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Microwave Spectroscopy on Heavyfermion Systems Phys. Status Solidi B 250, No. 3, 439–449 (2013) / DOI 10.1002/pssb.201200925 b Part of Special Issue on solidi pssstatus Quantum Criticality and Novel Phases www.pss-b.com physica basic solid state physics Microwave spectroscopy on Feature Article heavy-fermion systems: Probing the dynamics of charges and magnetic moments Marc Scheffler*,1, Katrin Schlegel1, Conrad Clauss1, Daniel Hafner1, Christian Fella1, Martin Dressel1, Martin Jourdan2,Jo¨ rg Sichelschmidt3, Cornelius Krellner3,4, Christoph Geibel3, and Frank Steglich3 1 Physikalisches Institut, Universita¨t Stuttgart, 70550 Stuttgart, Germany 2 Institut fu¨r Physik, Johannes Gutenberg Universita¨t, 55099 Mainz, Germany 3 Max-Planck-Institut fu¨r Chemische Physik fester Stoffe, 01187 Dresden, Germany 4 Physikalisches Institut, Goethe-Universita¨t Frankfurt, 60438 Frankfurt/Main, Germany Received 5 November 2012, revised 16 December 2012, accepted 17 December 2012 Published online 25 February 2013 Keywords electron spin resonance, heavy fermions, microwave spectroscopy, optics of metals * Corresponding author: e-mail scheffl@pi1.physik.uni-stuttgart.de, Phone: þ49 711 68564944, Fax: þ49 711 68564886 Investigating solids with light gives direct access to charge heavy fermions. Microwave studies with focus on quantum dynamics, electronic and magnetic excitations. For heavy criticality in heavy fermions concern the charge response, but fermions, one has to adjust the frequency of the probing light to also the magnetic moments can be addressed via electron spin the small characteristic energy scales, leading to spectroscopy resonance (ESR). We discuss the case of YbRh2Si2, the open with microwaves. We review general concepts of the questions concerning ESR of heavy fermions, and how these frequency-dependent conductivity of heavy fermions, includ- might be addressed in the future. This includes an overview of ing the slow Drude relaxation and the transition to a the presently available experimental techniques for microwave superconducting state, which we also demonstrate with studies on heavy fermions, with a focus on broadband studies experimental data taken on UPd2Al3. We discuss the optical using the Corbino approach and on planar superconducting response of a Fermi liquid and how it might be observed in resonators. ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Heavy-fermion materials are prime fundamental electronic properties are as follows: firstly, examples of metals with electronic properties that are the characteristic energy scales of heavy fermions are governed by strong electron–electron correlations. Though comparably low, and thus they can be tuned by conveniently the simpler examples of heavy-fermion metals are well accessible values of pressure or magnetic field. Secondly, the understood within theoretical frameworks based on the prime property of heavy fermions, namely their strongly Kondo lattice, the wide variety of unusual properties enhanced effective mass, causes strong signatures in experi- observed in different heavy-fermion materials continuously mental observables such as the specific heat, the suscepti- draws the attention of experimental and theoretical physi- bility, or the Fermi-liquid contribution to the transport cists. Two particular interesting features are unconventional scattering rate. This is even more the case because the low superconductivity and quantum criticality [1–4]. Here, characteristic energy scales require that the experiments heavy fermions have become model systems for other are performed at very low temperatures where other correlated electron system such as the cuprate supercon- contributions to these observables that are not caused by ductors. Concerning fundamental electronic properties, the electronic system, but e.g., by phonons, are very weak. main advantages of heavy-fermion materials compared to Therefore, the desired heavy-fermion response can be other correlated metals when it comes to studies of their observed as a strong signal on top of a comparably weak ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim b solidi p status s s physica 440 M. Scheffler et al.: Microwave spectroscopy on heavy-fermion systems background. Thirdly, heavy-fermion materials often have a component because the magnetic response usually is orders simple crystal structure, and in many cases single crystals of of magnitude weaker than the electrical one. The remainder exceptional quality and very low residual resistivity can be of this paper will first discuss microwave spectroscopy on grown. These virtues of heavy fermions as model systems heavy fermions addressing the charge response and later for correlated metals go hand in hand with an experimental microwave experiments that address the magnetic moments challenge: the small characteristic energy scales require that (via magnetic resonance). experiments be performed at very low temperatures, on the scale of 1 K or even on the mK scale, i.e., in dilution 2 Microwave spectroscopy Microwave spectro- refrigerators. Also, spectroscopic measurements have to be scopy on metals at cryogenic temperatures has remained an performed on these small energy scales, well below 1 meV experimental challenge. One reason is that for frequencies (1 K 86 meV 21 GHz). below the plasma edge, metals reflect almost 100% of These requirements can only be met by a few spectro- impinging light, and the difference to a reflectivity of unity is scopic techniques. In particular photoemission spec- the quantity that has to be determined and contains the troscopy, which otherwise is extremely helpful in information about the material under study [9]. With understanding the electronic properties of correlated metals decreasing frequency, the reflectivity of a metal increases, and which has been used successfully to study heavy- and at microwave frequencies the reflectivity typically fermion materials at higher energies and temperatures [5], exceeds 99%, which is very hard to measure with respect to cannot directly access many of the most interesting heavy- a 100% reference. Another difficulty arises from the large fermion states because it does not have sufficient energy wavelength of microwaves. This prevents the use of free- resolution and is incompatible with mK temperatures and space propagation and windows to send the signal to a the application of magnetic fields or pressure. Recently, sample in a cryostat. Instead, the microwaves have to scanning tunneling spectroscopy has managed to reach propagate in confining structures such as waveguides or sufficiently low temperature and energy resolution. This has coaxial cables. These cause substantial signal losses, which lead to studies of several heavy-fermion compounds at depend on frequency and temperature, and as such are temperatures of a few K [6–8], and corresponding studies at difficult to calibrate during the experiment. mK temperatures have become feasible. The traditional approach to overcome these difficulties Another rather direct energy-resolved access to the are cavity resonators [11]. If these have very high quality electronic properties of solids is optical spectroscopy [9, 10]. factors Q even in the presence of the sample, then the Incoming light directly interacts with the charges that are enhanced interaction between microwave and sample (of present in a sample, and therefore one can obtain information order Q compared to a single-bounce reflection measure- about the electronic properties of a material by measuring its ment) leads to measurable effects even for samples with optical properties. One big advantage of optical spec- rather low losses. Furthermore, the relevant observables are troscopy is that the probing energy can be adjusted to any the resonator frequency and the resonance linewidth, which relevant energy scale of a solid by choice of the appropriate are independent of the losses of the cables and therefore spectral range. Furthermore, optical spectroscopy can be rather robust quantities. Already since the 1980s, heavy- combined with low temperatures, high magnetic fields, and fermion materials have been studied with cavity resonators, high pressure (although these parameters might complicate and this has lead to the first experimental observations of the the experimental effort substantially). The most common slow Drude response of heavy fermions at GHz frequencies spectral range to study correlated metals with optics is the [12–14]. Cavity resonators are a very generic approach that infrared [10], typically covering photon energies 5 meV allows microwave measurements on very different material to 1 eV with Fourier transform spectrometers. For the classes, but there are two main drawbacks: firstly, because next lower spectral range, THz techniques are used which of geometric reasons (the sample is usually only a weak typically have photon energies down to a few hundred perturbation of the cavity fields, and the geometry of the meV. To optically probe a material with photon energies sample in the cavity has to be known to great detail for data of 100 meV and below, microwave techniques have to be analysis) it is difficult to obtain precise absolute values employed. Such experiments have to be performed in a of the microwave conductivity of the sample, in contrast fundamentally different manner than conventional optics: to relative changes, e.g., as a function of temperature or the wavelength of microwaves is so long (1 cm for frequency magnetic field [15]. The second drawback is that with 30 GHz 124 meV) that the light cannot be manipulated
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