Recently, a class of Ising anisotropic antiferromagnetic screw chain compounds ACo 2 V 2 O 8 (A =Ba,Sr) [16,17] attracts a lot of research attention. In these compounds, the easy-axis is along the chain direction (c-axis), and the intrachain exchange coupling J z ≈ 5-7 meV [18,19]. Both compounds order at fairly low temperatures (about 5 K), which implies the interchain exchange coupling J ′ ≪ J [20][21][22]. The magnetic order can be suppressed by a transverse field applied in the ab-plane [16,17]. Interestingly, the critical field values and the quantum critical behaviors are very different for fields applied along the [100] and the [110] direction [19,[23][24][25][26][27][28][29]. In BaCo 2 V 2 O 8 , separated 3D and 1D QCPs were suggested with field along the [110] direction at H 20 T [28]. For the field along the [100] direction, H C ∼ 10 T [24], much lower

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