PHYSICAL REVIEW B 90, 144405 (2014)
Spin-forbidden transitions in the molecular nanomagnet V
15
Maren Gysler,
1
Christoph Schlegel,
2
Tamoghna Mitra,
3
Achim M¨ uller,
3
Bernt Krebs,
4
and Joris van Slageren
1 , *
1
Institut f ¨ ur Physikalische Chemie, Universit¨ at Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
2
1. Physikalisches Institut, Universit¨ at Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
3
Fakult¨ at f ¨ ur Chemie, Universit¨ at Bielefeld, 33501 Bielefeld, Germany
4
Institut f ¨ ur Anorganische und Analytische Chemie, University M¨ unster, Corrensstrasse 36, 48149 M¨ unster, Germany
(Received 25 April 2014; revised manuscript received 17 September 2014; published 3 October 2014)
We performed electron spin-resonance measurements on single crystals of the molecular nanomagnet V
15
using a novel broadband spectrometer, both in parallel and in perpendicular modes, we see (B
1
‖ B
0
,B
1
⊥ B
0
).
Measurements were carried out in proximity of the spin level crossing at B
0
= 2.75 T. We observed spin-forbidden
transitions from the S = 1/2 zero-field ground state to the S = 3/2 excited state in parallel mode spectra.
Spin-forbidden transitions are employed for switching of coherent interactions between qubits in recent quantum
simulator proposals. Our theoretical investigations showed that the mixing of spin states can result from either
an antisymmetric exchange interaction or a combination of static distortion and hyperfine interaction.
DOI: 10.1103/PhysRevB.90.144405 PACS number(s): 75.50.Xx, 75.10.Dg, 75.10.Jm, 76.30.−v
I. INTRODUCTION
Molecular nanomagnets (MNMs) are promising candidates
for application as qubits in quantum information processing
(QIP) [1–3]. A crucial prerequisite for this purpose is a
sufficient quantum coherence time, which is the time available
for a quantum computation. This time must be longer than the
duration of all coherent manipulations of the qubits [4–6].
Trinuclear clusters are especially suitable as the exchange
interaction of triangular MNMs can be controlled by both
magnetic and electric fields [7,8] where the electric field
couples to the chirality of the spin states of the system.
In addition, they can exhibit long quantum coherence times
[6,9,10]. Performing quantum computations often requires
the possibility of switching the qubit coupling during gating
operations as well as addressing individual qubits [2,3].
Switching interactions between MNMs can be implemented by
the excitation of transitions to specific higher-lying spin states
[1] by means of microwave magnetic fields. These excitations
correspond to formally forbidden electron spin-resonance
(ESR) transitions. To allow such transitions, mixing between
spin states is required [7,11,12]. Mechanisms which allow
intermultiplet transitions are antisymmetric and anisotropic
exchange interactions [13], hyperfine interactions [14], as well
as single-ion zero-field splitting [12]. In the above context,
the MNM K
6
[V
15
As
6
O
42
(H
2
O)]8H
2
O[15,16] (abbreviated
V
15
) is an attractive candidate. It was shown that long-lived
coherent superpositions of spin states can be generated within
both the ground state (S = 1/2) and the first excited state
(S = 3/2) [6,17,18]. Coherent superposition states that involve
both the S = 1/2 and the S = 3/2 states at the same time.
Therefore, demonstrating mixing of spin states within V
15
is
a step towards achieving coherent superpositions of different
total spin multiplets. The MNM V
15
consists of 15 antiferro-
magnetically coupled V
4+
ions, arranged in a quasispherical
layered structure formed by a triangle sandwiched between
two hexagons [19,20] possessing overall D
3
symmetry. At
low temperatures, the spins within each hexagon are coupled
*
slageren@ipc.uni-stuttgart.de
to a total singlet spin S = 0[21]. Therefore, the low-lying
energy levels of V
15
can be described considering the three
spins of the triangle [22–24]. The ground state of this frustrated
triangle system consists of two S = 1/2 Kramers doublets with
the excited S = 3/2 quartet state separated from the ground
state by about E = 3.7K[19,24](≈2.6 cm
−1
)[25]. These
states are well separated (500 cm
−1
) from higher-lying spin
states [20,21]. The accidentally degenerate S = 1/2 doublets
are split by gaps of
0
= 0.06 cm
−1
(magnetic measurements
[22,26]) and
0
= 0.28 cm
−1
(inelastic neutron scattering
(INS) [27,28]). The microscopic origin of
0
still remains
unclear. INS suggested the cause to be distortions from D
3
symmetry [29,30], whereas theory and magnetization pointed
to antisymmetric exchange interactions [22,24,26,31,32]. In
an applied field of B
0
= 2.75 T, the S = 3/2 spin state
crosses the S = 1/2 state. In this region, mixing between
the two states might occur whose study might shed light
on the origin of
0
. In this paper, we present the results
of multifrequency ESR measurements in the proximity of
the level crossing. In parallel mode (B
1
‖ B
0
) we detected
intermultiplet transitions, clear evidence for mixing of spin
states. This paves the way to implement qubit interaction
switching for QIP. To gain insight into the mechanism of the
mixing of spin states in V
15
we discuss possible theoretical
models, such as antisymmetric exchange [32,33], isosceles
distortion, and hyperfine interactions.
II. EXPERIMENTAL SECTION
Single crystals (5 mg) of V
15
were prepared and were
characterized by published methods [15]. ESR measurements
of single V
15
crystals were carried out using a homebuilt
spectrometer [34]. All measurements were performed at 1.6 K
in the frequency range of 4–14 GHz. Frequencies lower
than 14 GHz were obtained by inserting dielectrics (Herasil
for 7–14 GHz, silicon for 4–7 GHz). No field modulation
was employed. ESR spectra were recorded for both parallel
B
1
‖ B
0
and perpendicular B
1
⊥ B
0
magnetic-field directions,
where B
1
is the microwave field. Here the sample is placed in
the middle of the cylindrical cavity or attached to the top plate
of the cavity, respectively [34,35]. The external magnetic field
1098-0121/2014/90(14)/144405(5) 144405-1 ©2014 American Physical Society