NMR Evidence for a Totally Symmetric Order Parameter in PrFe₄P₁₂

Intermetallic compounds with the filled-skutterudite structure RT₄X₁₂ (R = rare earth, T = transition metal, X = pnictogen) has attracted strong recent attention because of a variety of intriguing phenomena in a common crystal structure (Fig. 1 left) such as metal-insulator transitions, multipole orders, exotic superconductivity, and anomalous phonons [1]. Among them, PrFe₄P₁₂ shows a peculiar phase transition at T_A = 6.5 K. The low temperature (T ) phase has no spontaneous magnetic moment at zero field and is suppressed by a magnetic field of 4 - 7 T depending on the field directions (Fig. 1 right). The low-T phase has a structural modulation with the wave vector Q = (1,0,0), indicating loss of t (1/2, 1/2, 1/2) translation. Distinct electronic states for two Pr³⁺ ions in the bcc unit cell observed by resonant X-ray scattering, the field-induced staggered magnetization observed by neutron scattering, and elastic anomalies have all suggested an antiferro-quadrupole order likely to be of ƒ¡₂₃-type. However, direct identification of the order parameter has not been made yet.




Fig. 1. Crystal structure (left) and the phase diagram (right) of PrFe₄P₁₂

We have performed nuclear magnetic resonance (NMR) experiments on ³¹P nuclei for microscopic understanding of the low-T ordered phase [2]. We observed that all NMR lines in the high-T phase split into two upon entering into the low-T phase (Fig. 2) irrespective of the field direction. This should be ascribed to the distinction between two P₁₂ cages surrounding Pr sites at the corner and the body center of the original bcc lattice. Absence of any additional line splitting indicates that the 4f -electronic charge distribution of each Pr sites preserves the T_h point symmetry of the high-T phase. From group theoretical arguments [2] and phenomenological fitting of the angle dependence of splitting (Fig. 3 left) [3], we have established that the order parameter must belong to the totally symmetric ƒ¡₁ representation, ruling out any type of quadrupole order. The line splitting vanishes as the magnetic field is reduced to zero, indicating that the primary order parameter at zero field is electric, i.e. even-rank multipole moments. For Pr³⁺, the lowest order totally symmetric even-rank multipole is the hexadecapole shown in Fig. 3 (right).




Fig. 2 (left) ³¹P NMR spectra at T = 50 K. The numbers indicate assignment of each peak to the P sites (P1 - P6, see Fig. 1 left). (right) ³¹P NMR spectra at 6.0 K (above T_A) and at 4.6 K (below T_A) for the field of 1.6 T along [111]. NMR peaks from P1, P3, and P5 sites (P2, P4 and P6 sites) are shown by solid (open) circles.




Fig. 3. (left) The angle dependence of the NMR line splitting in the low-T phase (T = 4.2 K, H = 1.6 T). The lines are fitting to the phenomenological model described in ref. [3]. (right) Schematic illustration of a totally symmetric hexadecapole moment. Note that the cubic symmetry is preserved in spite of a highly anisotropic charge distribution.

What is the driving force for such a peculiar order ? A hint is provided by the band structure calculation showing a nesting feature of the conduction band with Q = (1,0,0) [4]. It is well known that electron-lattice coupling in the presence of Fermi surface nesting leads to a charge density wave order. A similar Fermi surface instability can be caused by coupling between the conduction band and 4f multipole moments. PrFe₄P₁₂ may be an example of such a novel type of order.


References
[1] Y. Kuramoto, JPJS Online-News and Comments [Apr. 13, 2007].
[2] J. Kikuchi, M. Takigawa, H. Sugawara and H. Sato, J. Phys. Soc. Jpn. 76 (2007) 043705 (Selected for JPSJ Editor's Choice).
[3] O. Sakai, J. Kikuchi, R. Shiina, H. Sato, H. Sugawara, M. Takigawa and H. Shiba, J. Phys. Soc. Jpn. 76 (2007) 024710.
[4] H. Harima and K. Takegahara, J. Phys.: Condens. Matter 15 (2003) S2081.