ESR bottleneck effect in the heavy-fermion metal YbRh2Si2

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Journal of Magnetism and Magnetic Materials 316 (2007) e393–e395 www.elsevier.com/locate/jmmm

ESR bottleneck effect in the heavy-fermion metal YbRh2Si2 V.A. Ivanshin MRS Laboratory, Faculty of Physics, Kazan State University, Kremlevskaya str. 18, 420008 Kazan, Russia Available online 2 March 2007

Abstract An approach related to the bottleneck effect is proposed for an origin of the electron spin resonance (ESR) of a Kondo ion (Yb3+) in the undoped Kondo-lattice systems YbRh2Si2 and YbIr2Si2. The effects observed for the effective ESR g-factor and the ESR linewidth in YbRh2Si2 are associated with the influence of the Kondo effect and the crystalline electric field splitting of the f-multiplet of ytterbium. A corresponding theory, which predicts the exchange-narrowed ESR linewidths in the temperature range 1–10 K, is discussed. r 2007 Elsevier B.V. All rights reserved. PACS: 71.27.+a; 75.20.Hr; 76.30v Keywords: Quantum criticality; Heavy-fermion; Yb-compound; Kondo effect; Electron spin resonance and relaxation

1. Introduction The magnetic and transport of ternary intermetallic RT2X2 compounds (RE ¼ rare earth, T ¼ transition metal and X ¼ Group IV or Group V element) are determined by the rare-earth moments, their conduction electron (CE)mediated exchange interaction, and the effects of the crystalline electric field (CEF) acting on the 4f electrons. The method of electron spin resonance (ESR) can yield important information on the electronic structure, on the interaction between the magnetic rare-earth spins and the CE, and on the spin correlations in the lattice. YbRh2Si2 is one of a few ytterbium-based heavy-fermion (HF) Kondo-metals exhibiting the properties of a so-called non-Fermi-liquid behavior (NFL) very close to a quantum critical point (QCP), where magnetic ordering via RKKY interactions is balanced by Kondo screening (see Ref. [1] and references therein). Anomalous behavior of the resistivity, specific heat and magnetic properties investigated in this compound suggests a fundamental breakdown of the Fermi liquid theory. Most remarkably, in contrast to the Ce-based NFL superconductors, YbRh2Si2 is not a superconductor at least at the lowest accessible temperature T ¼ 10 mK. Unraveling the intimate relationship Tel.: +7 843 231 51 75; fax: +7 843 292 74 18.

E-mail address: [email protected]. 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.02.160

between quantum criticality and superconductivity will remain a key issue in the physics of condensed matter [2]. 2. Experimental results and discussion An effective Kondo temperature of order 20–30 K was derived from different transport and magnetic measurements in YbRh2Si2 [1,2]. In the framework of known theories of the ESR for Kondo systems, such a Kondo temperature should be related to the ESR linewidth of 25–40 T [3]. An estimation of the dipole–dipole ESR linewidth only, caused by spin–spin interactions, yields in YbRh2Si2 the value of order 0.16 T [4]. Thus, the Kondo ion itself as a part of ground lattice is not an appropriate ESR probe, and it is necessary to dope HF systems with small amounts of ions with stable magnetic moments in order to observe any measurable ESR signal. Since the structure of the RET2X2 compounds is complicated, it is very difficult to obtain the information about magnetic exchange interactions from theoretical calculations. In addition, the character of the ground state in the HF compounds is often governed by several different microscopic interactions of comparable strength (Kondo effect, interatomic magnetic interactions and CEF). Therefore, such kind of doping induces different disorder effects, which also could substantially hinder a further evaluation of experimental ESR data. However, for the first time, a

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V.A. Ivanshin / Journal of Magnetism and Magnetic Materials 316 (2007) e393–e395

seemingly large (almost non-Kondo screened) but correlated fluctuating ytterbium magnetic moments were detected below the Kondo temperature in the ESR spectra of the YbRh2Si2 single crystals without additionally doped spin probes [4,5], and the corresponding characteristic linewidths related to the Yb3+-ions (4f13, J ¼ 7/2) were about 30 mT at the lowest temperature of measurements T ¼ 1.5 K. The interaction of the localized magnetic Yb3+ moments with CE influences two ESR parameters: the slope of the resonance linewidth DHppb ¼ dDHpp/dT and the effective g-factor, where the slope b is proportional to the squared electronic density of states N2(EF) at the Fermi energy [6]. The temperature dependence of both these values at To15 K (Fig. 1) shows the Kondo-type spin correlations which are typical for Kondo-lattice systems [7]. The Yb3+ ESR linewidth increases linearly below 15 K suggesting a Korringa mechanism which has been attributed to some remaining Yb3+ moments relaxing through correlated Fermi liquid [8]. However, a detailed study of the Kondo features will be possible only after ESR investigations at lower temperatures To1.5 K. At high temperatures, lattice vibrations modulate the CEF of ligands and cause spin–lattice relaxation via spin–orbit coupling. A highly anisotropic ESR relaxation can be related in YbRh2Si2 to a mutual influence of the Yb3+ spin–lattice relaxation [4,5] and RKKY interactions via CE [9], as it has been observed for the ESR of different HF Kondo-lattice compounds [3]. This leads to a substantial broadening of the ESR line and makes it unobservable above 25 K. The same spin–lattice relaxation mechanism caused by the thermal fluctuations of the lowest Yb3+ CEF states [4] can be also responsible for the temperature dependence of the g-factor above 15 K (Fig. 2). In this case, magnetic dipole–dipole and exchange interactions of the ytterbium ions with environment induce their random

Fig. 1. Temperature dependence of the ESR linewidth (upper panel) and the effective g-factor (lower panel) in YbRh2Si2. The solid line represents the fit using parameters shown in the inset.

Fig. 2. Temperature dependence of g-value in YbRh2Si2 measured at 34.1 GHz [4]. The solid line is the fit of Eq. (1) to the data, using gexc ? ¼ 1:0, Dg0? ¼ 2:58 and Dffi9.91 meV.

transitions from the ground Kramers doublet to the excited CEF levels with the activation energy DE9.91 meV. The contribution of this mechanism to the effective g-factors can be estimated using the relation   D ga ðTÞ ¼ g0 ðaÞ þ Dg0a exp  , (1) T where ga(0) and gaexc are the effective g-factors of the ground and first excited doublets of the ytterbium ion, Dga(0) ¼ gaexc–ga(0), and Dffi9.91 meV. Remarkably, very recent studies of YbRh2Si2, using the angle-resolved photoemission (ARPES) experiments, interpret this compound as a mixed-valent HF metal with the valency of the Yb-ion of approximately +2.88 [10]. The uppermost 4f band is located roughly 150 meV below the Fermy energy EF. The f-multiplet splits into j ¼ 7/2 and 5/2 excitations. The f7/2 multiplet is much closer to EF, hybridizing anisotropically with the Rh 4d-derived conduction band. The corresponding CEF splitting of the f-multiplet is of the order of 10 meV or less. Therefore, the value of the activation energy Dffi115 K9.91 meV derived from the temperature dependence of the ESR linewidth and the effective g-factor can be associated with the CEF splitting of the f-multiplet in YbRh2Si2. These findings can be also a partial reason of the reduction of the dipole–dipole and the whole ESR linewidth [4] under assumption that the concentration of the Yb3+ ions contributing to the ESR signal is essentially lower than it was expected. The ARPES studies for another relative to the YbRh2Si2 compound located close to the QCP, YbIr2Si2, have revealed very similar results [11]. Interestingly, in contrast to all other known undoped Yb-based HF intermetallics, the ESR was recently observed in YbIr2Si2 only [12]. It is natural to suggest that the ESR behavior has the same origin in both these systems. Our previous analysis [13] showed that the intermediate

ARTICLE IN PRESS V.A. Ivanshin / Journal of Magnetism and Magnetic Materials 316 (2007) e393–e395

ESR bottleneck effect can be responsible for the extremely narrow ESR linewidth in YbRh2Si2 in the temperature range 1–10 K. According to this approach, an anomalous reduction of the relaxation rate of the ytterbium spins could be understood in terms of exchange interactions between the subsystems of the localized Yb3+ magnetic moments and CE under conditions of their collective motion. The bottleneck appears, when the back-scattering rate deS of the CE to the Yb spins becomes comparable or larger than the scattering rate deL of the CE to the lattice. It indicates that CE interact more strongly with Yb spins than with the lattice. In the ESR measurements, the bottleneck behavior manifests itself by the decrease of the temperature slope of the linewidth b ¼ dDHpp/dT and by the shift of the g-value in comparison to the value for an ion in a nonmetallic host. In our case, the Yb3+-g-shift is negative: Dg/gE8% [5]. The corresponding estimation of the effective exchange Jeff between the Yb spins and the band states [6] in YbRh2Si2 according to the procedure described in the Ref. [14] gives the value of JeffE4.49 eV. An opening of the ESR bottleneck has been often observed in different Gd-based compounds [15–18]. It follows from these data that the ESR relaxation processes in RT2X2 are influenced by two effects: an increase in density of states at the Fermi level (leading to an increase in deS) and a change of the CE to more d character (increase in deL). The latter increase is larger, and when the number of d electrons in the transition element decreases, the temperature slope b increases. Moreover, the bottlenecked system can be opened by the addition of other magnetic ions, relaxing quickly to the lattice. Hence, the exchange interactions between Yb and either Rh or Ir can play a crucial role for the opening of the electron bottleneck in YbRh2Si2 and YbIr2Si2, respectively, and the possible ESR bottleneck effect should be weaker in the YbIr2Si2 compound. Our scenario is strongly supported by very recent ESR measurements on the isotope clean 174 YbRh2Si2 and on the doped compounds: YbRh2 (Si1xGex)2, Yb1xRxRh2Si2 (R ¼ La, Lu) [19,20]. In these experiments, introducing disorder by La- or Ge-doping causes a more effective Yb3+ ESR relaxation, and the ESR signal observed below 30 K in Yb1xLuxRh2Si2 vanishes with increasing Lu-concentration. A progressive reduction could be confirmed for the ESR linewidth by decreasing temperature in 174YbRh2Si2. The 174YbRh2Si2 samples show also a smaller residual linewidth and a strongly reduced thermal line broadening in the whole temperature region.

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3. Conclusions The ESR bottleneck effect and the Yb-valence fluctuations have been claimed as origins of the extremely narrow ESR linewidths in YbRh2Si2 and YbIr2Si2. At To15 K, the ESR linewidth and the effective g-factor in YbRh2Si2 are correlated with the Kondo effect and the Korringa relaxation mechanism. The spin–lattice relaxation caused by the influence of the CEF splitting of the ytterbium f-multiplet of the order of 10 meV determines the temperature dependence of both ESR parameters at higher temperatures. High-field ESR measurements in single crystals of both compounds should be performed in order to study the angular and frequency dependences of resonance lines which can be related to the Yb-, Rh-, and Ir-spins. Hopefully, such studies will also trigger theoretical investigations on localization effects in the NFL Kondolattice systems with stable magnetic moments.

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