Microscopic Theory Revealing Dual Field-Induced Transitions in Spin-1/2 Screw-Chain Magnets

Abstract

We develop a microscopic theory for pseudospin-$\frac{1}{2}$ screw-chain compounds with spin-orbit coupling that goes beyond the phenomenological site-dependent $g$-tensor description traditionally used for XXZ-like BaCo$_2$V$_2$O$_8$ and related materials. Starting from the symmetry-allowed $JKΓ$ Hamiltonian with Heisenberg $J$, Kitaev $K$, and off-diagonal $Γ$ interactions, we show that the $Γ$ interaction naturally generates the four-sublattice pattern associated with the crystal's screw symmetry. Using the density matrix renormalization group, we identify two distinct field-induced transitions. The first is a continuous transition into an intermediate phase, where the symmetry responsible for the two-fold ground-state degeneracy is broken. The second is a first-order transition into the high-field phase, characterized by a discontinuous jump in the spin-spin correlator. Entanglement-entropy scaling confirms that the first transition belongs to the Ising critical point with the central charge $1/2$. These results establish a microscopic framework for pseudospin-$\frac{1}{2}$ screw-chain systems such as Co$^{2+}$ materials, uncover an intermediate phase whose width increases with $Γ$, and provide guidance for systematic exploration of additional field orientations and structural distortions.

Figures (4)

• Figure 1: (a) Structure of the Co$^{2+}$ (red) screw chain with the zero-field moment directions (green). The $xyz$ coordinate system is aligned with the crystallographic $abc$ axes. $\alpha=1,2,3,4$, which denote the four sublattices, are shown in each octahedron. The green arrows represent the magnetic moments in the $zx$-plane under a magnetic field $h$ applied along the $y$-axis for (b) $h < h_{c_1}$ and (c) $h > h_{c_2}$. Here, the length of the arrow and the tilt angle $\phi$ are exaggerated for visibility.
• Figure 2: DMRG results for the on-site magnetizations $\langle S^{\gamma}_j \rangle$ with $\gamma = x,y,z$ in the middle region of a $N=200$-site chain showing distinct four-sublattice patterns in three representative regions: (a) low-field ($h=1.95$), (b) intermediate-field ($h=2.10$), and (c) high-field ($h=2.60$) regions.
• Figure 3: DMRG results for $J = 2.8$ , $K = -3.3$ and $\Gamma = 2$ as a function of the external field $h$ with $N = 800$ sites. (a) Energy susceptibility $\chi^e_h$ where the purple and pink dashed lines mark the transitions at $h_{c_1}=2.03$ and $h_{c_2}=2.54$, respectively. The inset shows the first derivative of energy indicating the first order transition at $h_{c_2}$. (b) Spin-spin correlator $\langle S^y_{1} S^y_j \rangle$ near the transitions as a function of $j$: $h (=1.95) <h_{c_1}$, $h_{c_1} < h (=2.10) < h_{c_2}$, and $h (= 2.60) > h_{c_2}$. (c) Spin-spin correlator $\langle S^y_{1} S^y_{n=100} \rangle$ taken at the central unit cell with $\alpha = 1-4$, i.e., $j=401-404$ as a function of the field. Note the sharp drop at $h_{c_2}$, indicating the first order transition consistent with the first derivative of the ground state energy shown in the inset of (a).
• Figure 4: DMRG results for the von Neumann entanglement entropy $S_{vN}$ as a function of the chain size $N$ for various values of $h$ near $h_{c_1}$. At $h = h_{c_1}$, it scales as $\ln(N/\pi)$ with central charge $c = 1/2$, indicating the Ising critical point, whereas its deviation at other fields indicates a finite gap. The inset shows the longitudinal spin--spin correlator $\langle S_1^l S_j^l \rangle$ for the $\alpha=1$ sublattice at $h = h_{c_1}$, showing power-law behavior with the exponent $\eta=1/4$.