Transport and Magnetic Properties of EuAl 4 and EuGa 4 Ai Nakamura 1,2+ , Taro Uejo 1 , Fuminori Honda 2 , Tetsuya Takeuchi 3 , Hisatomo Harima 4 , Etsuji Yamamoto 5 , Yoshinori Haga 5 , Kazuyuki Matsubayashi 6 , Yoshiya Uwatoko 6 , Masato Hedo 7 , Takao Nakama 7 , and Yoshichika Ōnuki 7 1 Graduate School of Engineering and Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan 2 Institute for Materials Research, Tohoku University, Oarai, Ibaraki 311-1313, Japan 3 Low Temperature Center, Osaka University, Toyonaka, Osaka 560-0043, Japan 4 Graduate School of Science, Kobe University, Kobe 657-8501, Japan 5 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan 6 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan 7 Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan (Received June 23, 2015; accepted October 8, 2015; published online November 26, 2015) We succeeded in growing a single crystal of the Eu-divalent compound EuAl 4 with the BaAl 4 -type tetragonal structure by the Al self-flux method and measured the electrical resistivity, magnetic susceptibility, magnetization, specific heat, and thermoelectric power. EuAl 4 orders antiferromagnetically below T N1 = 15.4 K, with three successive antiferro- magnetic transitions at T N2 = 13.2 K, T N3 = 12.2 K, and T N4 = 10.0 K. The latter two transitions are of the first-order. The corresponding magnetization curve indicates three successive metamagnetic transitions with hystereses and saturates above 16 kOe. We observed a plausible characteristic feature of the charge density wave (CDW) below T CDW = 140 K. We also studied an effect of pressure on the electronic state by measuring the electrical resistivity and thermoelectric power. T CDW is found to decrease with increasing pressure at a rate of dT CDW =dP = -54.7 K=GPa and becomes zero at about 2.5 GPa. The present antiferromagnetic ordering is, however, found to be stable at higher pressures up to 7 GPa in EuAl 4 . On the other hand, the different characteristic CDW was observed in EuGa 4 , not at ambient pressure but above 1 GPa, and T CDW increases with increasing pressure. Above 6 GPa, we found that the antiferromagnetic ordering is changed into another first-order-like phase transition. Its characteristic feature is similar to that of the valence transition, and the heavy fermion state is realized at low temperatures. 1. Introduction The f-electrons of rare-earth and actinide compounds are typical in exhibiting a variety of characteristic properties including spin and charge orderings, spin and valence fluctuations, heavy fermions, and anisotropic superconduc- tivity. 1) These are mainly competitive phenomena between the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction and the Kondo effect. The RKKY interaction enhances the long-range magnetic ordering, while the Kondo effect quenches the magnetic moment of almost localized f- electrons, forming the heavy-fermion state at low temper- atures. Eu compounds exhibit two types of valence state: Eu 2+ (4f 7 ) and Eu 3+ (4f 6 ). The former electronic state is magnetic and orders magnetically, following the RKKY interaction. The magnetic moment is the same as that of the correspond- ing Gd compound (J ¼ S ¼ 7=2, L ¼ 0), where J is the total angular momentum, S is the spin angular momentum, and L is the orbital angular momentum. On the other hand, the latter electronic state is non-magnetic (J ¼ 0, S ¼ L ¼ 3). Most Eu compounds are in the Eu-divalent electronic state. Eu-trivalent compounds are few. Very recently, we have succeeded in growing a high-quality single crystal of the typical Eu-trivalent compound EuPd 3 and clarified the Fermi surface properties. 2) Interestingly, the valence of the Eu-electronic state is changed by temperature, magnetic field, and pressure. For example, the experimental result of EuRh 2 Si 2 with the tetragonal structure is typical. 3) The electronic state of EuRh 2 Si 2 is divalent at ambient pressure and orders antiferromagnetically below a Néel temperature T N ¼ 23 K. With increasing pressure P, the electronic state is changed abruptly at the critical pressure P c ’ 1 GPa, revealing the first-order phase transition. Above P c , the electronic state is changed as a function of temperature. Namely, the valence of the Eu-electronic state in EuRh 2 Si 2 is divalent at temperatures higher than the characteristic temperature T v , while it becomes nearly trivalent or 2 þ  (< 1) below T v . Here, T v is called the valence transition temperature. The valence transition at T v under P>P c is of the second-order in the phase transition. Very recently, we have observed a plausible emergence of the charge density wave (CDW) in the electrical resistivity and thermoelectric power under pressures for EuGa 4 with the BaAl 4 -type tetragonal structure. 4) This occurs at about 150 K under a pressure of 2 GPa, for example. From the results of the de Haas–van Alphen (dHvA) experiments for EuGa 4 and energy band calculations for the non-4f reference compound SrGa 4 , the Fermi surface is found to consist of an ellipsoidal hole-Fermi surface and a cube-like electron Fermi surface with a vacant space in the center. We considered that the nesting effect might be realized for these Fermi surfaces and drive CDW in EuGa 4 . We continued the Fermi surface and magnetic studies for the similar compound EuAl 4 . This compound was known to be a Eu-divalent antiferromagnet, suggesting a Néel temper- ature T N ¼ 6 K. 5) The magnetization curve at 4.2 K indicates a metamagnetic transition at about 10 kOe and saturates above 20 kOe. This study was carried out using polycrystal samples. Recently, we have succeeded in growing a single crystal of EuAl 4 by the Al self-flux method. The Néel temperature of EuAl 4 is not 6 K but T N1 ¼ 15:4 K, with three successive antiferromagnetic transitions at T N2 ¼ 13:2 K, T N3 ¼ 12:2 K, and T N4 ¼ 10:0 K. We also observed a plausible character- Journal of the Physical Society of Japan 84, 124711 (2015) http://dx.doi.org/10.7566/JPSJ.84.124711 124711-1 © 2015 The Physical Society of Japan