Neutron Scattering

Figures 16 .10 and 16.11 show the magnetic diffuse neutron scattering of MnS2 at different
temperatures above TN and the magnetic Bragg peak at 4 .9 K (topmost figure). We can
clearly observe, how with decreasing temperature the diffuse scattering becomes shaiper in
reciprocal space and how the peak intensity increases strongly. However, for scans along
(1,k,0) the diffuse scattering is not centred at the low temperature Bragg position, while it is
centred for the perpendicular scans in the (h,k,0) plane. The magnetic short range order is
"incommensurate" wich the lattice . This means that the periodicity observed in the diffuse
magnetic scattering is not just a simple rational multiple of the chemical unit cell periodicity .
Figure 16 .9 shows the temperature variation of the incommensurate component of the vector
at which the diffuse scattering is centred . Note the jump characteristic for a first order
transition . Figure 16 .9 demonstrates that we can understand the paramagneticantiferromagnetic
phase transition in MnS2 as a transition from incommensurate short range
order to commensurate long range order . Now it is well established that such "lock-intransitions"
are of first order, which explains the unusual behaviour of MnS2 . The problem
remains which interaction leads to the shift of the diffuse peak as compared to the Bragg
reflection. This question can be solved with model calculations, such as the ones depicted in
figure 16 .8 [14] . It tums out that an anisotropy term in the Hamiltonian can give rise to the
observed effect .
Finally we want to show an example for a truc "classical" second order transition, the PM-AF
transition in MnF2 . In this case, we have performed the measurements with high energy
synchrotron x-rays due to the better reciprocal space resolution as compared to neutrons [15] .
Figure 16 .12 shows a double logarithmic plot of the reduced sublattice magnetisation m (m =
1VI/Ms, where Ms is the saturation value of the magnetisation) versus the reduces temperature
ti, defmed in eq. (16.15) . In this plot, the data points nicely line up along a straight line,
corresponding to a power law behaviour as expected from (16 .7) . The critical exponent ß of
the sub-lattice magnetisation can be obtained to great precision : ß = 0 .333 (3), corresponding
roughly to the exponent expected for an Ising system (n=1, d=3) according to table 16.1 .
However, the calculated and measured value do not quite coincide, at least to within two
standard deviations, which demonstrates that the precise values of the critical exponents are
still not very well established.
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