Isospin magnetic texture and intervalley exchange interaction in rhombohedral tetralayer graphene

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Abstract
The tunable band structure and non-trivial topology of multilayer rhombohedral graphene lead to a variety of correlated electronic states with isospin orders—meaning ordered states in the combined spin and valley degrees of freedom—dictated by the interplay of spin–orbit coupling and Hund’s exchange interactions. However, methods for mapping local isospin textures and determining the exchange energies are currently lacking. Here we image the magnetization textures in tetralayer rhombohedral graphene using a nanoscale superconducting quantum interference device. We observe sharp magnetic phase transitions that indicate spontaneous time-reversal symmetry breaking. In the quarter-metal phase, the spin and orbital moments align closely, providing a bound on the spin–orbit-coupling energy. We also show that the half-metal phase has a very small magnetic anisotropy, which provides an experimental lower bound on the intervalley Hund’s exchange interaction energy. This is found to be close to its theoretical upper bound. The ability to resolve the local isospin texture and the different interaction energies will allow a better understanding of the phase transition hierarchy and the numerous correlated electronic states arising from spontaneous and induced isospin symmetry breaking in graphene heterostructures.

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