Anisotropic Exchange Parameters Research Articles

Spatial data modeling by means of Gibbs–Markov random fields based on a generalized planar rotator model

We introduce a Gibbs–Markov random field for spatial data on Cartesian grids, which is based on the generalized planar rotator (GPR) model. The GPR model generalizes the recently proposed modified planar rotator (MPR) model by including in the Hamiltonian additional terms that better capture realistic features of spatial data, such as smoothness, non-Gaussianity, and geometric anisotropy. In particular, the GPR model can include an infinite number of higher-order harmonics with exponentially vanishing interaction strength, directional dependence of the bilinear interaction term between nearest neighbors, longer-distance neighbor interactions, and two types of an external bias field. Hence, in contrast with the single-parameter MPR, the GPR model features five additional parameters: the number n of higher-order terms and the decay-rate parameter α, the exchange anisotropy parameter Jnn, the further-neighbor interaction coupling Jfn, and the external field (bias) parameters K (or K′). We present numerical tests on various synthetic and real data which demonstrate the effects of the respective terms on the model’s prediction performance, and we discuss these results in connection with the data properties.

Ferrimagnetic spin waves in honeycomb and triangular layers of Mn3Si2Te6

The compound Mn${}_{3}$Si${}_{2}$Te${}_{6}$ consists of alternating honeycomb and triangular lattice layers of Mn sites along the $c$ axis. This geometry leads to competing antiferromagnetic interactions that result in ferrimagnetic order. This arrangement, coupled with a small spin-orbit coupling on the Mn sites, results in anisotropic thermodynamic measurements. Here, inelastic neutron scattering experiments are examined to refine the exchange interactions and to examine the extent of the spin-orbit coupling via quantification of the anisotropic exchange parameters.

The magnetic properties of mixed spin-(52,12) anisotropic Heisenberg model in the Oguchi approximation

We have used the Oguchi approximation to study the effects of longitudinal crystal (D) and longitudinal external magnetic (h) fields on the mixed spin-(52,12) anisotropic Heisenberg model. The thermal variations of sublattice and total magnetizations are exploited in detail for given values of D, exchange anisotropy parameter (Δ) and coordination numbers z=3,4 and 6 when h=0.0. Thus, the phase diagrams are constructed on the planes of (D/J,kBT/J) and (Δ,kBT/J). In this case, it is found that the model presents either first- or second-order phase transitions as well as tricritical points. In the presence of magnetic field, the hysteresis loops of the model are also analyzed and it was found that the coercive field and remanent magnetization decrease as the temperature increases and increase as the crystal field or the exchange anisotropy increases.

The transverse field XY model on the diamond chain

We consider the s=1/2 transverse field XY model on the frustrated diamond chain, considering anisotropic exchange parameters between nearest neighbor spins. To this end, we employ three different methodologies: mean-field approximations, and state-of-the-art exact diagonalizations (ED), and density matrix renormalization group (DMRG) simulations. Within a mean-field theory, the Hamiltonian is fermionized by introducing the Jordan–Wigner transformation, and the interacting (many-body) terms are approximated to single-particle ones by a Hartree–Fock approach. We analyze the behavior of the induced and spontaneous magnetization as functions of the external field, investigating the magnetic properties at the ground state, and at finite temperatures. Interestingly, the mean-field results are in reasonable agreement with the ED and DMRG ones, in particular for the distorted chain, or at an intermediate/large spin anisotropy parameter. As our key results, we present phase diagrams anisotropy × magnetic field at zero temperature, discussing the emergence of phases and its quantum critical points. Finally, our analysis at finite temperature provides a range of parameters in which an unusual behavior of the induced magnetization occurs — with it increasing as a function of temperature. This work presents a global picture of the XY model on the diamond chain, which may be useful to understand features of magnetism in more complex geometries.

Analyzing Anisotropic Exchange in a Pentanuclear Os2 Ni3 Complex.

Spin Hamiltonian parameters of a pentanuclear Os2III Ni3II cyanometallate complex are derived from ab initio wave function based calculations, namely valence‐type configuration interaction calculations with a complete active space including spin‐orbit interaction (CASOCI) in a single‐step procedure. While fits of experimental data performed so far could reproduce the data but the resulting parameters were not satisfactory, the parameters derived in the present work reproduce experimental data and at the same time have a reasonable size. The one‐centre parameters (local g matrices and single‐ion zero field splitting tensors) are within an expected range, the anisotropic exchange parameters obtained in this work for an Os−Ni pair are not exceedingly large but determine the low‐T part of the experimental χT curve. Exchange interactions (both isotropic and anisotropic) obtained from CASOCI have to be scaled by a factor of 2.5 to obtain agreement with experiment, a known deficiency of such types of calculation. After scaling the parameters, the isotropic Os−Ni exchange coupling constant is J=-4.2 cm−1 and the D parameter of the (nearly axial) anisotropic Os−Ni exchange is D=J∥-J⊥=18.8cm −1, so anisotropic exchange is larger in absolute size than isotropic exchange. The negative value of the isotropic J (indicating antiferromagnetic coupling) seemingly contradicts the large‐temperature behaviour of the temperature dependent susceptibility curve, but this is caused by the negative g value of the Os centres. This negative g value is a universal feature of a pseudo‐octahedral coordination with t2g5 configuration and strong spin‐orbit interaction. Knowing the size of these exchange interactions is important because Os(CN)63- is a versatile building block for the synthesis of 5d /3d magnetic materials.

Unravelling competing microscopic interactions at a phase boundary: A single-crystal study of the metastable antiferromagnetic pyrochlore Yb2Ge2O7

We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb$_{2}$Ge$_{2}$O$_{7}$. We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat. The exchange parameters so-determined are strongly correlated to the values determined for the $g$-tensor components, as previously observed for the related Yb pyrochlore Yb$_{2}$Ti$_{2}$O$_{7}$. To address this issue, we directly determined the $g$-tensor from electron paramagnetic resonance of 1% Yb-doped Lu$_{2}$Ge$_{2}$O$_{7}$, thus enabling an unambiguous determination of the exchange parameters. Our results show that Yb$_{2}$Ge$_{2}$O$_{7}$ resides extremely close to the classical phase boundary between an antiferromagnetic $\Gamma_5$ phase and a splayed ferromagnet phase. By juxtaposing our results with recent ones on Yb$_{2}$Ti$_{2}$O$_{7}$, our work illustrates that the Yb pyrochlore oxides represent ideal systems for studying quantum magnets in close proximity to classical phase boundaries.

High field magnetization ofFePS3

High field magnetization measurements in pulsed fields up to 65 T have been performed on ${\mathrm{FePS}}_{3}$, which is nominally a good example of a two-dimensional Ising-like antiferromagnet on a honeycomb lattice. Measurements with the field parallel to the moment direction confirm the presence of two first-order transitions above 35 T, to $M/{M}_{\mathrm{sat}}=1/2$ and $M/{M}_{\mathrm{sat}}=1$, respectively, at 4 K. The measurements are in contradiction with published estimates for the magnetic exchange parameters, but the contradiction can be resolved by allowing for anisotropic exchange parameters in the Hamiltonian. The magnetization with the field perpendicular to the moment direction is anisotropic, with no transitions observed for fields along the a axis while a cascade of first-order transitions is observed for fields above 50 T along the b axis, the latter case also showing a strong degradation of the sample after repeated pulses. The results indicate a strong magnetolattice coupling in ${\mathrm{FePS}}_{3}$. Temperature-dependent measurements hint at a possible tricritical point.

Investigations of Magnetic Properties Hg0.865Mn0.135Te by the Electron Spin Resonance Method

Mercury chalcogenide (Hg 0.865 Mn 0.135 Te) monocrystal was grown by crystallization from a two-phase mixture with replenishment of the melt from a tellurium solution and has n-type conductivity. The electron spin resonance (ESR) spectra of a single crystal were studied before and after X-irradiation. Only one intense anisotropic ESR line was observed at 4.2 K before X-irradiation. The anisotropy parameters were established from the angular dependence of the resonance field of the ESR line. After X-irradiation, three ESR lines were registered in the spectrum. The first and second lines with a large g -factor and unusual temperature dependencies were associated with charge carriers localized on defects with the strong exchange interaction with the manganese ion spins. The third ESR narrowed line was identified as signal from Mn 2+ ions. Estimated anisotropic exchange parameters from angular dependencies of magnetic resonance field depend on temperature. The temperature dependencies of ESR linewidths are well described by the Korringa law and spin-lattice relaxation contributions. The discontinuities in temperature dependencies of resonance field and linewidth at 18 and 65 K were observed.

Magnetic properties of XXZ Heisenberg antiferromagnetic and ferromagnetic core-shell nanowires

A cylindrical core-shell nanowire was described by an anisotropic XXZ Heisenberg model. The spontaneous magnetization, critical temperature, and hysteresis behavior were calculated by using the double-time spin Green's function method. For the nanowire with antiferromagnetic interfacial exchange interaction, the spin quantum fluctuation of the core is more obvious than that of the shell. The critical temperature of the system does not change for the same values of the antiferromagnetic or ferromagnetic interfacial exchange interaction, and it reduces to zero when the exchange anisotropy parameter reaches 1.0. The asymptotic value of the ratio of magnetizations from the shell to the core as the temperature approaches the critical temperature shows interesting behaviors during the interaction between spins in the core or the shell changing from Ising limit to Heisenberg limit. The magnetic hysteresis of the system with antiferromagnetic interfacial exchange interaction shows behaviors of magnetization plateaus, single loop, double loops, and tricyclic loops. When the interfacial exchange interaction is ferromagnetic, the hysteresis only shows single loops.

Dimer correlation amplitudes and dimer excitation gap in spin- 12 XXZ and Heisenberg chains

Correlation functions of dimer operators, the product operators of spins on two adjacent sites, are studied in the spin-$\frac{1}{2}$ XXZ chain in the critical regime. The amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field, through the combined use of bosonization and density-matrix renormalization group methods. In particular, for the antiferromagnetic Heisenberg model with SU(2) symmetry, logarithmic corrections to the dimer correlations due to the marginally-irrelevant operator are studied, and the asymptotic form of the dimer correlation function is obtained. The asymptotic form of the spin-Peierls excitation gap including logarithmic corrections is also derived.

Giant biquadratic interaction-induced magnetic anisotropy in the iron-based superconductorAxFe2−ySe2

The emergence of the electron-pocket only iron-based superconductor AxFe2-ySe2 (A = alkali metal) challenges the Fermi-surface nesting picture established in iron-pnictides. It was widely believed that magnetism is correlated with the superconductivity in AxFe2-ySe2. Unfortunately, the highly anisotropic exchange parameters and the disagreement between theoretical calculations and experimental results triggered a fierce debate on the nature of magnetism in AxFe2-ySe2. Here we find that the strong magnetic anisotropy is from the anisotropic biquadratic interaction. In order to accurately obtain the magnetic interaction parameters, we propose a universal method, which does not need including other high energy configurations as did in conventional energy mapping method. We show that our model successfully captures the magnetic interactions in AxFe2-ySe2 and correctly predicts the spin wave spectrum, in quantitative agreement with the experimental observation. These results suggest that the local moment picture, including the biquadratic term, can describe accurately the magnetic properties and spin excitations in AxFe2-ySe2, which sheds new light on the future study of the high-Tc iron-based superconductors.

Origin of Dissimilar Single-Molecule Magnet Behavior of Three MnII(2)MoIII Complexes Based on [MoIII(CN)7]4- Heptacyanomolybdate: Interplay of MoIII-CN-MnII Anisotropic Exchange Interactions.

The origin of contrasting single-molecule magnet (SMM) behavior of three MnII2MoIII complexes based on [MoIII(CN)7]4– heptacyanomolybdate is analyzed; only the apical Mn2Mo isomer exhibits SMM properties with Ueff = 40.5 cm(-1) and TB = 3.2 K, while the two equatorial isomers are simple paramagnets [Qian, K.; J. Am. Chem. Soc. 2013, 135, 13302]. A microscopic theory of anisotropic spin coupling between orbitally degenerate [MoIII(CN)7](4-) complexes (pentagonal bipyramid) and bound MnII ions is developed. It is shown that the [MoIII(CN)7](4-) complex has a unique property of uniaxial anisotropic spin coupling in the apical and equatorial MoIII-CN-MnII pairs, H̑eff = -Jxy(SMoxSMnx + SMoySMny) - JzSMozSMnz, regardless of their actual low symmetry. The difference in the SMM behavior originates from a different ratio between the anisotropic exchange parameters Jz and Jxy for the apical and equatorial Mo-CN-Mn groups. In the apical Mn2Mo isomer, an Ising-type anisotropic spin coupling (Jz = -34, Jxy = -11 cm(-1)) produces a double-well potential of spin states resulting in SMM behavior. Exchange anisotropy of an xy-type (|Jz| < |Jxy|) in the equatorial Mn2Mo isomers results in a single-well potential with no SMM properties. The prospects of anisotropic uniaxial spin coupling in engineering of high Ueff and TB values are discussed.

Magnetic properties of nearly stoichiometric CeAuBi2 heavy fermion compound

Motivated by the interesting magnetic anisotropy found in the heavy fermion family CeTX2 (T = transition metal and X = pnictogen), here, we study the novel parent compound CeAu1−xBi2−y by combining magnetization, pressure dependent electrical resistivity, and heat-capacity measurements. The magnetic properties of our nearly stoichiometric single crystal sample of CeAu1−xBi2−y (x = 0.92 and y = 1.6) revealed an antiferromagnetic ordering at TN = 12 K with an easy axis along the c-direction. The field dependent magnetization data at low temperatures reveal the existence of a spin-flop transition when the field is applied along the c-axis (Hc ∼ 7.5 T and T = 5 K). The heat capacity and pressure dependent resistivity data suggest that CeAu0.92Bi1.6 exhibits a weak heavy fermion behavior with strongly localized Ce3+ 4f electrons. Furthermore, the systematic analysis using a mean field model including anisotropic nearest-neighbors interactions and the tetragonal crystalline electric field (CEF) Hamiltonian allows us to extract a CEF scheme and two different values for the anisotropic JRKKY exchange parameters between the Ce3+ ions in this compound. Thus, we discuss a scenario, considering both the anisotropic magnetic interactions and the tetragonal CEF effects, in the CeAu1−xBi2−y compounds, and we compare our results with the isostructural compound CeCuBi2.

Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er2Ti2O7: A high-temperature series expansion study

We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er${}_{2}$Ti${}_{2}$O${}_{7}$ on its approach to the critical temperature ${T}_{c}$. We show that its anisotropic exchange parameters, ${{J}_{e}}$, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near ${T}_{c}$. While different $\mathbit{q}=0$ $XY$ order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear ``${\ensuremath{\psi}}_{2}$ state'' as found in Er${}_{2}$Ti${}_{2}$O${}_{7}$. Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at ${T}_{c}$ in this frustrated quantum spin-1/2 antiferromagnetic material.

Low-temperature structure anomalies in CuNCN. Manifestations of RVB phase transitions?

We propose a new frustrated Heisenberg antiferromagnetic model with spatially anisotropic exchange parameters Jc, Ja, and Jac, extending along the c, a, and a ± c (c–a–ca model) lattice directions, and apply it to describe the fascinating physics of copper carbodiimide, CuNCN, assuming the resonating valence bond (RVB) type of its phases. This explains within a unified picture the intriguing absence of magnetic order in CuNCN. We further present a parameters–temperature phase diagram of the c–a–ca-RVB model in the high-temperature approximation. Eight different phases including Curie and Pauli paramagnets (respectively, in disordered and 1D- or Q1D-RVB phases) and (pseudo)gapped (quasi-Arrhenius) paramagnets (2D-RVB phases) are possible. By adding magnetostriction and elastic terms to the model, we derive possible structural manifestations of RVB phase transitions. Assuming a sequence of RVB phase transitions to occur in CuNCN with decreasing temperature, several anomalies observed in the temperature course of the lattice constants are explained.

Green's function approach of an anisotropic Heisenberg ferrimagnetic system

We have investigated the influence of the exchange anisotropy parameter on the magnetization, critical and compensation temperatures and susceptibility of the anisotropic Heisenberg ferrimagnetic system with the single-ion anisotropy under an external magnetic field using the double-time temperature-dependent Green's function theory. In order to decouple the higher order Green's functions, Anderson-Callen's decoupling and random phase approximations have been used. This model is useful for understanding the temperature dependence of total magnetization of Lithium-chromium ferrites Li0.5Fe1.25Cr1.25O4 for which negative magnetization is characteristic. We observe that the critical temperature increases when the exchange anisotropy increases. When the system is under an external magnetic field, one obtains the first-order phase transition where the magnetization jumps for all the values of the exchange anisotropy parameters.

Pair correlations, short-range order, and dispersive excitations in the quasi-kagome quantum magnet volborthite

We present spatial and dynamic information on the $s=1/2$ distorted kagome antiferromagnet volborthite, Cu${}_{3}$V${}_{2}$O${}_{7}$(OD)${}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2$D${}_{2}$O, obtained by polarized and inelastic neutron scattering. The instantaneous structure factor, $S(Q)$, is dominated by nearest-neighbor pair correlations, with short-range order at wave vectors ${Q}_{1}=0.65(3)$ \AA{}${}^{\ensuremath{-}1}$ and ${Q}_{2}=1.15(5)$ \AA{}${}^{\ensuremath{-}1}$ emerging below 5 K. The excitation spectrum, $S(Q,\ensuremath{\omega})$, reveals two steep branches dispersing from ${Q}_{1}$ and ${Q}_{2}$, and a flat mode at ${\ensuremath{\omega}}_{f}=5.0(2)$ meV. The results allow us to identify the crossover at ${T}^{*}\ensuremath{\sim}1$ K in ${}^{51}$V NMR and specific-heat measurements as the buildup of correlations at ${Q}_{1}$. We compare our data to theoretical models proposed for volborthite, and also demonstrate that the excitation spectrum can be explained by spin-wave-like excitations with anisotropic exchange parameters, as suggested by recent local-density calculations.

Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots

The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in Baruffa et al. [Phys. Rev. Lett. 104, 126401 (2010)] is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: (i) the model stays valid even for maximal possible interdot coupling (a single dot), due to the absence of a coupling to the nearest excited level, a fact following from the dot symmetry. (ii) In a weak-coupling regime, the Heitler-London approximation gives quantitatively correct anisotropic exchange parameters even in a finite magnetic field, although this method is known to fail for the isotropic exchange. The small discrepancy between the analytical model (which employs the linear Dresselhaus and Bychkov-Rashba spin-orbit terms) and the numerical data for GaAs quantum dots is found to be mostly due to the cubic Dresselhaus term.

Mössbauer, electron paramagnetic resonance, and magnetic susceptibility studies on members of a new family of cyano-bridged 3d-4f complexes. Demonstration of anisotropic exchange in a Fe-Gd complex.

The synthesis and crystallographic characterization of a new family of M(mu-CN)Ln complexes are reported. Two structural series have been prepared by reacting in water rare earth nitrates (Ln(III) = La, Pr, Nd, Sm, Eu, Gd, Dy, Ho) with K(3)[M(CN)(6)] (M(III) = Fe, Co) in the presence of hexamethylenetetramine (hmt). The first series consists of six isomorphous heterobinuclear complexes, [(CN)(5)M-CN-Ln(H(2)O)(8)].2hmt ([FeLa] 1, [FePr] 2, [FeNd] 3, [FeSm] 4, [FeEu] 5, [FeGd] 6), while the second series consists of four isostructural ionic complexes, [M(CN)(6)][Ln(H(2)O)(8)].hmt ([FeDy] 7, [FeHo] 8, [CoEu] 9, [CoGd] 10). The hexamethylenetetramine molecules contribute to the stabilization of the crystals by participating in an extended network of hydrogen bond interactions. In both series the aqua ligands are hydrogen bonded to the nitrogen atoms from both the terminal CN(-) groups and the hmt molecules. The [FeGd] complex has been analyzed with (57)Fe Mossbauer spectroscopy and magnetic susceptibility measurements. We have also analyzed the [FeLa] complex, in which the paramagnetic Gd(III) is replaced by diamagnetic La(III), with (57)Fe Mossbauer spectroscopy, electron paramagnetic resonance (EPR), and magnetic susceptibility measurements, to obtain information about the low-spin Fe(III) site that is not accessible in the presence of a paramagnetic ion at the complementary site. For the same reason, the [CoGd] complex, containing diamagnetic Co(III), was studied with EPR and magnetic susceptibility measurements, which confirmed the S = 7/2 spin of Gd(III). Prior knowledge about the paramagnetic sites in [FeGd] allows a detailed analysis of the exchange interactions between them. In particular, the question of whether the exchange interaction in [FeGd] is isotropic or anisotropic has been addressed. Standard variable-temperature magnetic susceptibility measurements provide only the value for a linear combination of J(x), J(y), and J(z) but contain no information about the values of the individual exchange parameters J(x), J(y), and J(z). In contrast, the spin-Hamiltonian analysis of the variable-field, variable-temperature Mossbauer spectra reveals an exquisite sensitivity on the anisotropic exchange parameters. Analysis of these dependencies in conjunction with adopting the g-values obtained for [FeLa], yielded the values J(x) = +0.11 cm(-1), J(y) = +0.33 cm(-1), and J(z) = +1.20 cm(-1) (S(1).J.S(2) convention). The consistency of these results with magnetic susceptibility data is analyzed. The exchange anisotropy is rooted in the spatial anisotropy of the low-spin Fe(III) ion. The condition for anisotropic exchange is the presence of low-lying orbital excited states at the ferric site that (i) effectively interact through spin-orbit coupling with the orbital ground state and (ii) have an exchange parameter with the Gd site with a value different from that for the ground state. Density functional theory (DFT) calculations, without spin-orbit coupling, reveal that the unpaired electron of the t(2g)(5) ground configuration of the Fe(III) ion occupies the xy orbital, that is, the orbital along the plane perpendicular to the Fe...Gd vector. The exchange-coupling constants for this orbital, j(xy), and for the other t(2g) orbitals, j(yz) and j(xz), have been determined using a theoretical model that relates them to the anisotropic exchange parameters and the g-values of Fe(III). The resulting values, j(yz) = -5.7 cm(-1), j(xz) = -4.9 cm(-1), and j(xy) = +0.3 cm(-1) are quite different. The origin of the difference is briefly discussed.

Anisotropic exchange in ErIG

Anisotropic exchange parameters associated with the rare-earth-iron exchange in ErIG have been determined by fitting the energy levels of states of the Er +3 ions in the 4I 15/2 manifold. The exchange parameters are found to be nearly the same as those for the rare-earth ions in YbIG and EuIG. The effects of the anisotropic exchange vary depending on the particular state. This can be seen by a comparison of principal values of the exchange splittings with the g-values for the corresponding ErGaG states. The ground state splittings are used to calculate parameters associated with the noncollinear magnetic structure.