Low-energy spin dynamics in the [YPc_ {2}]^{0} S= 1/2 antiferromagnetic chain

Abstract

1H nuclear magnetic resonance (NMR) measurements in [YPc2]0, an organic compound formed by radicals stacking along chains, are presented. The temperature dependence of the macroscopic susceptibility of the NMR shift and of the spin-lattice relaxation rate 1/T1 indicate that the unpaired electron spins are not delocalized but rather form a S=1/2 antiferromagnetic chain. The exchange couplings estimated from those measurements are all in quantitative agreement. The low-energy spin dynamics can be described in terms of diffusive processes and the temperature dependence of the corresponding diffusion constant suggests that a spin gap at ~1 K might be present in this compound.

Full text

Page 1

arXiv:1011.1141v2 [cond-mat.str-el] 10 Jan 2011
Low-energy spin dynamics in the [YPc2]0S = 1/2 antiferromagnetic chain
F. Branzoli1, P. Carretta1, M. Filibian1, S. Klyatskaya2and M. Ruben2
1Department of Physics “A. Volta”, University of Pavia-CNISM, 27100 Pavia (Italy) and
2Institute of Nanotechnology, Karlsrhue Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen (Germany)
1H nuclear magnetic resonance (NMR) measurements in [YPc2]0, an organic compound formed
by radicals stacking along chains, are presented. The temperature dependence of the macroscopic
susceptibility, of the NMR shift and of the spin-lattice relaxation rate 1/T1indicate that the unpaired
electron spins are not delocalized but rather form a S = 1/2 antiferromagnetic chain. The exchange
couplings estimated from those measurements are all in quantitative agreement. The low-energy
spin dynamics can be described in terms of diffusive processes and the temperature dependence of
the corresponding diffusion constant suggests that a spin-gap around 1 K might be present in this
compound.
PACS numbers: 76.60.Es, 75.10.Pq, 75.40.Gb, 75.10.Jm
I. INTRODUCTION
Molecular solids have attracted much interest since
decades owing to the possibility to easily tune their prop-
erties either through a chemical bottom up approach or
by varying physical parameters as the external pressure.1
One of the most versatile families of molecular solids
is the one based on phthalocyanine (Pc= C32H16N8)
molecules.2In fact, the employment of these materials
in different areas, ranging from the fabrication of organic
light emitting diodes, to contrast agents or spintronics
materials, has been envisaged. Pc-based compounds have
attracted significant interest in the last decade after it has
been suggested that high temperature superconductivity
could be induced in these materials by alkali doping3and,
more recently, when it has been recognized that neutral
[LnPc2]0molecules, with Ln a lanthanide ion, are molec-
ular nanomagnets with extremely long coherence times at
liquid nitrogen temperature.4–8Owing to the flat shape of
Pc molecules, the structure of Pc-based materials is typ-
ically characterized by chains along which Pc molecules
tend to stack.9Accordingly some of the Pc-based mate-
rials show many similarities to the Beechgaard salts.10
Bis(phthalocyaninato) yttrium [YPc2]0compound can
be considered the parent compound of the aforemen-
tioned [LnPc2]0molecular magnets. In fact, it is charac-
terized by the absence of localized f electrons and the
microscopic properties are mainly associated with the
presence of an unpaired electron delocalized in the a2π
orbital, due to the one-electron oxidation of the [YPc2]−
unit.11Thus, [YPc2]0allows to investigate the spin dy-
namics associated only with this unpaired electron spin,
independently from the one due to f electrons. One of
the most suitable tools to address this aspect is nuclear
magnetic resonance (NMR) technique. In this work we
present an experimental study of the magnetic proper-
ties of [YPc2]0compound by means of magnetization and
nuclear magnetic resonance (NMR) measurements. The
temperature dependence of the macroscopic susceptibil-
ity, of the NMR shift and of the spin-lattice relaxation
rate 1/T1 clearly show that this system is a prototype
of a S = 1/2 antiferromagnetic chain, characterized by a
diffusive low-frequency spin dynamics and, possibly, by
the presence of a low-energy spin-gap.
1 10100
0.00
0.01
0.02
0.03
0.04
0.05

χS (emu/mole)
T(K)
FIG. 1: Temperature dependence of static uniform suscepti-
bility χS for [YPc2]0complex, derived from SQUID magneti-
zation measurements. The solid line shows the best fit of the
data to Curie-Weiss law.
II.EXPERIMENTAL RESULTS AND
DISCUSSION
[YPc2]0polycristalline samples were synthesized by us-
ing some modifications of the protocol published in Ref.
12. All reagents were purchased from Across or Aldrich
and used without further purification. A mixture of 1,2-
dicyanobenzene (42 mmol), Y(acac)3 ·4H2O (5 mmol),
and 1,8-diazabicyclo[5,4,0]undec-7-ene (DBU) (21 mmol)
in 50 mL of 1-pentanol was refluxed for 1.5 days. The
solution was allowed to cool to room temperature. The
precipitate was collected by filtration and washed with
n-hexane and Et2O. The crude purple product was re-
dissolved in 800 ml of CHCl3/MeOH (1/1) and undis-
solved PcH2 was filtered off. Both forms, blue (anionic

Page 2

2
[YPc2]−) and green (neutral [YPc2]0), were obtained si-
multaneously, as revealed by electronic absorption spec-
tra. In order to convert the unstabilized anionic form to
the neutral one, the reaction mixture was presorbed on
active (H2O-0%) basic alumina oxide. Purification was
carried out by column chromatography on basic alumina
oxide (deactivated with 4.6% H2O, level IV) with chloro-
form methanol mixture (10:1) as eluent. In general, the
yield was 30-35%. According to microelemental analysis
based on atomic spectroscopic methods (ICP) performed
at Mikroanalytisches Labor Pascher, the powder sample
contains molecules of [YPc2]0, water and CH2Cl2in ra-
tio 1:1:1/3. The molecules crystallized in the space group
P212121(γ-phase), as reported in Ref. 13.
DC magnetization (M) measurements have been per-
formed by using an MPMS-XL7 Quantum Design super-
conducting quantum interference device (SQUID) mag-
netometer. The magnetization was found to depend
linearly on the magnetic field intensity H, for H ≤ 5
kGauss, over all the explored temperature range and, ac-
cordingly, the macroscopic static uniform susceptibility
can be written as χS = M/H. The temperature de-
pendence of χSreveals the presence of antiferromagnetic
correlations. In fact, χS(T) can be nicely reproduced by
a Curie-Weiss (CW) law
χS(T) =
C
T + Θ+ χ0
, (1)
where C = g2µ2
the Bohr magneton, g the Land´ e factor, NAAvogadro’s
number and kBBoltzmann constant). Θ is the CW tem-
perature and χ0a temperature independent term mainly
due to diamagnetic and Van-Vleck corrections. By fitting
the data, leaving all three parameters free, we found an
antiferromagnetic CW temperature Θ = 5.37 ± 0.04 K
(Fig. 1) and a Curie constant C = 0.342 ± 0.002 erg
· K/G2, quite close to the value 0.375 erg·K/G2, ex-
pected for a S = 1/2 system. If we fixed C = 0.375
erg·K/G2the fit was still good and the CW temperature
Θ = 6.18 ± 0.03 K. The temperature dependence of χS
shows that the unpaired electron spins are localized along
the chains formed by [YPc2]0molecules, although a cer-
tain overlap of the π orbitals of adjacent molecules must
be present in order to justify the magnitude of the antifer-
romagnetic exchange coupling Je. In fact, although this
system should present a narrow half-filled band, the size-
able Hubbard Coulomb repulsion U ∼ 1eV prevents the
electron delocalization along the chain.14In this limit,
Je = Θ = 4t2/U, with t the hopping integral among
adjacent molecules. From the estimated value of Θ one
would derive a band width formed by the overlap of a2
orbitals in adjacent molecules W = 4t ∼ 0.05 eV≪ U,
justifying the spin localization along the chain.
The1H NMR spectra were obtained in the 1.6-300 K
temperature range for magnetic field intensities H = 9 T,
1 T and 0.3 T. The spectra were derived from the Fourier
transform of half of the echo formed after a π/2 − τ − π
pulse sequence, when the full NMR line could be irradi-
BS(S+1)NA/(3kB) is Curie constant (µB
050 100150200250300
0
30
60
90
120
150
?? ?? ? ?? ? ?
T(K)
? ? ?? ? ?? ? ?
? ?? ? ? ?
? ?? ? ?
?
? ?? ? ? ?


∆ν (kHz)
T(K)
H= 9 T, H= 1 T, H= 0.3 T


∆ν/ν0
FIG. 2: Temperature dependence of1H full NMR linewidth at
half intensity in [YPc2]0, at three different magnetic fields. In
the inset the linewidth is normalized by the Larmor frequency
after subtracting the constant linewidth due to nuclear dipole-
dipole interaction.
ated or, otherwise, from the envelope of the echo ampli-
tude upon varying the irradiation frequency. The line-
shape was gaussian in all the investigated temperature
range. For H = 9 T and H = 1 T a broadening of the
spectrum can be observed at low temperature, which is
more pronounced at higher field intensities (Fig. 2). On
the other hand, for H = 0.3 T the linewidth ∆ν is prac-
tically temperature independent and the broadening is
likely to be due just to nuclear dipole-dipole interaction.
The increase of the linewidth with H suggests that the
low temperature line broadening originates from some
anisotropy in the hyperfine coupling, which for a powder
gives rise to a linewidth proportional to the susceptibility.
In fact, it is noticed that if we subtract the T-independent
contribution at H = 0.3 Tesla from the raw data and di-
vide the linewidth by the Larmor frequency ν0, the data
at different fields overlap (inset to Fig.2). This result also
indicates that there is not an additional internal field due
to the onset of a long-range magnetic order down to 1.6
K.
The NMR paramagnetic shift ∆K = (νR−ν0)/ν0, with
νR the resonance frequency, shows a more pronounced
temperature dependence (Fig. 3). As expected, it was
found to increase upon cooling, according to
∆K =
AχS
2µBNA
,(2)
namely the temperature dependence of ∆K should be
the same of the macroscopic spin susceptibility. In fact,
also ∆K(T) is found to obey a Curie-Weiss law with a
Curie-Weiss temperature Θ = 7.4K ±0.3 K, close to the
one derived from SQUID magnetization measurements.
The small difference between those two type of measure-

Page 3

3
050 100 150200250
0.0000
0.0001
0.0002
0.0003
0.0004
? ? ? ? ?? ? ? ? ? ? ? ? ? ?
χ
? ? ?? ?? ? ? ? ??? ? ? ?
? ? ? ? ? ?
? ? ? ? ??
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ?
?


∆K
T(K)
H = 9 T


∆K
? (emu/mole)
FIG. 3: Temperature dependence of
∆K in [YPc2]0. The solid line shows the best fit of the data
to Curie-Weiss law. In the inset ∆K is reported as a function
of the macroscopic susceptibility. The solid line is the best fit
according for a linear dependence of ∆K vs χS.
1H paramagnetic shift
ments could be associated with a tiny amount of im-
purities which might affect the macroscopic susceptibil-
ity. Accordingly, the measurement of the microscopic
susceptibility with paramagnetic shift measurements is
expected to provide a more reliable estimate of the static
uniform spin susceptibility and of the Curie-Weiss tem-
perature. By plotting ∆K as a function of χS a linear
trend is attained (Fig. 3) and from the slope it is possible
to estimate the isotropic term of the hyperfine coupling
tensor A = 180 ± 10 Gauss.
The1H nuclear spin-lattice relaxation rate 1/T1 was
measured in the 1.6 - 300 K temperature range and for
different values of the external field. 1/T1was extracted
from the recovery of nuclear magnetization after a sat-
uration recovery pulse sequence. The recovery law was
found to be a single exponential in all the explored tem-
perature range (Fig. 4, inset). This result is an evidence
that the unpaired electron is delocalized onto a π orbital
within the molecule. In fact, since in the two phthalo-
cyanine rings a large number of inequivalent proton sites
is present, if the electron was on a more localized orbital
a distribution of hyperfine couplings would be present
and, accordingly, a stretched exponential recovery law
should be observed. Moreover, the fact that hyperfine
coupling seems quite isotropic indicates that it could orig-
inate from the contact interaction between the unpaired
electron spin in the a2π orbital and the1H nuclei.
The temperature dependence of 1/T1at different mag-
netic fields is shown in Fig. (4). In general, for a relax-
ation process driven by electron spin fluctuations one can
write
1
T1
=
γ2
2N
?
α,q
(|Aq|2Sα,α(q,ωL))⊥
, (3)
? ? ?? ? ?
?
?
?
?
110100
0
20
40
60
T=100 K
T=15 K


y(τ)
τ (ms)


1/T1 (s-1)
T(K)
H = 0.3 T
H = 0.5 T
H = 1 T
H = 9 T
FIG. 4:
dependence for [YPc2]0compound measured for different val-
ues of the applied field. In the inset the recovery of the nu-
clear magnetization as a function of the delay τ between the
saturating and the echo readout sequences is shown at two
different temperatures. The solid lines show the best fit for a
single exponential recovery.
1H nuclear spin-lattice relaxation rate temperature
where γ is the nuclear gyromagnetic ratio, |Aq|2the form
factor describing the hyperfine coupling with spin excita-
tions at wave-vector q and Sα,α(q,ωL) (α = x,y,z) the
component of the dynamical structure factor at the Lar-
mor frequency. In the high temperature limit, namely
when the thermal energy is much larger than the ex-
change energy (T ≫ Θ), the 1/T1 of a spin S = 1/2
antiferromagnet becomes temperature and field indepen-
dent and is given by15
1
T1
=γ2
2(A2
x+ A2
y)S(S + 1)
3
√2π
ωH
,(4)
where Ax ≃ Ay ≃ A are the components of the hyper-
fine coupling tensor which is basically isotropic, while
ωH = (JekB/?)?2zS(S + 1)/3 is the Heisenberg ex-
change frequency, with z = 2 the number of nearest
neighbour spins along the chain. By taking the mea-
sured value of 1/T1≃ 20 s−1at high temperature, from
Eq. (4) it is possible to estimate the exchange frequency
ωH≃ 9.2·1011rad/s, corresponding to an exchange cou-
pling constant Je≃ 7.0 K, in quite good agreement with
the value which can be estimated from the NMR shift
measurements. Upon decreasing the temperature, for 200
K≥ T ≥ 30 K, one observes a progressive slow increase
of 1/T1(Fig. (4)). In particular, it is noticed that nu-
clear spin-lattice relaxation rate increases on decreasing
temperature according to
1/T1∝ ln1/2(T0/T) . (5)
In fact, in Fig. (5) one observes that (1/T1)2is a linear
function of 1/T, when reported in logarithmic scale. Re-
markably, this logarithmic increase of 1/T1is expected in

Page 4

4
a S = 1/2 Heisenberg antiferromagnet, but for T ≤ Je16.
Here it is not clear why the logarithmic behavior extends
up to T ≫ Je.
0.01
1/T (K
0.1
0
400
800
1200
1600
2000


(1/T1)
2 (s
-2)
-1)
H= 9 T
H= 1 T
FIG. 5: The 1/T1 squared is plotted as a function of T−1, in
logarithmic scale, for two values of the external field (H = 9
T, circles and H = 1 T, squares). The dashed lines represent
the best fits to Eq. (5).
At about 20 K a peak in the nuclear spin-lattice re-
laxation rate appears (Fig. 4), whose intensity decreases
by increasing the external field intensity. Eventually, be-
low T ≃ 5 K, the 1/T1is only weakly temperature de-
pendent. The maximum in 1/T1, not associated with
molecular motions, could be due to a form factor, which
partially filters out the antiferromagnetic fluctuations as
the system gets more and more correlated.
0.1 0.20.30.4
20
25
30
35
40
45
50


1/T1 (s-1)
(ω0/2π)
-1/2 (MHz)
-1/2
T = 117 K
T = 27 K
T = 4.2 K
T = 1.6 K
FIG. 6: The1H spin-lattice relaxation time 1/T1 in [YPc2]0
is plotted as a function of (ω0/2π)−1/2for different selected
temperatures. The solid lines show the best fit according to
Eqs.6 and 7 in the text.
The magnetic field dependence of 1/T1 (Fig. 6) can
originate from the diffusive nature of the spin correlation
function, which in one dimension is characterized by long-
time tails yielding to a divergence of the low-frequency
spectral density J(ω).17In fact, in the presence of diffu-
sive processes for the spin excitations 1/T1can be written
in terms of the spectral density for the spin excitations
according to the following equation18:
1
T1
=γ2
2
kBTχ0
(gµB)2
?3
5A2
dJ(ω0) +
?
A2+7
5A2
d
?
J(ωe± ω0)
?
,
(6)
where Adis the anisotropic term of the hyperfine cou-
110100 120
0.0
0.2
0.4
0.6
0.8


D/ωH
T (K)
FIG. 7: Temperature dependence of the ratio D/ωH between
the spin diffusion coefficient D and the exchange frequency
ωH in [YPc2]0compound as derived from the slopes in the
1/T1 vs (ω0/2π)−1/2plots in Fig. 6. The solid line gives the
best fit according to D ∝ exp(∆/T) with ∆ = 1.2 ± 0.4 K.
pling, which hereafter shall be neglected since A2≫ A2
Then just the second term in square bracket can be con-
sidered. In Eq.6 χ0 is the static uniform susceptibility
per spin and ωe= ω0γe/γ is the electron resonance fre-
quency. This means that during the nuclear relaxation
process a simultaneous flip of the electron and nuclear
spins occur, involving an energy exchange ?(ωe± ω0),
and 1/T1thus probes the spin excitations at a frequency
close to ωe.
In a one dimensional system, the spectral density at
ωeis characterized by a low-frequency divergence given
by19
d.
J(ωe) =
1
√2D(ωc+?ω2
e+ ω2
c
ω2
e+ ω2
c
)1/2
,(7)
where ωcis a low-frequency cutoff accounting for the fi-
nite spin anisotropy and/or inter-chain coupling, while
D is the spin diffusion rate.
is plotted as a function of ν−1/2
trend further proves the one-dimensional nature of the
antiferromagnetic correlations.
of a low-frequency flattening in 1/T1plot indicates that
In Fig.
. The observed linear
(6), the 1/T1
0
Moreover, the absence

Page 5

5
spin diffusion occurs in the electronic frequency range
ωc≪ ωe≪ D. Thus, from the slopes of the curves it is
possible to deduce the spin diffusion coefficient at differ-
ent temperatures (Fig. 7) considering A ≃ 180 Gauss and
neglecting ωc≪ ωein Eqs (6-7). The estimated spin dif-
fusion coefficient is of the order of the exchange frequency
ωH and it is found to progressively decrease with tem-
perature and to become nearly constant above 20 K. It
is interesting to observe that D ∝ exp(∆/T), namely the
behaviour expected for one-dimensional antiferromagnets
in the presence of a spin-gap ∆ between singlet and
triplet excitations.20Here we find that ∆ = 1.2 ± 0.4
K suggesting that a small gap, either due to compet-
ing exchange interactions or to a dimerization might be
present in [YPc2]0. It is interesting to observe that, at
low temperature, when the Zeeman energy ?ωe≃ ∆ the
breakdown of Eq.7 is noticed. In fact, in Fig. (6) one
clearly notices that at T = 1.6 K the linear behaviour
is no longer obeyed at high fields (i.e. low values for
?2π/ω0) and 1/T1 ceases to decrease with increasing
field. This could be due to the modifications in the spin
correlations induced by the magnetic field for ?ωe≃ ∆,
possibly associated with the progressive closure of the
spin gap.
In conclusion, from magnetization,1H NMR param-
agnetic shift and T1measurements we have derived the
magnitude of the antiferromagnetic exchange interaction
in [YPc2]0compound and found an overall good agree-
ment. The low-energy spin excitations are of diffusive
character and characteristic of one-dimensional antiferro-
magnets. From the temperature dependence of the spin
diffusion rate derived from 1/T1vs. H measurements it
was found that a spin-gap around 1 K might be present
in this compound.
Acknowledgements
The research activity in Pavia was supported by Fon-
dazione Cariplo (Grant N. 2008-2229) research funds.
1see M. Scwoerer and H.C. Wolf in Organic Molecular
Solids, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
(2007)
2see The Porphyrin Handbook Vol. 19, K.M. Kadish, K.M.
Smith, R. Guilard, Academic Press New York (2000)
3E. Tosatti, M. Fabrizio, J. T´ obik, and G.E. Santoro, Phys.
Rev. Lett. 93, 117002 (2004).
4F. Branzoli, M. Filibian, P. Carretta, M. Ruben and S.
Klyatskaya, Phys. Rev. B 79, 220404 (2009)
5F. Branzoli, P. Carretta, M. Filibian, G. Zoppellaro, M.
J. Graf, J. R. Galan-Mascar´ os, O. Fuhr, S. Brink and M.
Ruben, J. Am. Chem. Soc. 131, 4387 (2009)
6S. Takamatsu, T. Ishikawa, S. Koshihara and N. Ishikawa,
Inorg. Chem. 46, 7250 (2007)
7N. Ishikawa, Y. Mizuno, S. Takamatsu, T. Ishikawa and S.
Koshihara, Inorg. Chem. 47, 10217 (2008)
8F. Branzoli, P. Carretta, M. Filibian, M. J. Graf, S. Kly-
atskaya, M. Ruben, F. Coneri, and P. Dhakal, Phys. Rev.
B 82, 134401 (2010)
9Y. Taguchi, T. Miyake, S. Margadonna, K. Kato, K. Pras-
sides, and Y. Iwasa, J. Am. Chem. Soc. 128, 3313 (2006).
10K. Bechgaard, C. S. Jacobsen, K. Mortensen, H. J. Peder-
sen and N. Thorup, Solid State Commun. 33, 1119 (1980)
11R. Rousseau, R. Aroca and M.L. Rodriguez-Mendez, J.
Mol. Struct. 356, 49 (1995)
12M. Moussavi, A. De Cian, J. Fischer and R. Weiss, Inorg.
Chem. 27, 1287 (1988); N. Koike, H. Uekusa, Y. Ohashi,
C. Harnoode, F. Kitamura, T. Ohsaka and K. Tokuda,
Inorg. Chem. 35, 5798 (1996); K. Kasuga, M. Tsutsui, R.
C. Petterson, K. Tatsumi, N. Van Opdenbosch, G. Pepe
and E. F. J. Meyer, J. Am. Chem. Soc. 102, 4835 (1980).
13K. Katoh, Y. Yoshida, M. Yamashita, H. Miyasaka, B.K.
Breedlove, T. Kajiwara, S. Takaishi, N. Ishikawa, H. Is-
shiki, Y.F. Zhang, T. Komeda, M. Yamagishi and J.
Takeya, J. Am. Chem. Soc. 131, 9967 (2009)
14M. S. Liao and S. Scheiner, J. Chem. Phys. 114, 9780
(2001).
15T. Moriya, Prog. Theor. Phys. 16, 23 (1956).
16M. Takigawa, O. A. Starykh, A. W. Sandvik and R. R. P.
Singh, Phys. Rev. B 56, 13681 (1997).
17H. Benner and J. P. Boucher, in Magnetic Properties of
Layered Transition Metal Compounds, edited by L. J. De
Jongh (Kluwer Academic, Norwell, MA, 1990), p. 323
18F. Devreux, J. P. Boucher and M. Nechtschein J. Phys.
France 35, 271 (1974).
19G. Soda, D. Jerome, M. Weger, J. Alizon, J. Gallice, H.
Robert, J.M. Fabre and L. Giral, J. Phys. France 38, 931
(1977); L. J. Azevedo, J. E. Schirber and J. C. Scott, Phys.
Rev. Lett. 49, 826 (1982).
20K. Damle and S. Sachdev, Phys. Rev. B 57, 8307 (1998)