Noncolinear spin polarization from frustrated antiferromagnetism: A possible scenario
for molecular oxygen at high pressure
R. Gebauer
CECAM– Centre Europe ´en de Calcul Atomique et Mole ´culaire, ENSL, 46 Alle ´e d’Italie, F-69364 Lyon Cedex 07, France
S. Serra, G. L. Chiarotti, and S. Scandolo
INFM– Istituto Nazionale di Fisica della Materia and SISSA– Scuola Internazionale Superiore di Studi Avanzati,
via Beirut 2/4, I-34014 Trieste, Italy
S. Baroni
CECAM– Centre Europe ´en de Calcul Atomique et Mole ´culaire, ENSL, 46 Alle ´e d’Italie, F-69364 Lyon Cedex 07, France
and INFM– Istituto Nazionale di Fisica della Materia and SISSA– Scuola Internazionale Superiore di Studi Avanzati,
via Beirut 2/4, I-34014 Trieste, Italy
E. Tosatti
INFM– Istituto Nazionale di Fisica della Materia and SISSA– Scuola Internazionale Superiore di Studi Avanzati,
via Beirut 2/4, I-34014 Trieste, Italy
and ICTP– The Abdus Salam International Centre for Theoretical Physics, I-34014 Trieste, Italy
Received 11 June 1999; revised manuscript received 23 August 1999
We perform density-functional calculations of the magnetic properties of a simplified structure aimed at
capturing some of the features of the elusive phase of molecular oxygen at high pressure. Starting with the
phase—which is a quasi-two-dimensional distorted triangular arrangement of antiferromagnetically ordered
molecules—pressure could decrease the b / a ratio in the basal planes pushing it toward the ideal triangular
value of 1/ 3, thus increasing magnetic frustration. We conjecture that when frustration takes over, the
magnetic order may turn into a 120° planar spin-spiral structure inside the phase, until at higher pressures
band-overlap metallization suppresses magnetization in the phase. This conjecture is substantiated by calcu-
lations that also represent the attempt to apply state-of-the-art pseudopotential techniques to the magnetic
properties of a frustrated antiferromagnet.
I. INTRODUCTION
Most magnetic materials are characterized by atomic mo-
ments or electronic spins, in an itinerant picture all aligned,
parallel or antiparallel, to the same direction everywhere in
space. A number of notable exceptions to this rule exist, in
which the direction of the magnetization varies from point to
point in space. Such exceptions include, e.g., spin spirals in
the lanthanides and the complex structures occurring in to-
pologically frustrated antiferromagnets.
Density-functional theory DFT calculations of noncolin-
ear magnetic structures have been available for more than a
decade.
1
Most of these studies, however, rely on some kind
of atomic-sphere approximation ASA in which different
spin quantization axes are chosen within different spheres.
The stable magnetic structure is then determined a posteriori
as the one that minimizes the total energy with respect to the
directions of the quantization axes chosen as inputs of the
calculation. Although spin colinearity may be broken even
within individual atoms by, e.g., spin-orbit effects,
2
the con-
cept that the same direction of magnetization is associated
with each atom is physically well motivated, and it has been
recently confirmed by calculations on iron clusters per-
formed without requiring ASA.
3
Nevertheless, going beyond
the ASA treatment of magnetic noncolinearity is important,
because only releasing all prior constraints on the magnetic
structure such as, notably, that on the relative orientation of
different quantization axes within different atomic spheres
can DFT calculations display their full predictive power.
In this paper we present a fully unconstrained calculation
of the magnetic structure of a topologically frustrated anti-
ferromagnet, following an approach whose bases are concep-
tually similar to that of Ref. 3. The system we choose to
study is a layered triangular arrangement of oxygen mol-
ecules aimed at capturing some of the features of the hitherto
ill-characterized phase of molecular oxygen at high pres-
sure.
II. OXYGEN AT HIGH PRESSURE
In the gas phase, the ground state of the O
2
molecule is a
triplet, as required by Hund’s rule. In solid, and Mott-
Hubbard insulating, O
2
, at low temperature and moderate
pressure, weak electron hopping gives rise to antiferromag-
netic intermolecular superexchange, whose magnitude rises
considerably with pressure,
4,5
from the zero-pressure value
of 5 meV Ref. 6 to hundreds of meV at tens of GPa.
7
The
relevant pre-1990 work on high-pressure phases and magne-
tism of oxygen is reviewed by Freiman.
8
Antiferromagnetic
order is realized in the insulating low-temperature crystalline
phase -O
2
,
9
which is stable up to 1 GPa. With tempera-
ture this converts to -O
2
, which is magnetically disordered.
PHYSICAL REVIEW B 1 MARCH 2000-I VOLUME 61, NUMBER 9
PRB 61 0163-1829/2000/619/61455/$15.00 6145 ©2000 The American Physical Society