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Final Report Summary - MAGNETOORBITAL (Magnetoelectric couplings in solids and related phenomena: First-principles theory)

This project deals with theoretical and computational studies of the
response of crystals to external electric and magnetic fields. It
explores the fundamental relation between the symmetry of the crystal
structure, and the way in which electrons responde to external
perturbations. The behavior is strikingly different depending on
whether the material is a metal or an insulator.

In conventional materials, an applied magnetic field B induces a
magnetization M, and an electric field E induces a polarization P (if
an insulator) or a current J (if a metal).

The main focus of the project are the cross "magnetoelectric" (ME)
responses, whereby B induces P or J, and E induces M.

The ME effect occurs in insulators when both spatial inversion and
time reversal symmetry are broken. We have developed and implemented
first-principles methods to compute this response from, and used them
to understand the ME response of Cr2O3, a prototypical ME insulator.

Much less understood is the ME response of metals. A major result of
the project is the development of a detailed microscopic
theory. Contrary to insulators, the ME effect in metals occurs in
non-magnetic samples. The symmetry requirements are precisely the same
as for the phenomenon of natural optical activity. Thus, spatial
inversion must be broken. A sufficient condition is that the structure
is either chiral (cannot be superimposed on its mirror image) or polar
(has a unique preferred direction).

We have obtained a quantum-mechanical expression for the ME response
in metals and doped semiconductors, showing that it is controlled by
the intrinsic magnetic moment (both spin and orbital) of the
conduction electrons.

We have carried out a detailed studied on the current-induced ME
effect and related effects in a chiral conducting crystal, doped
tellurium. In particular, we found that some of these "gyrotropic"
effects are strongly influenced by the presence of chiral band
touchings ("Weyl points") near the bottom of the conduction band
acting as sources and sinks of Berry curvature.

Motivated by the study of Weyl points in tellurium, we formulated a
systematic classification of the types of Weyl points stabilized by
screw-rotational symmetry, with and without time-reversal invariance.

We have carried out a systematic survey of the Weyl points in the
bandstructure of ferromagnetic bcc Fe, and how they induce a
non-trivial topology ("Chern numbers") on the Fermi-surface sheets.

We have studied the spontaneous orbital magnetization that occurs in
bulk ferromagnets such as iron, due to broken time-reversal symmetry.

Moreover, we have studied how shinning circularly-polarized light on
two-dimensional samples with broken inversion symmetry (monolayer
MoS2) leads to an anomalous Hall effect (AHE) where an in-plane electric
field produces a transverse current. Specifically, we investigated how
disorder affects this photoinduced anomalous Hall effect.

The ME effect in bulk insulators is accompanied by an AHE at the
surface, which becomes "half-quantized" in topological insulators.
The quantized part of the response depends on the specific surface
termination. We have studied how, given an insulator with a specific
surface termination, the quantized part of the ME coupling can be

This project has been instrumental for my career integration and
development. It has taken my research in new directions, allowed me to
initiate several new collaborations with colleagues in several
countries (Denmark, Italy, United States, and Germany), and to set up
my own research group in Spain.

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