Intersite Exchange Interactions Research Articles

Microscopic origin of magnetism in monolayer 3d transition metal dihalides

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $M{X}_{2}$ ($M$=V, Mn, Ni and $X$=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered $3d$ transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

Ferro-octupolar Order and Low-Energy Excitations ind2Double Perovskites of Osmium

Conflicting interpretations of experimental data preclude the understanding of the quantum magnetic state of spin-orbit coupled $d^2$ double perovskites. Whether the ground state is a Janh-Teller-distorted order of quadrupoles or the hitherto elusive octupolar order remains debated. We resolve this uncertainty through direct calculations of all-rank inter-site exchange interactions and inelastic neutron scattering cross-section for the $d^2$ double perovskite series Ba$_2M$OsO$_6$ ($M$= Ca, Mg, Zn). Using advanced many-body first principles methods we show that the ground state is formed by ferro-ordered octupoles coupled by superexchange interactions within the ground-state $E_g$ doublet. Computed ordering temperature of the single second-order phase-transition is consistent with experimentally observed material-dependent trends. Minuscule distortions of the parent cubic structure are shown to qualitatively modify the structure of gaped magnetic excitations.

Phase transitions in a model of BEDT-TTF compound electron subsystem

Model of electronic subsystem of (BEDT-TTF)2X family is studied theoretically within Green function equation of motion approach. The configurational representation of the model Hamiltonian which allows analytical calculation of the energy spectrum is developed. Effective Hamiltonian of the model takes into account the strong intra-site Coulomb, intersite exchange interaction of electrons and correlated hopping of electrons both within the conducting plane and in transversal direction. With rise of intraatomic Coulomb repulsion in the energy spectrum a gap opens and the transition to antiferromagnetic state is realized. At the external pressure and decreasing temperature the transition from insulator to metallic phase occurs. The experimental phase diagrams for quasi-twodimensional organic conductors with strong electron correlations and correlated hopping are discussed.

Longitudinal Spin Fluctuations and Magnetic Ordering Temperature in Metals: First-Principle Modeling and Phase Space Integration Measure

In magnetically ordered metals the magnitude of the local atomic moment become temperature dependent. To deal with this problem on the ab-initio level one need to employ a specific methodology for calculation of the electronic structure that takes into the account the magnetic disorder effects. In addition one needs to setup a special statistical models allowing simultaneously for ab-initio mapping and for the variation of the local spin magnitude. To this end here we discuss and employ methodology that is based on the Disordered Local Moment (DLM) formalism, spin-constraint Local Spin Density Approximation (LSDA) and Lichtenstein theorem for calculation of the inter-site exchange interactions. An extended classical Heisenberg Hamiltonian used for mapping allows for the variation of the lattice site spin magnitude. We consider here three representative canonical transition metals ferromagnets hcp Gd, bcc Fe and fcc Ni with quite a different character of the magnetic moment localization and illustrate the relative importance of the longitudinal spin fluctuations and the magnetic disorder induced electronic structure reconstruction. We use recently introduced linear measure [1] for integration over the longitudinal spin component in the classical configurational spin space.

First-principles study of the giant magnetic anisotropy energy in bulk Na4IrO4

In 5d transition metal oxides, novel properties arise from the interplay of electron correlations and spin--orbit interactions. Na4IrO4, where 5d transition-metal Ir atom occupies the center of the square-planar coordination environment, is synthesized. Based on density functional theory, we calculate its electronic and magnetic properties. Our numerical results show that the Ir-5d bands are quite narrow, and the bands around the Fermi level are mainly contributed by d_{xy},d_{yz} and d_{zx} orbitals. The magnetic easy-axis is perpendicular to the IrO4 plane, and the magnetic anisotropy energy (MAE) of Na4IrO4 is found to be very giant. We estimate the magnetic parameters by mapping the calculated total energy for different spin configurations onto a spin model. The next nearest neighbor exchange interaction J2 is much larger than other intersite exchange interactions and results in the magnetic ground state configuration. Our study clearly demonstrates that the huge MAE comes from the single-ion anisotropy rather than the anisotropic interatomic spin exchange. This compound has a large spin gap but very narrow spin-wave dispersion, due to the large single-ion anisotropy and relatively small exchange couplings. Noticing this remarkable magnetic feature originated from its highly isolated IrO4 moiety, we also explore the possiblity to further enhance the MAE.

Investigation of structural, morphological and electromagnetic properties of Mg0.25Mn0.25Zn0.5−xSrxFe2O4 ferrites

Polycrystalline Mg0.25Mn0.25Zn0.5−xSrxFe2O4 (0 ≤ x ≤ 0.20) ferrites were synthesized using the solid state reaction sintering at 1373 K and 1473 K for 4 h. The XRD patterns revealed the formation of single phase cubic spinel with Sr2FeO4 and SrFe12O19 as impurity phases. The decrement in the lattice parameter for Sr2+ substituted samples is attributed to the difference in ionic radii of cations. The crystallite size decreases with increase in Sr2+ content. Low frequency dielectric dispersion is attributed due to the Maxwell-Wagner interfacial polarization. The appearance of the peak in dielectric loss spectrum for x = 0.15 and 0.20 at 1373 K and x = 0.20 at 1473 K suggests the presence of relaxing dipoles. The loss peak shifts towards lower frequency side with Sr2+ content at 1373 K which is due to the strengthening of dipole–dipole interactions. The complex impedance spectra clearly revealed that the both grain and grain boundary effects on the electrical properties. A complex electric modulus spectrum indicates that a non-Debye type of conductivity relaxation exists. The saturation magnetization and remanence gradually decreases with Sr2+ substitution which may be due to the existence of non-magnetic phase in the space between the magnetic particles and the substitution of Zn2+ cation in Mg0.25Mn0.25Zn0.5Fe2O4 ferrite lattice by Sr2+ content. The permeability decreases significantly while the cut-off frequency increases with the Sr2+ content at 1373 K and decreases at 1473 K, obeying the Snoek's law.The decrease in permeability with Sr2+ content is attributed due to the decrease in magnetization because non-magnetic ions weaken the inter-site exchange interaction.

Theoretical prediction of antiferromagnetism in layered perovskite Sr2TcO4

We theoretically investigate magnetic properties of Sr$_2$TcO$_4$, a 4d transition-metal layered perovskite of the K$_2$NiF$_4$-type with half-filled t$_{2g}$ states. The effect of local Coulomb repulsion between the t$_{2g}$ orbitals is included within the density-functional theory (DFT)+U and DFT+dynamical mean-field theory (DMFT) methods. The DFT+DMFT predicts paramagnetic Sr$_2$TcO$_4$ to be close to the Mott insulator-to-metal transition, similarly to the cubic compound SrTcO$_3$. The inter-site exchange interactions computed within the DFT+DMFT framework point to a strong antiferromagnetic coupling between the neighboring Tc sites within the layer. We then evaluate the N\'eel temperature $T_N$ within a classical Monte Carlo approach including dipolar interactions, which stabilize the magnetic order in the frustrated K$_2$NiF$_4$ lattice structure. Our approach is applied to a set of layered and cubic perovskites. The obtained $T_N$ are in fair agreement with experiment. Within the same approach we predict $T_N$ of Sr$_2$TcO$_4$ to be in the 500-600K range.

Two-site fluctuations and multipolar intersite exchange interactions in strongly correlated systems

An approach is proposed for evaluating dipolar and multipolar intersite interactions in strongly correlated materials. This approach is based on the single-site dynamical mean-field theory (DMFT) in conjunction with the atomic approximation for the local self-energy. Starting from the local-moment paramagnetic state described by DMFT, we derive intersite interactions by considering the response of the DMFT grand potential to small fluctuations of atomic configurations on two neighboring sites. The present method is validated by applying it to one-band and two-band ${e}_{g}$ Hubbard models on the simple-cubic $3d$ lattice. It is also applied to study the spin-orbital order in the parent cubic structure of ternary chromium fluoride ${\mathrm{KCrF}}_{3}$. We obtain the onset of a G-type antiferro-orbital order at a significantly lower temperature compared to that in real distorted ${\mathrm{KCrF}}_{3}$. In contrast, its layered A-type antiferromagnetic order and N\'eel temperature are rather well reproduced. The calculated full Kugel-Khomskii Hamiltonian contains spin-orbital coupling terms inducing a misalignment in the antiferro-orbital order upon the onset of antiferromagnetism.

Investigation of the ground state of the anisotropic extended Hubbard chain at weak coupling

We study a one-dimensional anisotropic extended Hubbard model, where the inter-site density (V) and exchange (J) interactions are spin-dependent. Use of bosonization and renormalization helps investigate phase diagram. At half filling, the ground state characterizes insulating phases. The spin-dependent repulsion leads to a bond-spin-density-wave (BSDW) phase. The antiferromagnetic exchange enhances the bond-order-wave (BOW) phase while weakens the charge-density-wave (CDW) phase. When J>4V, the BSDW and CDW phases disappear. Away from half filling, the ground state exhibits superconducting behavior. The anisotropic interactions have an important effect on the phase structures.

Incommensurate spin correlations in highly oxidized cobaltates La2-xSrxCoO4.

We observe quasi-static incommensurate magnetic peaks in neutron scattering experiments on layered cobalt oxides La2−xSrxCoO4 with high Co oxidation states that have been reported to be paramagnetic. This enables us to measure the magnetic excitations in this highly hole-doped incommensurate regime and compare our results with those found in the low-doped incommensurate regime that exhibit hourglass magnetic spectra. The hourglass shape of magnetic excitations completely disappears given a high Sr doping. Moreover, broad low-energy excitations are found, which are not centered at the incommensurate magnetic peak positions but around the quarter-integer values that are typically exhibited by excitations in the checkerboard charge ordered phase. Our findings suggest that the strong inter-site exchange interactions in the undoped islands are critical for the emergence of hourglass spectra in the incommensurate magnetic phases of La2−xSrxCoO4.

Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter ${F}_{0}^{a}$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism---negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at ${F}_{0}^{a}=\ensuremath{-}1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter ${F}_{0}^{s}$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to ${F}_{0}^{a}$ at $J<0$ it requires an attraction beyond a critical value ${V}_{c}$ to generate the divergence of the charge susceptibility at ${F}_{0}^{s}=\ensuremath{-}1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.

Synthesis and Characterization of Frustrated Spin Ladders SrFe2S2O and SrFe2Se2O

AbstractChemical pressure was introduced by replacing Ba atoms with Sr atoms in the spin‐ladder compounds AEFe2Ch2O (AE = Ba, Sr; Ch = S, Se). Powders and small single crystals of SrFe2S2O and SrFe2Se2O were synthesized from SrO, Fe, and Ch (S, Se). X‐ray diffraction data were used to determine the crystal structures, which showed prominent magnetic ladderlike sublattices. The Mössbauer spectra of SrFe2S2O and SrFe2Se2O suggest the presence of localized divalent Fe ions in the FeCh3O structural units (distorted e3t23 configuration, S = 2). Single sharp hyperfine patterns at 5 K indicate the formation of simple antiferromagnetic ground states. The spin‐ordering transitions (TN) were determined by magnetic, resistivity, and specific heat data to be 216 and 228 K for SrFe2S2O and SrFe2Se2O, respectively. At ca. 540 K, both compounds exhibit a similar broad maximum in χ (Tχmax). In comparison with BaFe2S2O and BaFe2Se2O, the Sr homologues have higher Tχmax values, which suggest stronger intersite exchange interactions in accordance with the chemical pressure from the replacement of Sr atoms with Ba atoms. However, the lower Néel temperatures for the Sr homologues supports the idea that magnetic frustration is present, and it clearly has to be considered for this group of compounds.

Magnetic orderings and phase separations in a simple model of insulating systems

A simple effective model for a description of magnetically ordered narrow-band insulators is studied. The Hamiltonian considered consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbours. The phase diagrams and properties of this model for arbitrary chemical potential μ and arbitrary electron density n have been determined within several approaches: (i) the variational method (which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation) for any Jz,Jxy≠0 (exact in the limit of infinite dimensions), (ii) the Monte Carlo simulations on a square lattice with periodic boundary conditions for Jxy=0, and (iii) other approximate methods (inter alia: random phase approximation and spin-wave approximation) as well as (iv) rigorous treatment to obtain results concerning the ground state phase diagrams (the two last also for Jz,Jxy≠0). The investigations of the general case show that, depending on the values of interaction parameters and electron concentration n, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (Fα, α=z,xy) and nonordered (NO), but also phase separated states (PSα: Fα/NO). For a fixed n one finds the following phase transitions (both continuous and discontinuous ones) and their sequences, which can occur with increasing temperature: Fα→NO, PSα→NO, PSα→Fα→NO, PSα→Fα→PSα→NO. The system analysed exhibits also tricritical behaviour.

Exchange coupling and magnetic anisotropy at Fe/FePt interfaces

We perform fully relativistic first principles calculations of the exchange interactions and the magnetocrystalline anisotropy energy (MAE) in an Fe/FePt/Fe sandwich system in order to elucidate how the presence of Fe/FePt (soft/hard magnetic) interfaces impacts on the magnetic properties of Fe/FePt/Fe multilayers. Throughout our study we make comparisons between a geometrically unrelaxed system and a geometrically relaxed system. We observe that the Fe layer at the Fe/FePt interface plays a crucial role inasmuch its (isotropic) exchange coupling to the soft (Fe) phase of the system is substantially reduced. Moreover, this interfacial Fe layer has a substantial impact on the MAE of the system. We show that the MAE of the FePt slab, including the contribution from the Fe/FePt interface, is dominated by anisotropic inter-site exchange interactions. Our calculations indicate that the change in the MAE of the FePt slab with respect to the corresponding bulk value is negative, i.e., the presence of Fe/FePt interfaces appears to reduce the perpendicular MAE of the Fe/FePt/Fe system. However, for the relaxed system, this reduction is marginal. It is also shown that the relaxed system exhibits a reduced interfacial exchange. Using a simple linear chain model we demonstrate that the reduced exchange leads to a discontinuity in the magnetisation structure at the interface.

The magnetic field induced phase separation in a model of a superconductor with local electron pairing

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach (VA), which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case shows that the system can exhibit not only the homogeneous phases—superconducting (SS) and non-ordered (NO)—but also the phase separated states (PS: SS–NO). Depending on the values of interaction parameters, the PS state can occur in higher fields than the SS phase (field induced PS). Some ground state results beyond the VA are also presented.

Fe magnetic moment formation and exchange interaction in Fe2P: A first-principles study

Abstract Electronic structure and magnetic properties of Fe 2 P have been studied by a first-principles density functional theory calculation. The ground state is ferromagnetic and the calculated magnetic moments for Fe 1 (3 f ) and Fe 2 (3 g ) are 0.83 and 2.30 μ B , respectively. The nearest neighbor inter-site magnetic exchange coupling parameter at the Fe 1 layer (0.02 mRy) is much smaller than that at the Fe 2 layer (1.29 mRy). The Fe moment at the 3 f site is metastable and sensitive to the inter-site exchange interaction with its magnetic neighbors, which is responsible for the first order magnetic transition and large magneto-caloric effect around T C .

Antiferromagnetic ordering of itinerant systems with correlation and binary disorder

The itinerant model of antiferromagnetism (AF) is revisited. The solution of the Hubbard model is found using the Green function technique and the coherent potential (CP) decoupling for the on-site Coulomb repulsion. The AF state is obtained at large Coulomb repulsion and at the electron occupations 0.67≤n<1. In addition we take into account the inter-site exchange interaction, which causes occupationally dependent bandwidth. We find that the AF state is supported by the negative inter-site exchange interaction J. Subsequently, we include the binary disorder within the same approximation. It is found that the disorder weakens antiferromagnetism and decreases antiferromagnetic susceptibility.

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS–NO). The system considered exhibits interesting multicritical behaviour including tricritical points.

Interplay between crystal electric field and magnetic exchange anisotropies in the heavy-fermion antiferromagnet YbRhSb under pressure

We report the pressure effect on the magnetic ground state of the heavy-fermion (HF) canted antiferromagnet YbRhSb (orthorhombic $\ensuremath{\varepsilon}$-TiNiSi-type) by means of magnetization and resistivity measurements using a single crystal. At ambient pressure, this compound undergoes a transition at ${T}_{M1}=2.7$ K into a canted antiferromagnetic (AF) state with a small spontaneous moment of $3\ifmmode\times\else\texttimes\fi{}10$${}^{\ensuremath{-}3}\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}/$Yb. With increasing pressure $P$ above 1 GPa, another magnetic transition occurs at ${T}_{M2}$ above ${T}_{M1}$, and ${T}_{M1}(P)$ has a deep minimum of 2.5 K at 1.7 GPa. For $P\ensuremath{\ge}2$ GPa, the canted AF structure changes to a ferromagnetic (FM) one, where a large moment 0.4 ${\ensuremath{\mu}}_{B}/$Yb lies in the orthorhombic $b\ensuremath{-}c$ plane and a metamagnetic transition occurs at $B$ $||\phantom{\rule{0.16em}{0ex}}a$ $=$ 1.5 T. This unusual FM state below ${T}_{M3}\ensuremath{\cong}4.3$ K is ascribed to the balance between the single-ion crystalline electric field (CEF) anisotropy with easy direction $||\phantom{\rule{0.16em}{0ex}}a$ and the intersite exchange interaction with easy $b\ensuremath{-}c$ plane. Furthermore, we have investigated the pressure dependence of ${T}_{M3}$ up to 20.4 GPa using electrical resistivity measurements. The structural stability under pressures up to 19 GPa was examined by x-ray diffraction. We find that ${T}_{M3}$ above 2.5 GPa steeply increases up to about 7 K, showing a broad maximum and then slightly decreases with increasing pressure above 8 GPa, while the structure remains unchanged. We attribute the enhancement of ${T}_{M3}$ above 2.5 GPa to an increase of the CEF anisotropy with respect to magnetic exchange anisotropy. Finally, we compare and discuss the volume dependence of magnetic phase diagram of YbRhSb with the isostructural HF ferromagnet YbNiSn.

THE SPIN GLASS-KONDO COMPETITION IN DISORDERED CERIUM SYSTEMS

We discuss the competition between the Kondo effect, the spin glass state and a magnetic order observed in disordered Cerium systems. We present firstly the experimental situation of disordered alloys such as CeNi1-xCux and then the different theoretical approaches based on the Kondo lattice model, with different descriptions of the intersite exchange interaction for the spin glass. After the gaussian approach of the Sherrington-Kirkpatrick model, we discuss the Mattis and the van Hemmen models. Then, we present simple cluster calculations in order to describe the percolative evolution of the clusters from the cluster spin glass to the inhomogeneous ferromagnetic order recently observed in CeNi1-xCux disordered alloys and finally we discuss the effect of random and transverse magnetic field.