the Heisenberg spin exchange interaction, the Dzyaloshinskii-Moriya and spin dipole-dipole interactions are induced. As a result, $p$-wave superconductivity is induced with the gap function $d$-vector being not aligned with the internal magnetic field of the spin-orbit interaction. Most importantly, the ground state goes through transitions into gapless phases with split nodal points. The split nodal structure always results in Majorana modes for any interfaces that are not exactly in (100) or (010) directions. Hence for general interfaces, existence of Majorana bound edge states is a robust feature. Our results indicate that these Majorana modes would result in a small plateau in tunneling spectrum near zero bias peak and in 4 $\pi$ periodicity in typical SIS$'$ junctions . As a result, it is easy for a $\pi$-ring in tricrystal experiments to hold Majorana Ferimions and exhibit periods of two flux quanta in external magnetic fields. These phenomena may have been already observed in experiments and their connections to experimental results are discussed.

EPR line shifts and line shape changes due to Heisenberg spin exchange and dipole-dipole interactions of nitroxide free radicals in liquids: 9. An alternative method to separate the effects of the two interactions employing ¹⁵N and ¹⁴N.

A method to separate the effects of Heisenberg spin exchange (HSE) and dipole–dipole (DD) interactions on EPR spectra of nitroxide spin probes in solution by employing 15N and 14N nitroxide spin probes in parallel experiments is developed theoretically and tested experimentally. Comprehensive EPR measurements are reported of 4-oxo-2,2,6,6-tetramethylpiperidine-d16;1-15N-1-oxyl (perdeuterated 15N Tempone; 15pDT), in 70 wt % aqueous glycerol as functions of concentration and temperature. The method, termed the relative broadening constant method (RBCM), is demonstrated by using the present results together with those in the literature that employed perdeuterated 14N Tempone (14pDT) under identical conditions. In principle, the separation of DD and HSE is dependent on the model of diffusion and molecular-kinetic parameters; however, within present day experimental uncertainties, the RBCM method turns out to be insensitive to the model. The earlier methods to separate DD and HSE by measuring the dispersion component introduced by the two interactions shows general agreement with the RBCM; however, there are discrepancies larger than estimated uncertainties due to random errors. Thus, further support is found for Salikhov’s recent theory of the effects of DD and HSE on EPR spectra (Appl. Magn. Reson.2010, 38, 237); however, detailed confirmation is still lacking. The RBCM affords a possible approach to separate HSE and DD in spectra complicated by slow motion and/or overlap with other resonance lines, allowing the method to be used in situations more complicated than low-viscosity simple liquids.

Exploring the radical nature of a carbon surface by electron paramagnetic resonance and a calibrated gas flow.

While the first Electron Paramagnetic Resonance (EPR) studies regarding the effects of oxidation on the structure and stability of carbon radicals date back to the early 1980s the focus of these early papers primarily characterized the changes to the structures under extremely harsh conditions (pH or temperature)(1-3). It is also known that paramagnetic molecular oxygen undergoes a Heisenberg spin exchange interaction with stable radicals that extremely broadens the EPR signal(4-6). Recently, we reported interesting results where this interaction of molecular oxygen with a certain part of the existing stable radical structure can be reversibly affected simply by flowing a diamagnetic gas through the carbon samples at STP(7). As flows of He, CO2, and N2 had a similar effect these interactions occur at the surface area of the macropore system. This manuscript highlights the experimental techniques, work-up, and analysis towards affecting the existing stable radical nature in the carbon structures. It is hoped that it will help towards further development and understanding of these interactions in the community at large.

Exploring the Radical Nature of a Carbon Surface by Electron Paramagnetic Resonance and a Calibrated Gas Flow

While the first Electron Paramagnetic Resonance (EPR) studies regarding the effects of oxidation on the structure and stability of carbon radicals date back to the early 1980s the focus of these early papers primarily characterized the changes to the structures under extremely harsh conditions (pH or temperature)1-3. It is also known that paramagnetic molecular oxygen undergoes a Heisenberg spin exchange interaction with stable radicals that extremely broadens the EPR signal4-6. Recently, we reported interesting results where this interaction of molecular oxygen with a certain part of the existing stable radical structure can be reversibly affected simply by flowing a diamagnetic gas through the carbon samples at STP7. As flows of He, CO2, and N2 had a similar effect these interactions occur at the surface area of the macropore system. This manuscript highlights the experimental techniques, work-up, and analysis towards affecting the existing stable radical nature in the carbon structures. It is hoped that it will help towards further development and understanding of these interactions in the community at large.

Spin Excitation Assisted by Non-Softening Phonon for Spin-Peierls Model

We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum π. The phonon excitation spectrum is also influenced by the spin–phonon interaction. We discuss the possibility of observing the spin–phonon coupled features in inorganic spin-Peierls compound CuGeO 3 .

Spin Excitation and Phonon Effect for Frustrated Spin-Peierls Model

We study spin excitation for a spin-Peierls chain with nearest-neighbour and next-nearest-neighbour Heisenberg spin exchange interactions. Lattice degree of freedom is introduced as a gapped and dispersionless (Einstein) phonon, and its effect is renormalized to the spin exchange interactions. We apply a dynamical density matrix renormalization group method to calculate the dynamical spin structure factor of the renormalized spin model. By using this method, we can obtain differences in spin excitation between the spin-liquid phase and the dimer phase.

A new model for Overhauser enhanced nuclear magnetic resonance using nitroxide radicals

Nitroxide free radicals are the most commonly used source for dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance (NMR) experiments and are also exclusively employed as spin labels for electron spin resonance (ESR) spectroscopy of diamagnetic molecules and materials. Nitroxide free radicals have been shown to have strong dipolar coupling to (1)H in water, and thus result in large DNP enhancement of (1)H NMR signal via the well known Overhauser effect. The fundamental parameter in a DNP experiment is the coupling factor, since it ultimately determines the maximum NMR signal enhancements which can be achieved. Despite their widespread use, measurements of the coupling factor of nitroxide free radicals have been inconsistent, and current models have failed to successfully explain our experimental data. We found that the inconsistency in determining the coupling factor arises from not taking into account the characteristics of the ESR transitions, which are split into three (or two) lines due to the hyperfine coupling of the electron to the (14)N nuclei (or (15)N) of the nitric oxide radical. Both intermolecular Heisenberg spin exchange interactions as well as intramolecular nitrogen nuclear spin relaxation mix the three (or two) ESR transitions. However, neither effect has been taken into account in any experimental studies on utilizing or quantifying the Overhauser driven DNP effects. The expected effect of Heisenberg spin exchange on Overhauser enhancements has already been theoretically predicted and observed by Bates and Drozdoski [J. Chem. Phys. 67, 4038 (1977)]. Here, we present a new model for quantifying Overhauser enhancements through nitroxide free radicals that includes both effects on mixing the ESR hyperfine states. This model predicts the maximum saturation factor to be considerably higher by the effect of nitrogen nuclear spin relaxation. Because intramolecular nitrogen spin relaxation is independent of the nitroxide concentration, this effect is still significant at low radical concentrations where electron spin exchange is negligible. This implies that the only correct way to determine the coupling factor of nitroxide free radicals is to measure the maximum enhancement at different concentrations and extrapolate the results to infinite concentration. We verify our model with a series of DNP experimental studies on (1)H NMR signal enhancement of water by means of (14)N as well as (15)N isotope enriched nitroxide radicals.

Mechanism of relaxation enhancement of spin labels in membranes by paramagnetic ion salts: dependence on 3d and 4f ions and on the anions.

Progressive saturation EPR measurements and EPR linewidth determinations have been performed on spin-labeled lipids in fluid phospholipid bilayer membranes to elucidate the mechanisms of relaxation enhancement by different paramagnetic ion salts. Such paramagnetic relaxation agents are widely used for structural EPR studies in biological systems, particularly with membranes. Metal ions of the 3d and 4f series were used as their chloride, sulfate, and perchlorate salts. For a given anion, the efficiency of relaxation enhancement is in the order Mn(2+) > or = Cu(2+) > Ni(2+) > Co(2+) approximately Dy(3+). A pronounced dependence of the paramagnetic relaxation enhancement on the anion is found in the order ClO(-)(4) > Cl(-) > SO(2-)(4). This is in the order of the octanol partition coefficients multiplied by spin exchange rate constants that were determined for the different paramagnetic salts in methanol. Detailed studies coupled with theoretical estimates reveal that, for the chlorides and perchlorates of Ni(2+) (and Co(2+)), the relaxation enhancements are dominated by Heisenberg spin exchange interactions with paramagnetic ions dissolved in fluid membranes. The dependence on membrane composition of the relaxation enhancement by intramembrane Heisenberg exchange indicates that the diffusion of the ions within the membrane takes place via water-filled defects. For the corresponding Cu(2+) salts, additional relaxation enhancements arise from dipolar interactions with ions within the membrane. For the case of Mn(2+) salts, static dipolar interactions with paramagnetic ions in the aqueous phase also make a further appreciable contribution to the spin-label relaxation enhancement. On this basis, different paramagnetic agents may be chosen to optimize sensitivity to different structurally correlated interactions. These results therefore will aid further spin-label EPR studies in structural biology.

Spin-Exchange Term in the Solvent Equation of State Near the Critical Point for Electron-Transfer Reactions

Phenomenological equations of state (EOS) for fluids near their critical point have been obtained using literature compression factor data, Zc=PcVc/(nRTc)=0.40 to 0.10 in (Pc, Vc, and Tc are the pressure, volume per nmole, and the absolute temperature of the fluid at the critical point). The objective is to explain the deviations from the van der Waals value, Zc(vdW)=3/8 (−70% for molten Se and alkali metals up to 6% for molten Pb, Hg, and In) by including in the commonly used phenomenological thermodynamic relations a term which explicitly describes the Heisenberg spin-exchange interactions, in order to understand electron-transfer reactions in solvents near their critical point. Literature data near the critical point indicate that the 199,201Hg(Zc≅0.4) Knight shift pluments to zero while the alkali metals and Se (Zc=0.2 to 0.1) are paramagnetic fluids, and that the enhanced rates for free radical electron-exchange reactions in CO2, n-C2H6, and CHF3 with intermediate values of Zc, are correlated to Zc. The difference in the solvent behavior for electron-exchange reactions near its critical point is ascribed to spin-exchange interactions. The analysis shows that the solvated electron osmotic pressure in metal–ammonia solutions goes through a maximum where enhanced rates of electron exchange also attain a maximum versus the solvent density ρr=Vc/V≅0.5. The results can be applied to choose the best solvents, near their critical point, for the syntheses of new materials and heavy metal oxide extraction.

Electron spin resonance of Cu-porphyrin of dimer-type in Langmuir-Blodgett films

The electron spin resonance (ESR) spectra of mixed LB films of a conjugated dimer-type Cu-porphyrin and cadmium arachidate show a drastic change by adding a small amount of n-hexatriacontane as trigger molecules that cause a distinct change of orientation of porphyrins. Similar phenomenon has been observed in monomer-type Cu-porphyrin LB films. The marked difference between these cases is that the dimer films show a septet Cu hyperfine structure instead of a quartet of the monomer films with the total spectral span unchanged. This results from the Heisenberg spin exchange interaction between two Cu spins in a dimer, providing direct evidence for the existence of the dimer in LB films. The line-shape analysis of the ESR spectra observed at the X and K bands yields the detailed molecular orientation. The dimer plane is slightly more inclined toward the film plane compared with monomers in the presence of n-hexatriacontane.

Characterization of polyion complexed Langmuir-Blodgett films by electron spin resonance

Electron spin resonance spectra of the Langmuir-Blodgett films of 5-, 10-, and 16-doxylstearic acids (DXSTAs) and their mixtures with stearic acid complexed with polyallylamine, polyvinylmethylpyridinium iodide, and polyvinylbenzyltrimethylammonium chloride are measured at various angles between the magnetic field and the film normal. From the difference in the strength of Heisenberg spin exchange interaction among these three kinds of DXSTA films, it was indicated that the mobility of the methylene chain in these films increased with the distance from the head group. From the anisotropic properties of these spectra, it was also shown that the DXSTA molecules were well oriented with their methylene chain almost perpendicular to the film surface and were well arranged two dimensionally in the film plane.

Rotational diffusion and intermolecular collisions of a spin labeled alpha-helical peptide determined by electron spin echo spectroscopy.

Short peptides that are composed mainly of alanine have recently been shown to form alpha-helices in aqueous solution at low temperature (Marqusee, S., and R. L. Baldwin. 1987. Proc. Natl. Acad. Sci. 84:8898-8902; Marqusee, S., V. H. Robbins, and R. L. Baldwin. 1989. Proc. Natl. Acad. Sci. USA. 86:5286-5290). These peptides are excellent models for probing structure and dynamics in isolated helical domains. In previous work we have designed and synthesized spin labeled analogs of these helix-forming peptides and we have shown that these analogs retain the folding characteristics of the parent peptide (Todd, A. P., and G. L. Millhauser. 1991. Biochemistry. 30:5515-5523). Using conventional continuous wave electron spin resonance (CW ESR) we have further shown that local motion is more pronounced near the helix amino terminus than in the central region as the peptide is thermally unfolded (Miick, S. M., A. P. Todd, and G. L. Millhauser. 1991. Biochemistry. 30:9498-9503). In this present work we use electron spin echo (ESE) spectroscopy to further refine our understanding of the solution dynamics of the 3K-8 peptide, which is a 16-mer with a nitroxide spin label attached at position 8. We find that the spin echo decays are well described by a single exponential function and that the determined correlation times are close to those previously derived from CW experiments. Variable concentration ESE experiments have directly revealed Heisenberg spin exchange (HSE) interactions and we find that the interpeptide collision rate is near to that expected for a free species in solution. This provides strong evidence that the helical conformation of these peptides is not stabilized by intermolecular interactions.

Influence of Heisenberg spin exchange on conventional and phase-quadrature EPR lineshapes and intensities under saturation

The effects of the Heisenberg spin-exchange interaction on saturation-transfer EPR spectra are analyzed according to a simple analytical model which contains the essential features of anisotropic powder patterns and in which the saturation-transfer intensity is taken to be proportional to the effective spin-lattice relaxation time. Spectral diffusion induced by spin exchange is predicted to give rise to a large reduction in the overall spectral intensity, with relatively little change in the spectral lineshape. The effects at low exchange frequencies (of the order of or less than the intrinsic spin-lattice relaxation rate) are much greater than those on the saturation of the conventional EPR spectrum and are readily distinguishable from those of slow rotational diffusion due to the insensitivity of the spectral lineshape. The theoretical predictions are found to be in accord with experimental measurements on the spin-concentration dependence of the saturation-transfer EPR spectra of a spin-labeled phospholipid in model membrane systems.