Nearest-neighbour Exchange Interactions Research Articles

Symmetry considerations in exact diagonalization: spin-1/2 pyrochlore magnets

Abstract We describe how the methods of group theory (symmetry) are used to optimize the problem of exact diagonalization of a quantum system on a 16-site pyrochlore lattice. By analytically constructing a complete set of symmetrized states, the Hamiltonian can be completely block-diagonalized. As an example, we consider a spin-1/2 system with nearest-neighbour exchange interactions. We present the energy spectrum of a small system for a range of model parameters in the vicinity of the spin ice phase.

Exact diagonalization for a 16-site spin-1/2 pyrochlore cluster

We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore cluster with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding precise details about symmetry of the eigenstates, in particular those components which are spin ice states, in order to evaluate the spin ice density at finite temperature. At low enough temperatures, a ‘perturbed’ spin ice phase, where the ‘2-in-2-out’ ice rule is largely obeyed, is clearly outlined within the four parameter space of the general model of exchange interactions. The quantum spin ice phase is expected to exist within these boundaries.

Mean-Field Modeling of Magnetocaloric Effect of Antiferromagnetic Compounds

Antiferromagnetic compounds are known in the literature to present the inverse magnetocaloric effect (MCE). This effect is characterized by the negative adiabatic temperature change, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta T_{S}$</tex-math></inline-formula> , of an antiferromagnetic material when submitted to an applied magnetic field. In an isothermal process, a positive entropy change, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta S_{T}$</tex-math></inline-formula> , is also expected. More recently, the anisotropic character of antiferromagnetic compounds, due to spin-flop and spin-flip transitions, has been pointed out highlighting the applicability of the antiferromagnetic compounds in a rotary magnetocaloric device. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In this work, we systematically investigated a mean-field model that describes the antiferromagnetic behaviour of materials in a multisublattice approach. Our model includes the nearest and next-nearest neighbour exchange interaction, the Zeeman effect, and a uniaxial anisotropy energy. We investigated the effect of anisotropy on the spin-flop and spin-flip transitions on the usual and anisotropic MCE. We also demonstrated and verified an area rule for —<inline-formula><tex-math notation="LaTeX">$\Delta S_{T}$</tex-math></inline-formula> vs. T curves that can be used on compounds where the saturation magnetization is magnetic field dependent.

Effects of composition variation and site disorder on the magnetic interactions in Ru2Fe(Si1-xGex) alloys

X-ray diffraction studies on arc melted Ru2Fe(Si1-xGex) (0 ≤ x ≤ 1) alloys did not show the characteristic (111) and (200) super-lattice peaks of the stable L21 structure of full Heusler alloys. The alloy with x = 0 exhibited antiferromagnetic behaviour. However, with increase in x, the alloys became ferromagnetic. In order to understand the origin of the novel magnetic behavior of these alloys and its correlation with their crystal structure, ab initio study was carried out using spin-polarized relativistic Korringa-Kohn-Rostoker Green’s function method. The study shows that the antiferomagnetism in the alloy with x = 0 is due to the presence of B2 disorder. Due to this, the 2nd nearest neighbour (NN) exchange interaction between the Fe atoms at proper and improper sites, respectively, becomes strongly antiferromagnetic which dominates over the 1st NN ferromagnetic exchange interaction. With increase in x, the alloys become ferromagnetic with an improvement in L21 ordering which in turn makes the 1st NN interaction strongly ferromagnetic. The electronic structure calculations show no half metallic gap in either spin direction for all the alloys. Comparison of experimental and theoretically estimated properties of Ru2Fe(Si1-xGex) alloys provides insight to the variation in the magnetic interaction with the composition and the disorder present in the alloys.

On the magnetic ground state of lead-free complex perovskite Sr(Fe1/2Nb1/2)O3

We present here the results of dc magnetization (M) measurements as a function of temperature (T), field (H) and time (t) with different histories and ac susceptibility measurements as a function of temperature and frequency to understand the magnetic ground state of Sr(Fe1/2Nb1/2)O3 (SFN). We show that the zero-field cooled (ZFC) and field cooled (FC) magnetization curves (M(T)) not only bifurcate but also exhibit a short plateau with a dip in the FC M(T) curve suggesting that the observed history dependent irreversibility may be due to cluster spin-glass (CSG) freezing and not superparamagnetic (SPM) blocking. This is confirmed by ac susceptibility χ(ω, T) studies which reveal critical slowing down of the spin dynamics as per Vogel Fulcher and power laws with spin-glass transition temperature TSG ∼(24 ± 1) K. The attempt time obtained by these laws (τ0 ∼10−6 s) is found to be consistent with CSG picture. Further, the field dependent shift of Tf follows de Almeida-Thouless line in the T-H plane with a characteristic critical exponent m = 2/3. Further support for the existence of the spin-glass phase is obtained by the observation of non-exponential decay of the thermoremanent magnetization as well as aging, rejuvenation and memory effects below Tf. The non-zero value of remanent magnetization Mr without saturation below Tf is shown to vanish exponentially with increasing temperature as T → TSG in agreement with what is observed in spin-glass systems. We also present a critical comparison of the magnetic ground states of SFN with CaCu3Ti4O12 (CCTO) and other complex niobate perovskites in terms of the strength of the nearest neighbour exchange interaction parameter J1, the coordination polyhedral, the disorder/dilution level of the magnetic sublattices, the presence or absence of octahedral tilts and the possibility of alternative superexchange pathways in these compounds.

Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores

We use Monte Carlo simulations to evaluate the feasibility of detecting thermal order by disorder in real antiferromagnetic Ising pyrochlores, frustrated by a magnetic field applied in the $[110]$ direction. Building on an ideal system with only nearest-neighbour exchange interactions and a perfectly oriented field, we consider the effects of dipolar interactions and field misalignment. Our approach is special in that it relies more in the possibility to switch on and off the entropic drive towards order than in the absence of (or immunity to) a particular perturbation. It can then be applied, in principle, to other uncontrolled interactions expected to be naturally present in real {magnetic} materials. We establish the conditions under which entropic effects can be discerned from an interaction drive towards order, show how to use neutron scattering as a means to unveil this mechanism, and discuss possible materials where to test these ideas.

Ordering and frustrations in generalized Ising chain

The Ising model on a one-dimensional monoatomic equidistant lattice with different nearest-neighbour and second-neighbour exchange interactions is researched. Generalized Kramers-Wannier transfer-matrix with translation on two periods of a lattice is introduced. A property similar to supercooling and superheating is detected. At the triple points phases are not individualized, but completely frustrated which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for free energy, heat capacity and entropy including zero-temperature entropy are obtained. Various new special cases were analyzed and compared with all known results. All frustration fields for magnetization, frustration values for the zero-temperature entropy and magnetization are found.

Spin interactions and magnetic order in the iron oxychalcogenides BaFe2Q2O(Q=Sand Se)

The ability to tune the iron chalcogenides BaFe2Q3 from Mott insulators, to metals and then superconductors with applied pressure has renewed interest in low-dimensional iron chalcogenides and oxychalcogenides. We report here a combined experimental and theoretical study on the iron oxychalcogenides BaFe2Q2O (Q=S, Se) and show that their magnetic behaviour results from nearest-neighbour magnetic exchange interactions via oxide and selenide anions of similar strength, with properties consistent with more localised electronic structures than those of BaFe2Q3 systems.

Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet

Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realisation of topological magnons in three dimensions has not been reported so far. Here, by measuring spin excitations (magnons) of a three-dimensional antiferromagnet Cu3TeO6 with inelastic neutron scattering, we provide direct spectroscopic evidence for the coexistence of symmetry-protected Dirac and triply degenerate nodes, the latter involving three-component magnons beyond the Dirac–Weyl framework. Our theoretical calculations show that the observed topological magnon band structure can be well described by the linear-spin-wave theory based on a Hamiltonian dominated by the nearest-neighbour exchange interaction J1. As such, we showcase Cu3TeO6 as an example system where Dirac and triply degenerate magnonic nodal excitations coexist, demonstrate an exotic topological state of matter, and provide a fresh ground to explore the topological properties in quantum materials.

Exchange interactions in two-state systems: rare earth pyrochlores

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.

Spin dynamics and magnetoelectric coupling mechanism of Co4Nb2O9

Neutron powder diffraction experiments reveal that Co4Nb2O9 forms a noncollinear in-plane magnetic structure with Co2+ moments lying in the ab plane. The spin-wave excitations of this magnet were measured by using inelastic neutron scattering and soundly simulated by a dynamic model involving nearest and next-nearest neighbour exchange interactions, in-plane anisotropy and the Dzyaloshinskii-Moriya interaction. The in-plane magnetic structure of Co4Nb2O9 is attributed to the large in-plane anisotropy while the noncollinearity of the spin configuration is attributed to the Dzyaloshinskii-Moriya interaction. The high magnetoelectric coupling effect of Co4Nb2O9 in fields can be explained by its special in-plane magnetic structure.

Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-defined excitations even though integrability is broken.

Superexchange interaction in the A -site ordered perovskite YMn3Al4O12

Crystal structure and magnetic ordering in ${\mathrm{YMn}}_{3}{\mathrm{Al}}_{4}{\mathrm{O}}_{12}$ are determined by neutron powder diffraction measurement, indicating that $S=2$ spins of the ${A}^{\ensuremath{'}}$-site ${\mathrm{Mn}}^{3+}$ ions are ordered in G-type antiferromagnetic (AFM) arrangement in the $Im\overline{3}$ cubic crystal structure. Using the first-principles electronic structure calculations, it is found that the AFM spin structure is stabilized by the nearest-neighbour (NN) exchange interaction. The underlying mechanism of the NN exchange is revealed to be the antiferromagnetic Mn-O-Mn superexchange interaction from the calculations of electronic transfer integrals.

Special Modes in Spin Wave Spectra of Two-Dimensional Nanodots

Faculty of Physics, A. Mickiewicz University in Pozna«, Umultowska 85, 61-614 Pozna«, Poland We use a microscopic theory taking into account the nearest-neighbour exchange and dipolar interactions to study two-dimensional magnetic nanodots and nanorings. Magnetic con guration is assumed to form an inplane vortex (circular magnetization). We examine the dependence of the frequencies and pro les of spin waves on the dipolar-to-exchange interaction ratio d and the size of the dot (ring). Special attention is paid to some particular modes, including the lowest mode in the spectrum and the fundamental mode, the frequency of which proves almost independent of d. In the case of the lowest mode di erent pro les are observed: azimuthal, fundamental (quasiuniform) or highly localized, depending on d and the size. We also study the fundamental mode evolution including its hybridization and explain the selection rules. DOI: 10.12693/APhysPolA.127.365

Exotic Magnetism on the Quasi-fcc Lattices of thed3Double PerovskitesLa2NaB′O6(B′=Ru, Os)

We find evidence for long-range and short-range (ζ=70 Å at 4 K) incommensurate magnetic order on the quasi-face-centered-cubic (fcc) lattices of the monoclinic double perovskites La2NaRuO6 and La2NaOsO6, respectively. Incommensurate magnetic order on the fcc lattice has not been predicted by mean field theory, but may arise via a delicate balance of inequivalent nearest neighbor and next nearest neighbor exchange interactions. In the Ru system with long-range order, inelastic neutron scattering also reveals a spin gap Δ ∼ 2.75 meV. Magnetic anisotropy is generally minimized in the more familiar octahedrally coordinated 3d3 systems, so the large gap observed for La2NaRuO6 may result from the significantly enhanced value of spin-orbit coupling in this 4d(3) material.

Effects of the competition between the exchange and dipolar interactions in the spin-wave spectrum of two-dimensional circularly magnetized nanodots

We use a microscopic theory taking into account the dipolar and nearest-neighbour exchange interactions for exploring spin-wave excitations in two-dimensional magnetic dots in the vortex state. Normal modes of different profiles are observed: azimuthal and radial modes, as well as fundamental (quasiuniform) and highly localized modes. We examine the dependence of the frequencies and profiles of these modes on the dipolar-to-exchange interaction ratio and the size of the dot. Special attention is paid to some particular modes, including the lowest mode in the spectrum and the evolution of its profile, and the fundamental mode, the frequency of which proves almost independent of the dipolar-to-exchange interaction ratio. We also provide a selective overview of the experimental, analytical and numerical results from the literature, where different profiles of the lowest mode are reported. We attribute this diversity to the competition between the dipolar and exchange interactions. Finally, we study the hybridization of the modes, show the multi-mode hybridization and explain the selection rules.

Stability of the Landau state in square two-dimensional magnetic nanorings

We use a microscopic theory taking into account dipolar and nearest-neighbour exchange interactions to explore spin-wave excitations in two-dimensional square-shaped magnetic nanorings with the Landau state assumed as a magnetic state. From the spin-wave spectra, we determine the range of the dipolar-to-exchange interaction ratio in which the assumed state is stable. Various types of localized spin waves prove responsible for the transition to a new magnetic configuration. We found the transition forced by predominating exchange interactions size-independent in a wide range of both external and internal size of the ring.

Monte Carlo Simulation of Multiferroic Magnetic Order in Ca3Co2-xMnxO6 System

Ca3Co2-xMnxO6 (x≈1, CCMO) is a typical magnetic multiferroic material. The spins of Co2+ and Mn4+ have strong magnetic anisotropy, which are similar to Ising spins. Moreover, at low temperatures, CCMO forms a particular up-up-town-town (↑↑↓↓) spin order, the so-called E-type antiferromagnetic state. In this paper, a diatomic Ising chain model for CCMO system, with the nearest-neighbour exchange frustration, has been studied by Monte Carlo simulation. The zero-temperature phase diagram is calculated by the variational method, which contains the E-type antiferromagnetic phase. Monte Carlo simulations confirm the existence of E-type antiferromagnet. Based on the results of specific heat and spin structure factor, two phase transition temperatures have been revealed, which may correspond to two phase transitions in real CCMO. By continuously adjusting the intensity of nearest-neighbour exchange interaction in Monte Carlo simulations, the phase transition boundary between the G-type and E-type antiferromagnetic states shows critical phenomena. Near the phase boundary, the spin modulation period becomes incommensurate. The instability of E-type antiferromagnetic order in real CCMO with x=1, may just due to the low dimensional features of the 1D Ising spin chain and the exchange frustration.

The effect of the single-spin defect on the stability of the in-plane vortex state in 2D magnetic nanodots

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified.

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement.