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Valence fluctuation

In the rare-earth elements, 4f electrons are localized, because they are well shielded from an external charge by 5s2 and 5p6 closed shells. However, 4f electrons can be delocalized due to strong mixing with conduction electrons in some rare-earth compounds. When the configuration 4fn of a rare earth ion is nearly degenerate with a 4fn-1 state and a surplus conduction electron, the 4f state will fluctuate between two valence states. In other words, the 4f state fluctuates with time and space in the material due to electron hopping from ion to ion. This behavior is called valence fluctuation, intermediate valence or mixed valence.

Valence transition

The valence fluctuating state of Eu is realized between Eu3+(4f6) and Eu2+ (4f7) configurations. Among the valence fluctuation systems, Eu compounds are known to exhibit strong temperature dependence of the mean valence. In most cases, the mean valence shifts to three with decreasing temperature, because the trivalent state is nonmagnetic, whereas the divalent state has a large magnetic moment of 7 µB. In some cases, valence changes abruptly in its temperature dependence, which is the valence transition. Pressure stabilizes a trivalent state, because the atomic volume of Eu3+ is smaller than that of Eu2+. On the otherhand, we have demonstrated that a magnetic field also causes a valence transition in Eu(Pd1-xPtx)2Si2 and EuNi2(Si1-xGex)2 compounds (upper right panel). Quite recently, we have observed that EuRh2Si2 exhibits a valence transition under pressure. The T-P diagram is depicted in the lower left panel. The critical pressure is as low as 1 GPa. We are studying various physical properties of the compound under pressures. The lower right panel shows that the valence transition takes place under magnetic fields at 30-45 K. This field-induced valence transition is accompanied by large hysteresis.

Valence ordering

In other cases, the two valence states are ordered periodically below the characteristic temperature due to strong Coulomb repulsion between electrons. This is the charge ordering. In the case of 3d electron systems, the conduction electrons cannot move, when a charge order state is realized. Therefore, the system becomes an insulator or a semimetal with low carriers. For 4f electron systems, on the other hand, the system can be stayed in a metallic state, when the two valence states are ordered. So, we call this ordering “the valence ordering” .The ternary Eu pnictide, EuPtP has been believed to be a valence ordering system. The structure contains layers of Eu and Pt-P atoms alternating in the c-direction. This compound undergoes two first-order phase transitions at T1=235 K and T2= 190 K (see left panel).. Early reports suggested that the valence ordering takes place at T1 and another valence order state is relaized below T2. We successfully prepared single crystals of EuPtP by using a flux method. The resonant X-ray diffraction measurements were carried out by Inami (SPring 8) et al.  as collaboration work. They observed (1 1 1) forbidden reflection below T2 and superlattice reflections (1 1 2/3) and (1 1 4/3) between T1 and T2. These results indicate that the valence order patterns are Eu2+Eu3+Eu2+Eu3+ at T < T2 and Eu2+Eu2+Eu3+Eu2+Eu2+Eu3+  at T2 < T < T1 (right panel).  

YbPd is aother possible valence ordering system. The compound crystallizes in the cubic CsCl-type structure. The compound undergo first order phase transitions at T1 = 125 K and T2 = 105 K. The 170Yb Mossbauer spectra have revealed the presence of two kinds of Yb atoms, one is magnetic and the other is nonmagnetic, in nearly equal proportions at low temperatures, although there is a unique Yb site in the CsCl-type structure. In a simple model, magnetic and nonmagnetic states correspond to the trivalent (4f13) and divalent (4f14) configurations of Yb, respectively. However, the mean valence of YbPd is about 2.8 and it is temperature independent. These results suggest that a nonmagnetic state is in the non-integer valence state, as observed in metallic YbInCu4. We have found that the transition at T1 is accompanied by a structural transition from cubic to tetragonal. We also observed superlattice reflections such as (1/2 0 0) and (1/2 1/2 0) below T2. Based on these results, we discussed possible valence order structures. Another interesting feature of YbPd is the pressure dependence of magnetic ordering temperature. In contrast to many Yb compounds, the magnetic ordering is destabilized by pressure. Presumably, the magnetic ordering is closely associated with the valence ordering. The structural transition and valence ordering disappear above 4 GPa. As a result, the intermediate valence state would be realized in the ground state under high pressures. Studies on the high-pressure phase at low temperatures are in progress. The present work has been carried out in collaboration with Institute of Solid State Physics, University of Tokyo and Hiroshima University.temperature.
References

Valence transition

1. Field-induced valence transition of Eu(Pd1-xPtx)2Si2, A. Mitsuda, H. Wada, M. Shiga, H. Aruga Katori and T. Goto, Phys. Rev. B, vol. 55 (1997) 12474-9.

2. Temperature- and field-induced valence transitions of EuNi2(Si1-xGex)2, H. Wada, A. Nakamura, A. Mitsuda, M. Shiga, T. Tanaka, H. Mitamura and T. Goto, J. Phys., Condens. Matter, vol. 9 (1997) 7913-23.

3. Pressure-induced valence transition in antiferromagnet EuRh2Si2, A. Mitsuda , S. Hamano, N. Araoka, H. Yayama and H. Wada, J. Phys. Soc. Jpn. vol. 81 (2012) 023709.

4. Valence transition induced by pressure and magnetic field in antiferromagnet EuRh2Si2, Akihiro Mitsuda, Suguru Hamano and Hirofumi Wada, J. Korean Phys. Soc. vol. 62 (2013) 1787-1791.

 

Valence ordering

1. Origins of Phase Transitions in Valence Fluctuating YbPd, Akihiro Mitsuda, Masaki Sugishima, Takumi Hasegawa, Satoshi Tsutsui, Masahiko Isobe, Yutaka Ueda, Masayuki Udagawa, Hirofumi Wada, J. Phys. Soc. Jpn. vol. 82 (2013) 084712 (5 pages).

2. Observation of two charge ordering transitions in the valence-fluctuation EuPtP by resonant x-ray diffraction, T. Inami, S. Michimura, A. Mitsuda and H. Wada, Phys. Rev. B vol. 82 (2010) 195133 1(5 pages).

3. Field-induced valence transition in EuPtP1-xAsx, A. Mitsuda, T. Okuma, M. Sugishima, H. Wada, K. Sato and K. Kindo, Eur. Phys .J. B vol. 85 (2012) 2011396 (5 pages).
 

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