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Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long-range magnetic order in the family of pyrochlore iridates. As a consequence, Pr2Ir2O7 lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits an array of complex phenomena including the Kondo effect, biquadratic band structure, and metallic spin liquid. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning, density functional theory and theoretical modeling, we probe the local electronic states in Pr2Ir2O7 and find an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. These spatial nanoscale patterns display a fractal geometry with power-law behavior extended over two decades, consistent with being in proximity to a critical point. Our discovery reveals a nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration. 

Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long-range magnetic order in the family of pyrochlore iridates. As a consequence, Pr₂Ir₂O₇lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits an array of complex phenomena including the Kondo effect, biquadratic band structure, and metallic spin liquid. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning, density functional theory and theoretical modeling, we probe the local electronic states in Pr₂Ir₂O₇and find an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. These spatial nanoscale patterns display a fractal geometry with power-law behavior extended over two decades, consistent with being in proximity to a critical point. Our discovery reveals a nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration.

 

Search for novel electronically ordered states of matter emerging near quantum phase transitions is an intriguing frontier of condensed matter physics. In ruthenates, the interplay between Coulomb correlations among the 4delectronic states and their spin-orbit interactions, lead to complex forms of electronic phenomena. Here we investigate the double layered Sr₃(Ru_1−xMn_x)₂O₇and its doping-induced quantum phase transition from a metal to an antiferromagnetic Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope, we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap at the Fermi energy that develops with doping to form a weak Mott insulating state. Near the quantum phase transition, we discover a spatial electronic reorganization into a commensurate checkerboard charge order. These findings bear a resemblance to the universal charge order in the pseudogap phase of cuprates and demonstrate the ubiquity of charge order that emanates from doped Mott insulators.

 

Novel electronic phenomena frequently form in heavy-fermions because of the mutual localized and itinerant nature of f -electrons. On the magnetically ordered side of the heavy-fermion phase diagram, f -moments are expected to be localized and decoupled from the Fermi surface. It remains ambiguous whether Kondo lattice can develop inside the magnetically ordered phase. Using spectroscopic imaging with scanning tunneling microscope, complemented by neutron scattering, x-ray absorption spectroscopy, and dynamical mean field theory, we probe the electronic states in antiferromagnetic USb 2 . We visualize a large gap in the antiferromagnetic phase within which Kondo hybridization develops below ~80 K. Our calculations indicate the antiferromagnetism and Kondo lattice to reside predominantly on different f -orbitals, promoting orbital selectivity as a new conception into how these phenomena coexist in heavy-fermions. Finally, at 45 K, we find a novel first order–like transition through abrupt emergence of nontrivial 5 f -electronic states that may resemble the “hidden-order” phase of URu 2 Si 2 .