Toroidal moment in the molecular magnet V
15
A. K. Zvezdin,
1,2
V. V. Kostyuchenko,
3
A. I. Popov,
4
A. F. Popkov,
5
and A. Ceulemans
6
1
A.M. Prokhorov General Physics Institute, RAS, 119991 Moscow, Russia
2
Department of Materials Physics, Chemistry Faculty, Universidad del Pais Vasco UPV/EHU, San Sebastian, Spain
3
Institute of Physics and Technology, RAS, Yaroslavl Branch, 150007 Yaroslavl, Russia
4
Moscow Institute of Electronic Technology, 124489 Moscow, Russia
5
Zelenograd Research Institute of Physical Problems, 124460 Moscow, Russia
6
Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
Received 30 April 2009; revised manuscript received 28 July 2009; published 19 November 2009
Quantum-mechanical calculations predict the existence of toroidal spin structure in the molecular magnet
V
15
. It is shown that nonzero toroidal moment arises from symmetry violation of the exchange interactions
between spins of the base triangle of the V
15
molecule due to the Jahn-Teller effect. It is established that the
value of the toroidal moment is connected with value of total spin projection of V
15
on z axis. It enables to
induce the toroidal moment by external magnetic field and or to induce the magnetic moment by variable
electric field or by current.
DOI: 10.1103/PhysRevB.80.172404 PACS numbers: 75.50.Xx, 75.80.+q
Triangular antiferromagnets offer interesting quantum
systems, the spin states of which can be controlled and ma-
nipulated by external fields.
1–3
This opens perspectives for
the development of quantum devices for information han-
dling. Recently it was shown see Ref. 4 that electric
polarization of a Cu
3
antiferromagnet could induce a spin-
electric effect under certain conditions: a relativistic Hamil-
tonian is used, containing Dzyaloshinskii-Moriya DM spin-
exchange, spin-chirality, and spin-orbit interactions. In
addition a low-symmetry external electric field, e.g., pro-
vided by an approaching scanning tunnel microscope tip, is
required in this Brief Report to induce asymmetry. However
as we will demonstrate here, isotropic exchange coupling in
a spin triangle will give rise to spontaneous spin-electric ef-
fects, due to symmetry breaking. In the present case the
asymmetry is an intrinsic feature of the magnetoelastic inter-
action. The carrier of this spin-electric effect is an intrinsic
toroidal magnetic moment, as our subsequent quantum-
mechanical analysis will reveal. The resulting quantum struc-
ture provides ways to control and manipulate the qubit state
for use in quantum computation.
5,6
In particular, the exis-
tence of a toroidal moment provides the interaction between
spin and external current. It opens an important possibility
for the control of the qubit state.
4
On the more fundamental
level the treatment clearly shows the presence of a parity
nonconservation effect in a molecule.
At the present time the search for the toroidal moment is
on in chemistry and condensed-matter physics, particularly
in multiferroics.
7
In works
8,9
it has been experimentally
found that spin structure of some magnets with antiferromag-
netic interaction has a toroidal type of symmetry. Recently
toroics with a toroidal domain structure were discovered and
investigated.
10
The toroidal moment changes sign upon both
time and spatial reversal. This symmetry condition for the
appearance of toroidal moment in molecules can be achieved
by application of crossed electric and magnetic fields.
11,12
But intrinsic mechanisms of its spontaneous appearance at
zero field are not known. In work
13
it has been proposed that
toroidal moment can exist in some mesoscopic molecules.
But these ideas were not realized. Recently an interesting
hypothesis for the construction of toroidal moment in mag-
netic nanoclusters has been put forward.
14
The required spe-
cific magnetic anisotropy is realized in triangular Dy
3
complexes
2,3
but the question on its toroidal moment de-
mands further study. In present work the molecular magnet
V
15
is considered. According to the quantum-mechanical
analysis see below it may exhibit a toroidal moment. The
latter is caused by the Jahn-Teller JT activity of the frus-
trated ground state.
Molecular magnet K
6
V
15
IV
As
6
O
42
H
2
O ·8H
2
O hereafter
V
15
contains 15 ions V
4+
with S =1 / 2 Ref. 15 which are
arranged in the apices of two hexagons and the triangle lay-
ered between them. Thus we are dealing with three magnetic
subsystems which are formed by vanadium ions. The scheme
of exchange interaction between V
4+
ions is shown in Fig. 1.
The spin Hamiltonian of the molecular magnet see, e.g.,
Ref. 15 has D
3
symmetry. All exchange interactions be-
tween vanadium ions are antiferromagnetic leading to the
total spin S
=1 / 2 in the ground state. Nearly all contribu-
tions to the total spin are due to the spins arranged in the
apices of triangle. The contribution of ions arranged in the
apices of hexagons is rather small.
16
It is 2.8% of the tri-
angle contribution.
The exchange interaction between spins of triangle can be
described by the Hamiltonian
r1
r2
r3
1
2
3
x
y
1
2
3
4
5
6
7
8 9
10
11 12
13
14 15
(b)
(a)
FIG. 1. The structure of exchange interactions in the molecular
magnet V
15
.
PHYSICAL REVIEW B 80, 172404 2009
1098-0121/2009/8017/1724044 ©2009 The American Physical Society 172404-1