Umbrella-coplanar transition in the triangular XXZ model with arbitrary spin

Abstract

The quantum triangular XXZ model has recently enjoyed a wealth of new theoretical results, especially in relation to the modeling of the Ba${}_3$CoSb${}_2$O${}_9$ compound. In particular, it has been understood that in a longitudinal magnetic field the umbrella (cone) phase, classically stable in all the easy-plane region of the ground-state phase diagram, is considerably reduced by the effect of quantum fluctuations. We provide more quantitative information for this phenomenon at arbitrary value of the site spin $S$, by employing the dilute Bose gas expansion, valid in the high-field regime; our results improve the available estimates of the $1/S$ expansion. We quantify the extent to which a higher spin suppresses the effect of quantum fluctuations. Besides, we show how in three-dimensional layered systems a relatively small antiferromagnetic interlayer coupling has a similar consequence of bringing back the umbrella phase in some part of the phase diagram.

8 pages, 7 figures; v2 results unchanged, title and abstract slightly modified, introduction expanded, presentation generally improved, references added, matches published version

References in corpus (11)

• Unusual ordered phases of highly frustrated magnets: a review
• Static and Dynamical Properties of the Spin-1/2 Equilateral Triangular-Lattice Antiferromagnet Ba${}_3$CoSb${}_2$O${}_9$
• Critical magnetization behaviors of the triangular and Kagome lattice quantum antiferromagnets
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• Microscopic Model Calculations for the Magnetization Process of Layered Triangular-Lattice Quantum Antiferromagnets
• Ground States of Spin-1/2 Triangular Antiferromagnets in a Magnetic Field
• Phases of triangular lattice antiferromagnet near saturation
• Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number $s$
• Real-space perturbation theory for frustrated magnets: application to magnetization plateaus
• Magnon condensation with finite degeneracy on the triangular lattice
• Magnetization process of spin-1/2 Heisenberg antiferromagnets on a layered triangular lattice

Cited by in corpus (12)

• Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$
• Survival of itinerant excitations and quantum spin state transitions in YbMgGaO${}_4$ with chemical disorder
• Magnon topology and thermal Hall effect in trimerized triangular lattice antiferromagnet
• Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation
• Field-induced decays in $XXZ$ triangular-lattice antiferromagnets
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Quantum spin state transitions in spin-1 equilateral triangular lattice antiferromagnet Na${}_2$BaNi(PO${}_4$)${}_2$
• Continuous control of classical-quantum crossover by external high pressure in the coupled chain compound CsCuCl${}_3$
• Chiral crossroads in $\mathrm{H}{\mathrm{o}}_3\mathrm{Sc}{\mathrm{O}}_6$: a tale of frustration in maple leaf lattice
• Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method
• Quantum many-body scars in the Bose-Hubbard model with a three-body constraint
• Spin Excitation Continuum in the Exactly Solvable Triangular-Lattice Spin Liquid CeMgAl11O19