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We present the results of an extensive study of the phase diagram and spin wave excitations for a general spin model on a hexagonal AB-stacked kagome system. The boundaries of the magnetic phases are determined via a combination of numerical (Monte Carlo) and analytical (Luttinger-Tisza) methods. We also determine the phase coexistence regions by considering the instabilities in the spin wave spectra. Depending on the strength of the spin-orbit coupling (SOC), some spin and lattice rotations become decoupled, leading to considerably larger symmetry groups than typical magnetic groups. Thus, we provide a detailed symmetry description of the magnetic Hamiltonian with negligible, weak, and intermediate strength of SOC. The spin symmetry in these three cases has a strong effect on the splittings observed in the spin excitation spectra. We further identify a number of self-duality transformations that map the Hamiltonian onto itself. These transformations describe the symmetry of the parameter space and provide an exact mapping between the properties of different magnetic orders and lead to accidental degeneracies. Finally, we discuss the physical relevance of our findings in the context of $\mathrm{Mn}_3X$ compounds.

${\mathrm{Mn}}_{3}X$ compounds in which the magnetic $\mathrm{Mn}$ atoms form $AB$-stacked kagome lattices have received a tremendous amount of attention since the observation of the anomalous Hall effect in ${\mathrm{Mn}}_{3}\mathrm{Ge}$ and ${\mathrm{Mn}}_{3}\mathrm{Sn}$. Although the magnetic ground state has been known for some time to be an inverse triangular structure with an induced in-plane magnetic moment, there have been several controversies about the minimal magnetic Hamiltonian. We present a general symmetry-based model for these compounds that includes a previously unreported interplane Dzyaloshinskii-Moriya interaction, as well as anisotropic exchange interactions. The latter are shown to compete with the single-ion anisotropy which strongly affects the ground state configurations and elementary spin-wave excitations. Finally, we present the calculated elastic and inelastic neutron scattering intensities and point to experimental assessment of the types of magnetic anisotropy in these compounds that may be important.

A study of spherical maghemite nanoparticles on a two-dimensional triangular array was carried out using a stochastic Landau-Lifshitz-Gilbert approach. The simulation method was first validated with a triangular array of simple dipoles, where results show the expected phase transition to a ferromagnetic state at a finite temperature. The ground state exhibited a continuous degeneracy that was lifted by an order-from-disorder mechanism at infinitesimal temperatures with the appearance of a sixfold planar anisotropy. The nanoparticle array consisted of 7.5 nm diameter maghemite spheres with bulklike superexchange interactions between Fe ions in the core, and weaker exchange between surface Fe ions and a radial anisotropy. The triangular nanoparticle array ordered at the same reduced temperature as the simple dipole array, but exhibited different behavior at low temperatures due to the surface anisotropy. We find that the vacancies on the octahedral sites in the nanoparticles combine with the surface anisotropy to produce an effective random temperature-dependent anisotropy for each particle. This leads to a reduction in the net magnetization of the nanoparticle array at zero temperature compared to the simple dipole array.

Results are presented on analytic and computational analyses of the spin states associated with a 3D fcc lattice composed of ABC stacked kagome planes of magnetic ions with only long-range dipole-dipole interactions. Extending previous work on the 2D kagome system, where discrete six-fold discrete degeneracy of the ground state was revealed [Holden et al. Phys. Rev. B 91, 224425 (2015)], we show that the 3D lattice exhibits a continuous degeneracy characterized by just two spherical angles involving six sublattice spin vectors. Application of a Heat Bath Monte Carlo algorithm shows that thermal fluctuations reduce this degeneracy at very low temperature in an order-by-disorder process. A magnetic field applied along directions of high symmetry also results in lifting the continuous degeneracy to a subset of states from the original set of ground states. Metropolis Monte Carlo simulation results are also presented on the temperature and system size dependence of the energy, specific heat, and magnetization, providing evidence for a phase transition at T $\simeq$ 0.38 (in units of the dipole strength). The results can be relevant to a class of magnetic compounds having the AuCu$_3$ crystal structure., 13 pages, 23 figures

Exchange interactions up to fourth nearest neighbor are shown within a classical local-moment Heisenberg approach to be important to model inelastic neutron scattering data on the fcc kagome antiferromagnet IrMn$_3$. Spin wave frequencies are calculated using the torque equation and the magnetic scattering function, $S({\bf Q},\omega)$, is determined by a Green's function method, as an extension of our previous work, LeBlanc et al, Phys. Rev. B 90, 144403 (2014). Results are compared with intensity contour data on powder samples of ordered IrMn$_3$, where magnetic Mn ions occupy lattice sites of ABC stacked kagome planes. Values of exchange parameters taken from DFT calculations used in our model provide good agreement with the experimental results only if further-neighbor exchange is included. Estimates of the observed energy gap support the existence of strong cubic anisotropy predicted by DFT calculations., Comment: Submitted to Phys. Rev. B

A series of atomistic finite temperature simulations on a model of an FCC lattice of maghemite nanoparticles using the stochastic Landau-Lifshitz-Gilbert (sLLG) equation are presented. The model exhibits a ferromagnetic transition that is in good agreement with theoretical expectations. The simulations also reveal an orientational disorder in the orientational order parameter for $T < 0.5 T_c$ due to pinning of the surface domain walls of the nanoparticles by surface vacancies. The extent of the competition between surface pinning and dipolar interactions provides support for the conjecture that recent measurements on systems of FCC superlattices of iron-oxide nanoparticles provide evidence for dipolar ferromagnetism is discussed.

Techniques developed by previous authors to describe the effects of a random distribution of impurity spins on the excitations of a magnetically ordered system are extended to the case of long-range oscillatory types of order which are not necessarily commensurate with the lattice. For non-magnetic impurities, a spin-wave stability condition is used to determine a critical concentration for the onset of such long-range order. For long-range oscillatory exchange the critical concentration can be reduced significantly from the nearest-neighbour result. The results are in good agreement with recent experiments on dilute rare-earth-yttrium alloys.

The effects of both anisotropic exchange and magnetoelastic coupling on phase transitions involving flat, conical and tilted spiral phases are investigated. Also the conditions under which the magnon modes in conical and flat spiral phases may soften are examined when anisotropic exchange is taken into account. It is found that both anisotropic exchange and magnetoelastic coupling can inhibit the instability of the magnon mode with q=Q in the flat spiral phase, but that the nature of the transition which occurs is quite different in each case. These results are discussed with reference to the phase transitions which occur in holmium and erbium near 20K.

The role of topological excitations in frustrated Heisenberg antiferromagnets between two and three spatial dimensions is considered. In particular, the antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A phase transition that is purely topological in nature occurs at a finite temperature for all film thicknesses. The results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions. PACS Nos.: 75.10.Hk, 75.40.Cx, 75.40.Mg

We report room temperature electrical detection of spin injection from a ferromagnetic insulator (YIG) into a ferromagnetic metal (Permalloy, Py). Non-equilibrium spins with both static and precessional spin polarizations are dynamically generated by the ferromagnetic resonance of YIG magnetization, and electrically detected by Py as dc and ac spin currents, respectively. The dc spin current is electrically detected via the inverse spin Hall effect of Py, while the ac spin current is converted to a dc voltage via the spin rectification effect of Py which is resonantly enhanced by dynamic exchange interaction between the ac spin current and the Py magnetization. Our results reveal a new path for developing insulator spintronics, which is distinct from the prevalent but controversial approach of using Pt as the spin current detector., 5 pages, 4 figures

Spin wave calculations demonstrate that the macroscopic continuous degeneracy associated with the two-dimensional kagome Heisenberg spin lattice persists in the case of the stacked fcc structure giving rise to zero energy modes in three dimensions. The addition of an effective local cubic anisotropy is shown to remove this continuous degeneracy and introduce a gap in the spectrum as well as modify the inelastic scattering function $S({\bf q},\omega)$. This scenario supports earlier Monte Carlo simulations which indicate that the phase transition to long range $q=0$ magnetic order is driven to be discontinuous by critical fluctuations associated with the large degeneracy in the absence of anisotropy, but becomes continuous with the addition of anisotropy. The results are relevant to Ir-Mn alloys which are widely used in the magnetic storage industry in thin film form as the antiferromagnetic pinning layer in spin-valve structures., Comment: 11 pages, 3 figures

The nature of multimagnon excitations in alternating spin/bond ferromagnetic chains are studied using a combination of scaling methods and the recursion method. Two-magnon excitations for a Heisenberg chain with either alternating spin magnitudes, $S$ and ${S}^{\ensuremath{'}},$ or alternating nearest-neighbor couplings, ${J}_{1}$ and ${J}_{2}$ can be studied using real-space rescaling techniques. These results are then used to investigate three-magnon excitations using the recursion method.

We describe a method for obtaining an analytic form for an inverse of a class of symmetric semi-infinite banded matrices, which are, apart from a finite number of terms, of the Toeplitz type. The results are applied to the determination of the spectrum of two-magnon excitations in Heisenberg spin chains with next-nearest-neighbour interactions.

We describe a method for obtaining an analytic form for the inverse of a finite symmetric banded Toeplitz matrix. Explicit formulae are given for the tridiagonal and pentadiagonal cases and the results are applied to the evaluation of the Green's function for nearest and next-nearest neighbour one-dimensional tight-binding systems.

The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.

The critical behaviour of the fully frustrated classical antiferromagnet on the triangular lattice is studied using Monte Carlo methods. Numerical evidence for separate Kosterlitz - Thouless and Ising transitions is presented as a result of investigating the free-energy cost to create an isolated vortex, the finite-size scaling of the spin stiffness and the finite-size scaling of the chirality.

Micron-sized rectangular ferromagnetic bars have a variety of spin excitations, including a quasi-uniform mode, horizontal and vertical standing spin-wave modes, and edge and corner modes. When driven by a strong microwave field, these modes differ from those found in the linear regime. For example, the resonance field or frequency becomes amplitude dependent. We study the nonlinear spin dynamics in such microstrips, both experimentally and theoretically, for a geometry where the static magnetic field is perpendicular to the plane of the sample. Experimentally, it is found that, at a fixed microwave frequency, the resonance field for the uniform mode is significantly reduced as the microwave power is increased. In contrast, the resonance fields for the standing horizontal spin-wave modes are only slightly reduced. This behavior is confirmed theoretically using micromagnetic calculations, and an intuitive explanation for this behavior is developed.

Monte Carlo simulation results are reported on magnetic ordering in ABC stacked Kagom\'{e} layers with fcc symmetry for both XY and Heisenberg models which include exchange interactions with the eight near-neighbors. Well known degeneracies of the 2D system persist in the 3D case and analysis of the numerical data provides strong evidence for a fluctuation-driven first-order transition to well-defined long-range order characterized as the layered $q=0$ (120-degree) spin structure. Effects of varying the inter-layer coupling are also examined. The results are relevant to understanding the role of frustration in IrMn$_3$ alloys widely used by the magnetic storage industry as thin-films in the antiferromagnetic pinning layer in GMR and TMR spin valves. Despite the technological importance of this structure, it has not previously been noted that the magnetic Mn-ions of fcc IrMn$_3$ form Kagom\'{e} layers., Comment: 9 pages, 14 figures. Submitted to Phys. Rev. B

The nature of three-magnon excitations in general spin-S quantum spin chains is studied using the recursion method. The asymptotic behaviour of the recurrence coefficients can be used to identify the presence of bound states in the spectrum. Special features of integrable models are easily identified.

Micromagnetic simulations are used to examine the effects of cubic and axial anisotropy, magnetostatic interactions and temperature on M-H loops for a collection of magnetic dipoles on fcc and sc lattices. We employ a simple model of interacting dipoles that represent single-domain particles in an attempt to explain recent experimental data on ordered arrays of magnetoferritin nanoparticles that demonstrate the crucial role of interactions between particles in a fcc lattice. Significant agreement between the simulation and experimental results is achieved, and the impact of intra-particle degrees of freedom and surface effects on thermal fluctuations are investigated., Comment: 10 pages, 9 figures

The classical antiferromagnetic Heisenberg model on the triangular lattice is studied using Monte Carlo techniques. The behavior of the antiferromagnetic structure factor, antiferromagnetic correlation length, and spin stiffness at low temperatures is consistent with recent low-temperature renormalization-group predictions based on a nonlinear sigma model (NLσ) description of the system. Our results support the validity of the NLσ model approach to the study of frustrated systems

Experimental and theoretical evidence is presented which shows that orientational ordering of highly polar head groups in monolayers of amphiphilic molecules (zwitterionic 2 amino-tetradecanoic acid) at fluid interfaces produces a smooth continuous phase transition. Hence this supports the view that models which interpret the sharp ‘kink’ point phase transitions exhibited by phospholipid monolayers at oil/water interfaces as being purely due to reorientation are deficient in important respects and suggests that the model which is most likely to be applicable to lipids of biological interest at oil/water interfaces is a blend of chain melting and collective molecular orientational ordering.

The critical dynamics of the d=1 alternating bond Glauber-Ising model and related models is studied. There are two contributions to the critical slowing down. One is due to the long-range fluctuations near the critical point. It is characterized by the dynamic exponent z=2. The other contribution is a temperature dependence of the bare time scale, which is a result of short-range phenomena. In contrast to previous studies, it is shown that all these models belong to one universality class.

The critical dynamics of the Glauber-Ising model on nontranslationally invariant lattices is studied. Both a quasi-periodic and a fractal geometry are considered. The distribution of inverse relaxation times rho (1/ tau ) is calculated using a generating function method. The distribution consists of bands with an internal self-similar structure. In the limit 1/ tau to 0, rho (1/ tau ) diverges with a universal exponent related to the dynamic critical exponent z. The width of the lowest frequency band is determined by a nonuniversal bare time scale, which is related to the presence of metastable states.

Using a numerical transfer-matrix method, the authors have determined the number of zero-temperature metastable states and their distribution in energy and magnetization for random-field Ising chains. Both discrete and continuous distributions of the random fields are considered. The degeneracy and structure of the metastable states and ground states for the discrete case may be understood in terms of a domain picture. Algorithms for generating exact ground-state configurations for both discrete and continuous distributions are described, and these demonstrate that the ground states of the random-field Ising chain have a hierarchical structure.

The authors examine the distribution of metastable states in the p-state Potts model. The random-bond Potts model on a chain as well as the uniform bond model on a self-similar lattice are studied. Analytic results are obtained for arbitrary continuous distributions of nearest-neighbour bonds for the chain. When negative bonds are present, the ground state for p>2 is frustrated, in contrast to the Ising model which has p=2. The results for p>2 show similarity to the discrete random-field Ising model.

The critical dynamics of the alternating bond kinetic Ising model on a chain is examined. It is shown that previous nonuniversal results for the dynamical critical exponent z for single spin flip dynamics should be reinterpreted. The critical slowing down is due to two distinct contributions which, when separated, indicate that the value of z is universal. The exponent remains universal even when two spin flip dynamics are considered.

We report magnetic measurements on a macroscopic three-dimensional fcc array of iron-oxide nanoparticles. We observe typical nanomagnetism for the randomly packed configuration of nanoparticles, including dynamical freezing and superparamagnetism. By contrast, the nanoparticle "atoms" in the fcc configuration that form the crystal exhibit a low coercivity that is weakly temperature dependent with no superparamagnetism up to 400 K.

In this paper we examine the nature of two-magnon excitations in the alternating-bond ferrimagnetic spin chain for general values S and S of the two species of spin. Both a direct analytic approach as well as a method based on a scaling transformation are used to study the bound-state branches and their relationship to the two-magnon continuum.

The effects of interfacial coupling at the boundary of ferromagnetic and antiferromagnetic components in a nanoscale columnar-structured thin film of ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}∕\mathrm{Co}\mathrm{O}$ have been examined. Field-cooling the film results in very different temperature dependences of the enhanced coercivity and exchange-bias shift of the hysteresis loop. The exchange-bias temperature dependence is well described by thermal fluctuations of the interfacial spins while the coercivity temperature dependence indicates that single-domain-like columns are being coherently rotated by the thermal fluctuations of the interface spins. Furthermore, only a portion of the spins in the antiferromagnetic layer seem to be associated with the spin coupling that results in exchange bias. X-ray magnetic resonant scattering measurements show clearly the presence of canted Co interfacial moments that provide a local field which enables exchange bias at a significantly higher temperature than the onset of an enhanced coercivity.

A generalized model which describes a family of antiferromagnetic Heisenberg magnets on a three-dimensional stacked triangular lattice is studied. The model contains a constraint parameter which changes the details of the interactions but not the symmetry of the model. We investigate the question of whether a first or second order phase transition occurs in these systems using a short time dynamics method. The effective critical exponents are determined as a function of the constraint parameter. Our results provide strong evidence that the phase transition is first order. In addition, for a particular value of the constraint parameter, the model corresponds to a stacked kagome lattice. In this case, our results also indicate the existence of a finite temperature first order phase transition.

An unusual enhancement of the antiferromagnetic ordering (N\'eel) temperature is observed in a ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}∕{\mathrm{Co}}_{3}{\mathrm{O}}_{4}$ thin film. This significant increase of the N\'eel temperature indicates an exchange energy of interface spins between the ferromagnet (FM) and antiferromagnet (AF) that is significantly greater than that of spins in the bulk of the film. Exchange bias is established even when the thin film is zero field cooled. Field cooling the film sets a significantly stronger exchange coupling between the FM and AF spins at the interface with a concomitant increase in the exchange-bias field.

Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that XY antiferromagnetic systems undergo a (weak) first order phase transition., 4 pages, 6 figures, largely revised version

Using Monte Carlo simulations, we compute the spin stiffness of a site-random 3d Heisenberg model with competing ferromagnetic and antiferromagnetic interactions. Our results for the pure limit yield values of the the critical temperature and the critical exponent $\nu$ in excellent agreement with previous high precision studies. In the disordered case, a mixed "chiral" phase is found which may be in the same universality class as 3d Heisenberg spin glasses., Comment: 5 pages, 4 figures, accepted in PRB Rapid Communications

The antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A topological phase transition occurs at finite temperature for all film thicknesses. Our results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions.

Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets., 5 pages, 3 figures, minor changes, published version

We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagome lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.

Ni12xAlx(OH)2(CO3) x/2iyH2O. 2‐ 6 The Ni ions in Ni(OH)2 occupy the octahedral holes between alternate pairs of OH planes and thus form a triangular lattice identical to that adopted by the OH ions. The two planes of OH ions, with the plane of Ni atoms between them, form a brucitelike layer of the host structure. 7 Ni(OH)2 can exist in two polymorphous crystal structures denoted as a and b. Both structures consist of brucitelike layers that are well ordered in the b phase and randomly stacked in the a phase. The interlayer spacing ~gallery! in the a phase is usually significantly larger than that in the b phase due to the large number of water molecules and anionic species that can penetrate into the galleries. 8

We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura., Comment: 5 pages, 7 figures

By introducing a chiral term into the Hamiltonian of the three-state Potts model on a triangular lattice additional symmetries are achieved between the clockwise and anticlockwise antiferromagnetic states and the ferromagnetic state. This model is investigated using Monte Carlo methods. We investigate the full phase diagram and find evidence for a line of tricritical points separating the ferromagnetic and antiferromagnetic phases.

The technique of damage spreading is used to study the phase diagram of the easy axis anisotropic Heisenberg antiferromagnet on two geometrically frustrated lattices. The triangular and kagome systems are built up from triangular units that either share edges or corners respectively. The triangular lattice undergoes two sequential Kosterlitz-Thouless transitions while the kagome lattice undergoes a glassy transition. In both cases, the phase boundaries obtained using damage spreading are in good agreement with those obtained from equilibrium Monte Carlo simulations., Comment: 7 pages, 4 figures

The antiferromagnetic Heisenberg model with easy-axis exchange anisotropy on the Kagome lattice is studied by means of Monte Carlo simulations. From equilibrium properties, we find that the values of the critical exponents associated with the magnetization at the critical temperature $T_c$ vary with the magnitude of the anisotropy. On the other hand, the spin-spin autocorrelation functions have a stretched exponential behavior with a power law divergence of the relaxation time at a glass-like temperature $T_g \sim T_c$. From non-equilibrium dynamics at a fixed temperature below $T_g$, aging effects are found which obey the same scaling laws as in spin glasses and polymers., 9 pages, 10 figures

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz–Thouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition. PACS Nos.: 75.10Hk, 75.40Mg

We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis anisotropy on the triangular lattice. Both the free energy cost for long wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented., 8 pages, 10 figures