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The dependence of the velocity of surface acoustic wave (SAW) as a function of an external applied magnetic field is investigated in a Fe thin film epitaxially grown on a piezoelectric GaAs substrate. The SAW velocity is observed to strongly depend on both the amplitude and direction of the magnetic field. To interpret the experimental data a phenomenological approach to the relative change in SAW velocity is implemented. We find that the experimental velocity variation can be well reproduced provided that the spin wave dispersion is taken into account. The validity of this phenomenological model is attested by the comparison with a quasi-exact magnetoelastic one.

Alternating gradient force magnetometry and Brillouin light scattering (BLS) experiments were exploited to investigate the perpendicular magnetic anisotropy (PMA) localized at the CoFeB–MgO interface, both in Ta/CoFeB/MgO heterostructures (bottom samples) and in the inverted ones MgO/CoFeB/Ta (top samples). Thermal treatment was found to induce a marked increase of the PMA with respect to the as grown state. Using linear spin wave theory, an analysis of the spin wave frequencies was performed which allowed to estimate the thickness dependence of the PMA in the single CoFeB film. Magnetic tunnel junctions with the Ta/CoFeB/MgO/CoFeB/Ta structure were also studied by BLS. The analysis of the experimental results, performed via the linear spin wave theory, revealed that there is an antiferromagnetic interlayer exchange coupling between the free and the fixed CoFeB layers which increases after the annealing procedure.

In thin magnetic films with perpendicular magnetic anisotropy, a periodic “up-down” stripe-domain structure can be originated at remanence, on a mesoscopic scale (~100 nm) comparable with film thickness, by the competition between short-range exchange coupling and long-range dipolar interaction. However, translational order is perturbed because magnetic edge dislocations are spontaneously nucleated. Such topological defects play an important role in magnetic films since they promote the in-plane magnetization reversal of stripes and, in superconductor/ferromagnet hybrids, the creation of superconducting vortex clusters. Combining magnetic force microscopy experiments and micromagnetic simulations, we investigated the motion of two classes of magnetic edge dislocations, randomly distributed in an $${{\rm{N}}}_{2}^{+}$$ N 2 + -implanted Fe film. They were found to move in opposite directions along straight trajectories parallel to the stripes axis, when driven by a moderate dc magnetic field. Using the approximate Thiele equation, analytical expressions for the forces acting on such magnetic defects and a microscopic explanation for the direction of their motion could be obtained. Straight trajectories are related to the presence of a periodic stripe domain pattern, which imposes the gyrotropic force to vanish even if a nonzero, half-integer topological charge is carried by the defects in some layers across the film thickness.

Ferromagnetic thin films with moderate perpendicular magnetic anisotropy (PMA) are known to support weak stripe domains provided film thickness exceeds a critical value. In this work, we performed both an experimental and theoretical investigation of a peculiar phenomenon shown by weak stripe domains: namely, the stripe domains reorientation when a dc magnetic field is applied in the film plane along the direction perpendicular to the stripes axis. We focus on bct α′-Fe8N1−x thin films obtained by N 2 + implantation of α-Fe films epitaxially grown on ZnSe/GaAs(001). By using different ion implantation and heat treatment conditions, we show that it is possible to tune the PMA values. Magnetic force microscopy and vibrating sample magnetometer measurements prove the existence of weak stripe domains at remanence, and of a threshold field for the reorientation of the stripes axis in a transversal field. Using a one-dimensional model of the magnetic stripe domains, where the essential parameter is the maximum canting angle of the stripe magnetization out of the film plane, the various contributions to the magnetic energy can be separately calculated. A linear increase of the reorientation threshold field on the PMA is obtained, in qualitative agreement with experimental data in our Fe–N films, as well as in other thin films with weak stripe domains. Finally, we find that also the rotatable anisotropy field linearly increases as a function of the PMA magnitude.

Spin waves propagation in ferromagnetic films, several tens of nanometers thick, have recently received increasing attention, in view of the development of magnonic devices operating in the GHz range of frequencies. A detailed knowledge of the dispersion curves and of the spatial characteristics of the spin-wave modes is preliminary to any technological application, particularly in the ``mesoscopic range'' (50--200 nm) of film thickness, where several dipole-exchange modes may appear in the spectrum, exhibiting frequency crossing and hybridization as a function of their wave number. In this work, the mutual interaction and the hybridization of the dipole-exchange spin-wave modes was investigated in a nitrogen-implanted iron (Fe-N) film, 78-nm-thick, in-plane magnetized. The spin-wave dispersion curves were measured by using Brillouin light scattering, and the experimental results were interpreted combining micromagnetic simulations and theoretical calculations in the framework of a dipole-exchange spin-wave mode approach. A noticeable hybridization between the spin-wave modes was observed, due to the simultaneous presence of a marked perpendicular magnetic anisotropy and a rather high saturation magnetization. The hybridization was found to induce a very large gap ($\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}\ensuremath{\approx}5$ GHz) between the low-frequency spin waves at high wave vector ($k\ensuremath{\approx}{10}^{5}$ rad/cm). Consequently, in such a $k$ range the simultaneous presence of two spin-wave modes with sizeable (${v}_{g}\ensuremath{\approx}1.5$ km/s) but opposite group velocity was observed, opening a way for the potential use of Fe-N films in magnon spintronics.

In this work, we present a nuclear magnetic resonance (NMR) study of the spin dynamics in the rare-earth-based low-dimensional molecular magnetic chains $\mathrm{Eu}{(\mathrm{hfac})}_{3}\mathrm{NITEt}$ and $\mathrm{Gd}{(\mathrm{hfac})}_{3}\mathrm{NITEt}$ (in short, Eu-Et and Gd-Et). Although both samples are based on the same chemical building block, [(${\mathrm{hfac})}_{3}\mathrm{NITEt}]$, their magnetic properties change dramatically when the ${\mathrm{Eu}}^{3+}$ ion, which is nonmagnetic at low temperatures, is substituted by the magnetic ${\mathrm{Gd}}^{3+}$ ion. The present proton NMR investigation shows that, down to the lowest investigated temperature ($T=1.5$ K for Gd-Et and $T=3$ K for Eu-Et), the Eu-Et chain behaves as a one-dimensional Heisenberg model with antiferromagnetic exchange coupling ($J=\ensuremath{-}20$ K) between $s=1/2$ organic radicals, and has a $T$-independent exchange frequency (${\ensuremath{\omega}}_{e}=2.6\ifmmode\times\else\texttimes\fi{}{10}^{12}$ rad/s). In the Gd-Et chain, in contrast, a competition arises between nearest-neighbor ferromagnetic coupling and next-nearest-neighbor antiferromagnetic coupling; moreover, two phase transitions have previously been found, in agreement with Villain's conjecture: a first transition, at ${T}_{0}=2.2$ K, from a high temperature paramagnetic phase to a chiral spin liquid phase, and a second transition, at ${T}_{N}=1.9$ K, to a three-dimensional helical spin solid phase. Contrary to the Eu-Et chain (whose three-dimensional ordering temperature is estimated to insurge at very low, ${T}_{N}\ensuremath{\approx}0.3$ K), critical spin dynamics effects have been measured in the Gd-Et chain on approaching ${T}_{N}=1.9$ K: namely, a divergence of the proton nuclear spin-lattice relaxation rate $1/{T}_{1}$, which in turn produces a sudden wipe-out of the NMR signal in a very narrow ($\mathrm{\ensuremath{\Delta}}T\ensuremath{\sim}0.04$ K) temperature range above ${T}_{N}$. Below ${T}_{N}$, an inhomogeneous broadening of the NMR line indicates a complete spin freezing. At ${T}_{0}=2.2$ K, instead, such critical effects are not observed because NMR measurements probe the two-spin correlation function, while the chiral spin liquid phase transition is associated with a divergence of the four-spin correlation function.

Controlling the speed at which systems evolve is a challenge shared by all disciplines, and otherwise unrelated areas use common theoretical frameworks towards this goal. A particularly widespread model is Glauber dynamics, which describes the time evolution of the Ising model and can be applied to any binary system. Here we show, using molecular nanowires under irradiation, that Glauber dynamics can be controlled by a novel domain-wall kickoff mechanism. In contrast to known processes, the kickoff has unambiguous fingerprints, slowing down the spin-flip attempt rate by several orders of magnitude, and following a scaling law. The required irradiance is very low, a substantial improvement over present methods of magneto-optical switching. These results provide a new way to control and study stochastic dynamic processes. Being general for Glauber dynamics, they can be extended to different kinds of magnetic nanowires and to numerous fields, ranging from social evolution2 to neural networks and chemical reactivity.

We present Monte Carlo simulation data about Holmium magnetic thin film structures. As well known, this rare earth shows, at transition temperature T N , a helical order in the bulk phase. In contrast with the collinear ferromagnetic or antiferromagnetic thin films, recent experimental works have proven that the transition temperature T N ( n ) ( n being the film thickness) depends on n only by an empirical relation. In order to study the behavior of these film structures, we consider a Heisenberg model with easy-plane single ion anisotropy and seven coupling constant ( J 0 in the plane and J 1 − J 6 between plane of the Ho h c p structure), obtained by experimental neutron measurements.

The effect of graded anisotropy on static and dynamic magnetic properties of ${\mathrm{Ar}}^{+}$-irradiated FePt films has been investigated by static magnetometry, magnetic force microscopy, and Brillouin light scattering from thermally excited spin waves. A gradual variation of magnetic anisotropy with film thickness was obtained by ${\mathrm{Ar}}^{+}$ irradiation. The irradiation incidence angle influences the anisotropy profile: on decreasing $\ensuremath{\alpha}$, a decreasing thickness of the hard $\mathrm{L}{1}_{0}$ phase and an increasing thickness of the soft A1 phase were obtained. Accordingly, the zero-field spin-wave frequency gap was found to decrease. In the sample with the highest soft-phase thickness the spin-wave frequency gap takes a substantial value (${\ensuremath{\nu}}_{0}\ensuremath{\approx}6$ GHz), which could be reproduced assuming the presence of a nonzero ``rotatable'' anisotropy (i.e., any direction in the film plane can be established as the easy axis by the application of a saturating magnetic field along this direction). The hypothesis is supported by both magnetometry and magnetic force microscopy data.

PMCID: PMC4800001.-- et al., Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices., Financial support from Italian MIUR, Spanish MINECO (MAT2012-38318-C03-01), BW-Stiftung (Kompetenznetz Funktionelle Nanostrukturen), ERC StG-338258 “OptoQMol”, the Royal Society (URF fellowship and grant) and the AvH Stiftung (Sofja Kovalevskaja award).

We present NMR and μ+SR study of spin dynamics in one-dimensional and quasi-one-dimensional molecular magnets of recent synthesis. In particular, we focus on the so called Gd(hfac)3NIT-R and CoPhOMe magnetic chains families. For Gd-R helimagnets we show some differences between “weakly frustrated systems” and “fully frustrated systems”. The different behaviour is due to the different radical inserted in the chains (R = Me, Ph for “weakly frustrated systems” and R = iPr, Et for “fully frustrated systems”). The existence of different phase transitions, particularly to 3D long-range magnetic order in Gd-Ph and to chiral order in Gd-iPr, is remarked together with a comparison between results obtained from macroscopic and microscopic investigating techniques. As regards CoPhOMe slowly relaxing chain, the 1H NMR measurements confirm the freezing of the spins at low temperature, which prevents the 3D long-range order, and display the presence of two relaxation mechanisms related to distinct contributions to the local spin relaxation.

The in-plane rotation of magnetic stripe domains in a 65-nm magnetostrictive ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ epitaxial film was investigated combining magnetic force microscopy, vibration sample magnetometry, and x-ray resonant magnetic scattering measurements. We analyzed the behavior of the stripe pattern under the application of a bias magnetic field along the in-plane direction perpendicular to the stripe axis, and made a comparison with the analogous behavior at remanence. The experimental results have been explained by means of micromagnetic simulations, supported by energy balance considerations. Fields smaller than $\ensuremath{\sim}400$ Oe do not induce any stripe rotation; rather, a deformation of the closure domains pattern was evidenced. Larger fields produce a sudden rotation of the stripe structure.

The classical one-dimensional planar spin model with competing nearest neighbor (nn) and next nearest neighbor (nnn) exchange interactions (Jnn>0 and Jnnn

The metastable states of a finite-size chain of N classical spins described by the chiral XY-model on a discrete one-dimensional lattice are calculated by means of a general theoretical method recently developed by one of us. This method allows one to determine all the possible equilibrium magnetic states in an accurate and systematic way. The ground state of a chain consisting of N classical XY spins is calculated in the presence of (i) a symmetric ferromagnetic exchange interaction, favoring parallel alignment of nearest neighbor spins, (ii) a uniaxial anisotropy, favoring a given direction in the film plane, and (iii) an antisymmetric Dzyaloshinskii–Moriya interaction (DMI), favoring perpendicular alignment of nearest neighbor spins. In addition to the ground state with a non-uniform helical spin arrangement, which originates from the energy competition in the finite-size chain with open boundary conditions, we have found a considerable number of higher-energy equilibrium states. In the investigated case of a chain with N =10 spins and a DMI much smaller than the in-plane uniaxial anisotropy, it turns out that a metastable (unstable) state of the finite chain is characterized by a configuration where none (at least one) of the inner spins is nearly parallel to the hard axis. The role of the DMI is to establish a unique rotational sense for the helical ground state. Moreover, the number of both metastable and unstable equilibrium states is doubled with respect to the case of zero DMI. This produces modifications in the Peierls–Nabarro potential encountered by a domain wall during its displacement along the discrete spin chain.

A theoretical method is used to find, in an accurate and systematic way, all the possible equilibrium magnetic states of a finite-size one-dimensional chain of classical planar spins, interacting via ferromagnetic nearest-neighbor symmetric exchange and subjected to a uniaxial anisotropy which favors the orientation of the spins along an easy axis within the plane perpendicular to the chain. For a chain with $N$ spins, the energy is a function of $N$ absolute orientation angles $({\ensuremath{\theta}}_{i}$, $i=1,...,N)$ and, owing to the absence of energy competition, the ground state is collinear ferromagnetic and doubly degenerate (either ${\ensuremath{\theta}}_{i}=0$ $\ensuremath{\forall}i$, or ${\ensuremath{\theta}}_{i}=\ensuremath{\pi}$ $\ensuremath{\forall}i$). The ground state corresponds to a global minimum of the energy in the $N$-dimensional space, while metastable states correspond to local minima. As a function of $N$, we have numerically determined the minimal value ${\ensuremath{\gamma}}_{\mathrm{min}}$ to be assumed by the ratio $\ensuremath{\gamma}$ between the anisotropy and the exchange constant for the first noncollinear metastable state to appear. For $N\ensuremath{\le}13$, all the noncollinear equilibrium spin configurations of the system were calculated with great accuracy at two different values, $\ensuremath{\gamma}=0.18$ and 0.21. A stability analysis was subsequently performed, showing that metastable noncollinear states can appear in the model even in the absence of energy competition. The various kinds of metastable states can be classified, in order of increasing energy, on the basis of the increasing number of $\ensuremath{\pi}$ walls (including both domains and antidomains) which can be inserted into the discrete finite chain with open ends when $N$ and/or $\ensuremath{\gamma}$ are increased. The effects of open boundary conditions and finite size on the Peierls-Nabarro barrier (i.e., the difference between the energy of an unstable onsite-centered domain wall and the energy of a stable intersite-centered domain wall) were also investigated.

The observation of slow magnetic relaxation in molecular clusters is now considered as one of the most important achievements of molecular magnetism of the last few years. In fact systems like Mn12, Fe 8 have provided unique opportunities for the investigation of molecular magnetic hysteresis, quantum tunneling of the magnetization, and of phase interference (Berry phase). All these features depend on slow magnetic relaxation. While clusters can be considered as zero-dimensional materials, in principle slow relaxation of the magnetization can also be expected in one-dimensional (1D) materials, as suggested by Glauber in 1963. However, to date, it has not been possible to observe this behavior because no suitable experimental system has been produced. In fact the conditions to be met to observe slow magnetic relaxation in 1D materials are rather stringent: 1) the ratio of the interaction within the chain, J, and that between chains, J', must be rather high, larger than 10^4 ; 2) the material must behave as a 1D Ising ferro- or ferrimagnet. We have now found that slow relaxation of the magnetization and hysteresis effects which are not associated with three-dimensional (3D) order can be observed in [Co(hfac)2(NITPhOMe)]. We have shown here that these findings provide an experimental confirmation of Glauber's prediction and that magnetic bistability and the related memory effect can indeed be observed in such a 1D material without requiring any interchain interaction. These results may open exciting new perspectives including that of storing information in a single magnetic polymer as well as in the novel class of 1D materials where ionic structures are obtained inside carbon nanotubes.

The dependence on temperature of the layer magnetization of a Heisenberg ferromagnetic ultrathin film in presence of magnetocrystalline single-ion anisotropy was theoretically investigated in the framework of a Green's function approach using the random phase approximation (RPA). The effect of surface orientation and of film thickness N on the Curie temperature TC was carefully investigated in the case of face centered cubic (FCC) films: the steepest increase of TC(N) was found in the case of the FCC(1 1 1) orientation and the smoothest in the FCC(1 1 0) one. Our results for TC(N) were successfully fitted by a finite-size scaling relation [TC(∞)−TC(N)]/TC(N)=(N/N0)−λ, giving a shift exponent λ≃1.5, irrespectively of the surface orientation. Finally, the temperature evolution of the magnetization profile was analyzed, as well as its limiting shape at TC.

Low-temperature magnetic susceptibility, zero-field muon spin resonance and specific heat measurements have been performed in the quasi-one-dimensional (1D) molecular helimagnetic compound Gd ( hfac ) 3 NITEt . The specific heat presents two anomalies at T 0 = 2.19 ( 2 ) K and T N = 1.88 ( 2 ) K , while susceptibility and zero-field muon spin resonance show anomalies only at T N = 1.88 ( 2 ) K . The results suggest an experimental validation of Villain's conjecture of a two-step magnetic ordering in quasi-1D XY helimagnets: the paramagnetic phase and the helical spin solid phases are separated by a chiral spin liquid, where translational invariance is broken without violation of rotational invariance.

We present Monte Carlo simulations of Ho magnetic thin films. We consider a Heisenberg model with easy-plane single ion anisotropy and seven coupling constant, obtained by experimental neutron scattering measurements. For the analysed thicknesses ( n = 9 – 16 ) , increasing the temperature the films show, after the distorted helical configuration, a temperature range where the inner planes are disordered, while the surface ones appear in a block ordered state. At low temperatures, we also show that the progressive thickness reduction does not entail a sudden helical order suppression, but rather a gradual passage to a fan-like order is observed, driven by the helix distortion related to the surface effects.

We present numerical simulations, based on a mean-field calculation of the equilibrium configuration, for the magnetization reversal process in magnetic multilayers consisting of a hard (h) phase with large anisotropy, exchange coupled to a soft (s) phase with large magnetization. Starting from a trilayer made of $50h/100s/50h$ layers, and using realistic Hamiltonian parameters pertinent to epitaxial Sm-Co/Fe films, we separately investigate the effect of (i) increasing nanostructuration, while maintaining constant the overall hard/soft ratio, and (ii) decreasing the thickness of the hard phase, while keeping constant that of the soft phase. We find that the exchange-bias field and the coercive field strongly increase upon increasing nanostructuration and that the maximum energy product ${(\mathrm{BH})}_{\mathrm{max}}$ rapidly tends to the ideal value $(2\ensuremath{\pi}{M}_{\mathrm{sat}}{)}^{2}$. In contrast, upon reducing the thickness of the hard phase in a trilayer, the exchange-bias field and the coercive field remain nearly constant. Thus, combining both effects in an opportune way, we are able to determine the most convenient composition in order to obtain a permanent exchange-spring magnet with high performance, i.e., very high ${(\mathrm{BH})}_{\mathrm{max}}.$

We studied the low-temperature specific heat $C(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ of $\mathrm{Gd}(\mathrm{hfac}{)}_{3}\mathrm{NITiPr},$ a quasi-one-dimensional (1D) molecular magnetic chain with competing nearest-neighbor $(\mathrm{nn})$ and next-nearest-neighbor $(\mathrm{nnn})$ intrachain exchange interactions. The anomaly observed in $C(T)$ was reproducibly found at ${T}_{0}=2.09 \mathrm{K},$ although the $C(T)$ curves measured on different samples showed clear evidence for aging effects. For fresh, high-quality samples, the $\ensuremath{\lambda}$ shape of the anomaly and the negligible latent heat (less than $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3} \mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$ strongly suggest the presence of a phase transition of order higher than the first. In the best sample at temperatures well below ${T}_{0}$ (0.2--1 K), a linear C-vs-$T$ dependence was found, which we interpreted in the framework of 1D quantum free spin-wave theory. Strong aging effects were also found in the magnetic susceptibility $\ensuremath{\chi}(T)$ which, for the best and freshest sample, exhibits a very small anomaly close to ${T}_{0}$ (at ${T}_{\ensuremath{\chi}}=2.1 \mathrm{K}),$ superimposed to a diverging paramagnetic behavior at lower temperatures. The anomaly at ${T}_{0}(\ensuremath{\sim}{T}_{\ensuremath{\chi}})$ could be due to a transition to three-dimensional (3D) helical long-range order, but this is inconsistent with the observed linear C-vs-$T$ behavior, typical of a 1D magnet with strong intrachain antiferromagnetic interactions. An alternative interpretation, capable of explaining the $C(T)$ data both in the low-temperature and in the critical region, calls for the onset, below ${T}_{0},$ of nonconventional chiral long-range order due to interchain interactions. The chiral phase can be described as a collection of parallel corkscrews, all turning clockwise (or all counterclockwise), whereas their phases are random. An estimation of ${T}_{0}$ according to this model and using the exchange constants evaluated from the linear C-vs-$T$ slope supports this interpretation. The chiral order is compatible with the breaking of the chain into finite segments, due to aging effects, while the phase coherence necessary for the onset of 3D helical long-range order is destroyed. In this framework, a qualitative account for the very small anomaly observed in the magnetic susceptibility $\ensuremath{\chi}(T)$ can also be given.

A comprehensive investigation of rotatable anisotropy in a Fe${}_{0.8}$Ga${}_{0.2}$ thin film with a stripe domain structure has been performed comparing static and dynamic measurements. The stripes' domain formation and their rotation under a transverse magnetic field have been imaged by magnetic force microscopy. The rotatable anisotropy field ${H}_{\mathrm{rot}}$ was determined by fitting the frequency evolution of the dipole-dominated magnetostatic spin-wave mode versus the in-plane orientation of the stripe domains, measured by Brillouin light scattering in the absence of any dc or ac magnetic field. We obtained ${H}_{\mathrm{rot}}\ensuremath{\approx}1.35$ kOe, which is nearly ten times larger than the crystallographic in-plane anisotropy field. By applying a dc magnetic field along the stripes' axis, ${H}_{\mathrm{rot}}$ decreases, and eventually vanishes for saturated in-plane magnetization. At remanence, we established a quantitative relationship between static and dynamic properties, that is, the stripes' rotation angle and the in-plane angle dependence of spin-wave frequency.

A theoretical method recently developed is used to find all possible equilibrium magnetic states of a finite-size classical one-dimensional planar spin chain with competing nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions. The energy of a classical planar model with $N$ spins is a function of $N$ absolute orientational angles or equivalently, due to the absence of in-plane anisotropy, of $(N\ensuremath{-}1)$ relative orientational angles. The lowest energy stable state (ground state) corresponds to a global minimum of the energy in the $(N\ensuremath{-}1)$-dimensional space, while metastable states correspond to local minima. For a given value of the ratio, $\ensuremath{\gamma}$, between nnn and nn exchange couplings, all the equilibrium configurations of the model were calculated with great accuracy for $N\ensuremath{\le}16$, and a stability analysis was subsequently performed. For any value of $N$, the ground state was found to be ``symmetric'' with respect to the middle of the chain in the relative angles representation. For the chosen value of $\ensuremath{\gamma}$, the ground state consists of a helix whose chirality is constant in sign along the chain (i.e., all the spins turn clockwise, or all anticlockwise), but whose pitch varies owing to finite-size effects; e.g., for positive chirality we found that the chiral order parameter $\ensuremath{\chi}(N)g0$ increases monotonically with increasing $N$, approaching the value $(\ensuremath{\chi}=1)$ pertinent to the ground state in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. For finite but not too small values of $N$, we found metastable states characterized by one reversal of chirality, either localized just in the middle of the chain [``antisymmetric'' state, with chiral order parameter $\ensuremath{\chi}(N)=0$], or shifted away from the middle of the chain, to the right or to the left [pairs of ``ugly'' states, with equal and opposite values of $\ensuremath{\chi}(N)\ensuremath{\ne}0$; the attribute ``ugly'' refers to the absence of a definite symmetry in the relative angles representation]. Concerning the stability of these states with one reversal of chirality, two main results were found. First, the ``antisymmetric'' state is metastable for even $N$ and unstable for odd $N$. Second, an additional pair of ``ugly'' states is found whenever the number of spins in the chain is increased by 1; the states in each additional pair are unstable for even $N$ and metastable for odd $N$. Analysis of stable and metastable configurations in the framework of a discrete nonlinear mapping approach provides further support for the above results.

The classical one-dimensional (1D) planar spin model with competing nearest neighbor (nn) and next nearest neighbor (nnn) exchange interactions (Jnn>0 and Jnnn

Graphene is a potential component of novel spintronics devices owing to its long spin diffusion length. Besides its use as spin-transport channel, graphene can be employed for the detection and manipulation of molecular spins. This requires an appropriate coupling between the sheets and the single molecular magnets (SMM). Here, we present a comprehensive characterization of graphene-Fe4 SMM hybrids. The Fe4 clusters are anchored non-covalently to the graphene following a diffusion-limited assembly and can reorganize into random networks when subjected to slightly elevated temperature. Molecules anchored on graphene sheets show unaltered static magnetic properties, whilst the quantum dynamics is profoundly modulated. Interaction with Dirac fermions becomes the dominant spin-relaxation channel, with observable effects produced by graphene phonons and reduced dipolar interactions. Coupling to graphene drives the spins over Villain's threshold, allowing the first observation of strongly-perturbative tunneling processes. Preliminary spin-transport experiments at low-temperature are further presented.

La relaxation d'un spin dans un solide depend dans certains cas de l'effet tunnel entre deux etats de champ cristallin excites |a> et |b>. Le calcul de la frequence tunnel ω ab a la resonance est un probleme classique en l'absence d'amortissement. En presence d'amortissement, on peut deduire le temps de relaxation d'une equation maitresse ou l'effet tunnel est modelise par une probabilite de transition Γ ab entre |a> et |b>. Nous demontrons la formule Γ ab = 2ω ab 2 τ ab / [1 + τ ab 2 (E a - E b ) 2 /h 2 ], ou E a - E b est une fonction lineaire du champ magnetique, τ ab = τ a τ b /(τ a + τ b ), enfin τ a et τ b sont les temps de vie de |a> et |b>, qui dependent de l'interaction spin-phonon et peuvent etre calcules en l'absence d'effet tunnel. On propose une analogie mecanique qui donne une image intuitive du phenomene. Les equations maitresses sont identiques a celles qui decrivent la decharge de condensateurs dans un reseau electrique.

Spin-polarized low-energy electron diffraction combined with in situ Kerr magnetometry and a model calculation indicates that a six monolayer thick fcc Fe film undergoes a reversible transition from a room-temperature paramagnetic state to a low-temperature phase including antiferromagnetically coupled planes. The fcc Fe film was grown in an exchange field provided by an underlying Co layer.

The magnetic coupling of Fe(110) thin films through epitaxial (111) oriented noble-metal spacers has been investigated using a site-specific M\"ossbauer spectroscopy technique that is sensitive to changes in the interfacial Fe spin-wave spectrum. As the interlayer exchange oscillates, the interfacial spin-wave modes are alternately softened and stiffened. To qualitatively connect the observed spin-wave behavior to the effective exchange at the Fe/noble-metal interface, the system is modeled using two semi-infinite simple cubic ferromagnets which may interact either ferromagnetically or antiferromagnetically. Vibrating-sample magnetometry and superconducting quantum interference device magnetometry measurements determined that the interlayer coupling is always ferromagnetic. As the interlayer thickness is increased, the spin-wave behavior indicates an oscillatory component superimposed on a monotonic decrease in the ferromagnetic exchange coupling. The periodicities of the oscillatory component are 6 monolayers (ML) for Ag(111) and 4.5 ML for Cu(111), in close agreement with the expected periodicities from the bulk Fermi-surface spanning vectors. \textcopyright{} 1996 The American Physical Society.

In systems with free surfaces and interfaces, the absence of translational invariance may result in a completely different behavior with respect to the corresponding bulk system, so that many new and interesting phenomena may take place, as for example, the occurrence of a surface reconstruction phenomenon, characterized by an order at the surface different from the one which occurs deep in the sample. This article reviews the mean-field approach to surface and interface properties as a problem in nonlinear dynamics. We focus our attention on magnetic films and superlattices, whose properties are studied in terms of area-preserving maps; the emphasis is put on the effect of the surfaces, which are introduced as appropriate boundary condition, and which let exotic solution become physically relevant, though the infinitely extended system is trivially solvable. The importance of the discreteness of the lattice and of chaotic regimes in the map phase space is stressed. Some specific applications are given: (i) the magnetic field dependence of the ground state of semi-infinite uniaxial antiferromagnets and films, so that the anomalous behavior of the magnetic susceptibility experimentally observed in Fe/Cr(211) superlattices is easily accounted for as related to the chaotic nature of the corresponding map; (ii) the ground state and the temperature dependence of the magnetization of a ferromagnet with an enhanced surface exchange, and with a surface anisotropy favoring the spins to lie perpendicularly to the film plane, while a bulk anisotropy favors an in plane spin configuration.

Brillouin light scattering was applied to measure the evolution of spin waves in exchange-coupled [Co/Pd]-NiFe films with out-of-plane/in-plane magnetic anisotropy. Tunable tilting of the magnetization has important effects on the spin wave frequency gap: a substantial increase is observed with decreasing the soft NiFe thickness, while seemingly insignificant tilting angles cause a strong reduction with respect to a film with only the hard [Co/Pd] component. The spin wave frequency is reproduced also in samples, with increased thickness of the upper Pd layer, where a sudden modification in the tilting at the hard/soft interface is caused by the weakening of interlayer exchange.

Using a microscopic approach, we study the elementary excitations for a uniaxial antiferromagnetic film with an external magnetic field H applied along the easy axis. For H greater than a critical value, HS, the system has a non-uniform ground state which is obtained, very rapidly and with high accuracy, in terms of a two-dimensional area preserving map, where the surfaces are introduced as appropriate boundary conditions. The consequent spectrum is calculated in the whole Brillouin zone and the behaviour of the localized surface modes is carefully analysed. It is possible to observe that the lowest-energy modes have substantially a bulk character for low values of k/sub /// (the wavevector in the plane parallel to the surfaces), whilst the localized surface modes have the lowest energy for high values of k/sub ///. The relevance of our results for the superlattices composed by ferromagnetic films antiferromagnetically coupled across non-magnetic layers, which present the giant magnetoresistance phenomenon, is discussed, too.

We study a model which presents surface enhanced magnetic order and magnetic reconstruction using a nonlinear map with boundary conditions. Different temperature dependences are found for the parallel and perpendicular components of the magnetization. The relevance to recent experiments on Gd/W films is discussed.

The low temperature NMR investigation of Mn(hfac)2NITiPr, a one-dimensional ferrimagnet formed by manganese(II), spin S = 5/2, and nitronyl nitroxide NITiPr, spin S = 1/2, is reported. The main feature observed is a field dependent maximum in the 1H longitudinal relaxation rate. These data are explained assuming nonlinear excitations, like 2π sine-Gordon solitons. The theoretical modelling for solitons in 1D ferrimagnets is outlined. This is the first report of soliton spin dynamics in one-dimensional ferrimagnets.

Recent experimental measurements on Fe/Cr(211) superlattices (Wang et al. 1994 Phys. Rev. Lett. 72 920) show several peaks in the field dependence of magnetic susceptibility. We show that the presence of these peaks is due to the chaotic nature of the two-dimensional area-preserving map by which we determine the equilibrium configuration of the system. We find a large number of metastable states and that the ground state changes abruptly with increasing field, showing the fundamental role played by the discreteness of the lattice.

The phenomenon of surface magnetic reconstruction (i.e. a different orientation of the surface spins with respect to the bulk ones) is overviewed in the framework of mean-field theory as an area-preserving map, where the surfaces are introduced as appropriate boundary conditions. In this way, the nonuniform ground state both of semi-infinite systems and films, can be calculated very rapidly and with a great precision for a variety of magnetic models: (i) a uniaxial antiferromagnet in an applied magnetic field, a model able to describe Fe Cr (211) superlattices with antiferromagnetic interlayer coupling; (ii) a ferromagnet with enhanced surface exchange, and with a surface anisotropy favouring the spins to lie perpendicularly to the film surface, while the bulk anisotropy favours in-plane alignment, a model able to describe Gd(0001)/W(110) films.

We study the magnetic state of a thin film undergoing a reorientation transition, in the plane defined by the temperature T and the thickness N. In going beyond free spin wave theory, three distinct regions are found: one with perpendicular magnetization; one with in-plane magnetization and a third (high T)-region with no magnetization. We are able to determine the boundaries between these regions and the resulting phase diagram agrees with the existing experimental data. A possible maximum in the reorientation transition TR(N) is predicted. Further experimental work is necessary to check this possibility.

The relaxation time of the magnetization of a big magnetic molecule is evaluated. Isotropic exchange is assumed to be dominant, resulting in a fixed spin modulus s (equal to 20 in the case of interest). A perturbation of the form ASz2 results from spin-orbit coupling and produces an energy barrier As2 which separates positive and negative values of Sz. Spin-phonon interactions are treated by second-order perturbation theory. An upper limit of the pre-exponential factor in the Arrhenius law is obtained, which is consistent with the very large experimental value.

Making use of detailed classical Monte Carlo simulations, we study the critical properties of a two-dimensional planar spin model on a square lattice composed by weakly interacting helimagnetic chains. We find a large temperature window where the vector chirality order parameter, = , the key quantity in multiferroic systems, takes nonzero value in the absence of long-range order or quasi-long-range order. The phase diagram we obtain for different strengths of the interchain coupling clearly shows that the weakness of the interchain interaction plays an essential role in order to observe the vector chiral spin liquid phase in a temperature range of up to now unattained width ({approx_equal}7%, to be compared with {approx_equal}1% or less previously reported for fully frustrated models, the only well-investigated systems unambiguously displaying spin-chirality decoupling). The relevance of our results for three-dimensional models is also discussed.

The static and dynamic properties of the single-chain molecular magnet [Co(hfac)$_2$NITPhOMe] are investigated in the framework of the Ising model with Glauber dynamics, in order to take into account both the effect of an applied magnetic field and a finite size of the chains. For static fields of moderate intensity and short chain lengths, the approximation of a mono-exponential decay of the magnetization fluctuations is found to be valid at low temperatures; for strong fields and long chains, a multi-exponential decay should rather be assumed. The effect of an oscillating magnetic field, with intensity much smaller than that of the static one, is included in the theory in order to obtain the dynamic susceptibility $\chi(\omega)$. We find that, for an open chain with $N$ spins, $\chi(\omega)$ can be written as a weighted sum of $N$ frequency contributions, with a sum rule relating the frequency weights to the static susceptibility of the chain. Very good agreement is found between the theoretical dynamic susceptibility and the ac susceptibility measured in moderate static fields ($H_{\rm dc}\le 2$ kOe), where the approximation of a single dominating frequency turns out to be valid. For static fields in this range, new data for the relaxation time, $\tau$ versus $H_{\rm dc}$, of the magnetization of CoPhOMe at low temperature are also well reproduced by theory, provided that finite-size effects are included., Comment: 16 pages, 9 figures

The interlayer exchange coupling in Fe(110)/Ag(111) multilayer structures with parallel alignment of the Fe layer magnetizations has been investigated with a zero-field M\"ossbauer spectroscopy technique that is sensitive only to the spin-wave spectrum at the Fe/Ag interface. Model spin-wave calculations are presented to connect the coupling strength to the observed interfacial spin-wave behavior. As the Ag thickness was varied from 0 to 40 ML (monolayers), the interfacial spectra of the films showed oscillations in the coupling strength with a period of 6 ML, in close agreement with recent predictions.

The thermodynamical properties of an alternating spin (S,s) one-dimensional (1D) Ising model with competing nearest- and next-nearest-neighbor interactions are exactly calculated using a transfer-matrix technique. In contrast to the case S=s=1/2, previously investigated by Harada, the alternation of different spins (S\ensuremath{\ne}s) along the chain is found to give rise to two-peaked static structure factors, signaling the coexistence of different short-range-order configurations. The relevance of our calculations with regard to recent experimental data by Gatteschi et al. in quasi-1D molecular magnetic materials, R (hfac${)}_{3}$ NITEt (R=Gd, Tb, Dy, Ho, Er, . . .), is discussed; hfac is hexafluoro-acetylacetonate and NlTEt is 2-Ethyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide.

The proton nuclear spin–lattice relaxation rate in the molecular ring Fe10 is calculated by linear response theory, starting from the unperturbed eigenvalues and eigenvectors, and introducing dipolar superhyperfine interactions as a perturbation. A strong enhancement of the rate at critical values of the applied magnetic field, recently observed by solid-state NMR at low temperatures, is explained in terms of level crossing between states with |Δ S |=1 and |Δ M |=1.

The properties of helical thin films have been thoroughly investigated by classical Monte Carlo simulations. The employed model assumes classical planar spins in a body-centered tetragonal lattice, where the helical arrangement along the film growth direction has been modeled by nearest neighbor and next-nearest neighbor competing interactions, the minimal requirement to get helical order. We obtain that, while the in-plane transition temperatures remain essentially unchanged with respect to the bulk ones, the helical/fan arrangement is stabilized at more and more low temperature when the film thickness, n, decreases; in the ordered phase, increasing the temperature, a softening of the helix pitch wave-vector is also observed. Moreover, we show also that the simulation data around both transition temperatures lead us to exclude the presence of a first order transition for all analyzed sizes. Finally, by comparing the results of the present work with those obtained for other models previously adopted in literature, we can get a deeper insight about the entwined role played by the number (range) of interlayer interactions and surface effects in non-collinear thin films., Comment: 7 pages, 10 figures

Recent experimental data, showing a dimensional crossover of the T-dependent magnetization in molecular-beam-epitaxy grown Fe(110)/Ag(111) superlattices with different Ag-spacer thickness, are theoretically reanalyzed, using a simple free-spin-wave theory. We consider a Heisenberg model of localized spins with intraplane and interplane exchange interactions. As suggested by the experimental results, we also take explicitly into account the effect of easy-plane and easy-axis surface anisotropies, which are shown to play an important role in the stabilization of the long-range order, more evident for large thickness of the Ag spacer. The spin-wave dispersion curves and the magnetization are calculated in the framework of a Green's-function method and the correct asymptotic forms for the temperature dependence of the spin deviation in the quasi-two-dimensional regime (T lnT) and in the three-dimensional one (${\mathit{T}}^{3/2}$) are obtained. Further experimental investigation is suggested, in order to point up the anisotropy effects.

Motivated by recent experimental results in ultra-thin helimagnetic Holmium films, we have performed an extensive classical Monte Carlo simulation of films of different thickness, assuming a Hamiltonian with six inter-layer exchange constants. Both magnetic structure and critical properties have been analyzed. For n>16 (n being the number of spin layers in the film) a correct bulk limit is reached, while for lower n the film properties are clearly affected by the strong competition among the helical pitch and the surface effects, which involve the majority of the spin layers: In the thickness range n=9-16 three different magnetic phases emerge, with the high-temperature, disordered, paramagnetic phase and the low-temperature, long-range ordered one separated by an intriguing intermediate-temperature block phase, where outer ordered layers coexist with some inner, disordered ones. The phase transition of these inner layers displays the signatures of a Kosterlitz-Thouless one. Finally, for n, Comment: 29 pages, 14 figures

We investigate theoretically and experimentally the static magnetic properties of single crystals of the molecular-based Single-Chain Magnet (SCM) of formula [Dy(hfac)$_{3}$NIT(C$_{6}$H$_{4}$OPh)]$_{\infty}$ comprising alternating Dy$^{3+}$ and organic radicals. A peculiar inversion between maxima and minima in the angular dependence of the magnetic molar susceptibility $\chi_{M}$ occurs on increasing temperature. Using information regarding the monomeric building block as well as an {\it ab initio} estimation of the magnetic anisotropy of the Dy$^{3+}$ ion, this anisotropy-inversion phenomenon can be assigned to weak one-dimensional ferromagnetism along the chain axis. This indicates that antiferromagnetic next-nearest-neighbor interactions between Dy$^{3+}$ ions dominate, despite the large Dy-Dy separation, over the nearest-neighbor interactions between the radicals and the Dy$^{3+}$ ions. Measurements of the field dependence of the magnetization, both along and perpendicularly to the chain, and of the angular dependence of $\chi_{M}$ in a strong magnetic field confirm such an interpretation. Transfer matrix simulations of the experimental measurements are performed using a classical one-dimensional spin model with antiferromagnetic Heisenberg exchange interaction and non-collinear uniaxial single-ion anisotropies favoring a canted antiferromagnetic spin arrangement, with a net magnetic moment along the chain axis. The fine agreement obtained with experimental data provides estimates of the Hamiltonian parameters, essential for further study of the dynamics of rare-earths based molecular chains., Comment: 11 pages, 8 figures

Low-temperature specific heat, magnetic susceptibility, and zero-field muon spin resonance (MUSR) measurements have been performed in the quasi-one-dimensional molecular helimagnetic compound Gd(hfac)(3)NITEt. The specific heat presents two anomalies at T(0)=2.19 +/- 0.02 K and T(N)=1.88 +/- 0.02 K, which both disappear upon the application of a weak magnetic field. Conversely, magnetic susceptibility and mu SR data show the divergence of two-spin correlation functions only at T(N)=1.88 +/- 0.02 K. These results suggest an experimental validation of Villain's conjecture of a two-step magnetic ordering in quasi-one-dimensional XY helimagnets; i.e., the paramagnetic phase and the helical spin solid phase are separated by a chiral spin liquid phase, where translational invariance is broken without violation of rotational invariance.

We study the effect of antiferromagnetic interactions on the single spin-flip Glauber dynamics of two different one-dimensional (1D) Ising models with spin $\pm 1$. The first model is an Ising chain with antiferromagnetic exchange interaction limited to nearest neighbors and subject to an oscillating magnetic field. The system of master equations describing the time evolution of sublattice magnetizations can easily be solved within a linear field approximation and a long time limit. Resonant behavior of the magnetization as a function of temperature (stochastic resonance) is found, at low frequency, only when spins on opposite sublattices are uncompensated owing to different gyromagnetic factors (i.e., in the presence of a ferrimagnetic short range order). The second model is the axial next-nearest neighbor Ising (ANNNI) chain, where an antiferromagnetic exchange between next-nearest neighbors (nnn) is assumed to compete with a nearest-neighbor (nn) exchange interaction of either sign. The long time response of the model to a weak, oscillating magnetic field is investigated in the framework of a decoupling approximation for three-spin correlation functions, which is required to close the system of master equations. The calculation, within such an approximate theoretical scheme, of the dynamic critical exponent z, defined as ${1/\tau} \approx ({1/ {\xi}})^z$ (where \tau is the longest relaxation time and \xi is the correlation length of the chain), suggests that the T=0 single spin-flip Glauber dynamics of the ANNNI chain is in a different universality class than that of the unfrustrated Ising chain., Comment: 5 figures. Phys. Rev. B (accepted July 12, 2007)