Letter Origin of Drastic Change of Fermi Surface and Transport Anomalies in CeRhIn$_{5}$ under Pressure Shinji Watanabe and Kazumasa Miyake Division of Materials Physics, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan The mechanism of drastic change of Fermi surfaces as well as transport anomalies near P = P c ≈ 2 . 35 GPa in CeRhIn 5 is explained theoretically. The key mechanism is pointed out to be the interplay of magnetic order and Ce-valence fluctuations. We show that the antiferromagnetic state with “small” Fermi surfaces changes to the paramagnetic state with “large” Fermi surfaces with huge enhancement of effective mass of electrons with keeping finite c-f hybridization. This explains the drastic change of the de Haas-van Alphen signals. Furthermore, it is also consistent with the emergence of T -linear resistivity simultaneous with the residual resistivity peak at P = P c in CeRhIn 5 . KEYWORDS: CeRhIn 5 , Fermi surface, non-Fermi liquid, localized-itinerant transition, valence fluctuation arXiv:1001.2598v1 [cond-mat.str-el] 15 Jan 2010 The mechanism of instability of electronic states emerging when the magnetically-ordered temperature is suppressed to absolute zero by tuning material parame- ters has been one of the central issues in condensed mat- ter physics. 1–3 A heavy-electron metal CeRhIn$_{5}$ has been extensively studied as the prototypical material. Accu- mulated experiments, however, have revealed that the physics of CeRhIn$_{5}$ seem to be beyond conventional un- derstanding 1–3 and require an essentially new concept. CeRhIn$_{5}$ undergoes an antiferromagnetic (AF) tran- sition at T$_{N}$ = 3 . 8 K with an ordered vector Q = (1 / 2 , 1 / 2 , 0 . 297) at ambient pressure. 4 When pressure is applied under a magnetic field larger than the upper critical field, the AF order is suppressed at P = P$_{c}$ ≈ 2 . 35 GPa. 5–11 Interestingly, a drastic change of Fermi surfaces was discovered at P = P$_{c}$ by the de Haas-van Alphen (dHvA) measurement: 9 For 0 ≤ P < P$_{c}$ , the main dHvA frequencies are in good agreement with those of LaRhIn$_{5}$ where the 4f electron is absent. On the other hand, for P > P$_{c}$ , the dHvA frequencies were identi- fied to be approximately the same as those of CeCoIn$_{5}$, where 4f electrons are itinerant, contributing to the for- mation of the Fermi surface. The electrons on a typi- cal Fermi surface, the cylindrical β$_{2}$ blanch, shows the mass enhancement from m ∗ = 6 m$_{0}$ at P = 0 to 60 m$_{0}$ at P ≈ 2 . 2 GPa with m$_{0}$ being a free-electron mass. 9 For P > P$_{c}$ , the dHvA signal of the β$_{2}$ blanch is lost probably because of a too-large effective mass close to 100 m$_{0}$ , where the heavy-electron state is realized in the paramagnetic-metal phase. 9 So far, it has been thought that this drastic change of the Fermi surfaces might be explained in terms of the “lo- calized” to “itinerant” transition of f electrons. 12 How- ever, this conception encounters a serious difficulty in elucidating the experimental fact that the effective mass of electrons is enhanced even at P = 0 with the Som- merfeld constant γ ≈ 56 mJmol − $^{1}$K − $^{2}$,5 which is about 10 times larger than that of LaRhIn$_{5}$. 13, 14 Furthermore, resistivity measurements revealed that a striking anomaly emerges near P = P$_{c}$ : 7 The low- T re- On the basis of these observations, in this Letter, we present a theoretical explanation for resolving this out- standing puzzle in CeRhIn$_{5}$. We show that the drastic change of the Fermi surface from a “small” to a “large” one occurs at the phase transition from AF to paramag- netic metal with huge mass enhancement under pressure, as observed. An important point here is that these results are obtained with finite hybridization between f and con- duction electrons, which overcomes the difficulty of con- ventional scenario that f electrons undergo “localized” Recently, an important measurement has been per- formed under pressure and magnetic field. 11 G. Knebel et al . have measured the T 2 coefficient A in the resistiv- ity in the T → 0 limit at the magnetic field H = 15 T, and found that A increases as pressure increases toward P = P$_{c}$ $_{. They have shown that under pressure,}$√$_{A}$$_{shows}$ an enhancement similar to the effective mass of electrons m ∗ of the β$_{2}$ blanch obtained by the dHvA measure- ment, 9 satisfying the √$_{A/m}$ ∗ =const. scaling. This in- dicates that the mass enhancement is not caused by the quantum criticality of the AF spin fluctuations, since in the case of the 3D (2D) AF QCP, √$_{A/m}$ ∗ is expected to show the T − 1 / 4 ( T − 1 / $^{2}$) divergence.1–3 Namely, the √$_{A/m}$ ∗ =const. scaling strongly suggests that the mass enhancement near P = P$_{c}$ purely comes from the band effect. sistivity ρ ( T = 2 . 25 K) has a sharp peak at P = P$_{c}$ , suggesting that the residual resistivity ρ$_{0}$ is strongly en- hanced near P = P$_{c}$ . 7, 11, 12 The low-temperature resis- tivity also exhibits anomalous behavior: The T -linear registivity ρ ( T ) ∝ T emerges most prominently near P = P$_{c}$ with a wide- T range up to ∼ 10 K. 7, 11, 12 This behavior is quite different from that of normal metals described by the Fermi liquid ρ ∝ T 2 as well as the conventional quantum criticality scenario near the AF quantum critical point (QCP) in three dimension (3D) ρ ∝ T 1 . $^{5}$.1–3 The origin and mechanism of these trans- port anomalies as well as the drastic change of the Fermi surface at P = P$_{c}$ accompanied by huge mass enhance- ment have not been clarified so far.