Spectroscopic investigation of the heavy fermion problem

October 24, 2018

MPI-CPfS contributors (in alphabetical order): M. Brando, R. Daou, S. D. Edkins, S. Friedemann, C. Geibel, A. Hannaske, Z. Hüsges, C. Krellner, S. Lausberg, S. Lucas, A. P. Mackenzie, H. R. Naren, H. Pfau, S. Seiro, J. Sichelschmidt, F. Steglich, U. Stockert, O. Stockert, T. Westerkamp, S. Wirth

The heavy fermion problem, which was the main focus of the Solid State Physics department under the leadership of Frank Steglich, remains a key exemplar of the challenges of correlated electron physics. In the new PQM department, we have extended our study of heavy fermion physics, concentrating on techniques and probes that have not previously been widely applied to this class of material, and on high-profile external collaboration and use of external facilities. Angle- resolved photoemission [1], inelastic neutron scattering [2], spectroscopic scanning tunneling microscopy [3] and low temperature, field-dependent thermopower [4] have led to new insight on the temperature-dependent formation of the heavy fermion state, the mechanisms of heavy fermion superconductivity and the importance of Lifshitz transitions in field-tuned heavy fermion systems. Our world lead in the preparation of heavy fermion materials means that we anticipate a continued high-impact presence in this field.

Figure 1: The experimental ARPES spectra (lower panels) show the large Fermi surface in the large TK Kondo system YbRh2Si2, but the small one in the low TK system YbCo2Si2. In both cases the experimental results agree very nicely with the calculated ones (upper panels) [1]. — Figure 1: The experimental ARPES spectra (lower panels) show the large Fermi surface in the large TK Kondo system YbRh₂Si₂, but the small one in the low T_K system YbCo₂Si₂. In both cases the experimental results agree very nicely with the calculated ones (upper panels) [1].

Figure 1: The experimental ARPES spectra (lower panels) show the large Fermi surface in the large TK Kondo system YbRh₂Si₂, but the small one in the low T_K system YbCo₂Si₂. In both cases the experimental results agree very nicely with the calculated ones (upper panels) [1].

Figure 2: Isoenergy surfaces for B = 0 and the quasiparticle density-of-states (DOS) development in finite field in YbRh2Si2 calculated using the renormalized band method. The zero-field DOS in (a) is divided into four regions [blue (A), green (B), yellow (C), red (D)] distinguished by different topologies of the isoenergy surfaces shown in (b). In the yellow region (C), we show the jungle gym Fermi surface sheet exactly at the topological transition between B and C. (c) illustrates the magnetic field evolution of the DOS for selected fields, with the zero-field DOS in gray for comparison. Inset in (a): Energy-field map of the DOS interpolated in 1 T steps. One can assign the four energy regions and their isoenergy surfaces in (a) and (b) to the four field ranges and their Fermi surfaces [4]. — Figure 2: Isoenergy surfaces for B = 0 and the quasiparticle density-of-states (DOS) development in finite field in YbRh₂Si₂ calculated using the renormalized band method. The zero-field DOS in (a) is divided into four regions [blue (A), green (B), yellow (C), red (D)] distinguished by different topologies of the isoenergy surfaces shown in (b). In the yellow region (C), we show the jungle gym Fermi surface sheet exactly at the topological transition between B and C. (c) illustrates the magnetic field evolution of the DOS for selected fields, with the zero-field DOS in gray for comparison. Inset in (a): Energy-field map of the DOS interpolated in 1 T steps. One can assign the four energy regions and their isoenergy surfaces in (a) and (b) to the four field ranges and their Fermi surfaces [4].

Figure 2: Isoenergy surfaces for B = 0 and the quasiparticle density-of-states (DOS) development in finite field in YbRh₂Si₂ calculated using the renormalized band method. The zero-field DOS in (a) is divided into four regions [blue (A), green (B), yellow (C), red (D)] distinguished by different topologies of the isoenergy surfaces shown in (b). In the yellow region (C), we show the jungle gym Fermi surface sheet exactly at the topological transition between B and C. (c) illustrates the magnetic field evolution of the DOS for selected fields, with the zero-field DOS in gray for comparison. Inset in (a): Energy-field map of the DOS interpolated in 1 T steps. One can assign the four energy regions and their isoenergy surfaces in (a) and (b) to the four field ranges and their Fermi surfaces [4].

Unravelling the underlying physics in heavy-fermion systems continues to be a major challenge in the field of correlated electron physics. These systems are mostly intermetallic compounds containing rare-earth elements in which the mag- netic moments become screened below a characteristic temperature, the Kondo temperature T_K, due to hybridization of localized 4f electrons and conduction electrons. A central issue is how the 4f electronic degrees of freedom get involved in the Fermi surface when increasing the hybridization or when changing the temperature or applying a magnetic field. Another important question concerns magnetic ordering phenomena of incompletely screened 4f moments where the magnetic order is given by the nesting properties of the Fermi surface. We address the above issues by using different microscopic and macroscopic measurements on prototypical heavy-fermion compounds. Microscopic probes involve neutron scattering, electron spin resonance, optical spectroscopy, angle-resolved photo-electron spectroscopy (ARPES) and scanning tunneling spectroscopy at large-scale facilities and/or through high-profile external collaborations, while macroscopic measurements facilitate specialized, not widely used in-house techniques like low-temperature field-dependent thermopower. The compounds studied include among others CeCu₂Si₂, YbRh₂Si₂, YbCo₂Si₂ and CeCu_6-xAu_x.

Because of the Luttinger theorem the Fermi surface of a Kondo lattice with a Kondo temperature T_K sufficiently large to suppress magnetic order is known to include the f-electrons at low temperatures. Hence the Fermi surface is large. Suppressing T_K, increasing T , or applying a strong magnetic field is expected to expel the 4f-electrons from the Fermi surface and should therefore result in a small Fermi surface, but many aspects of this transition are unclear, both theoretically and experimentally. Especially the experimental determination of the Fermi surface in these systems is a difficult issue. Using ARPES we were recently able to disclose part of the Fermi surface in the seminal Kondo system YbRh₂Si₂, which presents a sizeable T_K, and in its small T_K counterpart YbCo₂Si₂. Comparison with appropriate calculations show that in the former one the observed Fermi surface perfectly corresponds to the large one, while in the latter one it perfectly corresponds to the small one. The observation of a large Fermi surface in YbRh₂Si₂ despite the fact that this system orders magnetically at low T, challenges the Kondo breakdown scenario proposed for this compound. Interestingly, our ARPES results on YbRh₂Si₂ revealed no change of the Fermi surface, either in size or shape, over a wide temperature range extending from well below to far above TK, which puts new constraints on and provides new insight into, how a Kondo lattice forms a coherent state upon decreasing T. On the other hand, our transport study on YbRh₂Si₂ in a magnetic field resulted in a very profound insight how the Fermi surface of a Kondo lattice is affected by a large magnetic field. Thermopower, thermal conductivity, resistivity, and Hall effect measurements as a function of magnetic field in the range up to 12 T give clear evidence of several Lifshitz transitions associated with the disappearance of part of the Fermi surface [4]. Our findings can be well explained by a renormalized band approach when including the effect of a magnetic field. The calculations predict a weakening of the Kondo effect and a large change of the Fermi surface due to the polarization of the flat 4f bands. Fig. 2 displays the density of states and the Fermi surfaces as a results of these calculations for the different magnetic field regions which are the result of the transport measurements. Hence, ARPES and transport measurements both confirm the existence of a large Fermi surface at low temperatures.

Magnetic order in heavy-fermion compounds can arise from incomplete screening of the 4f electrons, as is the case in CeCu_6-xAu_x with x > 0.1. Here the magnetic ordering wave vector is determined by the nesting properties of the Fermi surface. The quantum critical point in CeCu_6-xAu_x with TN = 0 can be tuned by Au concentration x or hydrostatic pressure p with the same quantum critical behavior in thermodynamic and transport properties. Our elastic neutron scattering experiments on CeCu_5.5Au_0.5 under pressure now demonstrate that the concentration–pressure equivalence even holds on a microscopic level [2]. The change in the magnetic ordering wave vector in CeCu_5.5Au_0.5 with pressure is shown in Fig. 3 and corresponds to the changes in the magnetic structure of CeCu_6-xAu_x with lower Au content at ambient pressure. The transitions seem to occur in first-order fashions and indicate slight changes in the nesting properties of the Fermi surface.

In addition to the physics of the normal state under studies, the superconducting state of heavy-fermion materials is a subject of considerable importance. Since the transition temperatures are relatively low, studying this physics requires the development of spectroscopies with extremely high energy resolution. As part of a long-standing international collaboration, we work on this problem with the Cornell-based group of Séamus Davis. The unique capabilities of the bespoke Cornell instruments allow energy-, position- and momentum-resolved information to be deduced from scanning tunneling spectroscopy performed over wide fields of view. Applying this to the famous heavy-fermion superconductor CeCoIn₅ allowed the measurement of the superconducting gap structure, as well as yielding previously inaccessible information about the mechanism of Cooper pairing in a heavy-fermion material [3]. Our collaborative work with the Davis group is not restricted to study of the heavy fermion problem; we also perform joint spectroscopic studies of other unconventional superconductors [5, 6], and our graduate student Stephen Edkins is based full-time at Cornell working on these and other problems of topical interest.

Figure 3: Color-coded neutron intensity map of the reciprocal (h 0 l) plane in CeCu5.5Au0.5 for pressures p = 0, 4:1, and 13:7 kbar at T < 110 mK. They show magnetic Bragg peaks at different Q positions which indicate changes in the magnetic ordering wave vector [2]. The color scales are adjusted individually for each plot to make also weak peaks visible (figure after V. Fritsch, O. Stockert, C.-L.Huang et al., Eur. Phys. J. Special Topics 224, 997 (2015)). — Figure 3: Color-coded neutron intensity map of the reciprocal (h 0 l) plane in CeCu_5.5Au_0.5for pressures p = 0, 4:1, and 13:7 kbar at T < 110 mK. They show magnetic Bragg peaks at different Q positions which indicate changes in the magnetic ordering wave vector [2]. The color scales are adjusted individually for each plot to make also weak peaks visible (figure after V. Fritsch, O. Stockert, C.-L.Huang et al., Eur. Phys. J. Special Topics 224, 997 (2015)).

Figure 3: Color-coded neutron intensity map of the reciprocal (h 0 l) plane in CeCu_5.5Au_0.5for pressures p = 0, 4:1, and 13:7 kbar at T < 110 mK. They show magnetic Bragg peaks at different Q positions which indicate changes in the magnetic ordering wave vector [2]. The color scales are adjusted individually for each plot to make also weak peaks visible (figure after V. Fritsch, O. Stockert, C.-L.Huang et al., Eur. Phys. J. Special Topics 224, 997 (2015)).

In the future we will continue working on topical unconventional superconductors and quantum critical compounds, plan to study the effect of uniaxial and hydrostatic pressure on the Fermi surface topology and the resulting magnetic order also in frustrated systems and intend to look for effects which have been mainly neglected so far in strongly correlated electron systems (like unusual crystalline-electric-field excitations or Dzyaloshinsky-Moriya interaction in the presence of Kondo and RKKY-interactions).