Will spin-relaxation times in molecular magnets permit quantum information processing?
ABSTRACT Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in molecular nanomagnets for the first time. In Cr7M heterometallic wheels, with M=Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the molecule. In deuterated samples T2 reaches 3 micros at low temperatures, which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of molecular nanomagnets in quantum information applications.
- SourceAvailable from: Rachel S Edwards[show abstract] [hide abstract]
ABSTRACT: A multi- high-frequency electron paramagnetic resonance method is used to probe the magnetic excitations of a dimer of single-molecule magnets. The measured spectra display well-resolved quantum transitions involving coherent superposition states of both molecules. The behavior may be understood in terms of an isotropic superexchange coupling between pairs of single-molecule magnets, in analogy with several recently proposed quantum devices based on artificially fabricated quantum dots or clusters. These findings highlight the potential utility of supramolecular chemistry in the design of future quantum devices based on molecular nanomagnets.Science 12/2003; 302(5647):1015-8. · 31.20 Impact Factor
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ABSTRACT: The substitution of one metal ion in a Cr-based molecular ring with dominant antiferromagnetic couplings allows the engineering of its level structure and ground-state degeneracy. Here we characterize a Cr7Ni molecular ring by means of low-temperature specific-heat and torque-magnetometry measurements, thus determining the microscopic parameters of the corresponding spin Hamiltonian. The energy spectrum and the suppression of the leakage-inducing S mixing render the Cr7Ni molecule a suitable candidate for the qubit implementation, as further substantiated by our quantum-gate simulations.Physical Review Letters 06/2005; 94(20):207208. · 7.94 Impact Factor
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ABSTRACT: Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.Nature 05/2001; 410(6830):789-93. · 38.60 Impact Factor
arXiv:quant-ph/0609143v5 16 Jan 2007
Will spin-relaxation times in molecular magnets permit quantum information
Arzhang Ardavan, Olivier Rival, John J.L. Morton, and Stephen J. Blundell
Clarendon Laboratory, Department of Physics, University of Oxford, OX1 3PU, United Kingdom
Alexei M. Tyryshkin
Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, United States
Grigore A. Timco and Richard E.P. Winpenny
Department of Chemistry, University of Manchester,
Oxford Road, Manchester, M13 9PL, United Kingdom
(Dated: February 1, 2008)
Using X-band pulsed electron spin resonance, we report the intrinsic spin-lattice (T1) and phase
coherence (T2) relaxation times in molecular nanomagnets for the first time. In Cr7M heterometallic
wheels, with M = Ni and Mn, phase coherence relaxation is dominated by the coupling of the electron
spin to protons within the molecule. In deuterated samples T2 reaches 3 µs at low temperatures,
which is several orders of magnitude longer than the duration of spin manipulations, satisfying a
prerequisite for the deployment of molecular nanomagnets in quantum information applications.
Certain computational tasks can be efficiently imple-
mented using quantum logic, in which the information-
carrying elements are permitted to exist in quantum su-
perpositions .To achieve this in practice, a physi-
cal system that is suitable for embodying quantum bits
(qubits) must be identified.
employ electron spins in the solid state, for example
phosphorous donors in silicon , quantum dots , het-
erostructures  and endohedral fullerenes [5, 6], mo-
tivated by the long electron-spin relaxation times ex-
hibited by these systems. An alternative electron-spin
based proposal exploits the large number of quantum
states and the non-degenerate transitions available in
high spin molecular magnets [7, 8]. Although these ad-
vantages have stimulated vigorous research in molecular
magnets [9, 10, 11], the key question of whether the in-
trinsic spin relaxation times are long enough has hith-
erto remained unaddressed. Here we show, using pulsed
electron spin resonance experiments on heterometallic
wheels, that the relaxation times in molecular magnets
can significantly exceed the duration of coherent manipu-
lations, a prerequisite for the deployment of these systems
in quantum information applications.
Molecular magnets comprising clusters of exchanged
coupled transition metal ions have been studied exten-
sively in recent years . They can exhibit a substan-
tial ground state spin with a large and negative zero-
field splitting (ZFS), leading to a spontaneous magnetic
moment parallel to the easy axis. In the absence of a
magnetic field, the configurations in which the moment
is ‘up’ or ‘down’ relative to the easy axis are degener-
ate, and this bistable nature has stimulated interest in
the application of magnetic clusters as classical  or
quantum [7, 8, 9, 11] information elements.
Molecules in this class have been synthesised with
widely varying properties, from the S = 10 highly
Some proposed scenarios
Cr8F8Piv16 [15, 16].
is the the development of procedures for magnetically
‘doping’ a diamagnetic cluster to synthesise paramag-
netic molecules in a systematic and controllable way .
Thus, substituting a Cr3+(s = 3/2) by a Mn2+(s = 5/2)
or a Ni2+(s = 1) generates the S = 1 Cr7Mn or the
S = 1/2 Cr7Ni respectively.
Many clusters have been investigated using thermody-
namic probes such as magnetization  and heat capac-
ity , and spectroscopic probes such as neutron scat-
tering [20, 21, 22] and electron spin resonance [23, 24].
These strategies have been very successful in determin-
ing the energy spectra and magnetic structures, but apart
from a limited number of observations of ‘demagnetisa-
tion tunnelling’ there are few  reports of definitive
measurements of relaxation times. However, the feasibil-
ity of many of the most interesting proposed applications,
in particular those involving classical or quantum infor-
mation processing, is critically dependent on the intrinsic
spin-lattice (T1) and phase coherence (T2) times.
Bruker Elexsys 580 X-band pulsed ESR spectrometers,
employing4He flow cryostats for temperature control.
The relaxation times were obtained using standard tech-
niques : T2 from the decay of a 2-pulse Hahn echo
A key recent chemical advance
π/2 − τ − π − τ − echo,(1)
with τ varying; T1from the recovery of the magnetisation
(measured with a spin echo) after an inversion pulse,
π − T − π/2 − τ − π − τ − echo,(2)
with T varying and τ fixed and short.
Two factors conspire to complicate the measurement
of intrinsic lifetimes in anisotropic magnetic clusters.
Firstly, in a crystal the magnetic cores are typically sep-
arated by rather small distances of the order of 1 nm
to 10 nm, and are therefore coupled by dipolar interac-
tions. For two free electron spins, the dipolar interaction
is of the order of 100/r3MHz·nm3, so this dipolar
coupling is the dominant relaxation mechanism limiting
T2in crystals of clusters. Secondly, clusters tend to ex-
hibit strongly axial behaviour with significant zero-field
splittings; this lifts the degeneracy of the ∆mS = ±1
transitions in high spin (S > 1/2) molecules, and leads
to a strong dependence of the transition energies on the
orientation with respect to the external magnetic field.
Thus if we are to study a particular transition in an
ensemble of identical molecules, they must be orienta-
tionally ordered. The standard approach to solving the
first problem, dissolving the crystal (thereby increasing
the average separation of the clusters), leads to a second
problem, an ensemble of randomly oriented, highly axial
We chose the two compounds studied here with these
factors in mind.Cr7Ni has a ground state spin of
S = 1/2, so it exhibits a single ESR transition and, there-
fore, no zero-field splitting; the anisotropy of the g-factor,
which is small, is the only contribution to a dependence
of the transition energy on external magnetic field ori-
entation. A dilute dissolved sample of this material is
therefore amenable to ESR measurements without caus-
ing problems associated with the orientational disorder.
Cr7Mn is a very closely related compound with a ground
state spin of S = 1; the similarity in its structure leads
us to expect that it should share relaxation mechanisms
with Cr7Ni, but its higher spin allows us to examine the
consequences of the zero-field splitting. For example, a
modulation of the zero-field splitting, which might occur
as a result of coupling with thermally excited mechani-
cal deformations of the molecule, provides further spin-
lattice and phase-coherence relaxation mechanisms .
Samples were prepared as reported elsewhere , and
dissolved in toluene. The solution was diluted progres-
sively until the results reported below were no longer
dependent on concentration, indicating that the dipo-
lar coupling between clusters had become negligible;
this occurred for concentrations below approximately
0.2 mg/ml, corresponding to a mean separation of clus-
ters in excess of about 25 nm.
Figure 1 shows echo-detected ESR as a function of the
applied magnetic field measured at 4.5 K for (A) Cr7Ni
and (B) Cr7Mn. The spectrum for Cr7Ni shows a single
narrow line, as expected for an S = 1/2 species. The
line shape is approximately gaussian, with a width of
about 0.01 T, suggesting that the broadening is due to
inhomogeneity of the cluster environment. In contrast,
the spectrum for Cr7Mn is broad and contains structure
that is characteristic of an S = 1 species with a zero-field
splitting exceeding the microwave energy. Also shown is
a simulated powder spectrum  for an S = 1 species
FIG. 1: (Color online) X-band echo-detected ESR as a func-
tion of magnetic field for (A) Cr7Ni and (B) Cr7Mn mea-
sured at 4.5 K (blue), and the simulated powder spectrum for
a species with S = 1, g = 2, D = 21 GHz, E = 1.9 GHz
(green). In this experiment, the intensity of a Hahn-echo sig-
nal with short (τ = 300 ns) delays is measured as a function
of the applied magnetic field. Selective pulses, of 64 ns for
a π/2-pulse and 128 ns for a π-pulse, ensure that only spins
within a window of about 0.3 mT are excited. Using a broad
integration window suppresses1H ESEEM effects. The echo
intensity is proportional to the ESR excitation spectrum. The
fine structure in the data close to 0.33 T is an artifact of the
with the Hamiltonian
H = gµB · S + DS2
with parameters g = 1.9, D = 21 GHz and E = 1.9 GHz,
which reproduces the main features of the data (green
line in Figure 1(B)); deviations are probably due to the
fact that in the experiment, the pulses deviate from per-
fect π and π/2 rotations at different parts of the spectrum
because the transition probabilities depend strongly on
orientation. Both spectra show some low-amplitude fine
structure close to 0.33 T; these lines arise from impuri-
ties in the cavity and are present in the absence of the
Figure 2(A) shows the intensity of Hahn echos mea-
sured in Cr7Ni as a function of the delay time τ (de-
fined in equation 1), for long, selective pulses (blue)
and short, broadband pulses (cyan). The echo gener-
ated by broadband pulses exhibits very strong modula-
tions (electron spin echo envelope modulation, or ES-
EEM) with some second harmonic content, associated
with coupling of the electron spin to nearby nuclear mo-
ments . The nuclear frequency extracted from the
modulation, 16.6 ± 0.1 MHz, indicates that the relevant
nuclei are protons. This ESEEM can be suppressed by
using longer, selective pulses, as shown by the blue line in
Figure 2(A); this echo decay is well-described by a mono-
exponential fit (green dashed line), yielding a coherence
time of T2= 379 ± 1 ns at 4.5 K.
FIG. 2: (Color online) (A) Decay of the Hahn echo inten-
sity in Cr7Ni as a function of delay time for long, selective
pulses (64 ns π/2-pulse, 128 ns π-pulse, blue) and for short
broadband pulses (16 ns π/2-pulse, 32 ns π-pulse, cyan). (B)
Decay of the Hahn echo intensity for long, selective pulses in
per-deuterated Cr7Ni. Dashed green lines indicate fits to the
data. The fit in (B) assumes that the ESEEM effect is domi-
nated by a single harmonic at the2D Zeeman frequency .
(Note the different horizontal axis scales.)
The strong coupling to protons may provide an effi-
cient phase decoherence path, reducing T2. A direct
test of whether this is indeed an important relaxation
mechanism is to measure the same Hahn echo decay in
the per-deuterated analogue compound, as shown in Fig-
ure 2(B).2D has a gyromagnetic ratio about six times
smaller than1H; the ESEEM frequency is correspond-
ingly about six times smaller at 2.556± 0.005 MHz, and
T2is about six times longer, at 2210 ± 20 ns. This con-
firms that the coupling to protons dominates the spin
decoherence in the hydrogenated sample. (Note that we
were unable to decrease the bandwidth of the pulses suf-
ficiently to suppress the lower frequency ESEEM in the
Figure 3 shows the temperature dependences of T1and
T2 for each compound. T1 is comparable between the
Cr7Ni and Cr7Mn, and increases rapidly as the temper-
ature falls. This suggests that thermal processes (such
as couplings to phonons) are responsible for the longitu-
dinal relaxation. At low temperatures, there is a varia-
tion of a factor of about two in T1 measured at differ-
ent points in the spectrum of Cr7Mn. Exciting different
parts of the powder spectrum corresponds to selecting
sub-populations of molecules by orientation. These ori-
entational sub-populations relax at different rates, show-
ing that the magnetic anisotropy plays at least some rˆ ole
in the longitudinal relaxation, probably through spectral
diffusion effects . There is no such variation of T2.
In each compound, T2 also increases as the tempera-
ture is decreased, though less dramatically than T1, and
FIG. 3: (Color online) (A) T1 as a function of temperature in
Cr7Ni (blue open circles) and Cr7Mn (red open squares). (B)
T2 as a function of temperature for Cr7Ni (blue open circles),
Cr7Mn (red open squares) and per-deuterated Cr7Ni (blue
there are signs that it begins to saturate at tempera-
tures below about 2 K. There are two interesting obser-
vations: first, there is very little difference between the
hydrogenated Cr7Ni and Cr7Mn, despite the strong mag-
netic anisotropy of the latter; second, the factor of about
six between the decoherence times for the per-deuterated
and hydrogenated Cr7Ni is retained over the whole tem-
perature range over which a Hahn echo is measurable.
Both observations support the hypothesis that dipolar
coupling with1H or2D nuclei (which belong to organic
ligands of the magnetic cluster and are well-distributed
about the core ) dominates the phase decoherence in
these materials. Phase decoherence arising from fluctua-
tions of the zero field splitting in Cr7Mn is negligible in
comparison over the temperature range studied here.
In conclusion, we have measured intrinsic spin-lattice
(T1) relaxation times and, for the first time (to the best
of our knowledge), the phase coherence (T2) relaxation
times in molecular magnets. We find that in the het-
erometallic clusters Cr7Ni and Cr7Mn, T1 is long and
somewhat dependent on the magnetic anisotropy of the
cluster, but that T2is dominated by the coupling to the
nuclear moments of protons in the vicinity of the cluster.
There is no evidence of coupling between the magnetic
cluster and the fluorine nuclei, which had previously been
identified as a potential decoherence path . Futher-
more, we find that the intrinsic phase coherence time T2
exceeds previous (worst-case) expectations by three or-
ders of magnitude, reaching 0.55 µs at 1.8 K, and 3.8 µs
for the per-deuterated analogue.
ratus, the timescale for coherent manipulations of the
electron spin is of the order of 10 ns; if heteromagnetic
clusters of this class were to be used as elements of a
quantum information processing device, this would lead
to a single-qubit figure of merit of several hundred. The
identification of coupling to the1H or2D nuclei as the
main decoherence path offers a strategy for synthesising
structures with even better coherence properties by re-
ducing as far as possible the number of hydrogens and
other magnetic nuclei in the vicinity of the cluster. Our
results are very encouraging for the prospects of con-
structing and manipulating non-trivial quantum states
within individual clusters [7, 8] and between clusters in
We would like to thank C. Kay of University Col-
lege London, and S.A. Lyon of Princeton Univer-
sity for the use of their spectrometers and helpful
discussions. This work was supported by EPSRC
grants No. GR/S57396/01, No. GR/T27341/01 and No.
EP/D048559/1. A.A. is supported by the Royal Society.
J.J.L.M. is supported by St John’s College, Oxford.
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