The spin-polarized scanning tunneling microscope (SP-STM) operated in the constant current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. The potential of this approach is demonstrated by successfully resolving the magnetic structure of Cr͞Ag(111), which is predicted on the basis of ab initio vector spin-density calculations to be a coplanar noncollinear periodic 120 ± Néel structure. Different operating modes of the SP-STM are discussed on the basis of the model of Tersoff and Hamann. DOI: 10.1103/PhysRevLett.86.4132 PACS numbers: 75.30.Fv, 68.37.Ef, 75.70.Ak, 75.70.Rf Exploiting the spin, rather than the charge degrees of freedom, is the core vision behind the current excitement driving the rapid developments in magneto-and spin electronics. Some of the key issues relate to the understanding of the magnetic properties of nanoscale magnets with competing exchange interactions between neighboring atoms. Examples are (ultrathin) ferromagnetic films in contact with antiferromagnetic ones, as is common for exchangebias systems [1] used in the magnetic recording industry. In many cases, the geometrical arrangement of the atoms does not allow one to satisfy the competing exchange interactions between neighboring atoms, which leads to frustrated spin structures. Frustration gives rise to a wide variety of complex spin structures on the atomic scale, such as antiferromagnetism, spiral spin-density waves (SSDW), or general noncollinear states [2]. These spin structures are still poorly understood because of the inability of traditional techniques to spatially determine the magnetic structure. Even the currently most advanced techniques, the x-ray spectromicroscopy [3] and the spin polarized scanning tunneling microscope (SP-STM) in the spectroscopy mode [4,5], have no atomic-scale resolution.In this paper we introduce a new powerful method -the SP-STM operated in the constant current mode -to image complex magnetic structures at surfaces on the atomic scale. By applying the Tersoff-Hamann model [6] to the case of a SP-STM and considering the effect of the vacuum barrier on the lateral resolution of the STM, we show that in general the SP-STM image of any periodic magnetic superstructure of otherwise chemically equivalent atoms displays a pronounced pattern corresponding to the magnetic configuration and not to the geometric arrangement of the atoms. This is in contradiction to the conventional wisdom that spin polarization is a small effect and that therefore the nonspin-polarized STM image reflecting the atomic structure will be only slightly modulated in the SP-STM experiment.This approach opens up a new route for using the STM, namely, besides the exploration of the topological, chemical, and ferromagnetic structure of surfaces, and also the inherently much more difficult investigation of surfaces with noncollinear spin structures with ultimate, i.e., atomic, resolution. This new concept was very recently applied for the first ...

The massively parallelized full-potential linearized augmented plane-wave bulk and film program FLEUR for first-principles calculations in the context of density functional theory was adapted to allow calculations of materials with complex magnetic structures-i.e., with noncollinear spin arrangements and incommensurate spin spirals. The method developed makes no shape approximation to the charge density and works with the continuous vector magnetization density in the interstitial and vacuum region and a collinear magnetization density in the spheres. We give an account of the implementation. Important technical aspects, such as the formulation of a constrained local moment method in a full-potential method that works with a vector magnetization density to deal with specific preselected nonstationary-state spin configurations, the inclusion of the generalized gradient approximation in a noncollinear framework, and the spin-relaxation method are discussed. The significance and validity of different approximations are investigated. We present examples to the various strategies to explore the magnetic ground state, metastable states, and magnetic phase diagrams by relaxation of spin arrangements or by performing calculations for constraint spin configurations to invest the functional dependence of the total energy and magnetic moment with respect to external parameters.

We investigate hcp Gd and the Gd(0001) surface on the basis of density functional theory. The localized 4f states of Gd, which represent a challenge for first-principles theory, are treated in four different models, employing consistently the full-potential linearized augmented plane-wave method. Our results support previous findings that within the local density approximation (LDA) or generalized gradient approximation (GGA) the itinerancy of the 4f states is overestimated. In particular, the large density of states at the Fermi energy due to the minority 4f electrons is unphysical, and our results show that this is the origin of the incorrect prediction of the antiferromagnetic ground state for hcp Gd by many LDA and GGA calculations. We show that different models of removing these states from the region close to the Fermi energy, for example the treatment of the 4f electrons as localized core electrons or by using the LDA + U formalism, lead to the prediction of the correct ferromagnetic ground state for the bulk and a ferromagnetically coupled (0001) surface layer. With these models ground-state properties such as the magnetic moment and structural parameters can be determined in good agreement with experiment. The energetic positions of the surface states of the Gd(0001) surface are compared with experimental data.

Based on first-principles vector spin-density total-energy calculations of the magnetic and electronic structure of Cr and Mn transition-metal monolayers on the triangular lattice of a (111) oriented Cu surface, we propose for Mn a three-dimensional noncollinear spin structure on a two-dimensional triangular lattice as magnetic ground state. This new spin structure is a multiple spin-density wave of three row-wise antiferromagnetic spin states and comes about due to magnetic interactions beyond the nearest neighbors and due to higher order spin interactions (i.e., four spin). The magnetic ground state of Cr is a coplanar noncollinear periodic 120 ± Néel structure. DOI: 10.1103/PhysRevLett.86.1106 In the frontier field of nanomagnetism, understanding the effect of frustration on magnetic properties is one of the current key issues. Exchange bias [1], for example, is a technologically important effect for the magnetic recording industry and the magnetoelectronics, for which frustration plays an important role. In magnetic systems the term frustration refers to the inability to satisfy the competing exchange interactions between neighboring atoms. Frustration is known to be responsible for a number of diverse phenomena such as spin-glass behavior, noncollinear and incommensurate magnetic order, and unusual critical properties. One of the most evident examples of frustration is the so-called geometric frustration of an antiferromagnet on a triangular lattice. In fact, triangular antiferromagnets can be crystallized, e.g., in the form of stacked antiferromagnets. Typical compounds are RbNiCl 3 , VCl 2 , or CuCrO 2 [2], and they are localized spin systems. The magnetic properties of these triangular antiferromagnets are almost exclusively described within the framework of model Hamiltonians, the simplest of which is the classical Heisenberg modelwhere J ij describes the pairwise (two-spin) exchange interaction between spins at lattice sites i and j. S is the classical spin vector related to the magnetic moment vector m of localized atomic moments m 2gm B S. Localized spin systems are often well described by restricting the interaction to the antiferromagnetic nearestneighbor (n.n.) one, J ij 0 for all i, j, except for J ͑n.n.͒ J 1 (J 1 , 0). In this case the minimum energy configuration is the periodic 120 ± Néel state in the ͑ p 3 3 p 3 ͒R30 ±[3] unit cell (cf. Fig. 1b), a two-dimensional noncollinear structure with three atoms per surface unit cell, which consists of coplanar spins forming 6120 ± angles between nearest neighbors.Until now there has been no investigation of twodimensional (2D) itinerant antiferromagnets on a triangular lattice beyond model Hamiltonians. In itinerant magnets, the electrons that are responsible for the formation of the magnetic state do participate in the formation of the Fermi surface and hop across the lattice. Thus, it is by no means clear how far a short-ranged n.n. interaction or even how far the Heisenberg model can go in giving a sufficiently good description of the physics of i...

We report on a set of systematic first-principles electronic structure investigations of the magnetic spin moments, the magnetic spin configurations, and the magnetic coupling of ultrathin magnetic films on (001)- and (111)-oriented noble-metal substrates and on the Fe(001) substrate. Magnetism is found for 3d-, 4d-, and 5d-transition-metal monolayers on noble-metal substrates. For V, Cr, and Mn on (001) substrates a c(2 × 2) antiferromagnetic superstructure has the lowest energy, and Fe, Co, Ni are ferromagnetic. On (111) substrates, for Cr the energy minimum is found for a 120° non-collinear magnetic configuration in a ( × )R30° unit cell, and for Mn a row-wise antiferromagnetic structure is found. On Fe(001), V and Cr monolayers prefer the layered antiferromagnetic coupling, and Fe, Co, and Ni monolayers favour the ferromagnetic coupling to Fe(001). The magnetic structure of Mn on Fe(001) is a difficult case: at least two competing magnetic states are found within an energy of 7 meV. The Cr/Fe(001) system is discussed in more detail as the surface-alloy formation is investigated, and this system is used as a test case to compare theoretical and experimental scanning tunnelling spectroscopy (STS) results. The possibility of resolving magnetic structures by STS is explored. The results are based on the local spin-density approximation and the generalized gradient approximation to the density functional theory. The calculations are carried out with the full-potential linearized augmented-plane-wave method in film geometry.