432
M. Reissner
perature. Different values for quadrupole splitting, center shift, B ind , and B cl are
used for the different Fe environments, whereby the hyperfine fields were assumed
to increase with increasing number of Fe atoms in the surrounding. According to
the zero-field measurements quadrupole splitting is independent of temperature and
centre shift changes only according to second order Doppler shift. These changes
were assumed to be the same for all configurations, which means that the Debye
temperature does not depend on the local environment. This assumption seems to be
reasonable for a metal. Because the quadrupole interaction is much smaller than the
magnetic one, in the magnetic split spectra the change in quadrupole splitting has no
influence on the shape of the spectra within the given measuring accuracy. Therefore
the quadrupole splitting was assumed to be field independent. Line widths are fixed
to the values of the calibration α-Fe foil. Asymmetry parameter was set to zero. The
number of subspectra and their intensity was fixed by the number of nearest neighbour environments and their probability calculated by binomial distribution. To take
into account that an iron atom in a specific surrounding may be part of clusters of
different size, two or more subspectra for each surrounding were used. Figure 8.53
gives an example. The spectrum is fitted by five subspectra, each corresponding to a
specific surrounding. Each of these subspectra is the sum of two subspectra with different dynamical parameters. The sum intensity of these two subspectra are still fixed
to the value obtained from the binomial distribution and the only allowed parameters
to change are the two dynamical parameters τ and α τ . Close to T f it is necessary to
admit an angle θ between B cl and B a , because in the spin glass regime below T f the
clusters are frozen and applied field is not able to align the inner fields. For simplicity
θ was assumed not to change during reestablishment of the correlation. Field and
temperature dependence of θ for two concentrations is shown in Fig. 8.54. All measured spectra could be fitted reasonably well within this model. Typical examples
are shown in Fig. 8.47. It has to be stressed once more, that the number of subspectra
remains the same for zero- and in-field measurements. Thus the distinction between
individual iron environments remains. During τ of f the iron atom is not part of a correlated region. Therefore it must show paramagnetic behaviour. The field acting on the
nucleus during this time B ind is only caused by the moment of the probe atom. In that
case paramagnetic behaviour is expected to show a Brillouin-like behaviour, which
is really found for all Fe environments (Fig. 8.55). B ind increases with the number of
iron neighbours. For temperature T < ∼ T f B cl is antiparallel to the external field
B a . Near T f the cluster field is not fully aligned, even at the highest field of 13.5 T.
The obtained B cl fields decrease with temperature and are only mildy dependent on
the Fe concentration x for a given environment (Fig. 8.56). With these two fields a
field B n can be defined by B n = (B cl τ on cos θ + B ind τ of f )/(τ on + τ of f ). Because B n
acts on the Fe nucleus, it should be proportional to the macroscopic measured magnetization σ . Since for Y(Fe 0.75 Al 0.25 ) 2 , as mentioned above, the core contribution
is the dominant part of the hyperfine field, B n should be directly proportional to the
bulk magnetization. In the comparison (Fig. 8.57) there is only the hyperfine field
constant a free parameter, which turns out to be 11 T/μ B for all temperatures, in good
agreement with values often obtained from standard Mössbauer experiments. This
strongly supports the used model. The deviations 4.5 T are due to the fact that because
M. Reissner
perature. Different values for quadrupole splitting, center shift, B ind , and B cl are
used for the different Fe environments, whereby the hyperfine fields were assumed
to increase with increasing number of Fe atoms in the surrounding. According to
the zero-field measurements quadrupole splitting is independent of temperature and
centre shift changes only according to second order Doppler shift. These changes
were assumed to be the same for all configurations, which means that the Debye
temperature does not depend on the local environment. This assumption seems to be
reasonable for a metal. Because the quadrupole interaction is much smaller than the
magnetic one, in the magnetic split spectra the change in quadrupole splitting has no
influence on the shape of the spectra within the given measuring accuracy. Therefore
the quadrupole splitting was assumed to be field independent. Line widths are fixed
to the values of the calibration α-Fe foil. Asymmetry parameter was set to zero. The
number of subspectra and their intensity was fixed by the number of nearest neighbour environments and their probability calculated by binomial distribution. To take
into account that an iron atom in a specific surrounding may be part of clusters of
different size, two or more subspectra for each surrounding were used. Figure 8.53
gives an example. The spectrum is fitted by five subspectra, each corresponding to a
specific surrounding. Each of these subspectra is the sum of two subspectra with different dynamical parameters. The sum intensity of these two subspectra are still fixed
to the value obtained from the binomial distribution and the only allowed parameters
to change are the two dynamical parameters τ and α τ . Close to T f it is necessary to
admit an angle θ between B cl and B a , because in the spin glass regime below T f the
clusters are frozen and applied field is not able to align the inner fields. For simplicity
θ was assumed not to change during reestablishment of the correlation. Field and
temperature dependence of θ for two concentrations is shown in Fig. 8.54. All measured spectra could be fitted reasonably well within this model. Typical examples
are shown in Fig. 8.47. It has to be stressed once more, that the number of subspectra
remains the same for zero- and in-field measurements. Thus the distinction between
individual iron environments remains. During τ of f the iron atom is not part of a correlated region. Therefore it must show paramagnetic behaviour. The field acting on the
nucleus during this time B ind is only caused by the moment of the probe atom. In that
case paramagnetic behaviour is expected to show a Brillouin-like behaviour, which
is really found for all Fe environments (Fig. 8.55). B ind increases with the number of
iron neighbours. For temperature T < ∼ T f B cl is antiparallel to the external field
B a . Near T f the cluster field is not fully aligned, even at the highest field of 13.5 T.
The obtained B cl fields decrease with temperature and are only mildy dependent on
the Fe concentration x for a given environment (Fig. 8.56). With these two fields a
field B n can be defined by B n = (B cl τ on cos θ + B ind τ of f )/(τ on + τ of f ). Because B n
acts on the Fe nucleus, it should be proportional to the macroscopic measured magnetization σ . Since for Y(Fe 0.75 Al 0.25 ) 2 , as mentioned above, the core contribution
is the dominant part of the hyperfine field, B n should be directly proportional to the
bulk magnetization. In the comparison (Fig. 8.57) there is only the hyperfine field
constant a free parameter, which turns out to be 11 T/μ B for all temperatures, in good
agreement with values often obtained from standard Mössbauer experiments. This
strongly supports the used model. The deviations 4.5 T are due to the fact that because