Incommensurate magnetic ordering in CrB2.

Incommensurate magnetism in CrB2is studied in terms of a spin model based on density functional theory calculations. Heisenberg exchange interactions derived from the paramagnetic phase using the disordered local moment (DLM) theory show significant differences compared with those resulting from the treatment of the material as a ferromagnet; of these two methods, the DLM theory is found to give a significantly more realistic description. We calculate strongly ferromagnetic interactions between Cr planes but largely frustrated interactions within Cr planes. Although we find that the ground state ordering vector is sensitive to exchange interactions over a large number of neighbour shells, theq-vector of the incommensurate spin spiral state is satisfactorily reproduced by the theory (0.213 compared with the known ordering vector0.285×(2π)/(a/2)along Γ-K). The strong geometric frustration of the exchange interactions causes a rather low Néel temperature (about 97 K), also in good agreement with experiment.

Magnetic ground state of supported monatomic Fe chains from first principles.

A new computational scheme is presented based on a combination of the conjugate gradient and the Newton-Raphson method to self-consistently minimize the energy within local spin-density functional theory, thus to identify the ground state magnetic order of a finite cluster of atoms. The applicability of the newab initiooptimization method is demonstrated for Fe chains deposited on different metallic substrates. The optimized magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good comparison is found with those obtained from an extended Heisenberg model containing first principles based interaction parameters. Moreover, the effect of the different bilinear spin-spin interactions in the formation of the magnetic ground states is monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite rotational sense are found as compared to previous spin-model results which hints on the importance of higher order chiral interactions. The wavelength of the spin-spiral states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling microscopy experiments.

Role of temperature-dependent spin model parameters in ultra-fast magnetization dynamics.

In the spirit of multi-scale modelling magnetization dynamics at elevated temperature is often simulated in terms of a spin model where the model parameters are derived from first principles. While these parameters are mostly assumed temperature-independent and thermal properties arise from spin fluctuations only, other scenarios are also possible. Choosing bcc Fe as an example, we investigate the influence of different kinds of model assumptions on ultra-fast spin dynamics, where following a femtosecond laser pulse, a sample is demagnetized due to a sudden rise of the electron temperature. While different model assumptions do not affect the simulational results qualitatively, their details do depend on the nature of the modelling.

Improved efficiency of heat generation in nonlinear dynamics of magnetic nanoparticles.

The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific loss power in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field. We propose a new type of applied field, which is "simultaneously rotating and alternating," i.e., the direction of the rotating external field changes periodically. We show that a more efficient heat generation by magnetic nanoparticles is possible with this new type of applied field and we suggest its possible experimental realization in cancer therapy which requires the enhancement of loss energies.

Magnetism of Gadolinium: A First-Principles Perspective.

By calculating the spectral density of states in the ferromagnetic ground state and in the high temperature paramagnetic phase we provide the first concise study of finite temperature effects on the electronic structure of the bulk and the surface of gadolinium metal. The variation of calculated spectral properties of the Fermi surface and the density of states in the bulk and at the surface are in good agreement with recent photoemission experiments performed in both ferromagnetic and paramagnetic phases. In the paramagnetic state we find vanishing spin splitting of the conduction band, but finite local spin moments both in bulk and at the surface. We clearly demonstrate that the formation of these local spin moments in the conduction band is due to the asymmetry of the density of states in the two spin channels, suggesting a complex, non-Stoner behavior. We, therefore, suggest that the vanishing or nearly vanishing spin splitting of spectral features cannot be used as an indicator for Stoner-like magnetism.

Magnetic correlations beyond the Heisenberg model in an Fe monolayer on Rh(0 0 1).

Motivated by a recent experimental observation of a complex magnetic structure (Takada et al 2013 J. Magn. Magn. Mater. 329 95) we present a theoretical study of the magnetic structure of an Fe monolayer deposited on Rh(0 0 1). We use a classical spin Hamiltonian with parameters obtained from ab initio calculations and go beyond the usual anisotropic Heisenberg model by including isotropic biquadratic interactions. Zero-temperature Landau-Lifshitz-Gilbert spin dynamics simulations lead to a complex collinear spin configuration that, however, contradicts experimental findings. We thus conclude that higher order multi-spin interactions are likely needed to account for the magnetic ordering of the system.

Magnetic anisotropy and chirality of frustrated Cr nanostructures on Au(1 1 1).

By using a fully relativistic embedded cluster Green's function technique we investigated the magnetic anisotropy properties of four different compact Cr trimers (equilateral triangles) and Cr mono-layers deposited on the Au(1 1 1) surface in both fcc and hcp stackings. For all trimers the magnetic ground state was found to be a frustrated 120° Néel configuration. Applying global spin rotations to the magnetic ground state, predictions of an appropriate second order spin Hamiltonian were reproduced with high accuracy by first principles calculations. For the Cr trimers with adjacent Au atoms in similar geometry, we obtained similar values for the in-plane and out-of-plane anisotropy parameters, however, the Dzyaloshinskii-Moriya (DM) interactions appeared to differ remarkably. For two kinds of trimers we found an unconventional magnetic ground state showing 90° in-the-plane rotation with respect to the high symmetry directions. Due to higher symmetry, the in-plane anisotropy term was missing for the mono-layers and distinctly different DM interactions were obtained for the different stackings. The chiral degeneracy of the Néel configurations was lifted by an energy less than 2 meV for the trimers, while this value increased up to about 15 meV per 3 Cr atoms for the hcp packed mono-layer.

Langevin spin dynamics based on ab initio calculations: numerical schemes and applications.

A method is proposed to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers are discussed in the case of a one-dimensional Heisenberg chain with nearest-neighbour interactions. We performed detailed investigations for a monatomic chain of ten Co atoms on top of a Au(0 0 1) surface. We found a spiral-like ground state of the spins due to Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic behaviour of the system was well described by a nearest-neighbour Heisenberg model including easy-axis anisotropy.

Spin-correlations and magnetic structure in an Fe monolayer on 5d transition metal surfaces.

We present a detailed first principles study on the magnetic structure of an Fe monolayer on different surfaces of 5d transition metals. We use the spin-cluster expansion technique to obtain parameters of a spin model, and predict the possible magnetic ground state of the studied systems by employing the mean field approach and, in certain cases, by spin dynamics calculations. We point out that the number of shells considered for the isotropic exchange interactions plays a crucial role in the determination of the magnetic ground state. In the case of Ta substrate we demonstrate that the out-of-plane relaxation of the Fe monolayer causes a transition from ferromagnetic to antiferromagnetic ground state. We examine the relative magnitude of nearest neighbour Dzyaloshinskii-Moriya (D) and isotropic (J) exchange interactions in order to get insight into the nature of magnetic pattern formations. For the Fe/Os(0 0 0 1) system we calculate a very large D/J ratio, correspondingly, a spin spiral ground state. We find that, mainly through the leading isotropic exchange and Dzyaloshinskii-Moriya interactions, the inward layer relaxation substantially influences the magnetic ordering of the Fe monolayer. For the Fe/Re(0 0 0 1) system characterized by large antiferromagnetic interactions we also determine the chirality of the 120° Néel-type ground state.

Exchange bias driven by Dzyaloshinskii-Moriya interactions.

The exchange bias effect in a compensated IrMn3/Co(111) system is studied using multiscale modeling from ab initio to atomistic spin model calculations. We evaluate numerically the out-of-plane hysteresis loops of the bilayer for different thicknesses of the ferromagnetic layer. The results show the existence of a perpendicular exchange bias and an enhancement of the coercivity of the system. To identify the origin of the exchange bias, we analyze the hysteresis loops of a selected bilayer by tuning the different contributions to the exchange interaction across the interface. Our results indicate that the exchange bias is primarily induced by Dzyaloshinskii-Moriya interactions, while the coercivity is increased mainly due to a spin-flop mechanism.

Relativistic and thermal effects on the magnon spectrum of a ferromagnetic monolayer.

A spin model including magnetic anisotropy terms and Dzyaloshinsky-Moriya interactions is studied for the case of a ferromagnetic monolayer with C2v symmetry like Fe/W(110). Using the quasiclassical stochastic Landau-Lifshitz-Gilbert equations, the magnon spectrum of the system is derived using linear response theory. The Dzyaloshinsky-Moriya interaction leads to asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown that, in the presence of lattice defects, both the Dzyaloshinsky-Moriya interactions and the two-site anisotropy lead to a softening of the magnon energies. Two methods are developed to investigate the magnon spectrum at finite temperatures. The theoretical results are compared to atomistic spin dynamics simulations and good agreement is found between them.

Interatomic exchange interactions for finite-temperature magnetism and nonequilibrium spin dynamics.

We derive ab inito exchange parameters for general noncollinear magnetic configurations, in terms of a multiple scattering formalism. We show that the general exchange formula has an anisotropiclike term even in the absence of spin-orbit coupling, and that this term is large, for instance, for collinear configuration in bcc Fe, whereas for fcc Ni it is quite small. We demonstrate that keeping this term leads to what one should consider a biquadratic effective spin Hamiltonian even in the case of collinear arrangement. In noncollinear systems this term results in new tensor elements that are important for exchange interactions at finite temperatures, but they have less importance at low temperature. To illustrate our results in practice, we calculate for bcc Fe magnon spectra obtained from configuration-dependent exchange parameters, where the configurations are determined by finite-temperature effects. Our theory results in the same quantitative results as the finite-temperature neutron scattering experiments.

Effect of stacking faults on the magnetocrystalline anisotropy of hcp Co: a first-principles study.

In terms of the fully relativistic screened Korringa-Kohn-Rostoker method we investigate the effect of stacking faults on the magnetic properties of hexagonal close-packed (hcp) cobalt. In particular, we consider the formation energy and the effect on the magnetocrystalline anisotropy energy (MAE) of four different stacking faults in hcp cobalt-an intrinsic growth fault, an intrinsic deformation fault, an extrinsic fault and a twin-like fault. We find that the intrinsic growth fault has the lowest formation energy, in good agreement with previous first-principles calculations. With the exception of the intrinsic deformation fault which has a positive impact on the MAE, we find that the presence of a stacking fault generally reduces the MAE of bulk Co. Finally, we consider a pair of intrinsic growth faults and find that their effect on the MAE is not additive, but synergic.

The effect of a Pt impurity layer on the magnetocrystalline anisotropy of hexagonal close-packed Co: a first-principles study.

On the basis of the fully relativistic screened Korringa-Kohn-Rostoker method we investigate the variation in the magnetocrystalline anisotropy energy (MAE) of hexagonal close-packed cobalt with the addition of platinum impurities. In particular, we perform calculations on a bulk cobalt system in which one of the atomic layers contains a fractional, substitutional platinum impurity. Our calculations show that at small concentrations of platinum the MAE is reduced, while at larger concentrations the MAE is enhanced. This change in the MAE can be attributed to an interplay between on-site Pt MAE contributions and induced MAE contributions on the Co sites. The latter are subject to pronounced, long-ranged Friedel oscillations that can lead to significant size effects in the experimental determination of the MAE of nanosized samples.

Chiral asymmetry of the spin-wave spectra in ultrathin magnetic films.

We raise the possibility that the chiral degeneracy of the magnons in ultrathin films can be lifted due to the presence of Dzyaloshinskii-Moriya interactions. By using simple symmetry arguments, we discuss under which conditions such a chiral asymmetry occurs. We then perform relativistic first principles calculations for an Fe monolayer on W(110) and explicitly reveal the asymmetry of the spin-wave spectrum in the case of wave vectors parallel to the (001) direction. Furthermore, we quantitatively interpret our results in terms of a simplified spin model by using calculated Dzyaloshinskii-Moriya vectors. Our theoretical prediction should inspire experiments to explore the asymmetry of spin waves, with a particular emphasis on the possibility to measure the Dzyaloshinskii-Moriya interactions in ultrathin films.

Magnetic ordering in Fe/Co sandwiches on Cu(100).

We investigate magnetic correlations and local magnetic moments at finite temperatures of some Fe and Co multilayers on Cu(100) substrates, such as Co(m)Fe(n)Co(m)/Cu(100) and Fe(m)Co(n)Fe(m)/Cu(100). We use an ab initio mean-field theory of magnetic fluctuations for layered materials based on the first-principles local spin-density functional theory implemented through the screened Korringa-Kohn-Rostoker method. We find that the presence of Fe layers in the neighbourhood of a Co layer always leads to a reduction in the magnetic moment of the Co atoms, whereas that of the Fe atoms is enhanced. Of particular interest is the lack of local moment formation on the single fcc-Co layer sandwiched between two fcc-Fe layers. However, a Co layer completely immersed in a Cu environment remains ferromagnetic. The Curie temperature of the Co(m)Fe(n)Co(m)/Cu(100) system oscillates as the Fe layer thickness is increased whereas that of the Fe(m)Co(n)Fe(m)/Cu(100) system increases almost monotonically with Co layer thickness.

Effect of spin-orbit interaction on a magnetic impurity in the vicinity of a surface.

We propose a new mechanism for surface-induced magnetic anisotropy to explain the thickness dependence of the Kondo resistivity of thin films of dilute magnetic alloys. The surface anisotropy energy, generated by spin-orbit coupling on the magnetic impurity itself, is an oscillating function of the distance d from the surface and decays as 1/d2. Numerical estimates based on simple models suggest that this mechanism, unlike its alternatives, gives rise to an effect of the desired order of magnitude.

Exotic Kondo effect from magnetic trimers.

Motivated by the recent experiments of Jamneala et al. [Phys. Rev. Lett. 87, 256804 (2001)] by combining ab initio and renormalization group methods, we study the strongly correlated state of a Cr trimer deposited on gold. Internal orbital fluctuations of the trimer lead to a huge increase of T(K) compared to the single ion Kondo temperature explaining the experimental observation of a zero-bias anomaly for the trimers. The strongly correlated state seems to belong to a new yet hardly explored class of non-Fermi-liquid fixed points.

Temperature dependent magnetic anisotropy in metallic magnets from an ab initio electronic structure theory: L1(0)-ordered FePt.

Using a first-principles, relativistic electronic structure theory of finite temperature metallic magnetism, we investigate the variation of magnetic anisotropy K with magnetization M in metallic ferromagnets. We apply the theory to the high uniaxial K material, L1(0)-ordered FePt, and find its magnetic easy axis perpendicular to the Fe/Pt layers for all M and K to be proportional to M2 for a broad range of values of M. For small M, near the Curie temperature, the calculations pick out the easy axis for the onset of magnetic order. Our ab initio results for this important magnetic material agree well with recent experimental measurements, whereas the single-ion anisotropy model fails to give the correct qualitative behavior.

Onset of magnetic order in fcc-Fe films on Cu(100).

On the basis of an ab initio theory of metallic magnetism in layered materials, we investigate the onset of magnetic order in thin (2-8 layers) fcc-Fe films on and embedded in Cu(100) substrates. In particular, we find an oscillatory dependence of the Curie temperatures on embedding depth, in excellent agreement with experimental data. The thermally induced spin fluctuations are treated within a mean-field disordered local moment picture and give rise to layer-dependent "local exchange splittings" in the electronic structure even in the paramagnetic phase. These features determine the magnetic intralayer and interlayer interactions which are strongly influenced by the presence and extent of the Cu cap.