8 Mössbauer Spectroscopy in External Magnetic Fields
419
methods. With decreasing characteristic measuring time freezing temperature should
increase. This illustrates why T f for magnetization measurements (τ m ∼ 1 − 10
−4
s) is smaller than for Mössbauer measurements (τ m ∼ 10
−9 s) and much smaller for
neutron measurements (τ m ∼ 10
−9
− 10
−12 s). Further, in this model it is clear that
magnetic correlations are present far above the freezing temperature. Only at much
higher temperatures, when the short range order of the clusters is destroyed, pure
paramagnetic behaviour is found. Mössbauer spectroscopy in external magnetic field
is an excellent method to investigate the magnetic dynamics above the freezing temperature, because the applied field changes the relaxation frequency of the clusters.
If fields are large enough, they can shift the characteristic time of the dynamics into
the Mössbauer time window, so that the approximation of fast relaxation limit is no
longer fulfilled and the spectra show typical shape of so-called relaxation spectra.
This will be shown exemplarily in the following for the spin-glass-system Y(Fe,
Al) 2 .
8.5.4 Y(Fe, Al) 2
Y(Fe x Al 1−x ) 2 is a Laves phase, which crystallizes, with the exception of a small
region near x = 0.5, in the cubic MgCu 2 structure type. Whereas YAl 2 is a Pauli paramagnet with a nearly temperature independent susceptibility of 0.8 · 10
−6 emu/g at
room temperature, YFe 2 is a ferrimagnet with an Fe moment of 1.77 ± 0.08μ B and
a strongly delocalized yttrium moment of −0.67 ± 0.04μ B [63, 138]. For x ≥ 0.78
reciprocal susceptibility χ
-1 data are linear in temperature following a Curie-Weiss
law (Fig. 8.38 right). For lower iron concentrations x the χ
−1
(T ) data are strongly
curved (Fig. 8.38 left). They could be fitted by the relation χ = χ 0 + C/(T − )
where χ 0 describes the Pauli paramagnetic matrix contribution. The Weiss temperature scatters around zero on the Al-rich side and increase strongly on the Fe
rich side (Inset Fig. 8.39). From the Curie constant C the mean effective moment
μ e f f = gμ B
√
S(S + 1) is obtained, which is nearly concentration independent.
Above x ≥ 0.78 it is nearly constant equal to the value obtained for YFe 2 (3.02
μ B ) [139, 140] in contrast to the spontaneous moment which strongly decreases
(Fig. 8.39). On the Al-rich side it decreases slightly to below 2 μ B /Fe for x = 0.1
[123]. Although no long range magnetic order could be found down to 30 mK even
at 70% Fe, the magnetization curves on the Al-rich side are still strongly curved.
They could be fitted to M = N ¯
μL( ¯
μH/kT ) + χ H , with L the Langevin function.
The first term describes the magnetization of iron atoms gathered in clusters with the
mean cluster moment ¯
μ and N the number of mean clusters. The second term is a
susceptibility term coming from the moments which are not part of a cluster. Calculation gives mean cluster sizes of 3–4 magnetic atoms. Their concentration is a few
percent. This finding is confirmed by diffuse neutron scattering on two compounds
with x = 0.25 and 0.65, where the magnetic scattering was interpreted as arising from
small clusters of less than 10 Å at temperatures far above the freezing temperature
[142]. These clusters are formed by short range ferromagnetic correlations. There is
419
methods. With decreasing characteristic measuring time freezing temperature should
increase. This illustrates why T f for magnetization measurements (τ m ∼ 1 − 10
−4
s) is smaller than for Mössbauer measurements (τ m ∼ 10
−9 s) and much smaller for
neutron measurements (τ m ∼ 10
−9
− 10
−12 s). Further, in this model it is clear that
magnetic correlations are present far above the freezing temperature. Only at much
higher temperatures, when the short range order of the clusters is destroyed, pure
paramagnetic behaviour is found. Mössbauer spectroscopy in external magnetic field
is an excellent method to investigate the magnetic dynamics above the freezing temperature, because the applied field changes the relaxation frequency of the clusters.
If fields are large enough, they can shift the characteristic time of the dynamics into
the Mössbauer time window, so that the approximation of fast relaxation limit is no
longer fulfilled and the spectra show typical shape of so-called relaxation spectra.
This will be shown exemplarily in the following for the spin-glass-system Y(Fe,
Al) 2 .
8.5.4 Y(Fe, Al) 2
Y(Fe x Al 1−x ) 2 is a Laves phase, which crystallizes, with the exception of a small
region near x = 0.5, in the cubic MgCu 2 structure type. Whereas YAl 2 is a Pauli paramagnet with a nearly temperature independent susceptibility of 0.8 · 10
−6 emu/g at
room temperature, YFe 2 is a ferrimagnet with an Fe moment of 1.77 ± 0.08μ B and
a strongly delocalized yttrium moment of −0.67 ± 0.04μ B [63, 138]. For x ≥ 0.78
reciprocal susceptibility χ
-1 data are linear in temperature following a Curie-Weiss
law (Fig. 8.38 right). For lower iron concentrations x the χ
−1
(T ) data are strongly
curved (Fig. 8.38 left). They could be fitted by the relation χ = χ 0 + C/(T − )
where χ 0 describes the Pauli paramagnetic matrix contribution. The Weiss temperature scatters around zero on the Al-rich side and increase strongly on the Fe
rich side (Inset Fig. 8.39). From the Curie constant C the mean effective moment
μ e f f = gμ B
√
S(S + 1) is obtained, which is nearly concentration independent.
Above x ≥ 0.78 it is nearly constant equal to the value obtained for YFe 2 (3.02
μ B ) [139, 140] in contrast to the spontaneous moment which strongly decreases
(Fig. 8.39). On the Al-rich side it decreases slightly to below 2 μ B /Fe for x = 0.1
[123]. Although no long range magnetic order could be found down to 30 mK even
at 70% Fe, the magnetization curves on the Al-rich side are still strongly curved.
They could be fitted to M = N ¯
μL( ¯
μH/kT ) + χ H , with L the Langevin function.
The first term describes the magnetization of iron atoms gathered in clusters with the
mean cluster moment ¯
μ and N the number of mean clusters. The second term is a
susceptibility term coming from the moments which are not part of a cluster. Calculation gives mean cluster sizes of 3–4 magnetic atoms. Their concentration is a few
percent. This finding is confirmed by diffuse neutron scattering on two compounds
with x = 0.25 and 0.65, where the magnetic scattering was interpreted as arising from
small clusters of less than 10 Å at temperatures far above the freezing temperature
[142]. These clusters are formed by short range ferromagnetic correlations. There is