Field-induced phase transitions and anisotropic magnetic properties of the Kiteav-Heisenberg compound Na$_2$Co$_2$TeO$_6$

Spin systems with honeycomb structures have recently attracted a great deal of attention in connection with the Kitaev quantum spin liquid state (QSL) predicted theoretically. One possible Kitaev QSL candidate is Na$_2$Co$_2$TeO$_6$ realizing a honeycomb lattice of pseudo-spin-1/2. Field-dependent single-crystal neutron diffraction technique allows us to determine the microscopic spin-spin correlations across the field induced phase transitions for H//a and H//a* in plane field directions. Our results reveal phase transitions, initially to a canted zigzag antiferromagnetic state at approximately 60 kOe, followed by a possible transition to a partially polarized state over the range of 90-120 kOe, and finally to a field-induced fully polarized state above 120 kOe. We observe distinct field dependencies of the magnetic peak intensities for H//a and H//a*. In addition, low-temperature electron spin resonance in magnetic fields H//c yields a complete softening for one of the antiferromagnetic resonances at ~ 40 kOe, revealing a field-induced phase transition. The present work, thus, provides new insights into the field evolution of the important Kitaev-Heisenberg spin system Na$_2$Co$_2$TeO$_6$.