8.4 Superparamagnetic Particles in the Mößbauer Spectrum 167
The fluctuation frequency of the magnetization is lower than the Larmor frequency. This is the standard case, the average magnetic field at the nucleus is
equal to the external field, as a consequence a sextet is observed. The other extreme
case is found in the situation where the frequency of the thermal fluctuation is
higher than the Larmor frequency. In this case, the average magnetic field, felt by
the nucleus during one revolution, is nil. Therefore, one observes the doublet
stemming from quadrupole splitting. In Figure 8.20 the Mößbauer spectrum of a
nearly ideal superparamagnetic ferrite, in this case MnFe 2 O 4 measured at 300 K,
is presented.
Figure 8.20 does not show any sign of the sextet. This allows the conclusion to
be drawn that this material is superparamagnetic with relaxation time of the
thermal fluctuations of the magnetization of less than 10
−9 s. Lastly, the examples
given in Figures 8.19 and 8.20 show that a Mößbauer experiment is the ultimate
proof for Néel superparamagnetis. (The Brownian superparamagnetism does not
influence the Mößbauer spectrum, as its relaxation time is by far too long.) From
Figure 8.19, where the doublet and the sextet occur, one can conclude that,
in this example, the specimen had a relatively broad particlesize distribution;
so some of the particles were superparamagnetic and others not. Nowadays, a
material is called superparamagnetic if there is only the doublet visible in the
Mößbauer spectrum.
From the viewpoint of solidstate physics, analyzing a Mößbauer spectrum may
give a lot of information. From the splitting of the energy levels, which is proportional to the magnetic field, one can calculate the magnetic crystal field and connected to this, an exact value of the blocking temperature. Figure 8.21 displays
such an example. This figure displays the magnetic crystal field of ferrite, γFe 2 O 3
particles as a function of the temperature. At low temperature, in this case 4 K, a
magnetic field of 50 T was calculated. With increasing temperature, a decrease of
this field was calculated. At a temperature of 80 K a value of 0 T was found.
Figure 8.20 Mößbauer spectrum of MnFe 2 O 4 using a polymer as distance holder determined
at 300 K. This spectrum shows the doublet stemming from the electric quadrupole splitting.
The specimen was perfectly superparamagnetic.
–10 –8 –6 –4 –2 0
2
4
6
8
10
velocity [mm s
–1
]
0.98
0.985
0.99
0.995
1
1.005
transmission
Fitted spectrum
Experimental data
The fluctuation frequency of the magnetization is lower than the Larmor frequency. This is the standard case, the average magnetic field at the nucleus is
equal to the external field, as a consequence a sextet is observed. The other extreme
case is found in the situation where the frequency of the thermal fluctuation is
higher than the Larmor frequency. In this case, the average magnetic field, felt by
the nucleus during one revolution, is nil. Therefore, one observes the doublet
stemming from quadrupole splitting. In Figure 8.20 the Mößbauer spectrum of a
nearly ideal superparamagnetic ferrite, in this case MnFe 2 O 4 measured at 300 K,
is presented.
Figure 8.20 does not show any sign of the sextet. This allows the conclusion to
be drawn that this material is superparamagnetic with relaxation time of the
thermal fluctuations of the magnetization of less than 10
−9 s. Lastly, the examples
given in Figures 8.19 and 8.20 show that a Mößbauer experiment is the ultimate
proof for Néel superparamagnetis. (The Brownian superparamagnetism does not
influence the Mößbauer spectrum, as its relaxation time is by far too long.) From
Figure 8.19, where the doublet and the sextet occur, one can conclude that,
in this example, the specimen had a relatively broad particlesize distribution;
so some of the particles were superparamagnetic and others not. Nowadays, a
material is called superparamagnetic if there is only the doublet visible in the
Mößbauer spectrum.
From the viewpoint of solidstate physics, analyzing a Mößbauer spectrum may
give a lot of information. From the splitting of the energy levels, which is proportional to the magnetic field, one can calculate the magnetic crystal field and connected to this, an exact value of the blocking temperature. Figure 8.21 displays
such an example. This figure displays the magnetic crystal field of ferrite, γFe 2 O 3
particles as a function of the temperature. At low temperature, in this case 4 K, a
magnetic field of 50 T was calculated. With increasing temperature, a decrease of
this field was calculated. At a temperature of 80 K a value of 0 T was found.
Figure 8.20 Mößbauer spectrum of MnFe 2 O 4 using a polymer as distance holder determined
at 300 K. This spectrum shows the doublet stemming from the electric quadrupole splitting.
The specimen was perfectly superparamagnetic.
–10 –8 –6 –4 –2 0
2
4
6
8
10
velocity [mm s
–1
]
0.98
0.985
0.99
0.995
1
1.005
transmission
Fitted spectrum
Experimental data