Exchange Constants Research Articles

Orbital magnetic field effects in Mott insulators with strong spin-orbit coupling

We study the effect of a magnetic field on the low energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realisation of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\Gamma$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.

Magnetic structure factors Heisenberg model for magnetic ordered graphene like structure

We have theoretically studied the magnetic structure factors of Heisenberg model on honeycomb lattice in the presence of anisotropic Dzyaloshinskii–Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the frequency dependence of both longitudinal and transverse dynamical spin susceptibilities has been investigated for various physical parameters in the model Hamiltonian. Using Holstein–Primakoff bosonic transformations, the behavior of magnetic susceptibilities properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of static spin susceptibilities on Dzyaloshinskii–Moriya interaction strength for various next nearest neighbor interaction strengths. We have found the dependence of static longitudinal spin structure factor on Dzyaloshinskii–Moriya interaction strength shows a divergence behavior at phase transition point for various next nearest neighbor exchange constants. Also our results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to lower frequency with next nearest neighbor coupling constant.

Reduced Exchange Interactions in Magnetic Tunnel Junction Free Layers with Insertion Layers

Perpendicularly magnetized CoFeB layers with ultra-thin non-magnetic insertion layers are very widely used as the electrodes in magnetic tunnel junctions for spin transfer magnetic random access memory devices. Exchange interactions play a critical role in determining the thermal stability of magnetic states in such devices and their spin torque switching efficiency. Here the exchange constant of free layers incorporated in full magnetic tunnel junction layer stacks, specifically CoFeB free layers with W insertion layers is determined by magnetization measurements in a broad temperature range. A significant finding is that the exchange constant decreases significantly and abruptly with W insertion layer thickness. The perpendicular magnetic anisotropy shows the opposite trend; it initially increases with W insertion layer thickness and shows a broad maximum for approximately one monolayer (0.3 nm) of W. These results highlight the interdependencies of magnetic characteristics required to optimize the performance of magnetic tunnel junction devices.

Helical antiferromagnetic ordering in EuNi1.95As2 single crystals

The Eu{+2} spins-7/2 in EuNi2As2 with the body-centered tetragonal ThCr2Si2 structure order antiferromagnetically below the Neel temperature TN =15 K into a helical antiferromagnetic (AFM) structure with the helix axis aligned along the tetragonal c axis and the Eu ordered moments aligned ferromagnetically within the ab plane as previously reported from neutron diffraction measurements [T. Jin, et al., Phys. Rev. B 99, 014425 (2019)]. Here we study the crystallographic, magnetic, thermal, and electronic transport properties of Bi-flux-grown single crystals using single-crystal x-ray diffraction, anisotropic magnetic susceptibility chi, isothermal magnetization M, heat capacity Cp, and electrical resistivity rho measurements versus applied magnetic field H and temperature T. Vacancies are found on the Ni sites corresponding to the composition EuNi{1.95}As2. The chi{ab}(T) data below TN are fitted well by molecular field theory (MFT), and the helix turn angle kd and the Eu-Eu Heisenberg exchange constants are extracted from the fit parameters. The kd value is in good agreement with the neutron-diffraction result. The magnetic contribution to the zero-field heat capacity below TN is also fitted by MFT. The isothermal in-plane magnetization Mab exhibits two metamagnetic transitions versus H, whereas Mc(T = 2 K) is nearly linear up to H =14 T, both behaviors being consistent with MFT. The Mc(H,T), rho(Hc,T), and Cp(Hc,T) data yielded a Hc-T phase diagram separating the AFM and paramagnetic phases in good agreement with MFT. Anisotropic chi(T) literature data for the ThCr2Si2-type helical antiferromagnet EuRh2As2 are also fitted well by MFT. A comparison is made between the crystallographic and magnetic properties of ThCr2Si2- type EuM2Pn2 compounds with M = Fe, Co, Ni, Cu, or Rh, and Pn = P or As, where only ferromagnetic and c-axis helical AFM structures are found.

Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model with and without magnetic field

We investigate phase transitions in the two-dimensional dipolar Heisenberg model with uniaxial anisotropy with a specific ratio between the exchange and dipolar constants, $\delta=1$. We obtain the $\eta$--$T$ (anisotropy vs. temperature) phase diagrams for typical values of magnetic field by a Monte Carlo method with an $O(N)$ algorithm. We find that at lower fields, the $\eta$--$T$ phase diagram consists of the planar ferromagnetic (F), (perpendicular) stripe-ordered (SO), and paramagnetic (P) phases, and is characterized by the triple point. In the SO phase realized at larger $\eta$ and smaller $T$, the SO pattern changes depending on the field. On the other hand, we find that at higher fields, the SO phase does not exist, while the planer F phase robustly remains. We study the properties of the phase boundaries by employing finite-size-scaling analyses. We find that the slope of the spin-reorientation-transition line is positive with and without field, i.e., $\frac{d\eta}{dT}>0$, which implies that the planar F phase changes to the SO phase with lowering temperature. In the phase diagrams we observe a characteristic shape of the P--planer F phase-transition line, whose maximum point of $\eta$ is located at an intermediate temperature. This structure leads to the temperature-induced reentrant transition associated with P and planar F phases, which appears in successive phase transitions with lowering temperature: P $\rightarrow$ planar F $\rightarrow$ P $\rightarrow$ SO phase at lower fields and P $\rightarrow$ planar F $\rightarrow$ P phases at higher fields.

The Spin Pumping Effect in a Ferromagnetic Insulator/Normal Metal System: A Simple Quantum Mechanical Model

A simple quantum mechanical model of the spin pumping effect upon the excitation of a ferromagnetic resonance in a magnetic dielectric having a flat interface with a nonmagnetic metal is constructed. The model is based on the solution of the Schrodinger equation for conduction electrons in metal. It is shown that the reflection of electrons from the insulator with an oscillating magnetization with a spin flip gives rise to both a direct and alternating (oscillating with the frequency of the resonance-exciting microwave field) spin fluxes from the ferromagnet to the insulator. In this case, the effect of direct current is small compared to the effect of the alternating current; the role of a small parameter is played by the ratio of the exchange constant of a ferromagnet to the potential barrier between the metal and the dielectric (which is higher than the Fermi energy). The result obtained is consistent with known experimental data. The model constructed provides a simple and clear picture of the origination of the phenomenon and enable one to analyze the dependence of the effect on the system parameters.

Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions.

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (h_{n}) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h_{n} to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h_{n}-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

Successive phase transitions and magnetization plateau in the spin-1 triangular-lattice antiferromagnet Ba2La2NiTe2O12 with small easy-axis anisotropy

The crystal structure and magnetic properties of the spin-1 triangular-lattice antiferromagnet Ba$_2$La$_2$NiTe$_2$O$_{12}$ are reported. Its crystal structure is trigonal $R\bar{3}$, which is the same as that of Ba$_2$La$_2$NiW$_2$O$_{12}$ [Y. Doi et al., J. Phys.: Condens. Matter 29, 365802 (2017)]. However, the exchange interaction $J/k_{\mathrm{B}}\simeq19$ K is much greater than that observed in the tungsten system. At zero magnetic field, Ba$_2$La$_2$NiTe$_2$O$_{12}$ undergoes successive magnetic phase transitions at $T_{\mathrm{N}1}=9.8$ K and $T_{\mathrm{N}2}=8.9$ K. The ground state is accompanied by a weak ferromagnetic moment. These results indicate that the ground-state spin structure is a triangular structure in a plane perpendicular to the triangular lattice owing to the small easy-axis-type anisotropy. The magnetization curve exhibits the one-third plateau characteristic of a two-dimensional triangular-lattice Heisenberg-like antiferromagnet. Exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate the large difference in the exchange constants between tellurium and tungsten systems and the good two-dimensionality of the tellurium system.

Spin-orbit excitons in CoO

CoO has an odd number of electrons in its unit cell, and therefore is expected to be metallic. Yet, CoO is strongly insulating owing to significant electronic correlations, thus classifying it as a Mott insulator. We investigate the magnetic fluctuations in CoO using neutron spectroscopy. The strong and spatially far-reaching exchange constants reported in [Sarte et al. Phys. Rev. B 98 024415 (2018)], combined with the single-ion spin-orbit coupling of similar magnitude [Cowley et al. Phys. Rev. B 88, 205117 (2013)] results in significant mixing between $j_{eff}$ spin-orbit levels in the low temperature magnetically ordered phase. The high degree of entanglement, combined with the structural domains originating from the Jahn-Teller structural distortion at $\sim$ 300 K, make the magnetic excitation spectrum highly structured in both energy and momentum. We extend previous theoretical work on PrTl$_{3}$ [Buyers et al. Phys. Rev. B 11, 266 (1975)] to construct a mean-field and multi-level spin exciton model employing the aforementioned spin exchange and spin-orbit coupling parameters for coupled Co$^{2+}$ ions on a rocksalt lattice. This parameterization, based on a tetragonally distorted type-II antiferromagnetic unit cell, captures both the sharp low energy excitations at the magnetic zone center, and the energy broadened peaks at the zone boundary. However, the model fails to describe the momentum dependence of the excitations at high energy transfers, where the neutron response decays faster with momentum than the Co$^{2+}$ form factor. We discuss such a failure in terms of a possible breakdown of localized spin-orbit excitons at high energy transfers.

Magnetic and magnetoelectric properties of AFeF5 (A = Ca, Sr) spin-chain compounds

Fluorides in general are characterized by big variety of crystal structures, whereas those containing transition metals also often show sizable magnetic properties. The tendency of fluorine to form linear chain structures in many cases results in low-dimensional magnetism. Despite the plethora of magnetic phenomena in fluorides, their magnetoelectric properties are less studied than those of oxides. In the present work we theoretically study the magnetic and magnetoelectric properties of spin-chain compounds CaFeF$_5$ and SrFeF$_5$. The density functional theory is employed for determination of magnetic exchange constants, which are then used in Monte Carlo calculations. The symmetry analysis reveals that CaFeF$_5$ does not show magnetoelectric properties, whereas SrFeF$_5$ is a multiferroic.

Local Magnetic Anisotropy of the Co-Based Amorphous Alloy

The magnetization, initial magnetic susceptibility, and magnetostriction of a multicomponent Co-based amorphous alloy have been studied. The exchange constant a and the Curie temperature TC of the alloy are determined. On the basis of a method based on the theory of stochastic magnetic structure for amorphous ferromagnets and using the magnetization curves, the correlation field Hℓ, the field Ha, the effective constant of local magnetic anisotropy Keff, and the stochastic characteristics of local anisotropy – the mean square field fluctuations and the correlation radius – have been calculated. The temperature behavior of the examined magnetic characteristics is analyzed. The results of magnetostriction research allow a conclusion to be drawn that the local magnetic anisotropy of the alloy has a single-ion origin.

Time-reversal invariance violation in neutron-nucleus scattering

Planning and interpretation of the experiments searching for the time reversal (T) and parity (P) violation in neutron reactions require values of the matrix elements of the T,P-violating nuclear forces between nuclear compound states. We calculate the root mean square values and the ratio of the matrix elements of the T,P-violating and P-violating interactions using statistical theory based on the properties of chaotic compound states and present the results in terms of the fundamental parameters in four different forms: in terms of the constants of the contact nuclear interaction, meson exchange constants, QCD theta-term and quark chromo-EDMs. Using current limits on these parameters, we obtain the upper bounds on the ratio of the matrix elements.

Current-Induced Modulation of the Interfacial Dzyaloshinskii-Moriya Interaction.

The Dzyaloshinskii-Moriya (DM) interaction is an antisymmetric exchange interaction that is responsible for the emergence of chiral magnetism. The origin of the DM interaction, however, remains to be identified albeit the large number of studies reported on related effects. It has been recently suggested that the DM interaction is equivalent to an equilibrium spin current density originating from spin-orbit coupling, an effect referred to as the spin Doppler effect. The model predicts that the DM interaction can be controlled by spin current injected externally. Here we show that the DM exchange constant (D) in W/CoFeB-based heterostructures can be modulated with external current passed along the film plane. At higher current, D decreases with increasing current, which we infer is partly due to the adiabatic spin transfer torque. At lower current, D increases linearly with current regardless of the polarity of current flow. The rate of increase in D with the current density agrees with that predicted by the model based on the spin Doppler effect. These results imply that the DM interaction at the heavy-metal-ferromagnetic-metal interface partly originates from an equilibrium interface spin (polarized) current which can be modulated externally.

Dynamical and static spin structure factors of Heisenberg antiferromagnet on honeycomb lattice in the presence of Dzyaloshinskii-Moriya interaction

We have theoretically studied the spin structure factors of Heisenberg model on honeycomb lattice in the presence of longitudinal magnetic field, i.e. magnetic field perpendicular to the honeycomb plane, and Dzyaloshinskii-Moriya interaction. The possible effects of next nearest neighbor exchange constant are investigated in terms of anisotropy in the Heisenberg interactions. This spatial anisotropy is due to the difference between nearest neighbor exchange coupling constant and next nearest neighbor exchange coupling constant. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to higher frequency with magnetic field. Also the intensity of dynamical transverse spin structure factor is not affected by magnetic field. However the Dzyaloshinskii Moriya interaction strength causes to decrease the intensity of dynamical transverse spin structure factor. The increase of magnetic field does not varied the frequency position of peaks in dynamical longitudinal spin susceptibility however the intensity reduces with magnetic field. Our results show static transverse structure factor is found to be monotonically decreasing with magnetic field and temperature for different values of next nearest neighbor coupling exchange constant.

Exchange interactions from a nonorthogonal basis set: From bulk ferromagnets to the magnetism in low-dimensional graphene systems

We present a computational method to determine the exchange constants in isotropic spin models. The method uses the Hamiltonian and overlap matrices computed from density functional schemes that are based on nonorthogonal basis sets. We demonstrate that the new method as implemented in the SIESTA code reproduces the Heisenberg interactions of simple metallic bulk ferromagnets as obtained from former well--established computational approaches. Then we address $sp$ magnetism in graphene nanostructures. For fluorinated graphene we obtain exchange interactions in fairly good agreement with previous calculations using maximally localized Wannier functions and we confirm the theoretical prediction of a 120$^\circ$ N\'eel state. Associated with the magnetic edge-states of a zigzag graphene nanoribbon we find rapidly decaying exchange interactions, however, with an unconventional distance dependence of $\exp(-\sqrt{r/\delta})$. We show that the stiffness constant derived from the exchange interactions is consistent with previous estimate based on total energy differences of twisted spin configurations. We highlight that our method is an efficient tool for the analysis of novel hybrid nano-structures where metallic and organic components are integrated to form exotic magnetic patterns.

Ordering of Fe and Zn Ions and the Magnetic Properties of FeZnMo3O8

In the present paper electronic, magnetic, and structural properties of a novel system FeZnMo$_3$O$_8$ with a polar crystal structure are investigated using GGA+U calculations. It is shown that Fe ions preferably occupy octahedral and Zn ions tetrahedral positions. This structural feature is caused by different ionic radii of these ions and not by the exchange coupling. The calculated exchange constants naturally explain magnetic structure observed in this material.

Controlling Ferromagnetic Ground States and Solitons in Thin Films and Nanowires Built from Iron Phthalocyanine Chains

AbstractIron phthalocyanine (FePc) is a molecular semiconductor whose building blocks are 1D ferromagnetic chains. It is shown that its optical and magnetic properties are controlled by the growth strategy, obtaining extremely high coercivities of over 1 T and modulating the exchange constant between 15 and 29 K through switching from thin films with controlled orientations, to ultralong nanowires. Magnetization measurements are analyzed using concepts and formulas with broad applicability to all 1D ferromagnetic chains. They show that FePc is best described by a xy model with moments preferentially lying in the molecular planes. The chain Hamiltonian is very similar to that for the classic inorganic magnet CsNiF3, but with ferromagnetic rather than antiferromagnetic interchain interactions. The dominant degrees of freedom are topological excitations called solitons, namely moving 1D magnetic domain walls, and at low temperatures and fields a “super‐Curie–Weiss” law characteristic of nearly 1D xy and Heisenberg ferromagnets, where susceptibility scales as 1/(T2–θ2), is observed. The ability to control the molecular orientation and ferromagnetism of FePc systems, and produce them on flexible substrates, together with excellent transistor characteristics reported previously for phthalocyanine analogues, makes them potentially useful for magneto‐optical and spintronic devices.

Exciton Fine Structure in Perovskite Nanocrystals.

The bright emission observed in cesium lead halide perovskite nanocrystals (NCs) has recently been explained in terms of a bright exciton ground state [ Becker et al. Nature 2018 , 553 , 189 - 193 ], a claim that would make these materials the first known examples in which the exciton ground state is not an optically forbidden dark exciton. This unprecedented claim has been the subject of intense experimental investigation that has so far failed to detect the dark ground-state exciton. Here, we review the effective-mass/electron-hole exchange theory for the exciton fine structure in cubic and tetragonal CsPbBr3 NCs. In our calculations, the crystal field and the short-range electron-hole exchange constant were calculated using density functional theory together with hybrid functionals and spin-orbit coupling. Corrections associated with long-range exchange and surface image charges were calculated using measured bulk effective mass and dielectric parameters. As expected, within the context of the exchange model, we find an optically inactive ground exciton level. However, in this model, the level order for the optically active excitons in tetragonal CsPbBr3 NCs is opposite to what has been observed experimentally. An alternate explanation for the observed bright exciton level order in CsPbBr3 NCs is offered in terms of the Rashba effect, which supports the existence of a bright ground-state exciton in these NCs. The size dependence of the exciton fine structure calculated for perovskite NCs shows that the bright-dark level inversion caused by the Rashba effect is suppressed by the enhanced electron-hole exchange interaction in small NCs.

Super-exchange theory for polyvalent anion magnets

The Goodenough–Kanamori–Anderson (GKA) rules have been widely applied for explaining the magnetic properties induced by super-exchange interaction. As conclusions of the super-exchange theory, they reveal the antiferromagnetic (ferromagnetic) ordering along with bond angle of 180° (90°) in the cation–anion–cation interaction path, in which the theory sets a pre-condition that the electronic states of cations in all paths are identical. We observed that the GKA rules are in fact not universal and even invalid to materials containing anions with different valence states, for example, the layered CrOCl crystal (with two valence states of anions: O2− and Cl−). In this study, we propose an extended super-exchange theory (ESET) related to superposed electronic states of cation in a specific path. ESET is capable of predicting not only the sign and relative magnitude of magnetic exchange constants in different cation–anion–cation paths, but also the magnetic ground state. Through our proposed theory, we conclude that the magnetic ordering along with bond angle of 90° in Cr–Cl–Cr path is moderately antiferromagnetic and of 180° in Cr–O–Cr path is strongly ferromagnetic, which are opposite to the contents of GKA rules. Moreover, we clarify that monolayer CrOCl has antiferromagnetic ordering rather than ferromagnetic as reported recently. The reliability of ESET is verified via first-principles calculation and previous experimental report as well, and its universality is also demonstrated. Thus, our theory is powerful to predict the magnetic properties, which makes it possible to design new high Curie temperature two-dimensional semiconducting ferromagnets with polyvalent anion materials.

Thiosemiquinoid Radical-Bridged CrIII2 Complexes with Strong Magnetic Exchange Coupling.

Semiquinoid radical bridging ligands are capable of mediating exceptionally strong magnetic coupling between spin centers, a requirement for the design of high-temperature magnetic materials. We demonstrate the ability of sulfur donors to provide much stronger coupling relative to their oxygen congeners in a series of dinuclear complexes. Employing a series of chalcogen donor-based bis(bidentate) benzoquinoid bridging ligands, the series of complexes [(TPyA)2Cr2(RL4-)]2+ (OLH4 = 1,2,4,5-tetrahydroxybenzene, OSLH4 = 1,2-dithio-4,5-dihydroxybenzene, SLH4 = 1,2,4,5-tetrathiobenzene, TPyA = tris(2-pyridylmethyl)amine) was synthesized. Variable-temperature dc magnetic susceptibility data reveal the presence of weak antiferromagnetic superexchange coupling between CrIII centers in these complexes, with exchange constants of J = -2.83(3) (OL4-), -2.28(5) (OSL4-), and -1.80(2) (SL4-) cm-1. Guided by cyclic voltammetry and spectroelectrochemical measurements, chemical one-electron oxidation of these complexes gives the radical-bridged species [(TPyA)2Cr2(RL3-•)]3+. Variable-temperature dc susceptibility measurements in these complexes reveal the presence of strong antiferromagnetic metal-semiquinoid radical coupling, with exchange constants of J = -352(10) (OL3-•), - 401(8) (OSL3-•), and -487(8) (SL3-•) cm-1. These results provide the first measurement of magnetic coupling between metal ions and a thiosemiquinoid radical, and they demonstrate the value of moving from O to S donors in radical-bridged metal ions in the design of magnetic molecules and materials.