Minute splitting of magnetic excitations
in CsFeCl3 due to dipolar interaction observed
by polarised neutron

B. Dorner (ILL), M. Baehr (HMI Berlin), D. Petitgrand (LLB Saclay).

Using inelastic neutron scattering with polarisation analysis it was possible, for the first time, to observe simultaneously the two magnetic modes split due to dipolar interaction. This would not have been possible with energy resolution only. An analysis of eigenvectors was also performed.

Dipolar interactions in magnetic materials are created by the magnetic field around one or more oriented elementary magnetic moments. They are most often weak compared to exchange interactions which arise from an overlap of the wavefunctions of magnetic electrons. Contrary to exchange interactions, dipolar forces are of long range. This is the reason why they may become important near magnetic phase transitions. Here we present an experimental study on CsFeCl3, where the use of polarised neutrons made it possible to observe the minute splitting, caused by dipolar interaction, of originally doubly degenerate states.

Due to this splitting the dispersion curves of the magnetic excitations are changed so that minima in energy, originally located at commensurate positions in reciprocal space, such as the K-points, (1/3, 1/3, 0) and (2/3, 2/3, 0), are moved to incommensurate positions. In the "soft mode" picture of phase transitions the minima in the excitation energy correspond to positions where Bragg peaks of the ordered magnetic structure appear.

For this study we chose CsFeCl3 which is isostructural with the quasi one-dimensional magnetic system RbFeCl3. The latter orders below 2.5 K into an incommensurate structure which is explained by dipolar interactions between the chains of Fe2+ ions which are ferromagnetically aligned along the hexagonal (z) axis with an antiferromagnetic interaction between neighbouring chains. CsFeCl3 does not order magnetically down to the lowest temperature so that the dipolar interactions can be studied without being disturbed by temperature dependent excitation energies (soft modes). The lowest excitation energies appear for the dispersion curve perpendicular to the chain direction and the main features of the dispersion correspond to the antiferromagnetic exchange interaction between the chains. The influence of dipolar forces is strongest on these low frequency modes, see Fig. 1.

The experiment with polarised neutrons was performed on the three-axis spectrometer IN14, with a sample of volume 0.5 cm3. The experimental set-up was such that magnetic fluctuations of Sx type (see Fig. 3) show up in the non-spin-flip (NSF) channel, while Sy fluctuations are detected in the spin-flip (SF) channel.

Figure 1 (left): Dispersion of the magnetic excitations in the y-direction [xx0], perpendicular to the chain direction, which are split due to dipolar interaction. NSF (blue) and SF (red) correspond respectively to Sx and Sy fluctuations (see Fig. 3). The curves represent a least squares fit of a dispersion relation containing exchange interaction between neighbouring chains and dipolar forces.
Figure 2 (right): A series of constant-Q scans at different positions along the y-direction, Q = [xx2]. Blue and red symbols correspond to NSF and SF, respectively.

Fig. 2 shows a series of scans, where the shift between the SF and the NSF signals can be seen. Each pair of curves was measured simultaneously: the instrument was positioned for one energy transfer and then a polarisation flipper was activated or disactivated to measure SF or NSF. Then the instrument was moved to the next position in energy transfer. Due to this procedure the small shifts between the signals are only influenced by the statistical uncertainties of the measured data but not by positioning inconsistencies of the spectrometer. Anyway, the sequence of measured frequencies, like a chain of pearls in Fig. 1, confirms the reliability of the experimental technique.

One part of the results consists in the first observation of the splitting of the modes (degenerate in the absence of dipolar interaction) and in the shift of the minima of the dispersion curves away from the commensurate K-points, see Fig. 1, thus indicating the possibility for an incommensurate magnetic order. In fact such an incommensurate magnetic structure appears not only in RbFeCl3 but also in CsFeCl3 , if an external magnetic field is applied parallel to the chain direction. The other part of the results is connected to the correlation between SF/NSF and Sy/Sx fluctuations. This correlation makes it possible to derive eigenvectors of the observed modes.

Fig. 3a shows the eigenvectors at small wavevector q = 2p/l (wavelength l >> a, where a is the lattice parameter in the hexagonal plane). It is obvious that the Sy-mode has to have the higher frequency because here the dipolar interaction is "stretched" contrary to the case for the Sx-mode. Fig. 3b gives the eigenvectors of the degenerate modes at the K-point (l = 3a/2) and Fig. 3c displays the eigenvectors at the M-point (1/2, 1/2, 0) (l = a). Here the Sy mode has the lower frequency.

It is remarkable that this Sy eigenvector is equal to the static order in the isostructural substance CsNiF3 , where the dipolar interactions dominate over the exchange between the chains.

This experiment demonstrates in a convincing way the possibilities of polarised neutrons: For the first time the two modes, split due to dipolar interaction, were measured simultaneously. This would not be possible with energy resolution only. Polarisation analysis also made it possible to extract the eigenvectors of the modes. These eigenvectors confirm the qualitative predictions of the incommensurate magnetic structure in RbFeCl3 near the K-point and the commensurate structure of CsNiF3 at the M-point.

Figure 3: Eigenvectors of the magnetic fluctuations at different wavevectors q: a) at small q, b) at q = 4p/3a (K-point), c) at q = 2p/a (M-point). The red and blue arrows indicate Sy and Sx fluctuations, respectively.