Forschungszentrum Jülich GmbH
Peter Grünberg Institut & Institute for Advanced Simulation
D52425 Jülich
Research
Interests of G.
Bihlmayer 
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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 abinitio 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 quantummechanical 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) lowdimensional 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
http://www.flapw.de/ pages or in a review on the FLAPW method
[B6] . As allelectron
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 spinorbit coupling effects (DzyaloshinskiiMoriya
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 spinorbit 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 noncollinear magnetism can be
treated in the FLAPW method was describes in a Psik Highlight
[B3] and reference [37] . Noncollinear 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 spinorbit coupling effect, the
DzyaloshinskiiMoriya (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 DMinteractions (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 spinorbit coupling influences the magnetic structure via the DM
interaction, e.g. it can lead to a chiral magnetic spinspiral 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 twodimensional 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 spintransistor.
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 Rashbasplit 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
spinorbit 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 spinorbit splittings beyond the (linear) Rashba effect can be
observed and new investigations can directly show the spinmixing 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 Rashbaeffect disappears
for quantum well states is also observed by spinpolarized 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 Rashbaeffect is a fundamental ingredient in many spintronic devices, as it allows spinaccumulation
(e.g. for spinsources) [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 spinpolarization, generally also bulk states can be locally spinpolarized near the surface
[110] . Interesting effects can be observed when the
Rashbatype spinsplitting is combined with exchangesplittings, e.g. at magnetic surfaces
[50] , thin films [164] ,
or in hybrid structures [172] .


Topological insulators
A spectacular manifestation of spinorbit interaction at surfaces is realized
in a class of materials calls topological insulators: Here, spinorbit split
surface or edgestates form Fermisurface contours, that do not allow the
backscattering of an electron without changing its spin. This leads to the socalled
quantum spinHall 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 edgestates form, that support the QSHE. While these edge currents
are protected by timereversal 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 angleresolved 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 smallgap insulators in a small range of composition, some
Bi compounds like TlBiSe_{2} have robust bandgaps and have been identified as TIs
[119] .
Apart from these 3DTIs (i.e. bulk material that show a protected edgestate at the surface) also twodimensional
TIs exist, where the edgestates support the quantum spinHall effect (QSHE).
E.g. a Bi(111) nanoribbon has onedimensional topologically protected edgestates
[120] at a zigzag termination that carry
dissipationless spin currents. In contrast,
BiSb alloy films are not necessarily 2DTIs  at least not if they have chemically ordered layers
[107] .
In the presence of an external magnetic field, 2DTIs 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 timereversal symmetry, also other, crystalline symmetry
elements can distinguish topological phases: the topological crystalline insulators (TCIs). We found
twodimensional 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 spinorbit 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 materialdependence is achieved by extensive abinitio calculations.
The picture on the right shows magnetic chains on a stepped substrate with a
possible noncollinear spinstructure as explored by Schweflinghaus et al. in
[177] .


More on Co wires on stepped Pt surfaces can be found in Ref. [61] ,
on multistranded 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. Selforganization of chainlike 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 DMinteractions in onedimensional
magnetic systems (wires at stepedges), where the low symmetry allows an even richer space of possible solutions
[177] .
A different way to stabilize onedimensional magnets are metalorganic 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 spinpolarised [62]
or not [57]. Recent work on transition metal dichalcogenides
(TMDCs) like MoS_{2} [175] and ReS_{2}
[194] explore e.g. spinorbit 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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