Forschungszentrum Jülich GmbH
Peter Grünberg Institut & Institute for Advanced Simulation
D-52425 Jülich


Research Interests of G. Bihlmayer back to homepage


Electronic and magnetic structure of surfaces, interfaces and nanostructures

Insight into the ground state properties of condensed matter is provided by density functional theory. With ab-initio calculations we achieve an accurate and realistic description of advanced materials. Properties like magnetic structure, elastic constants or response to electric fields can be calculated on a quantum-mechanical basis. Using what is considered to be the one of the most precise electronic structure method in solid state physics, we concentrate on magnetic properties of (quasi) low-dimensional systems like surfaces or interfaces.

More information on the full potential linearized augmented planewave (FLAPW) method and code development (FLEUR code) can be found on our pages or in a review on the FLAPW method [B6] . As all-electron method, our code can be used to test and compare to other methods [173] (see also press release).


Noncollinear magnetism

Contrary to ferro- or antiferromagnetic structures, in a noncollinear magnetic arrangement the direction of the magnetization may change from atom to atom by arbitrary angles. These structures might be formed by competing exchange interactions, topological frustration (e.g. on a triangular lattice) or spin-orbit coupling effects (Dzyaloshinskii-Moriya interaction). The image shows a layered material consisting of a magnetic bilayer (red) where the noncollinear structure, a skyrmion, is formed and two nomnagnetic bilayers (blue, green) that tune the exchange coupling and the spin-orbit coupling strength, respectively. How to combine materials that realize such skyrmions with moderate external magnetic fields is decribed in [176] (see also press release).

A general introduction into magnetism in density functional theory is presented in a IFF Spring School lecture [B9] , how non-collinear magnetism can be treated in the FLAPW method was describes in a Psi-k Highlight [B3] and reference [37] . Non-collinear magnetism arises in topologically frustrated lattices, like hexagonal thin films [17] , [23] or bulk systems e.g. manganides [42] , [77] .
Complex magnetic structures can be induced in ultrathin magnetic fields not only by varying the magnetic overlayer [55], but also by tuning the substrate to favor specific exchange interactions [84]. E.g. for an Fe layer on Ir(111) an intriguing magnetic pattern was observed [67] , [86] . We could identify a spin-orbit coupling effect, the Dzyaloshinskii-Moriya (DM) interaction as the source of this magnetic ground state, that is a topologically protected magnetic structure, known as skyrmion [122] . In multilayer structures it is possible to tune the exchange- and DM-interactions (DMI) to realize skyrmions of different sizes also near room temperature and with moderate external magnetic fields [176] . A systematic investigation of the DMI at 3d/5d interfaces can be found in [181] .
On heavy substrates like W or Pt, the spin-orbit coupling influences the magnetic structure via the DM interaction, e.g. it can lead to a chiral magnetic spin-spiral as groundstate of a thin magnetic film [80] . This is a phenomenon that can influence magnetic structures on an atomic scale [91] or occur in long ranged magnetic structures like in domain walls of thin magnetic films [96]. The complex interplay of exchange interactions, anisotropy and DM interaction can lead to a wide variety of magnetic ground states analysed in [117]. An overview and the connection to the Rashba effect on surfaces (see below) can be found in [B10].


Rashba effect at metallic surfaces

A surface state forms a two-dimensional electron gas (2DEG), that is subject to a potential gradient (i.e. an electric field) as a consequence of the dipole moment formed on all surfaces. Due to a relativistic effect, the motion of the electrons in this 2DEG leads to a magnetic field, that couples to the spin of the electrons. In semiconductor physics, this is called the Rashba effect. But this effect can also be observed at metallic surfaces,even magnetic ones. Depending on their spin, the electrons of the surface state show different dispersion curves and move with different velocities. This effect can be exploited in a spin-transistor. In certain situations, the Rashba effect can also lead to singular touching points in the bandstructure as shown on the right. This can occur in the presence of magnetism [172] or when different Rashba-split bands realize a touching protected by mirror symmetry as shown here for W(110) [189] . Such structures bear resemblence to topological crystalline insulators discussed below.

The Rashba effect on metallic surfaces is a phenomenon, which originates both from atomic spin-orbit coupling and the loss of inversion symmetry. A short history of the effect and new applications are summarized in [167] . A very active field is the investigation of the Rashba effect on interfaces and metallic surfaces of heavy elements [64] . E.g., it is particularly strong in Bi surfaces [42] , but occurs also in magnetic lanthanides [50] as well as nonmagnetic ones [99] . Very strong effects have also been found for surface alloys as formed by Bi or Pb on Ag(111) surfaces [78] and on Cu(111) [104] . In these alloys also states with spin-orbit splittings beyond the (linear) Rashba effect can be observed and new investigations can directly show the spin-mixing that occurs in these bands [155] , .
This phenomenon can also be observed in thin films
[71] , [74] , where the spin polarization depends on the penetration depth of the electronic state, i.e. whether the states are surface states or quantum well states [94] . That the Rashba-effect disappears for quantum well states is also observed by spin-polarized photoemission [85] on Bi films. But depending on the interface of the film to the substrate also quantum well states can show a spin polarization, e.g. for Pb films on Si(111) [98] or in the unoccupied states of an ultrathin Bi film on Cu(111) [106] .
The Rashba-effect is a fundamental ingredient in many spintronic devices, as it allows spin-accumulation (e.g. for spin-sources) [82] . Due to their semimetallic character, Bi films are good candidates here [88] , [89] . It should be noticed, that not only surface states in Bi have a spin-polarization, generally also bulk states can be locally spin-polarized near the surface [110] . Interesting effects can be observed when the Rashba-type spin-splitting is combined with exchange-splittings, e.g. at magnetic surfaces [50] , thin films [164] , or in hybrid structures [172] .


Topological insulators

A spectacular manifestation of spin-orbit interaction at surfaces is realized in a class of materials calls topological insulators: Here, spin-orbit split surface- or edge-states form Fermi-surface contours, that do not allow the backscattering of an electron without changing its spin. This leads to the so-called quantum spin-Hall effect (QSHE), which allows a dissipationless spin current at the surface. Whether a material is a topological insulator (TI) or not can be determined from its bulk properties, at the interface between a TI and a normal insulator (or vacuum) topologically protected edge-states form, that support the QSHE. While these edge currents are protected by time-reversal symmetry in 2D systems, there are also other symmetries that can lead to topologically protected edge states, also in 3D. In some systems, even several protection mechanisms can be combined: as example we show the surface states of a dual TI on the right (upper panel: experiment, lower panel: theory) [176] (see also press release).

One of the first known examples of topological insulators (TIs) are surfaces of Bi/Sb alloys, where spin- and angle-resolved photoemission and DFT calculations have revealed that the surface states are topogically protected, i.e., they cannot be removed by external, nonmagnetic, perturbations [100] . While Bi/Sb alloys are only small-gap insulators in a small range of composition, some Bi compounds like TlBiSe2 have robust bandgaps and have been identified as TIs [119] .
Apart from these 3D-TIs (i.e. bulk material that show a protected edge-state at the surface) also two-dimensional TIs exist, where the edge-states support the quantum spin-Hall effect (QSHE). E.g. a Bi(111) nanoribbon has one-dimensional topologically protected edge-states [120] at a zig-zag termination that carry dissipationless spin currents. In contrast, Bi-Sb alloy films are not necessarily 2D-TIs - at least not if they have chemically ordered layers [107] . In the presence of an external magnetic field, 2D-TIs can undergo a phase transition into a quantum anomalus Hall insulator (QAHI) state where the dissipationless spin current is transformed into a dissipationless charge current [140] .
While the characteristic symmetry of TIs is time-reversal symmetry, also other, crystalline symmetry elements can distinguish topological phases: the topological crystalline insulators (TCIs). We found two-dimensional examples in thin films and quantum well structures [163] , [178] . By applying external strain even a phase transformation between a TCI and a TI phase can be realized [173] . Also topological semimetals, in particular in two dimension, are in our focus: we mention here Dirac semimetals [182] and toplogical line node semimetals [190] in 2D.


Low dimensional magnets and magnetocrystalline anisotropy

Magnetic recording would not be possible without a relativistic effect called spin-orbit coupling. It determines the orientation of the spins with respect to the crystal lattice, or the magnetocrystalline anisotropy. The strength of this effect determines the storage density on an magnetic storage device. Therefore, finding new materials with large magnetocrystalline anisotropies is of substantial importance and the theoretical understanding of this material-dependence is achieved by extensive ab-initio calculations. The picture on the right shows magnetic chains on a stepped substrate with a possible noncollinear spin-structure as explored by Schweflinghaus et al. in [177] .

More on Co wires on stepped Pt surfaces can be found in Ref. [61] , on multi-stranded wires in Ref. [65] . How the large the magnetocrystalline anisotropy can get in freestanding chains was investigated in [66] , while in [75] chains on a substrate were studied. Self-organization of chain-like structures can also be found on Pt(110) surfaces [79] or InAs(110) substrates [97] . We also studied the interplay of magnetocrystalline anisotropy, exchange- and DM-interactions in one-dimensional magnetic systems (wires at step-edges), where the low symmetry allows an even richer space of possible solutions [177] .
A different way to stabilize one-dimensional magnets are metal-organic sandwich structures [68] that can form finite chains or (almost) infinite wires [87] . The magnetic properties of these wires can be easily manipulated, making them candidates for magnetoelectronic devices [90] .


More research topics

Our studies center around magnetism in low dimensions. Thin films and wires are of course the most studies examples, but low dimensional magnetic structures can occur also in unexpected contexts, e.g. in defects in perovskite materials and other oxide materials: a linear defect titanium dioxide (figure right) is one example [165]. These defects are important for the transport properties of the otherwise insulating crystal, see e.g. [63]. But also magnetic perovskites show a large variety of phenomena, that provide a fascinating playground for our calculations [70].

Among other research interests, I just mention here the lanthanides [27] , [36] (nice comparisons to spectroscopical data are found in [81] and [95] and their surfaces [62]. Moreover ultrathin magnetic films on early transition metal surfaces [B8], and of course all the nice work related with scanning tunneling microscopy methods, be it spin-polarised [62] or not [57]. Recent work on transition metal dichalcogenides (TMDCs) like MoS2 [175] and ReS2 [194] explore e.g. spin-orbit effects in these materials, even in elemental magnets like iron these still hold surprises to explore experimentally and theoretically [180] . What is not mentioned here explicitly can be found among the list of publications .


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