Physical Review X published the research of Li Yuan, Peng Yingying's research group and collaborators on the candidate material of Kitaev model, sodium, cobalt, antimony and oxygen

Recently, the research group of Associate Professor Li Yuanchangping of the Center for Quantum Materials Science, School of Physics, Peking University, successfully grew large-size, high-quality Na3Co2SbO₆ single crystals.
He also studied the quantum magnetic characteristics
in crystals together with collaborators such as the research group of Assistant Professor Peng Yingying of the Center for Quantum Materials Science.
Experimental results show that Na3Co2SbO6 has some key properties of Kitaev quantum spin liquid model, and has good controllability in the outer field, which is promising to be used to find novel magnetic quantum states
.
Related research results are "Giant Magnetic In-Plane Anisotropy and.
" Competing Instabilities in Na₃Co₂SbO_6"), published online in the prestigious comprehensive physics journal Physical Review X) on
.

Kitaev quantum spin liquids have attracted a lot of attention
from researchers in recent years.
Unlike previous ideas that use isotropic magnetic interactions and geometrically frustrated lattices (such as antiferromagnetic Heisenberg models on cage lattices) to find quantum spin liquids, the Kitaev honeycomb model has a strictly solvable ground state of zero-temperature quantum spin liquids, but each set of magnetic interactions in the model has a high degree of anisotropy
.
This local anisotropy, combined with the symmetry of the lattice as a whole, prevents the generation
of magnetic length programs at low temperatures.
This feature also makes it easier for the Kitaev cellular model to form rich magnetic order states after adding other kinds of magnetic
interactions.
Therefore, it can also be considered that the implementation of Kitaev quantum spin liquid in the ideal model is the result of
the fierce competition between multiple magnetic ordered states.

The "evenly matched" competition between multiple ordered states can be compared to the unstable point
in the mechanical system.
Near the point of instability, any tiny factor that upsets the equilibrium can have physically consequences that are extremely amplified
.
In previous theoretical studies (PRL125, 047201, 2020), the crystalline material Na3_Co2SbO6 is considered to be exactly such a material, which is near the junction of ferromagnetic and antiferromagnetic order in the interaction parameter space (biased to the antiferromagnetic side, the material will appear antiferromagnetic order below 7K), And it is possible that a quantum spin-liquid phase
may exist under parameter conditions not far from this location.
Like important Kitaev model_{candidates such as Na2IrO3}and α-RuCl3, Na3Co2SbO6 has a monoclinic crystal structure with lower spatial group symmetry than ideal Kitaev cellular models
。 In the vast majority of previous studies, these materials are still approximated to have the symmetry of the Kitaev honeycomb model, including the sixfold rotational symmetry around the normal of the honeycomb plane
.

In this research work, Li Yuan's group successfully grew large-size, high-quality Na3_Co2SbO₆ single crystals
.
In particular, they found that a small number of crystals are single-domain (without twins), which can show the magnetic anisotropy
of the system's intrinsic nature.
Detailed measurements show that although the monoclinic crystal structure only causes a shape change of less than 0.
2% of the honeycomb plane, it makes the crystal produce an extremely anisotropic response to the external magnetic field at low temperatures, completely losing the six-fold rotational symmetry (Figure 1): both in terms of magnetic susceptibility and from the critical magnetic field that triggers the phase transition, the degree of magnetic anisotropy in the honeycomb plane exceeds 200%, which is 3 orders of magnitude
greater than the anisotropy of the shape.
This is just in line with the judgment that the various magnetic order competitions mentioned earlier make the system near the unstable point
.
Inspired by these results, the research group further completed a series of neutron diffraction measurements
under low temperature and external magnetic field conditions with multiple neutron scattering teams in the United States, Japan and Australia.
Experimental results verify the physical image
of magnetically ordered competition.
With the application of an external magnetic field, the system successively enters a variety of different antiferromagnetic and ferromagnetic ordered states with different wave vectors and a potential commonality (Figure 2): there is a chain-like ferromagnetic spin association
on the edge of the zigzag of the honeycomb lattice.
By increasing the temperature of the sample so that the ferroflux chains appear independent of each other, a "six-pointed star" shaped signal
in reciprocal space can be observed in neutron diffraction.
These experimental results show thatNa3Co2SbO6 possesses some of the key properties of the Kitaev quantum spin-liquid model, and has good controllability in the outer field, which is promising to be used to find novel magnetic quantum states.

To this end, relevant research groups are carrying out follow-up experimental exploration
.

Figure 1.
(left) shows the magnetic susceptibility of single-domain crystals in an in-plane magnetic field in different directions; (middle) shows a magnetic field-induced phase transition in the AB direction; (right) shows the angular distribution of the critical magnetic field with respect to the cellular lattice

Figure 2.
(left) Magnetically ordered wavevector changes behind phase transitions induced by in-plane magnetic fields in two different directions; (right) Potential commonalities of multiple magnetic orders: chain-like spin correlation along the sawtooth edge of the honeycomb lattice, which corresponds to a diffuse scattering pattern in the shape of a "six-pointed star" in reciprocal space

Xintong Li, postdoctoral fellow of the Liberal Arts Program, Yuchen Gu, undergraduate student Yuchen and doctoral student Yue Chen, School of Physics, Peking University, are co-first authors of the paper, and Yuan Li, Xintong Li, and Igor A.
Zaliznyak of Brookhaven National Laboratory are co-corresponding authors
of this paper.
X-ray diffraction and angle magnetization measurements for single-domain crystals were completed
in collaboration with Peng Yingying's research group (Ph.
D.
Xiao Lead and Zheng Xixian) and Dr.
Ye Zirong from the Public Materials Characterization Laboratory.
Neutron scattering experiments were all completed through remote experiments during the epidemic, and these experiments were strongly supported
by scientists from Oak Ridge National Laboratory in the United States, J-PARC neutron source in Japan, and Neutron Scattering Center in Australia.
The above research work was supported
by the National Key Research and Development Program of China and the National Natural Science Foundation of China.