Stripe-Type Antiferromagnetic Phase

• Stripe-type antiferromagnetic phase is a magnetic order featuring parallel ferromagnetic spin stripes that are antiferromagnetically coupled in the transverse direction.
• It is stabilized by competing exchange interactions, anisotropy, and geometric frustration, often modeled using extended Heisenberg Hamiltonians (J1–J2–J3).
• Experimental signatures include characteristic magnetic Bragg peaks, anisotropic susceptibility, and specific heat anomalies that reveal underlying symmetry breaking and spin fluctuations.

Stripe-type antiferromagnetic (AFM) phases are characterized by the spontaneous formation of collinearly aligned ferromagnetic spin “stripes” that are antiferromagnetically coupled in the transverse direction. This motif arises in a broad class of quantum materials and model systems under conditions of geometric frustration, competing interactions, or multi-orbital degrees of freedom. Stripe-type AFM order signifies a symmetry breaking that reduces lattice rotational (e.g., C₄ to C₂) or point group symmetry and can occur in both periodic and aperiodic geometries, as well as in systems with itinerant or localized electrons, hardcore bosons, or Ising spins.

1. Fundamentals of Stripe-Type Antiferromagnetic Order

Stripe AFM order generically involves parallel chains (stripes) of spin alignment, with neighboring stripes exhibiting opposite moment direction. In canonical representations such as the square lattice J₁–J₂–J₃ Heisenberg models, stripe order is stabilized for next-nearest neighbor exchange $J_2 \gg J_1$, resulting from a nearly degenerate manifold of magnetic states in geometrically frustrated magnets. The propagation vector for stripe order in reciprocal space, such as $(\frac{1}{2}, 0, \frac{1}{2})$ (orthorhombic units), translates to stripe modulation along one axis and ferromagnetic alignment along the other, as in BaCoS₂ (Abushammala et al., 2023), BaMoP₂O₈ (Hembacher et al., 2018), and various Fe-based superconductors (Myers et al., 2024, Sapkota et al., 2014).

In triangular or honeycomb lattices, bond-dependent anisotropy, next-nearest or third-neighbor couplings, and crystal field environments can likewise drive stripe-yz or other stripe variants, often with spins locked in-plane perpendicular to selected bond axes (Xie et al., 2023, Kulbakov et al., 2021, Xing et al., 2020, Asai et al., 2017).

2. Microscopic Models and Stabilization Mechanisms

Stripe AFM phases are typically realized within Hamiltonians incorporating competing exchanges:

$$H = J_1 \sum_{\langle ij \rangle} S_i \cdot S_j + J_2 \sum_{\langle\langle ij \rangle\rangle} S_i \cdot S_j + J_3 \sum_{\langle ij \rangle_c} S_i \cdot S_j - D \sum_i (S_i^z)^2 + \cdots$$

Here, $J_1$ is the nearest-neighbor, $J_2$ the next-nearest neighbor, $J_3$ the third-neighbor (or interlayer), and $D$ the single-ion anisotropy (Abushammala et al., 2023, Hembacher et al., 2018, Asai et al., 2017). The stripe phase typically emerges when $J_2/J_1$ exceeds a critical threshold, e.g., $J_2/J_1 \gtrsim 0.55$ (quantum/mean-field) or 0.5 (classical), triggering a transition from Néel to stripe order (Erlandsen et al., 2020).

In itinerant systems, such as Fe-based pnictides and chalcogenides, Fermi surface topology, orbital differentiation (e.g., preferential filling of $d_{x^2-y^2}$ vs $d_{z^2}$), and Hund’s coupling engender stripe order by selecting particular nesting vectors or favoring electronic nematicity (Myers et al., 2024, Wang et al., 2015). In triangular and honeycomb geometries, anisotropic exchanges and crystal field splitting determine whether collinear stripes or coplanar 120° order are stabilized (Xie et al., 2023, Kulbakov et al., 2021, Xing et al., 2020).

3. Experimental Signatures and Thermodynamic Properties

Stripe-type antiferromagnetism manifests via neutron diffraction/magnetic Bragg peaks at characteristic wave vectors, anisotropic magnetic susceptibility, and specific heat anomalies. Table 1 catalogs select systems and key parameters:

Material	Propagation Vector	$T_N$	Ordered Moment
BaCoS₂	$(\frac{1}{2}, 0, \frac{1}{2})$	290 K	In-plane, $\sim$ $S=1/2$
BaMoP₂O₈	$(\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$	21 K	$1.42(9)\, \mu_B$ @ 1.5 K
Rb₁₋δFe₁.₅₋σS₂	$(0.5, 0.5, L)$, $L$ odd	450 K	$2.8\, \mu_B$/Fe
KErSe₂	$(\frac{1}{2}, 0, \frac{1}{2})$	0.2 K	$3.06\, \mu_B$/Er
KCeS₂	$(0, \frac{1}{2}, \frac{1}{2})$	0.43 K	$0.32\, \mu_B$/Ce
Ba₂NiTeO₆	$(0, 0.5, 1)$ (orthorhombic)	5.5 K	$S=1$, easy-axis along $c$

Experimental probes additionally reveal strong two-dimensional spin fluctuations near $T_N$, Schottky anomalies signaling (sub)meV-scale nearly degenerate orbital/magnetic states, and reduced ordered moments due to quantum and spin–orbit effects (Abushammala et al., 2023, Hembacher et al., 2018, Xing et al., 2020).

4. Stripe Phases in Strongly Correlated Electron and Bosonic Systems

Stripe phases are foundational in quantum doped antiferromagnets, where charge carriers self-organize into partially-filled, π-shifted domain walls that disrupt AFM correlations—seen in both the fermionic and bosonic t–J models (Harris et al., 2024). Density Matrix Renormalization Group calculations find partially-filled vertical stripes for $0 < \delta < \delta^{*}_{PP}$ (e.g., $\delta^*_{PP} \approx 0.12$ for $t/J = 3$ in bosonic systems). Here, holes maximize kinetic energy along the stripes by mitigating frustration at the cost of AF superexchange, while spin and charge structure factors reveal peaks at incommensurate wave vectors indicative of stripe period and spin modulation.

In the bosonic case, stripes differ qualitatively from their fermionic analogs: absence of bound pair formation along stripes, more robust coherence due to bosonic statistics, and a direct tuning of stripe filling with $t/J$ (Harris et al., 2024).

5. Stripe Order in Quasiperiodic and Frustrated Lattices

Geometric frustration and local environment effects in aperiodic (e.g., Ammann–Beenker) quasicrystals induce stripe-type order with novel symmetry breaking (Teixeira et al., 12 Jun 2025). For $J_2/J_1 > 0.8$ in the $J_1$–$J_2$ Ising model, long-range stripe order appears, but is softened by competing domains nucleated at coordination-$z=8$ sites. Table 2 summarizes critical temperatures:

$J_2/J_1$	$T_N/J_1$ (Néel)	$T_S/J_1$ (stripe)
0.50	1.223(4)	–
1.00	–	0.14(1)
2.00	–	0.84(3)

The stripe order parameter is defined via Fourier components at symmetry-related modulation vectors, and residual ground-state entropy signals the retention of domain flexibility at $z=8$ sites. Critical exponents for the stripe phase deviate modestly from standard universality classes, reflecting the modified criticality on quasiperiodic backgrounds.

6. Two-Dimensionality, Competing Phases, and Electronic Nematicity

The stripe phase exhibits a fluctuation regime governed by dimensionality and proximity to other magnetic/orbital configurations. In BaCoS₂, two-dimensional thermal fluctuations dominate, and the transition is “purely electronic,” with magnetic entropy substantially reduced compared to the expected $R\ln2$ for localized $S=1/2$ moments (Abushammala et al., 2023). Competing checkerboard or ferromagnetic phases are energetically close (within $\lesssim$ 1 meV), enhancing susceptibility to disorder and external perturbations.

In FeSe and related pnictides, stripe order is the ground-state configuration for accurate exchange–correlation functionals (e.g., $r^2$SCAN meta-GGA), with unreported interlayer couplings of order 1–2 meV/atom, confirming the necessity of constraint-based DFT for resolving intricate multi-orbital magnetic energetics (Myers et al., 2024).

7. Stripe-Type AFM and Spin-Fluctuation-Mediated Superconductivity

In proximity-coupled systems, stripe-phase antiferromagnets can mediate attractive electron–electron interactions via their low-energy spin fluctuations (Erlandsen et al., 2020). The Schwinger boson mean-field approach reveals that the superconducting $T_c$ is maximized at an uncompensated interface and is further enhanced near the stripe–Néel boundary due to softening of bosonic modes and elevated magnon coherence factors, favoring triplet $S_z = 0$ pairing channels.

A plausible implication is that the stripe phase, by offering a highly structured low-energy spectrum and enhanced fluctuations, can serve as an optimal platform for spin-fluctuation-driven superconductivity or novel odd-parity pair states.

• “Two-dimensional fluctuations and competing phases in the stripe-like antiferromagnet BaCoS₂” (Abushammala et al., 2023)
• “Stripe order and magnetic anisotropy in the $S=1$ antiferromagnet BaMoP₂O₈” (Hembacher et al., 2018)
• “Mott localization in a pure stripe antiferromagnet Rb₁₋δFe₁.₅₋σS₂” (Wang et al., 2015)
• “Stripe Antiferromagnetic Ground-State Configuration of FeSe Revealed by Density Functional Theory” (Myers et al., 2024)
• “Lattice distortion and stripe-like antiferromagnetic order in Ca₁₀(Pt₃As₈)(Fe₂As₂)₅” (Sapkota et al., 2014)
• “Spin Dynamics in a Stripe-ordered Buckled Honeycomb Lattice Antiferromagnet Ba₂NiTeO₆” (Asai et al., 2017)
• “Stripe magnetic order and field-induced quantum criticality in the perfect triangular-lattice antiferromagnet CsCeSe₂” (Xie et al., 2023)
• “Stripe antiferromagnetic ground state of ideal triangular lattice KErSe₂” (Xing et al., 2020)
• “Stripe disorder and dynamics in the hole-doped antiferromagnetic insulator La₅/₃Sr₁/₃CoO₄” (Lancaster et al., 2013)
• “Schwinger boson study of superconductivity mediated by antiferromagnetic spin-fluctuations” (Erlandsen et al., 2020)
• “Kinetic magnetism and stripe order in the antiferromagnetic bosonic ${t-J}$ model” (Harris et al., 2024)
• “Stripe order in quasicrystals” (Teixeira et al., 12 Jun 2025)
• “Stripe-yz magnetic order in the triangular-lattice antiferromagnet KCeS₂” (Kulbakov et al., 2021)