Orbital dynamics of the 4f shell in DyB₂C₂

U. Staub (SLS), A. M. Mulders (ANSTO, Curtin U. & SLS), O. Zaharko and S. Janssen (ETH), T. Nakamura (SPring-8) and S. W. Lovesey (SPring-8 and Diamond)

For the first time, fluctuations in the Dy quadrupole (orbital) moment have been observed in DyB2C2 using inelastic neutron scattering. The observed quasi-elastic response is decomposed into two components, one reflecting transitions within the doublets (narrow) and the other transitions between the doublets (broad) of the effective Dy quartet ground state.

The widths of the narrow and broad components are shown to arise from fluctuations in the magnetic dipole and the electric quadrupole moments, respectively.

Orbital degrees of freedom have attracted significant interest in recent years, as they are believed to be important for the occurrence or suppression of the colossal magneto-resistance in manganites as well as the occurrence of metal-insulator transitions in many transition metal oxides [1].

Orbital ordering can also play an important role in f-electron materials. Orbitals (quadrupoles or higher multipoles) may order independently of the magnetic dipoles; which causes discussions about the order parameter involved in the phase transition as e.g. in NpO2 [2-4].

Inelastic neutron scattering (INS) is a technique, which accesses the multipole dynamics through its influence on the dipole magnetic excitations of the f states. The INS experiments were performed at the time-of-flight spectrometer FOCUS at the spallation neutron source SINQ of PSI. Incident neutron energy of 7 meV was used.

The system DyB2C2 is an excellent candidate to study multipole dynamics because it exhibits the highest antiferroquadrupole (AFQ) transition with TQ = 24.7 K [5], which is significant higher than the magnetic dipole transition occurring at TN=14.7 K. Such a high TQ indicates that the energies of the quadrupole-quadrupole interaction are in the range of a few meV and the effects should be observable.

The ground state without the f-f interactions (dipole or quadrupole) has been determined to be a doublet followed by the first excited doublet at 1.4 meV [6]. It is the quadrupole pair interaction that turns these two doublets states into an effective quartet and AFQ ordering is induced. Only when the AFQ interaction overcomes the energy separation between the two doublets orbital order occurs.

This is similar to magnetic order induced in a singlet ground state of a non Kramers f-ion [7]. Figure 1 Neutron difference spectra of 28 K - 16 K (filled circles), together with a fit (full line is total) of a negative Voigt (broken lines; Lorentzians convoluted with the instrumental Gaussian type resolution function) and two positive Voigt functions (dotted lines). The inset shows the spectra rescaled.

Diagram 1

Figure 1 (right) shows the difference between INS spectra taken at various temperatures, and a spectrum taken at 16 K > TN = 14.7 K. This is the best way to get intrinsic information from the raw data as strong absorption makes the background correction of individual spectra inaccurate. This has the advantage that the non-magnetic contribution, e.g. the incoherent elastic intensity, does not appear as it is at most very weakly temperature dependent.

Therefore, the observed negative as well as positive contributions to the difference spectra are both of magnetic origin. At 16 K a single Voigt function describes the quasi elastic response well but at higher temperature two Voigt functions are needed to accurately describe the data; a broad and a narrow component. For increasing temperatures, the width of both components of the the quasi-elastic response is increasing.

The magnetic quasi-elastic neutron cross section of a polycrystalline material is a direct measure of the local susceptibility in the paramagnetic state of the 4f ion (moment averaged) similar as obtained by NMR or EPR. The width of the quasi-elastic peak is commonly related to the time scale of the dipole fluctuations; however, here the situation is more complex.

Diagram 2

Figure 2 (below) Temperature dependence of the intensity (upper part) and the full width at half maximum (lower part) of the two components. The vertical line represents TQ and the solid line through the points reflects the relaxation. The inset shows in the enlarged scale. The temperature dependence of the corresponding fit parameters, the widths and and integrated intensities IA and IB are shown in Figure 2. At 16 K, IB is zero and IA reflects the total magnetic scattering within the quasi-quartet.

The neutron cross section exhibits two components, a quasi-elastic with transition probability MA, reflecting the transition within the doublet and an inelastic excitation with transition probability MB between the two doublets as illustrated in Figure 3. reflects therefore the 'dynamical splitting' within the doublets and the 'dynamical splitting' between the doublets. Physically, the width directly relates to the fluctuation time of the dipole moments.

The broadening must be due to the interaction with the quadrupoles. In this regime a strong decrease of IB is observed. This decrease suggests that the quadrupole mean-field causes a strong change in the 4f wave functions suppressing the dipole transition for neutrons between the two doublets. In analogy with the quasi-elastic broadening of the doublets reflecting the dynamics of the magnetic dipoles, the broadening due to the transition between the two doublets reflects the dynamics of the quadrupoles.

To our knowledge this is the first time that the fluctuation times of the quadrupoles (orbitals) have been directly determined. There are many techniques able to determine dipole fluctuation timescales, (µSR, M?ssbauer etc.), yet, little is known in this time window on quadrupole fluctuations. It is interesting to see that the fluctuation time of the quadrupoles is significantly faster at all temperatures than those of the dipoles by approximately one order of magnitude.

The linear temperature dependence indicates that for DyB2C2 the RKKY interaction is the dominating interaction for AFQ. Figure 3 (below right) Qualitative energy level diagram of the ground state of the Dy3+ ions in DyB2C2 in four cases: I (top left) dilute Dy3+ ion (valid for strong dilution with non magnetic Y); II (top right) the paramagnetic state; III (bottom left) the AFQ state and IV (bottom right) the AFM + AFQ state. The broadening of the energy levels observed in the INS spectra is presented schematically at the right of every diagram and reflects the CEF splitting.

Diagram 3

We have measured the temperature dependence of the quasi elastic response of the Dy3+ ions in DyB2C2. Two components are observed that are related to the scattering within the doublets and between the doublets in the effective quartet ground state.

The broadening of these two components reflects the fluctuation time of the dipoles and the quadrupoles allowing us, for the first time, to determine a temperature dependence of the quadrupole dynamics of the f-shell. It is shown that the AFQ interaction is mediated by the conduction electrons.

These results indicate that INS might be a good tool to study orbital liquids. This work was performed at SINQ of the Paul Scherrer Institut, Villigen PSI, Switzerland. Details of this work can be found in ref [8].

References

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8. U. Staub, A. M. Mulders, O. Zaharko, S. Janssen, T. Nakamura and S. W. Lovesey, Phys. Rev. Lett. 94, 036408 (2005) Orbital dynamics of the 4f shell in DyB2C2
9. U. Staub (SLS), A. M. Mulders (ANSTO, Curtin U. & SLS), O. Zaharko and S. Janssen (ETH), T. Nakamura (SPring-8) and S. W. Lovesey (SPring-8 and Diamond)