The heavy-fermion compound CePdAl with ZrNiAl-type crystal structure (hexagonal space group P 62m) was investigated by powder neutron diffraction. The triangular coordination symmetry of magnetic Ce atoms on site 3f gives rise to geometrical frustration. CePdAl orders below T N = 2.7 K with an incommensurate antiferromagnetic propagation vector k = [1/2, 0, τ], τ ≈ 0.35, and a longitudinal sine-wave (LSW) modulated spin arrangement. Magnetically ordered moments at Ce(1) and Ce(3) coexist with frustrated disordered moments at Ce(2). The experimentally determined magnetic structure is in agreement with group theoretical symmetry analysis considerations, calculated by the program MODY, which confirm that for Ce(2) an ordered magnetic moment parallel to the magnetically easy c-axis is forbidden by symmetry. Further low-temperature experiments give evidence for a second magnetic phase transition in CePdAl between 0.6 and 1.3 K. Magnetic structures of CePdAl are compared with those of the isostructural compound TbNiAl, where a non-zero ordered magnetic moment for the geometrically frustrated Tb(2) atoms is allowed by symmetry.

There has been tremendous research activity in the field of magneto-electric (ME) multiferroics after Kimura et al. [1] showed that antiferromagnetic and ferroelectric order coexist in orthorhombically distorted perovskite TbMnO 3 and are strongly coupled. It is now generally accepted that ferroelectricity in TbMnO 3 is induced by magnetic long range order that breaks the symmetry of the crystal and creates a polar axis [2]. One remaining key question is whether magnetic order can induce ferroelectric polarization that is as large as that of technologically useful materials. We show that ferroelectricity in orthorhombic (o) TmMnO 3 is induced by collinear magnetic order, and that the lower limit for its electric polarization is larger than in previously investigated orthorhombic heavy rare-earth manganites. The temperature dependence of the lattice constants provides further evidence of large spin-lattice coupling effects. Our experiments suggest that the ferroelectric polarization in the orthorhombic perovskites with commensurate magnetic ground states could pass the 1µC/cm 2 threshold, as suggested by theory [3,4].

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Lattice effects in a cerium based clathrate compound Ce 3 Pd 20 Ge 6 with a cubic Cr 23 C 6 -type structure have been investigated by ultrasonic and thermal expansion measurements. Elastic softenings of (C 11 ϪC 12 )/2 and C 44 proportional to the reciprocal temperature 1/T above T Q1 ϭ1.25 K are well described in terms of the quadrupole susceptibility for the ground state ⌫ 8 quartet. A huge softening of 50% in (C 11 ϪC 12 )/2 and a spontaneous expansion ⌬L/Lϭ1.9ϫ10 Ϫ4 along the ͓001͔ direction in particular indicate the ferroquadrupole ordering of O 2 0 below T Q1 . The elastic anomalies associated with the antiferromagnetic ordering at T N2 ϭ0.75 K and the incommensurate antiferromagnetic ordering are also found. Notable frequency dependence of C 44 around 10 K is accounted for by the Debye-type dispersion indicating a ⌫ 5 rattling motion of an off-center Ce ion along the ͓111͔ direction with eight fractionally occupied positions around the 4a site in a cage. The thermally activated ⌫ 5 rattling motion obeying a relaxation time ϭ 0 exp (E/k B T) with an attempt time 0 ϭ3.1ϫ10 Ϫ11 sec and an activation energy Eϭ70 K dies out with decreasing temperature, and then the off-center tunneling state of Ce ion in the 4a-site cage will appear at low temperatures.