Nearest-neighbor Exchange Constants Research Articles

Microscopic Spin Hamiltonian for a Dipolar Heisenberg Magnet LiGdF4 from EPR Measurements

Low-temperature electron paramagnetic resonance measurements are performed on single crystals of LiY1 ‒xGdxF4 with low x = 0.005 and moderate x = 0.05 concentration of Gd ions. Modeling of the experimental spectra allows us to precisely determine microscopic parameters of the spin Hamiltonian of the parent LiGdF4 material, including the nearest-neighbor exchange constant. The obtained parameters are further tested by comparing a strongly anisotropic Curie–Weiss temperature obtained for LiGdF4 in our static magnetization measurements with theoretically computed values. We find a fine balance between principal magnetic interactions in LiGdF4, which results in a hidden magnetic frustration presumably leading to a delayed magnetic ordering and an enhanced magnetocaloric effect at low temperatures.

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb2

${\mathrm{EuMnSb}}_{2}$ is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. Here we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline $^{151}\mathrm{Eu}$ M\"ossbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below ${T}_{{\text{N}}_{\text{Mn}}}=323(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Mn magnetic moment ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below ${T}_{{\text{N}}_{\text{Eu1}}}=23(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Eu magnetic moment ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ canted away from the layer normal and ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ retaining its higher temperature order. ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $P{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}{a}^{\ensuremath{'}}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below ${T}_{{\text{N}}_{\text{Eu2}}}=9(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ reveals a third AFM phase where ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ remains unchanged but ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ develops an additional substantial in-plane canting. This phase has MSG $P11\frac{{2}_{1}}{{a}^{\ensuremath{'}}}$. We also find some evidence of short-range magnetic correlations associated with the Eu between $12\phantom{\rule{4pt}{0ex}}\text{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}30\phantom{\rule{4pt}{0ex}}\text{K}$. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in ${\mathrm{EuMnSb}}_{2}$ and their potential for tuning topological properties.

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.

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.

Thermodynamic properties of Heisenberg model for magnetic ordered graphene sheet

We study the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the 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 temperature dependence of specific heat has been investigated for various physical parameters in the model Hamiltonian. Using Holstein-Primakoff bosonic transformations, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of specific heat and magnetization on Dzyaloshinskii-Moriya interaction strength for various next nearest neighbor interaction strengths. At low temperatures, the specific heat is found to be monotonically increasing with temperature. We have found the dependence of specific heat on Dzyaloshinskii-Moriya interaction strength shows a monotonic increasing behavior for various next nearest neighbor exchange constants. Also we have studied the temperature dependence of staggered magnetization for different next nearest neighbor coupling constants. Our results show the critical temperature moves to higher amounts with reduction of Dzyaloshinskii-Moriya interaction strength.

Three-state Potts model on triangular lattice with nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions

Using Monte Carlo simulations, we investigated phase transitions and frustrations in the three-state Potts model on a triangular lattice with allowance for antiferromagnetic exchange interactions between nearest-neighbors J1 and next-nearest-neighbors J2. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r=J2/J1 is chosen within the range of 0≤r≤2. Based on the analysis of the entropy, specific heat, system state density function, and fourth order Binder cumulants, the phase transitions in the Potts model with interactions J1<0 and J2<0 are shown to be found in value ranges of 0≤r<0.2 and 1.25≤r≤2.0. In an intermediate range of 0.2≤r≤1.0 the phase transition fails and the frustrations are revealed.

Effective spin-12exchange interactions inTb2Ti2O7

We derive an effective spin-$\frac{1}{2}$ exchange model for non-Kramers ${\mathrm{Tb}}^{3+}$ states in the pyrochlore ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. The four anisotropic nearest-neighbor exchange constants, as well as next-neighbor exchange constants, are derived for the effective model. This work goes beyond the independent tetrahedra model by considering all nearest-neighbor exchange paths on the pyrochlore lattice. Estimates of the exchange constants reveal that ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ is described by a quantum spin ice Hamiltonian.

Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice

Phase transitions in two-dimensional arrays described by the three-vertex Potts model involving the interactions between magnetic moments located at the nearest-neighbor and next-nearest-neighbor sites of a triangular lattice are studied using the Monte Carlo method. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r = J2/J1 is chosen within the 0–1 range. The analysis of the low temperature behavior of the entropy and density of states in the system, as well as of the fourth-order Binder cumulants, shows that in the range 0 ≤ r < 0.2, this model exhibits a first-order phase transition, whereas at r ≥ 0.2, frustrations arise in such a system.

Exchange integrals in Mn- and Co-doped II-VI semiconductors

Exchange integrals between nearest-neighbor (NN) transition metal ions in II-VI diluted magnetic semiconductors (DMSs) are calculated within a local superexchange model, which includes orbital-dependent transfer, on-site Coulomb repulsion and Hund's exchange between $3d$ electrons, and ligand field effects. This extended model gives a quantitative account for the available experimental data on the NN exchange constants in all II-VI DMS family (wurtzite and zinc-blende) doped by cobalt or manganese. As expected, all obtained exchange integrals are antiferromagnetic. Remarkably, the model input parameters are taken directly from the photoemission spectroscopy. We show that in the case of Co-doped compounds, as compared to Mn-doped ones, the exchange process has at least two salient features. The first one is that the electron transfer between NN $\mathrm{Co}{}^{2+} 3d$ orbitals strongly depends on their symmetry positions in the crystal lattice. The second one is related to a peculiar virtual process, involving empty and occupied $\mathrm{Co}{}^{2+} 3d$ orbitals, which leads to an additional ferromagnetic contribution to the exchange constant. We argue that our systematic study of the superexchange opens a pathway toward an understanding of other exchange mechanisms occurring in DMSs.

Complex trend of magnetic order in Fe clusters on4dtransition-metal surfaces. II. First-principles calculations

We use first-principles calculations based on density functional theory to investigate the magnetic exchange interaction of Fe clusters on Rh(111) and Ru(0001). We consider dimers, trimers, tetramers, and pentamers of different shape in fcc and hcp stacking as well as infinite atomic and biatomic chains. From the dimer calculations, we extract the exchange interaction as a function of adatom distance by mapping total energies to a Heisenberg model. The nearest-neighbor (NN) exchange constant is about one order of magnitude smaller than reported for other substrates due to the strong hybridization between the Fe atoms and the partly filled $4d$ band of the surface. We also find a transition from a ferromagnetic NN exchange interaction for Fe dimers on Rh(111) to an antiferromagnetic one on Ru(0001). The distance-dependent exchange coupling displays a RKKY-like oscillatory behavior, which is nearly inverted for Fe dimers on the Rh(111) surface compared to those on Ru(0001). Unexpectedly, for Fe clusters beyond dimers, a complex trend of the magnetic ground state is observed which alternates between ferro- and antiferromagnetic configurations depending on cluster size and shape. In view of the exchange constants obtained for dimers, it is surprising that on both surfaces small compact clusters are ferromagnetic while open structures such as linear trimers or tetramers become antiferromagnetic. We demonstrate that both vertical and lateral structural relaxations of the clusters are crucial in order to understand this unexpected trend of magnetic order and connected to the competition of direct ferromagnetic exchange among Fe atoms in the cluster and the hybridization with the substrate.

Calculation of Exchange Constants in Spinels Chromites ZnxCo1−xCr2O4

The exchange interactions of the nearest-neighbor exchange constant between tetrahedral and octahedral sublattices (JAB(x)), nearest-neighbor exchange constant inside tetrahedral sublattice (JAA(x)) and nearest-neighbor exchange constant inside octahedral sublattice (JBB(x)) in cobalt and zinc chromites are calculated using the probability distribution. The Curie—Weiss temperature and the critical temperature are deduced using the mean field and the high temperature series expansion theories in ZnxCo1−xCr2O4. The critical exponent associated with the magnetic susceptibility (γ) is deduced for CoCr2O4.

Inelastic neutron scattering studies on the odd-membered antiferromagnetic wheel Cr8Ni

$[{{(}^{i}{C}_{3}{H}_{7})}_{2}N{H}_{2}][C{r}_{8}Ni{F}_{9}{({O}_{2}CCMe)}_{18}]$, or $C{r}_{8}Ni$, is a prominent example of an odd-membered antiferromagnetic ``wheel.'' A detailed characterization of the magnetic properties of $C{r}_{8}Ni$ has been conducted. Inelastic neutron scattering (INS) is used to investigate the energy and momentum transfer dependence of the low-lying spin excitations, including excited states inaccessible by other experimental techniques. The richness of the INS data, in conjunction with microscopic spin Hamiltonian simulations, enables an accurate characterization of the magnetic properties of $C{r}_{8}Ni$. Nearest-neighbor exchange constants of ${J}_{\mathrm{CrCr}}$ = 1.31 meV and ${J}_{\mathrm{CrNi}}$ = 3.22 meV are determined, and clear evidence of axial single-ion anisotropy is found. The parameters determined by INS are shown to fit magnetic susceptibility. The spectroscopic identification of several successive $S=1$ excited total spin states and lowest spin band excitations show that the rotational band picture, valid for bipartite AFM wheels, breaks down for this odd-numbered wheel. The exchange constants determined here differ from previous efforts based on bulk measurements, and possible reasons are discussed. The large ${J}_{\mathrm{CrNi}}/{J}_{\mathrm{CrCr}}$ ratio in $C{r}_{8}Ni$ puts this wheel into a regime with strong quantum fluctuations in which the ground state can be described with a valence bond solid state picture.

Optical phonons, spin correlations, and spin-phonon coupling in the frustrated pyrochlore magnetsCdCr2O4andZnCr2O4

We report on infrared, Raman, magnetic susceptibility, and specific heat measurements on CdCr2O4 and ZnCr2O4 single crystals. We estimate the nearest-neighbor and next-nearest neighbor exchange constants from the magnetic susceptibility and extract the spin-spin correlation functions obtained from the magnetic susceptibility and the magnetic contribution to the specific heat. By comparing with the frequency shift of the infrared optical phonons above TN , we derive estimates for the spin-phonon coupling constants in these systems. The observation of phonon modes which are both Raman and infrared active suggest the loss of inversion symmetry below the Neel temperature in CdCr2O4 in agreement with theoretical predictions by Chern and coworkers [Phys. Rev. B 74, 060405 (2006)]. In ZnCr2O4 several new modes appear below TN, but no phonon modes could be detected which are both Raman and infrared active indicating the conservation of inversion symmetry in the low temperature phase.

Multiple nearest-neighbor exchange model for the frustrated magnetic molecules{Mo72Fe30}and{Mo72Cr30}

Our measurements of the differential susceptibility $\ensuremath{\partial}M/\ensuremath{\partial}H$ of the frustrated magnetic molecules ${{\text{Mo}}_{72}{\text{Fe}}_{30}}$ and ${{\text{Mo}}_{72}{\text{Cr}}_{30}}$ reveal a pronounced dependence on magnetic field $(H)$ and temperature $(T)$ in the low $H$--low $T$ regime, contrary to the predictions of the existing models. Excellent agreement with experiment is achieved upon formulating a nearest-neighbor classical Heisenberg model where the 60 nearest-neighbor exchange interactions in each molecule, rather than being identical as has been assumed heretofore, are described by a two-parameter rectangular probability distribution of values of the exchange constant. We suggest that the probability distribution provides a convenient phenomenological platform for summarizing the combined effects of multiple microscopic mechanisms that disrupt the idealized picture of a Heisenberg model based on a single value of the nearest-neighbor exchange constant.

Exchange between deep donors in semiconductors: A quantum defect approach

Exchange interactions among defects in semiconductors are commonly treated within effective-mass theory using a scaled hydrogenic wave function. However, such a wave function is only applicable to shallow impurities; here, we present a simple but robust generalization to treat deep donors, in which we treat the long-range part of the wave function using the well-established quantum defect theory, and include a model central-cell correction to fix the bound-state eigenvalue at the experimentally observed value. This allows us to compute the effect of binding energy on exchange interactions as a function of donor distance; this is a significant quantity given recent proposals to carry out quantum information processing using deep donors. As expected, exchange interactions are suppressed (or increased), compared to the hydrogenic case, by the greater localization (or delocalization) of the wave functions of deep donors (or ``supershallow'' donors with binding energy less than the hydrogenic value). The calculated results are compared with a simple scaling of the Heitler-London hydrogenic exchange; the scaled hydrogenic results give the correct order of magnitude but fail to reproduce quantitatively our calculations. We calculate the donor exchange in silicon including intervalley interference terms for donor pairs along the {100} direction, and also show the influence of the donor type on the distribution of nearest-neighbor exchange constants at different concentrations. Our methods can be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.

A Computational Study of Nickel Ferrite

Magnetic properties and electronic structure of nickel ferrite are studied using hybrid density functional theory. In the calculation, the exchange correlation is a mixture of Fock exchange, local spin density approximation (LSDA) and generalized gradient approximation (GGA). The weighting factor ( w) of the Fock term and a scaling factor of the 3d orbitals of Fe 3+ ( α) are introduced as fitting parameters. All nearest neighbor exchange constants for inter and intra A and B sites of the spinel structure of nickel ferrite are calculated from the energies of different magnetic structures. Local magnetic moments of the ions on the A and B sites are calculated by the Mülliken population analysis. Moreover, the density of states is calculated to show the insulating nature of nickel ferrite. The band gap and intra-site Coulomb repulsion are extracted from the calculated density of states. The charge density map is calculated to visualize the electrons in nickel ferrite.

Calculation of exchange constants in spinel ferrites with magnetic S-state ions

The exchange constants in spinel ferrites with S-state ions, including magnesium ferrite, lithium ferrite, and manganese ferrite, were calculated using modified Becke’s three-parameter density functional, where the percentage of Hartree–Fock exchange in total exchange was introduced as a variable parameter (w) to match the experimental results of exchange constants by controlling the localization and delocalization of the electrons. Consistently, the scaling factor of the 3d orbitals of ferric ions was also introduced as a variable parameter (α). From the calculation, the values of parameters w and α matching the experimental results of JAB (nearest-neighbor exchange constant between tetrahedral and octahedral sublattices) were concentrative, while those matching the experimental results of JAA (nearest-neighbor exchange constant inside tetrahedral sublattice) and JBB (nearest-neighbor exchange constant inside octahedral sublattice) were dispersive. Observing that JAB is dominant in most practical ferrimagnetic spinel ferrites and the current accuracy of the measurements of JBB and JAA may be insufficient to support more accurate conclusion, it is suggested that there may be an empirical universal law of parameters w and α for spinel ferrites with S-state ions.

Competition between helimagnetism and commensurate quantum spin correlations in LiCu2O2.

Neutron diffraction and bulk measurements are used to determine the nature of the low-temperature ordered state in LiCu2O2, a S=1/2 spin-chain compound with competing interactions. The spin structure is found to be helimagnetic, with a propagation vector (0.5,zeta,0), zeta=0.174. The nearest-neighbor exchange constant and frustration ratio are estimated to be J(1)=5.8 meV and J(2)/J(1)=0.29, respectively. For idealized quantum spin chains, these parameter values would signify a gapped spin-liquid ground state with commensurate spin correlations. The observed temperature dependence of the magnetic propagation vector in LiCu2O2 is attributed to a competition between incommensurate helimagnetism in the classical spin model and commensurability in the quantum case. It is also proposed that long-range ordering in LiCu2O2 is facilitated by intrinsic nonstoichiometry.

Determination of hole-induced ferromagnetic exchange between nearest-neighbor Mn spins in p-type Zn1−Mn Te

Abstract The first direct determination of the hole-induced ferromagnetic contribution to the nearest-neighbor (NN) Mn–Mn exchange in Zn 1− x Mn x Te is reported. The difference between the NN exchange constants for insulating and strongly p-type samples was found by comparing inelastic magnetic neutron scattering from NN Mn–Mn pairs in the specimens.

Magnetic properties of ZnO-based diluted magnetic semiconductors

We report a study of the magnetic properties of transition-metal doped Zn1−xTMxO (TM=Mn, Co, Fe). Polycrystalline powder samples were synthesized by both solid-state and liquid-phase reactions. From the Curie–Weiss behavior of susceptibility at high temperatures, it was found that the TM–TM interaction is dominated by antiferromagnetic coupling with effective nearest-neighbor exchange constants J=−90 to −30 K. The magnetization data measured at low temperature as a function field H are fit to a parameterized Brillouin function to obtain the effective concentration xeff of magnetically active TM2+ ions. As x increases, the fraction of magnetically active ions, xeff/x, decreases. This is ascribed to an increase in average AF interaction between doped magnetic spins as the average distance between them decreases with an increase in x.