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Magnetismus Poster: Do., 13:00–15:30 D-P237
Magnets with two order parameters and order parameters with two components
Ulrich Köbler 1 , Andreas Hoser 2,1
1 IFF Forschungszentrum Jülich, 52425 Jülich – 2 Institut für Kristallographie, RWTH-
Aachen
In the interpretation of the observed magnetic excitation spectra it is necessary to
distinguish between the excitations for finite wave vector values, i.e. for q�=0 on the
one hand and for q=0 on the other hand. The excitations with q�=0 are material specific
non universal features on the length scale of the inter-atomic distance. On this length
scale the short range Heisenberg interactions seem to be the relevant interactions.
On the other hand, the spin dynamics at the stable fixed points T=Tc and T=0
shows universality. Universality is represented by power functions of temperature with
exponents that do not depend on microscopic details such as spin structure and lattice
symmetry.
Under the continuous symmetry of the long range ordered state distinction between
individual spins on a discrete lattice is no longer possible. The relevant interactions
are at the Γ point of the Brillouin zone, i.e. at q=0. Continuum theories are more
appropriate than atomistic models. Unfortunately, the long range interactions at q=0
are extremely small because they couple all spins of the sample.
In many magnetic materials a magnetic excitation gap is observed at q=0. We show
that in two dimensional (2D) magnets (K2NiF4) and in one dimensional (1D) magnets
(MnF2) the gap has identical temperature dependence as the order parameter. The
gap, therefore, seems to be a second component of the order parameter. On the other
hand, isotropic 3D magnets with integer spin also exhibit a magnetic excitation gap
(LaVO3). From the different temperature dependencies of gap and order parameter
(UO2) it can be concluded that the gap is a second order parameter. 3D magnets with
half-integer spin have continuous excitation spectra.
As a conclusion, it appears that in 2D and 1D magnets the order parameter has two
components while in 3D magnets two distinguished order parameters can be identified.
These observations cannot be explained assuming only short range Heisenberg interactions.
The only known long range interactions are dipole-dipole interactions. In a
classical treatment dipole-dipole interactions seem not to be able to explain a different
behaviour for integer and half-integer spin values [1]. As a conclusion, a new type of
long range interaction has to be found that is able to explain universality, long range
magnetic order in two and one dimension and different universality classes for integer
and half-integer spin values.
[1] U. Köbler, A. Hoser, Physica B 362 (2005) 295.