Heavy Fermion 4f Band in the “Localized” AF Ordering Regime of CeIn₃

Recently, the nature of the quantum critical point (QCP) of 4f compounds has attracted interest because unconventional superconductivity frequently appears near it [1]. The QCP is realized when the Néel temperature (T_N) at which transition from the paramagnetic heavy fermion (HF) state to the antiferromagnetic (AF) ordered state occurs is tuned to T = 0 K by controlling the pressure and/or magnetic field. There are two possible scenarios for how it occurs. The first scenario is based an ordinary spin density wave (SDW) in which electrons on the Fermi surface (FS) connected by the wave number vector characterizing the AF state are mainly reconstructed [2]. Electrons on the other area of the FS corresponding to the HF band are not strongly affected in the AF state. The second one is a local QCP scenario in which the transition occurs at the level of local magnetic moment formation [3]. The HF component disappears from the FS. Many experimental results that partly support either of the scenarios were obtained for various compounds. Among them, CeIn₃ may be a unique material because it has very simple crystal structure [4]. It has the AF ground state with T_N = 10 K at the ambient pressure, and it is believed to have a localized 4f state. T_N decreases to 0 K at a pressure of about 2.7 GPa, at this pressure, superconductivity appears at very low temperatures.

Recently, Iizuka et al. obtained a new insight into the 4f electron state near the QCP of CeIn₃ by performing detailed infrared reflectivity measurement [5]. A peak grows in the optical conductivity (OPC) of the infrared region as shown in Fig. 1 when the pressure is increased. It is well known that in HF materials a peak appears in the infrared region of the OPC when the temperature is decreased [6,7]. Iizuka et al. emphasized that, interestingly, the peak is observed even in the AF regime of this compound. A part of the FS of the HF band survives in the AF state, or at least, the 4f state in the AF regime does not change drastically from that of the HF state in the excitation energy region of 15 meV. Recently, a band calculation for the AF state of CeIn₃ was carried out, and it was shown that a very shallow 4f level is needed to reproduce the band structure of the AF state [8]. This seems to be consistent with the experimental result of ref. [5]. We should, however, note that there are suggestions of another scenario based on the analysis of the high-field de Haas–van Alphen effect experiments [9].

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Fig. 1 (a) Pressure dependence of the reflectivity, and (b) the optical conductivity (OPC) of CeIn₃ in the infrared region. The solid triangles in (b) show the positions of peaks inherent in HF states. It is noted that peaks are observed even in the pressure region of the AF state p < p_c(= 2.7 GPa). Figure is taken from Fig. 2 of Ref. 5.

The general description of QCP is still controversial. Results of different experiments seem to indicate different scenarios for the same material. Systematic studies by various experimental methods for various materials are needed. For example infrared measurements under pressure for materials that are similar to CeIn₃ such as CeRhIn₅ and CeRh₂Si₂ are desirable. For theoretical studies on the QCP, a recently proposed model including the d–f Coulomb interaction [10] seems to be promising because it controls the type of transition as an underlying mechanism. Actually, the existence of conflicting experimental results may indicate some underlying mechanics on which the observed quantities depend.

The band calculations based on the local density approximation (LDA) were carried out in Ref. 7 to investigate the origin of the peak of the OCP in HF materials. The calculation results show that the optical excitation from the occupied part of the c–f hybridized bands to unoccupied 4f bands accounts for the peak systematically for many materials. It should be noted, however, that the LDA calculation does not usually reproduce the single particle excitation spectra of 4f states. An effective exciton effect due to the d–f Coulomb interaction seems to be included in the LDA potential.

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