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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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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)

The problem of finite size effects in s=1/2 Ising systems showing slow dynamics of the magnetization is investigated introducing diamagnetic impurities in a Co$^{2+}$-radical chain. The static magnetic properties have been measured and analyzed considering the peculiarities induced by the ferrimagnetic character of the compound. The dynamic susceptibility shows that an Arrhenius law is observed with the same energy barrier for the pure and the doped compounds while the prefactor decreases, as theoretically predicted. Multiple spins reversal has also been investigated., 4 pages, 5 figures. Physical Review Letters, accepted for publication

We use a surface‐sensitive Mossbauer spectroscopy technique to examine the spin‐wave spectrum, at the Fe(110)/NM(111) interface only, of a multilayer structure with a noble metal (NM) interlayer. We find that the temperature dependence of the hyperfine field follows a Bloch law (1−BT3/2), and use spin‐wave calculations to connect the surface spin‐wave stiffness parameter, B, to the interlayer exchange coupling. Films grown with Ag(111) interlayers show clear oscillations with a period of 6 ML, in good agreement with recent predictions.

Using a microscopic and quantum approach, we study the ground state configuration and the spin‐wave excitations of a model of two ferromagnetic monolayers, interacting via both bilinear and biquadratic exchange, and subject to an easy‐plane anisotropy, a quartic in‐plane anisotropy, and an external field. Peculiar features are found in the field dependence of the acoustic and optical frequency gaps in correspondence to the critical fields for which the canting angle between the magnetizations of the two coupled layers presents discontinuities. In particular, we suggest that a minimum in the optical gap at the saturation field could be experimentally observed by Brillouin light scattering in real systems, like Fe/Cr/Fe trilayers.

The slow dynamics (10^-6 s - 10^4 s) of the magnetization in the paramagnetic phase, predicted by Glauber for 1d Ising ferromagnets, has been observed with ac susceptibility and SQUID magnetometry measurements in a molecular chain comprising alternating Co{2+} spins and organic radical spins strongly antiferromagnetically coupled. An Arrhenius behavior with activation energy Delta=152 K has been observed for ten decades of relaxation time and found to be consistent with the Glauber model. We have extended this model to take into account the ferrimagnetic nature of the chain as well as its helicoidal structure., 4 pages, 4 figures (low resolution), 16 references. Submitted to Physical Review Letters

Using a microscopic and quantum approach, we study the ground-state configuration and the spin-wave excitations of a model of two ferromagnetic monolayers, interacting via both bilinear and biquadratic exchange, and subject to an easy-plane anisotropy, a quartic in-plane anisotropy and an external field. In the framework of a Green's-function method, we obtain analytical results for the spin-wave dispersion curves. Peculiar features are found in the field dependence of the acoustic and optical frequency gaps, in correspondence to the critical fields for which the canting angle between the magnetizations of the two coupled layers presents discontinuities. In particular, a minimum for the optical gap at the saturation field is predicted, which could be experimentally observed by Brillouin light scattering in real systems.

We study the reorientation transition in a thin ferromagnetic film between a perpendicularly magnetized state and an in-plane magnetized one, at the growing of the temperature T and the number of planes N . In the framework of a renormalization group approach, we find the boundaries between the three (perpendicularly magnetized, in-plane magnetized, paramagnetic) regions. A maximum in the reorientation temperature T R ( N ) is predicted.

Some recent experimental data on the magnetic susceptibility and the low-temperature magnetization of the (La, Ce)B6 system are discussed in the light of the theoretical results. A value of the s-f exchange constant J is estimated which is also consistent with the results obtained from both the Kondo effect and the RKKY interaction.

The problem of computing the lattice thermal conductivity and the phonon-drag contribution to the electrical resistivity in presence of normal phonon–phonon processes is examined in the framework of the Boltzmann-Callaway equation. A previous treatment for the lattice thermal conductivity of insulating crystals by Callaway and Krumhansl is appropriately extended in order to treat the properties of interest. The so-obtained expressions for the lattice thermal conductivity and the phonon-drag contribution are presented. Some inconsistences of recent works on the same arguments are discussed in reference to the results obtained. Das Problem, die Gitter-Warmeleitfahigkeit und den Beitrag des Phonon-Drag zu der elektrischen Leitfahigkeit in Gegenwart der normalen Phonon–Phonon-Prozesse zu berechnen, wird im Rahmen der Boltzmann-Callaway-Gleichung untersucht. Eine fruhere Entwicklung von Callaway und Krumhansl fur die Gitter-Warmeleitfahigkeit der dielektrischen Kristalle wird richtig erweitert, um die spezifischen Eigenschaften zu behandeln. Die erlangten Ausdrucke fur die Gitter-Warmeleitfahigkeit und fur die Mitwirkung des Phonon-Drag werden vorgestellt. Einige Inkonsistenzen in kurzlich publizierten Werten werden diskutiert.

We have developed a theory which makes the expression for temperature‐dependent magnon energies, obtained by means of boson representations of spin operators, kinematically consistent. The theory is applied to FeCl2, a S = 1 ferromagnet with rather large anisotropy, to calculate the temperature dependence of the energy gap of the uniform mode. Both a self‐consistently renormalized spin‐wave theory and an exact calculation at low temperatures by a T‐matrix approach seem to indicate the presence of an anisotropic exchange in addition to easy‐axis single‐ion anisotropy. Comparison with experimental data shows the fundamental role of the correct treatment of the anisotropy.

The Curie temperature T C of a Heisenberg ferromagnetic ultrathin film with uniaxial single-ion anisotropy and face-centered cubic (FCC) structure was calculated in the framework of a Green's function approach using the random phase approximation (RPA). The effect of surface orientation on T C ( N ), where T C is the Curie temperature and N the film thickness, was carefully investigated. The results follow a finite-size scaling relation with shift exponent λ ≃1.5.

Longitudinal spin susceptibility, energy susceptibility and related properties of classical ferromagnetic chains in a field are calculated by means of an interacting spin-wave theory. The validity of the theory is checked by exact numerical calculations by the transfer matrix method and excellent agreement is found.

The exchange energy fluctuations of the classical Heisenberg chain with an applied field are theoretically studied by a non-perturbative interacting-boson theory. Computer simulations are also presented at different wavevectors and found in satisfactory agreement.