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interaction responsible for level mixing 29,30 . Due to the strong
anisotropy, the magnetic moment freezes along one of the two
easy directions at low temperatures.
FIG. 7: Principle of molecular
magnetism as shown for the
{Mn12012-(CH3COO)16(H2O)4]
. 2CH3COOH . 4H20 spin cluster.
In the absence of an externalfield,
a set of double degenerate
levels exists, the lowest
with |mS |= S, if D < 0. Interconversion
between degenerate
bevels is termed “tunnelling“.
FIG. 8: (Left) Frequency-domain zero field magnetic resonance spectra of
Mn12-acetate as a function of temperature. At elevated temperatures additional
resonances at lower frequency are detected, originating from |mS | = 9 and |mS | = 8
levels. (Courtesy M. Dressel, Stuttgart.)
FIG. 9: (Right) Time evolution of the transmission spectra at T = 1.96 K after the
magnetic feld is reversed from +0.9 T to -0.9 T. The narrow absorption dip within the
broad feature is due to resonant quantum tunnelling between pairs of coinciding
energy levels. Also shown is the zero-field absorption line. From ref. 28 .
The energy barrier ∆E ≅ 60 K between the two lowest-lying
states mS = ±10 controls thermally activated relaxation of the
magnetization. Below a blocking temperature of about 3 K, only
resonant quantum tunnelling is possible, which was discovered
in the form of steps in the hysteresis loops of the magnetization
at regular intervals of the applied magnetic fi eld, corresponding
to a coincidence of the zero-fi eld energy levels. This was confi rmed
by direct spectroscopic evidence by observing the time dependence
of the EMR signal after reversal of the external fi eld
direction 28 . Reorientation of the local magnetization vector, i. e.,
conversion from positive mS to negative mS or vice versa, is
resonantly enhanced if degenerate levels are involved. Performing
the experiment with a given BO, “absorption holes“ and
“antiholes“ developed as function of time at expected fi eld positions,
as shown in Fig. 9.
106
As mentioned in the introduction, the quantization of closed orbits
of electronic motion can be used to determine the effective
mass of carriers and, even more interestingly, to identify their
dispersion relation. Periodic-orbit resonance in a quasi-onedimensional
organic metal (TMTSF)2Cl04 (TMTSF standing for
tetramethyl-tetraselenafulvalene) was observed when applying
a magnetic fi eld transverse to the chain direction 6 . The effect
was detected via the resonance in the mw conductivity. This
resonance phenomenon is closely related to cyclotron resonance
observed in metals with closed Fermi surfaces. Another
beautiful example, although not invoking mw fi elds, is given by
the observation of Landau Ievels in graphene, single sheets
of graphite, for which the predicted linear dispersion relation
of apparently massless fermions was detected by Scanning
Tunnelling Spectroscopy (STS) 31 . In this experiment the quadratic
dependence of the closed loop area of cyclic electron
motion on the Landau quantum number was verifi ed, leading
to a square root dependence of level spacings as function of
quantizing fi eld. This was in contrast to the “normal“ dispersion
relation, in which a quadratic dependence of the energy of “free“
carriers on the momentum leads to a linear relationship instead.
B. CHEMISTRY
BUNSEN-MAGAZIN · 10. JAHRGANG · 3/2008
lt would be far beyond the scope of this article to give a comprehensive
review of EPR activities in chemistry. Here we want to restrict
ourselves to topics, which could only recently be studied with the
help of high frequency techniques. This narrows the examples
down to high spin paramagnetic centers with large enough ZFS
to either render them silent in standard 9 GHz EPR, or to prevent
exploration of the full electronic spin multiplet. As examples we
present recent results obtained from transition metal ions, being of
importance in material science or coordination chemistry.
As shown in Fig. 10, the full set of EPR parameters of octahedral
Fe(II) in its high spin S = 2 state could be determined by invoking
a special variant of high-frequency EPR 32 . In such an
experiment, a series of EMR spectra is recorded, each with a
fi xed mw frequency, which is subsequently varied quasi continuously
from 150 to 700 GHz 10 . Without external magnetic
fi eld, the fi ve-fold degenerate S = 2 state is split by ZFS into 3
levels, one of it necessarily being a singlet state. According to
the positive sign of the ZFS constant, this singlet level here is
lowest in energy. Allowed EPR transitions can connect only to
one of the upper ZFS Ievels, out of range for 9.4 GHz mw quanta.
The data set displayed in the fi gure lists peaks observed in
the spectra of the powder sample, corresponding to van Hove
singularities, which are originating from canonical orientations
of the molecule. These orientations are defi ned by the principal
axes of the dominant terms in the spin Hamiltonian. The fi gure
exemplifi es that full information about the spin system can only
be obtained by recording absorption lines with variation of the
mw frequency (being shown as vertical lines in the fi gure) over
a wide range. The vast gain in information obtainable is obvious
when expanding the frequency range beyond the commercially
available range. Note that no signal would be observed with
standard X-band EPR for this particular sample, and even when
using the commercial 94 GHz spectrometer, only three signals
within its fi eld range would be accessible. No elucidation of the
spin Hamilton parameters would be possible. It should also be
noted that not only full frequency coverage but also magnetic
fi elds up to 17 T were necessary to perform the analysis. Admittedly,
the example has been chosen deliberately to exemplify