Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d- or f-orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron-electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth's core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
Deep Dive into Local magnetic moments in iron and nickel at ambient and Earths core conditions.
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d- or f-orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron-electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth’s core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
ARTICLE
Received 6 Jun 2016 | Accepted 25 May 2017 | Published 12 Jul 2017
Local magnetic moments in iron and nickel at
ambient and Earth’s core conditions
A. Hausoel1, M. Karolak1, E. S¸as¸iog˘lu2,3, A. Lichtenstein4, K. Held5, A. Katanin6,7, A. Toschi5
& G. Sangiovanni1
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch
electrons by pre-localization due to the band-structure properties. Another known source of
electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which
leads to the formation of local magnetic moments. The combination of these two effects is
usually considered of little relevance to strongly correlated materials. Here we show that it
represents, instead, the underlying physical mechanism in two of the most important fer-
romagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on
the magnetism. As a result, the electron–electron scattering rate is linear in temperature, in
violation of the conventional Landau theory of metals. This is true even at Earth’s core
pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of
geomagnetism may have therefore to be reconsidered.
DOI: 10.1038/ncomms16062
OPEN
1 Institut fu¨r Theoretische Physik und Astrophysik, Universita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany. 2 Peter Gru¨nberg Institut and Institute for
Advanced Simulation, Forschungszentrum Ju¨lich and JARA, 52425 Ju¨lich, Germany. 3 Institut fu¨r Physik, Martin-Luther-Universita¨t Halle-Wittenberg, 06120 Halle
(Saale), Germany. 4 Institut fu¨r Theoretische Physik, Universita¨t Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany. 5 Institute of Solid State Physics,
TU Wien, 1040 Vienna, Austria. 6 M. N. Mikheev Institute of Metal Physics, 620990 Ekaterinburg, Russia. 7 Ural Federal University, 620002 Ekaterinburg, Russia.
Correspondence and requests for materials should be addressed to G.S. (email: sangiovanni@physik.uni-wuerzburg.de).
NATURE COMMUNICATIONS | 8:16062 | DOI: 10.1038/ncomms16062 | www.nature.com/naturecommunications
1
I
ron and nickel are two of the most well-known ferromagnets,
that is, conducting materials with a permanent magnetization1.
Their
importance
comes
primarily
from
the
invaluable
technological
uses,
ranging
from
invars
with
low
thermal
expansion, permalloys having high permeability, to maraging
steel, high-resistance nichrome and corrosion-resistant coatings.
Iron is also a cardinal ingredient of Earth’s magnetism and its
transport properties at high pressure are presently the object of a
lively debate2–6. At first sight, nickel should not play a role in
generating the Earth’s magnetic field as it originates in the outer
core, which is made of liquid iron. In current models, however
there seems to be not enough energy to sustain the geodynamo
through heat convection. Therefore, the importance of the inner
core, B20% of which is believed to be made of nickel, is being
critically reconsidered7.
Surprisingly, we still lack a complete theoretical comprehen-
sion of these two textbook materials. The reason can be ascribed
to the intrinsic quantum many-body nature of their electronic
structure, which makes a standard treatment in terms of
independent electrons and conventional band theory inapplic-
able. The calculated Coulomb interaction is large and comparable
in size in iron and nickel, which instead differ in the number of
3d electrons filling the bands close to the Fermi level. Iron is not
too far from half filling, where the Coulomb interaction has the
strongest effect and can easily drive a system Mott insulating. On
the contrary, nickel has an almost full shell, a situation in which
the Landau theory of Fermi liquids is in general recovered, even if
the Coulomb interaction is significant. Yet, nickel was originally
considered
the
more
correlated
of
the
two,
because
of
photoemission satellites far away from the Fermi level, believed
to originate from spectral weight transfer due to the Coulomb
interaction8,9. A theoretical study by one of us10 put the two
materials on a similar level, stressing the existence in both of
them of well-formed local moments, despite their marked
itinerant character.
Here we go a step further and perform electronic structure
calculations including the full local Coulomb interaction. This
way we demonstrate that nickel would not be a strong-coupling
quantum magnet without the van Hove singularities of its
fcc density of states (DOS). In fact, it turns out that only
the combined influence of its peculiar DOS11 and of the electron–
electron interaction can explain the Curie behaviour of its local
spin susceptibility. This reflects in what we call pre-localized
moments and a scattering rate, which is unexpectedly linear in
temperature. The most important implication of our results for
nickel comes from the observation that even at a pressure of
hundreds of GPa, the position and the shape of these s
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