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K. Golcuk et al. / Spectrochimica Acta Part A 60 (2004) 303–309
has been obtained by using Lorentzian lineshape function as
seen in Fig. 5.
A statistically and randomly oriented powder system con-
tains some crystallites in resonance at all fields, BR varying
between B and B . For a general orientation of a single
ꢀ
⊥
crystalline granular (or molecular unit) containing param-
agnetic center, the solution of the Eq. (1) gives a resonance
field as:
hf
hf
BR
=
[g⊥2 sin2 θ + gꢀ2 cos2 θ]−1/2
(2)
geffβe
βe
where θ is the angle between the magnetic field and the
symmetry axis direction of any particular spin species in the
powder complex. In Eq. (2) the symbol h and f represent
the Plank’s constant and the microwave frequency, respec-
tively. The number of the paramagnetic centers making an
angle θ with the field is proportional to sin θ. By using this
weighing factor together Eq. (2), one can obtain the follow-
ing expression [24] for the amplitude factor, A;
Fig. 6. X-band EPR spectrum of [CuBr2(mMA)2] at room temperature.
interaction between neighboring electronic spins, then any
spin on a particular Cu (II) ion can move around and interacts
with the nuclear spins of other Cu(II) ions having statistically
distributed different nuclear state. The average values of the
nuclear spin of different Cu(II) ion cancel out. Thus, the
observed EPR spectrum of [CuBr2(pMA)2] does not give
any hyperfine features. In this case, the hyperfine structure
is completely compressed. That is, the exchange interaction
is remarkably strong. The g and g values are related by an
B⊥2 (BR2 + Bꢀ2)
A =
(3)
B B2 [(B2 − B2 )(B2 − B2 )]1/2
ꢀ
R
R
⊥
ꢀ
⊥
that is proportional to the number of paramagnetic centers
giving a resonance absorption at BR.
⊥
ꢀ
On the other hand, the resonance curve of any individual
magnetic center has its own intrinsic line shape and width.
This curve reaches its maximum at the resonance field BR.
That is regardless how far from the exact resonance field,
comes unobservable experimentally. The contribution from
any center to the whole absorption line at any field depends
on intrinsic line width.
expression G = (g −2)/(g −2) and found to be less than 4,
ꢀ
⊥
supports the exchange interaction among Cu(II) ions [25] as
well.
The EPR signal taken from powdered [CuBr2(mMA)2]
complex and simulated spectra are shown in Fig. 6. The
X-band EPR spectrum shows isotropic character and does
not contain any hyperfine lines. The agreement of simulated
line with the experimental one supports the isotropic Zee-
man interaction between magnetic ion and static field. The
Hamiltonian describing the isotropic Zeeman interaction can
be written as:
By using Eq. (3) for amplitude factor, we have tried both
line of randomly oriented centers to reproduce experimental
spectra. The fitting parameters are as follows: B = 3410
⊥
G, B = 3197 G, line width = 34 G. As can be seen from
ꢀ
Hiso = gβeB · J
(4)
Fig. 5, there is a satisfying agreement between experimental
and simulated spectra for Lorentzian line. The simulated
spectrum gives almost all the features of the experimental
one. That is the magnetic center has an axially symmetric
(or at most tetragonal) crystalline local electric field.
where g is Lande splitting factor, βe Bohr magneton and J
is total angular momentum of magnetic ion.
The best simulation for experimental spectrum was ob-
tained by using the first-derivative Lorentzian lineshape
function and line width of 200 G. But there is a significant
discrepancy between Gaussian line and experimental data.
The spectroscopic splitting parameter (g = 2.12) is com-
pletely symmetric. This situation may occur if the crystalline
field is cubic (or equivalently if there is perfect tetrahedrally
or octahedrally coordinated magnetic ion). We could not
observe any hyperfine structure in [CuBr2(mMA)2]. Since
the exchange interaction between Cu(II) electrons is quite
strong.
The spectra of the complexes do not exhibit any hyperfine
lines at both perpendicular and parallel parts of spectrum
as reported in some Cu(II) complexes [25,26]. The reason
must be the exchange-narrowing effect between Cu(II) ions.
It should be noted that the paramagnetic center in our case
is Cu(II) ion. Therefore, one can expect hyperfine structure
in the EPR spectra due to the magnetic interactions between
electronic S ( = 1/2) and nuclear spins, I ( = 3/2). Generally,
this interaction can give rise a splitting about a few tens
oersteds which is easily measurable in most of the cases.
The absence of hyperfine structure suggests the existence
of exchange interactions between electronic spins of Cu(II)
ions in the chain. If there is sufficiently strong exchange
The values of magnetic moment of [CuBr2(pMA)2] and
[CuBr2(mMA)2] have been found by using Evans method
as 1.68 and 1.62 B, respectively. The magnetic moments
of the complexes are slightly lower than the spin-only value