Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules

Abstract

In many quantum magnets, especially the rare-earth ones, the low-lying crystal-field states are not well separated from the excited ones and thus they are insufficient to describe the low-temperature magnetic properties. Inspired by this simple observation, we develop a microscopic theory to describe the magnetic physics due to the collapses of the weak crystal-field states. We find two cases in which the excited crystal-field states should be seriously included in the theory. One case is when the bandwidth of the excited crystal-field states is comparable to the crystal-field gap. The other case is when the exchange-energy gain between the low-lying and the excited crystal-field states overcomes the crystal-field gap. Both cases could drive a phase transition and result in magnetic orders by involving the excited crystal-field states. We dub the above physics 'upper branch magnetism and phase transition.' We discuss the multitude of magnetic phases and the emergent selection rules for the detection of the underlying excitations. We expect that our results will help improve the understanding of many rare-earth magnets with weak crystal-field gaps such as Tb2Ti2O7 and Tb2Sn2O7, and will also provide a complementary perspective to the prevailing local 'J' physics in 4d/5d magnets.