[Paper Review] Electronic and magnetic phase diagrams of Kitaev quantum spin liquid candidate Na$_2$Co$_2$TeO$_6$

Shengzhi Zhang, Sangyun Lee+9 more|arXiv (Cornell University)|Dec 7, 2022

Advanced Condensed Matter Physics4 citations

TL;DR

This study maps the complete temperature–magnetic field phase diagram of Na₂Co₂TeO₆, a Kitaev quantum spin liquid candidate, using magnetization, specific heat, dielectric constant, electric polarization, and magnetostriction. It identifies three field-induced magnetic phases before saturation, reveals strong magnetoelectric coupling without net electric polarization, and provides evidence favoring a zigzag spin order over a triple-Q structure at zero field, constraining the search for a Kitaev spin liquid phase.

ABSTRACT

The 3$d^7$ Co$^{2+}$-based insulating magnet \NCTO{} has recently been reported to have strong Kitaev interactions on a honeycomb lattice, and is thus being considered as a Kitaev quantum spin liquid candidate. However, due to the existence of other types of interactions, a spontaneous long-range magnetic order occurs. This order is suppressed by applied magnetic fields leading to a succession of phases and ultimately saturation of the magnetic moments. The precise phase diagram, the nature of the phases, and the possibility that one of the field-induced phases is a Kitaev quantum spin liquid phase are still a matter of debate. Here we measured an extensive set of physical properties to build the complete temperature-field phase diagrams to magnetic saturation at 10 T for magnetic fields along the $a$- and $a^*$-axes, and a partial phase diagram up to 60 T along $c$. We probe the phases using magnetization, specific heat, magnetocaloric effect, magnetostriction, dielectric constant, and electric polarization, which is a symmetry-sensitive probe. With these measurements we identify all the previously incomplete phase boundaries and find new high-field phase boundaries. We find strong magnetoelectric coupling in the dielectric constant and moderate magnetostrictive coupling at several phase boundaries. Furthermore, we detect the symmetry of the magnetic order using electrical polarization measurements under magnetic fields. Based on our analysis, the absence of electric polarization under zero or finite magnetic field in any of the phases or after...

Motivation & Objective

• To establish a complete temperature–magnetic field phase diagram for Na₂Co₂TeO₆, a candidate Kitaev quantum spin liquid material.
• To resolve the nature of magnetic phases, particularly the origin of successive field-induced transitions up to magnetic saturation.
• To investigate the role of magnetoelectric coupling and symmetry-sensitive probes like electric polarization in identifying magnetic order.
• To determine whether the zero-field ground state is a zigzag or triple-Q spin structure based on symmetry and experimental constraints.
• To characterize the order of phase transitions and entropy changes across the phase boundaries.

Proposed method

• Measured magnetic, thermodynamic, and elastic responses across a wide range of temperatures (down to 20 mK) and magnetic fields (up to 60 T) along multiple crystallographic axes (a, a*, c).
• Employed dc and ac magnetization, specific heat, magnetocaloric effect, magnetostriction, dielectric constant, and electric polarization under magnetic fields to probe phase transitions.
• Used electric polarization as a symmetry-sensitive probe to distinguish between possible magnetic ground states (zigzag vs. triple-Q) based on selection rules.
• Analyzed phase boundaries and transition order (first- or second-order) via hysteresis and entropy change analysis in magnetization and specific heat data.
• Mapped the evolution of spin gap and lattice response across phases, particularly near the transition to the spin-polarized phase (IV).
• Combined data from multiple probes to identify magnetoelectric coupling, especially the peak in dielectric constant at the III–IV phase boundary.

Experimental results

Research questions

• RQ1 What is the complete temperature–magnetic field phase diagram of Na₂Co₂TeO₆, including field-induced phases up to saturation?
• RQ2 Which magnetic order—zigzag or triple-Q—best describes the zero-field ground state, as constrained by symmetry and electric polarization measurements?
• RQ3 How strong is the magnetoelectric coupling in Na₂Co₂TeO₆, and what is the nature of the dielectric response at phase boundaries?
• RQ4 What is the microscopic origin of the three successive field-induced magnetic phases (I, II, III), and how do their spin entropies and lattice responses differ?
• RQ5 Is there evidence for a Kitaev quantum spin liquid phase in the high-field regime, and what role do Majorana excitations or electric dipoles play?

Key findings

• Three distinct field-induced magnetic phases (I, II, III) are identified before magnetic saturation at 10 T, with phase boundaries H₁ and H₂ largely independent of temperature, indicating magnetic frustration.
• The dielectric constant shows sharp peaks at all magnetic phase transitions, demonstrating strong magnetoelectric coupling despite the absence of measurable net electric polarization.
• Electric polarization measurements under zero or finite magnetic fields show no net polarization in any phase, supporting a zigzag spin structure over a triple-Q structure at zero field due to symmetry constraints.
• Phase IV, the spin-polarized state, is reached at 10 T with a continuously increasing magnetization up to 60 T, consistent with a Van Vleck contribution, and a spin gap opens with increasing field.
• A strong peak in the dielectric constant at the III–IV boundary suggests a concurrent antiferroelectric or disordered-electric phase transition, possibly linked to magnetic excitations.
• The absence of a tricritical point in H∥a but its apparent presence in H∥a* for T_N, H₂, and H₃ suggests possible first-order character or symmetry-breaking at this point, challenging conventional second-order transition models.