>K9m 2014, TOM 145, bmii. 5, rap. 866 870
© 2014
EVOLUTION OF THE 4/ ELECTRON LOCALIZATION FROM YbRh2Si2 to YbRh2Pb STUDIED BY ELECTRON SPIN RESONANCE
V. A. Ivanshina'€* T. O. Litvinova", N. A. Ivanshinb, A. Pdpplc, D. A. Sokolovd, M. C. Aronson
aMB.S Laboratory, Kazan Federal (Volga Region) University 42000S, Kazan, Russia
bKazan State University of Architecture and Engineering 420043, Kazan, Russia
cFaculty of Physics and Earth Sciences, University of Leipzig D-04103, Leipzig, Germany
d School 071 Physics and CSEC, University of Edinburgh EH 3JZ, Edinburgh, UK
''Department of Physics and Astronomy, Stony Brook University 11794-3800, Stony Brook, NY, USA
1 Condensed Matter Physics and Materials Department, Brookhaven National Laboratory
11973-5000, Upton, NY, USA
Received November 4, 2013
We report electron spin resonance (ESR) experiments on the Heusler alloy YbRli^Pb and compare its spin dynamics with that of several other Yb-based intermetallics. A detailed analysis of the derived ESR parameters indicates the extremely weak hybridization, more localized distribution of the 4/ states, and a smaller RKKY interaction in YbRli^Pb. These findings reveal the important interplay between hybridization effects, chemical substitution, and crystalline electric field interactions that determines the ground state properties of strongly correlated electron systems.
DOI: 10.7868/S0044451014050097
1. INTRODUCTION
Olio interesting aspect of the heavy-fermion (HF) compounds is the evolution from high-temperature unscreened localized / electrons to itinerant heavy quasi-particlos with effective masses hundords of times that of bare electrons at low temperature [1]. Recent experimental and theoretical studies 011 the HF Yb-based materials have revealed a rich physics of transport and magnetic properties of these systems (see, e.g., Rof. [2] for a review). I11 principle, the Yb systems are the 4/-holo analogue of the Co-based compounds [3] and their ground state properties strongly depend 011 the Yb valence and the strength of hybridization between the 4/ electrons (holes) and the conduction d-, or
E-mail: Vladimir.Ivanshin'&kpfu.ru
•s-electroiis. The most essential role belongs here, 011 the one hand, to the Kondo coupling that screens the Yb or Co magnetic moment and creates a paramagnetic ground state with enhanced masses of quasiparti-cles and, 011 the other hand, to the Ruderman Ivittel Ivasuya Yoshida (RKKY) exchange interaction, which causes a magnetic ordering [4]. A key for understanding the behavior of HF compounds is the interplay between both these phenomena. At a low value of Kondo exchange, the conduction electrons are carriers of longrange magnetic interactions, and the local moments of / shells are ordered in the weak Kondo coupling limit. With an increase in the Kondo effect, the ordered state is suppressed, creating a screening of moments in the strong Kondo coupling regime. As presented 011 the Doniach phase diagram [5], a quantum phase transition occurs between these two regimes.
>K3TO, TOM 145, Bi>in. 5, 2014
The ESR technique could directly probe the local moments of / electrons and their interaction with conduction electrons [6]. However, as a rule, no concentrated HF systems (including Ivondo lattices) can be studied using ESR because of a very fast relaxation of the resonating spin, which leads to a huge ESR linewidth, too broad to be observable and proportional to the Ivondo temperature. One expects the ESR to be washed out by the Ivondo effect because the lattice of local moments is strongly coupled to conduction electrons. Therefore, it is necessary to dope small amounts of ions with localized magnetic moments, such as Co3+ or Gd3+, into the compound under investigation. Surprisingly, during the last two decades, the low-temperature ESR signals have been detected in some undoped Yb-based intermetallies, e.g., mixed-valence compound YbCuAl [7], quantum critical system YbRh2Si2 [8], its parent compounds YbIr2Si2 [9] and YbCo2Si2 [10], and in several other Co- and Eubased alloys [11].
Different theoretical approaches [12 15] show that the narrow anisotropic ESR can be observed in some dense HF compounds in a broad range of magnetic fields as a result of hybridization between 4/ and conduction electrons in conjunction with ferromagnetic (FM) fluctuations [16], which can significantly reduce the ESR linewidth and make it observable. Finally, very recent results of inelastic neutron scattering experiments [17] explain the ESR mode in YbRh2Si2 as a mesoscopic spin resonance of localized droplets of Yb3+ spins and conduction electrons due to a coherent precession of the spin density, extending the distance 6 ± 2 A beyond the Yb site. Such ESR absorption is not caused by the purely localized Yb3+ ions and is not associated with correlated effects over long length scales. In this work, the spin dynamics in YbRh2Pb probed by ESR is compared to that of some relative Yb materials.
2. EXPERIMENTAL PROCEDURE
Samples of YbRh2Pb were obtained from Pb flux as described previously in [18]. They crystallize in a distorted Heusler alloy structure with dimensions a = 4.5235(4) A and c = 6.9864(6) A, and a probable space group I4/mmm. The ESR spectra (ESR linewidth AH = 600 2300 Oe) were taken in the Bruker ESM/'plus X-band (9.4 GHz) [19] and in the EMX 10 40 Q-band (34.1 GHz) spectrometers. In both cases, we used the Oxford continuous-flow liquid-helium cryostats in the temperature range
Evolution of the 4/ electron localization ...
clP/dH
H, KOO
Fig. 1. Derivative of the absorption ESR signal at T = 5 K at the Q-band frequency (34.1 GHz) in YbRliiPb. Inset: The X-band (9.45 GHz) ESR spectrum at T = 4.2 K. The arrow indicates the parasitic signal from the microwave cavity
4.2 Iv < T < 25 Iv. Above 25 Iv, no ESR signal was observed. A multiply twinned crystal structure of the investigated small grains (1 2 mm2 surface area), which was established with a Bruker Smart charged-coupled device X-ray diffractometor, has prevented an orientation of samples and an accurate determination of the local symmetry of paramagnetic centers.
The X- and Q-band ESR spectra of YbRh2Pb are shown in Fig. 1 for 5 Iv. The intensity of the X-band ESR spectrum was comparable with that of the cavity background signal, which is indicated by arrow on the inset in Fig. 1. Its intensity was approximately 20 30 times smaller than that for YbRh2Si2 as measured by identical experimental conditions on the samples of very similar size and weight [8,20]. The measurements at the Q-band frequency allowed us to obtain a higher resolution of the ESR line with a much better signal-to-noise ratio.
No significant deviation from the linear behavior was observed below 15 Iv for the temperature dependence of the ESR linewidth AH at the Q-band frequency (Fig. 2). On a further increase in temperature, the ESR lineshape was essentially distorted, and this was accompanied by an even faster increase in its linewidth. The temperature dependences of the ESR (/-factor are given in Fig. 3 for both frequencies.
V. A. Ivanshin, T. 0. Litvinova, N. A. Ivanshin et al.
>K3TO, TOM 145, Bi>in. 5, 2014
AH, nOe 2.5
2.0
1.5
1.0
0.5
Fig. 2. Temperature evolution of the ESR linewidth at 34.1 GHz in YbRliiPb. The dashed line is the theoretical curve obtained from Eq. (1)
9
T, K
Fig. 3. Temperature effective ESR (/-factor dependence for X-band at 9.45 GHz (triangles) [19] and Q-band at 34.1 GHz (squares) in YbRli^Pb. Solid lines represent the best fits using Eq. (2)
3. DISCUSSION
Wo suppose that the ESR signal in YbRh-iPb originates from the hybridization of 4/ Yb electrons with conduction electrons in the presence of FM fluctuations, as was also proposed for YbRh-iSi-i and YbIr2Si2 [8,9]. In accordance to Refs. [8] and [20], the temperature dependence of AH of ESR spectra in YbRh2Pb at 34.1 GHz can be well fitted (see the dashed line in Fig. 2) by the formula
AH = A + BT+Cox]>(-A/T), (1)
where the measured Korringa rate B « 27 ± 2 Oe/K is within the usual order of magnitude of ytterbium, and the activation energy of the first excited Stark sublevel of the Yb3+ ion is A « 73.5 K. This value of A corresponds very well to the estimation of the first excited crystal electric field level of this ion, Ai = = 68 ± 5 K, which has been derived after heat capacity and magnetic susceptibility measurements in YbRh-iPb [18]. The residual ESR linewidth ,4 changes approximately from 420 to 470 Oe upon passing from the X-to the Q-band experiments. Finally, the parameter C = 69.5±2 kOo (X-band) [19] or 9.0±1 kOo (Q-band). The exponential term is caused by random transitions from the ground sublevel of the Yb3+ ion to the first excited crystal electric field level separated by the distance A [8]. This electronic mechanism of thermal fluctuations can nicely explain the temperature dependence of the effective ESR (/-factor in YbRh-iPb above 10 K (see Fig. 3), also with the same value A « 73.5 K, using the expression
.9(T) = .9o + A.9ooxi)(-A/r), (2)
where Ago = gcrc — go, go and gcrc are respectively the effective ESR (/-factors of the ground and first excited sublevels of the ytterbium ion. At the Q-band frequency, Ago = —2.23 and gcrc = 1.509 are found to be more reasonable values than those reported after the fitting procedure of the X-band ESR spectra in YbRh2Pb (Ago = —18.5 and .</,,, = -15.1) [19]. A huge difference between both sets of the parameters is caused by errors during simulation of the extremely broad and weak X-band ESR signals in the temperature range between 13 and 20 K. Moreover, both these Q-band values are in close agreement with the corresponding fitting parameters obtained from the Q-band ESR experiments on YbRli2Si2 [8], Ago = —2.58 and gfc = 1.0. Recently, Ramires and Coleman [15] showed that a very similar ESR (/-factor shift with temperature in the another HF metal /i-YbAlB4 can be understood as a result of the development of a cohere
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