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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.

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.

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 ${(\mathrm{BH})}_{\mathrm{max}}.$

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.

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.

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.

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.

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.

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

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.

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

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)

Ultrathin ferromagnetic films of Co, grown on a stepped Cu(100) substrate, exhibit shifted magnetization curves. We calculate the shift field of a film consisting of N planes. Our model includes a four-fold bulk anisotropy k/sub 4/, a uniaxial anisotropy k/sub u/ and a magnetic field applied perpendicularly to the easy magnetization axis. Even if k/sub u/ is limited to the outermost plane, a finite shift field h/sub s/ exists, which, for k/sub u//spl Lt/k/sub 4/, is proportional to k/sub u//N. This result explains some experimental data.

10 pages, 7 figures.-- PACS nrs.: 57.10.Pq; 75.30.-m; 75.30.Gw; 78.70.Dm.-- Published online Oct 22, 2005., We present a combined experimental and theoretical study of the magnetization of one-dimensional atomic cobalt chains deposited on a platinum surface. We discuss the intrinsic magnetization parameters derived by X-ray magnetic circular dichroism measurements and the observation of ferromagnetic order in one dimension in connection with the presence of strong, dimensionality-dependent anisotropy energy barriers of magnetocrystalline origin. An explicit transfer matrix formalism is developed to treat atomic chains of finite length within the anisotropic Heisenberg model. This model allows us to fit the experimental magnetization curves of cobalt monatomic chains, measured parallel to the easy and hard axes, and provides values of the exchange coupling parameter and the magnetic anisotropy energy consistent with those reported in the literature. The analysis of the spin–spin correlation as a function of temperature provides further insight into the tendency to magnetic order in finite-sized one-dimensional systems., We would like to acknowledge the contribution to the experiments reported in this work by A. Dallmeyer, K. Maiti, M.C. Malagoli, and W. Eberhardt (Forschungszentrum Jülich), P. Ohresser, S.S. Dhesi, N.B. Brookes, and K. Larsson (beamline ID12B at the ESRF), and K. Kern (EPF Lausanne and MPI Stuttgart). A. Vindigni, A. Rettori, and M.G. Pini acknowledge financial support from the Italian MIUR (projects FISR ‘Nanotecnologie per dispositivi di memoria’ and FIRB ‘Microsistemi e nanomateriali magnetici’).

The use of magnetic nanowires as memory units is made possible by the exponential divergence of the characteristic time for magnetization reversal at low temperature, but the slow relaxation makes the manipulation of the frozen magnetic states difficult. We suggest that finite-size segments can show a fast switching if collective reversal of the spins is taken into account. This mechanism gives rise at low temperatures to a scaling law for the dynamic susceptibility that has been experimentally observed for the dilute molecular chain Co(hfac)2NitPhOMe. These results suggest a possible way of engineering nanowires for fast switching of the magnetization., Comment: 9 pages, 3 figures, 20 references

A double-peaked structure was observed in the {\it in-situ} Brillouin Light Scattering (BLS) spectra of a 6 \AA$ $ thick epitaxial Fe/GaAs(001) film for values of an external magnetic field $H$, applied along the hard in plane direction, lower than a critical value $H_c\simeq 0.9$ kOe. This experimental finding is theoretically interpreted in terms of a model which assumes a non-homogeneous magnetic ground state characterized by the presence of perperpendicular up/down stripe domains. For such a ground state, two spin-wave modes, namely an acoustic and an optic mode, can exist. Upon increasing the field the magnetization tilts in the film plane, and for $H \ge H_{c}$ the ground state is homogeneous, thus allowing the existence of just a single spin-wave mode. The frequencies of the two spin-wave modes were calculated and successfully compared with the experimental data. The field dependence of the intensities of the corresponding two peaks that are present in the BLS spectra was also estimated, providing further support to the above-mentioned interpretation.

We report evidences for long-range antiferromagnetic (AF) order in iron oxyhydroxides Fe19metheidi and (enH2)2Fe6 clusters that at low temperature behave like single molecule magnets with total spin S=33/2 and S=5, respectively. Anomalies are clearly observed at 1.19 K in the heat capacity and in the low-field magnetization of Fe19metheidi while for (enH2)2Fe6 a broad λ-peak is found at 0.99 K in the heat capacity. Since dipolar interactions are estimated to be ∼190 mK and ∼40 mK for Fe19metheidi and (enH2)2Fe6, respectively, the origin of the AF ordering is due to super-exchange in these cases.

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 report evidence of antiferromagnetic (AF) transition in ${\mathrm{Fe}}_{19}metheidi,$ a molecular nanomagnet with a total spin $S=33/2.$ The temperature (T) dependence of the specific heat (C) shows a \ensuremath{\lambda} anomaly at 1.19 K and at the same temperature an anomaly is also observed in the low-field $(Bl0.12\mathrm{T})$ magnetization M-vs-T curves. Since the dipolar interaction between clusters is estimated to be \ensuremath{\sim}190 mK, the origin of the AF transition is probably due to superexchange. Analysis of the specific heat at very low temperature reveals an exponential T scaling of C, which we ascribe to the presence of an energy gap in the spin-wave spectra and, below 150 mK, a hyperfine $C/R\ensuremath{\sim}4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{T}^{\ensuremath{-}2}$ term mainly due to the protons closest to iron.

Recent experimental data, showing a dimensional crossover of the T‐dependent magnetization in MBE‐grown Fe(110)/Ag(111) superlattices with different Ag spacer thickness, are theoretically reanalyzed, using a Heisenberg model of localized spins with intraplane and interplane exchange interactions and including easy‐plane and easy‐axis surface anisotropies. The latter ones 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‐2D regime (T ln T) and in the 3D one (T3/2) are obtained.

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

Epitaxial Cu/Ni/Cu/Si(001) magnetic films have been studied in the thickness range (17–120 A) where a uniaxial anisotropy favoring the direction perpendicular to the film plane is dominant over the easy-plane dipolar interaction. Using magneto-optic magnetometry and Brillouin light scattering we show that on decreasing an in-plane magnetic field the perpendicular component of the magnetization breaks into domains.

We study the magnetic relaxation of a system of localized spins interacting through weak dipole interactions, at a temperature large with respect to the ordering temperature but low with respect to the crystal field level splitting. The relaxation results from quantum spin tunneling but is only allowed on sites where the dipole field is very small. At low times, the magnetization decrease is proportional to $\sqrt{t}$ as predicted by Prokofiev and Stamp, and at long times the relaxation can be described as an extension of a relaxed zone. The results can be directly compared with very recent experimental data on Fe_8 molecular clusters., 9 pages, 11 figures; accepted for publication on Eur. Phys. J. B

We investigate the relaxation time, τ , of a dilute Glauber kinetic Ising chain obtained by ac susceptibility and SQUID magnetometry on a Co(II)-organic radical Ising 1D ferrimagnet doped with Zn(II). Theoretically we predicted a crossover in the temperature-dependence of τ , when the average segment is of the same order of the correlation length. Comparing the experimental results with theory we conclude that in the investigted temperature range the correlation length exceeds the finite length also in the pure sample.

We study the elementary excitations for a multilayer of spins represented by a Heisenberg ferromagnet with nearest-neighbor and next-nearest-neighbor exchange. In addition to the bulk modes, and the usual monotonic surface ones characterized by an exponential decay of the amplitude of the spin fluctuations, we find for opportune conditions other localized modes that present a \ensuremath{\pi} phase variation when passing from a layer to the adjacent one. Furthermore we show that the surface-plane magnetization is much more affected by the surface modes in a film than in a semi-infinite system. Also the effects of surface single-ion anisotropies and of dipolar interactions are investigated using the Green's-function method. Some analytical expressions are obtained for the energy of the lowest mode of the multilayer, which makes it possible to find the dependence on the number of layers N. Finally, we derive a formal expression for the magnetization profile which is valid for systems with a nondiagonal quadratic boson Hamiltonian.

We studied the transition between the antiferromagnetic and the surface spin-flop phases of a uniaxial antiferromagnetic [Fe(14 \AA)/Cr(11 \AA]$_{\rm x20}$ superlattice. For external fields applied parallel to the in-plane easy axis, the layer-by-layer configuration, calculated in the framework of a mean-field one-dimensional model, was benchmarked against published polarized neutron reflectivity data. For an in-plane field $H$ applied at an angle $\psi \ne 0$ with the easy axis, magnetometry shows that the magnetization $M$ vanishes at H=0, then increases slowly with increasing $H$. At a critical value of $H$, a finite jump in $M(H)$ is observed for $\psi5^{\rm o}$. A dramatic increase in the full width at half maximum of the magnetic susceptibility is observed for $\psi \ge 5^{\rm o}$. The phase diagram obtained from micromagnetic calculations displays a first-order transition to a surface spin-flop phase for low $\psi$ values, while the transition becomes continuous for $\psi$ greater than a critical angle, $\psi_{\rm max} \approx 4.75^{\rm o}$. This is in fair agreement with the experimentally observed results., Comment: 24 pages, 7 figures

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.

One of the more interesting features of magnetic chains is the lack of spontaneous magnetisation at any finite temperature.In one dimension (1-D) this result is quite general and holds irrespective of the quantum or classical nature of the system, as well as of the presence of exchange or single-ion anisotropies [1]. In the classical Heisenberg case, which we shall explicitly consider in the following, all the thermodynamic quantities of the system can be evaluated analytically at any temperature in zero external field [2]. Unfortunately, in the presence of a magnetic field H, the statistical properties of the model can be determined only in a numerical way, e.g. by transfer matrix techniques [3]. At very low temperatures and for H≠ 0, non-interacting spin-wave theory predicts results in good agreement with the numerical data [4, 5]. Larger and larger discrepancies, however, appear as the field is decreased, until for H=0 spin-wave calculations predict a magnetisation →−∞, in sharp contrast with the exact result = 0. This dramatic failure of an approach which is so successful in the usual 3-D magnets clearly indicates a breakdown in the conventional many-body techniques based on perturbation theory, and requires a new treatment.