Since the original proposal by Anderson on spin liquid being a possible mechanism for high-Tc superconductivity, electrical transport in frustrated quantum spin systems has always been one of the most enticing topics in condensed matter physics. However, a majority of quantum spin ice and spin liquid candidates are good insulators, making it challenging for standard electrical transport techniques. In contrast, in the few cases of metallic frustrated spin systems, transport experiments usually lead to surprising discoveries.
In this collaborative work, through electrical transport experiments on a recently identified metallic kagome spin ice compound HoAgGe, we made another surprising discovery: There exists a time-reversal-like degeneracy for certain noncollinear ice-rule states on field-induced magnetic plateaus, which have the same energy and magnetization, but different sizes of the anomalous Hall effect (AHE). Since the AHE transforms as a pseudovector with fixed length under all magnetic group operations, the symmetry operation underlying such a degeneracy is beyond the standard paradigm of magnetic space group for classifying magnetic structures.
Through comprehensive neutron refinement and numerical search in the degenerate ice-rule manifold, we are able to nail down the spin structures of the degenerate states and to come up with a microscopic model for calculating their transport properties. Again surprisingly, we find that the degenerate spin structures have exactly the same band structure, but different Berry curvatures in momentum space, and hence different sizes of the anomalous Hall effect. Although the Berry curvature is more related to the geometric properties of the Bloch wavefunctions than to the eigenenergies, it is hard to imagine without seeing that real physical systems with identical band structures can have different Berry curvatures.
Our systematic experimental and theoretical efforts elucidated the rather subtle symmetry operation that connects the degenerate states, which critically relies on a reversal of lattice distortion in the structure of HoAgGe. Since the Berry connection inherently depends on the atomic location in a unit cell, while the latter is largely invisible to the momentum space Hamiltonian, the distortion reversal in such a quasi-symmetry operation eventually changes the size of the AHE but not the band structure.
Our work is built upon the active research in the topical areas of quantum spin ice systems and anomalous transport in noncollinear antiferromagnets, but advances these fields by cross-disciplinary findings that crucially require ingredients from both: The massive ground state degeneracy of frustrated spin systems provides a reservoir for novel noncollinear spin configurations that host characteristic anomalous transport properties. Our work also points to the special role of lattice distortion and distortion reversal in quantum spin systems. In particular, our theoretical analysis indicates that similar phenomena should generally occur in quantum spin systems with nontrivial lattice distortion and relatively weak spin-orbit coupling.
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