Ferromagnetic Order of Reduced Magnetic Moments in a Frustrated Sawtooth Chain of the Magnetic Semiconductor ZnYb$_2$S$_4$

Abstract: In a sawtooth spin chain, competing nearest- and next-nearest-neighbor interactions suppress long-range order, yielding novel quantum states such as a spin-dimer singlet, 1/2 magnetization plateau, and spin contraction. Here, we investigate the magnetic properties of the orthorhombic semiconductor ZnYb$2$S$_4$, in which Yb$^{3+}$ ions with an effective spin-1/2 form a sawtooth chain along the $b$-axis. The specific heat exhibits a sharp peak at ${T}{\rm m}$ $=$ 1.4 K, at which the magnetic entropy $S_{\rm m}$ reaches only 27% of $R$ln2. This reduced $S_{\rm m}$ at $T_{\rm m}$ indicates the entropy release of the ground state doublet of Yb$^{3+}$ even for $T$ $>$ $T_{\rm m}$. The isothermal magnetization $M(B)$ at 0.28 K exhibits hysteresis for $\left|B\right| \leq 0.2$ T and increases monotonically for $B > 0.2$ T. The spontaneous magnetization is only 0.1 ${\it μ}{\rm B}$$/$Yb, an order of magnitude smaller than that expected for the ground state doublet of Yb$^{3+}$. Moreover, in powder neutron diffraction measurements, no superlattice reflections due to antiferromagnetic order are observed for $T$ $<$ $T{\rm m}$. Therefore, in the ground state, the Yb moments are ferromagnetically aligned, but their amplitude is reduced by magnetic frustration in the sawtooth Yb chain.

• The paper reveals a frustrated sawtooth chain in ZnYb2S4 where ferromagnetic order emerges with significantly reduced Yb3+ moments.
• It employs synthesis, powder diffraction, and magnetic measurements to detail anisotropic exchange effects and marked entropy suppression.
• Results challenge classical models by showing the absence of expected magnetization plateaus and suggesting the role of additional inter-chain interactions.

Ferromagnetic Order of Reduced Magnetic Moments in Frustrated Sawtooth Chains of ZnYb$_2$S$_4$

Introduction and Motivation

Geometric frustration in quantum spin systems continues to be a central topic for research into emergent quantum states such as spin-dimer singlets, magnetization plateaus, and quantum spin liquids, particularly in systems with strong spin-orbit coupling and significant crystalline electric field (CEF) effects. Rare-earth-based compounds with effective spin-1/2 moments, notably those involving Yb$^{3+}$ ions, provide novel platforms for investigating highly anisotropic exchange physics and unconventional ground states. The sawtooth spin chain, characterized by competing nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) exchange interactions, furnishes a unique 1D motif for studying frustration-induced phenomena. The extensive theoretical literature predicts a range of ground states—antiferromagnetic (AFM), spin-dimer, and noncollinear orders—dependent on the ratio $J_2/J_1$, including magnetization plateaus and spin contraction effects, yet robust experimental realizations in $4f$-electron sawtooth chain systems remain absent.

Experimental Approach

Polycrystalline ZnYb$_2$S$_4$ was synthesized by a solid-state reaction and structurally characterized via powder X-ray diffraction and EPMA, confirming the olivine-type orthorhombic ($Pnma$) lattice and a sawtooth chain formation along the $_4$0-axis involving two crystallographically distinct Yb sites. Magnetic susceptibility measurements, specific heat analysis, isothermal magnetization, and powder neutron diffraction were conducted across low temperatures and variable magnetic fields to probe the magnetic ground state and frustration effects.

Crystal Field Effects and Spin-1/2 Realization

Magnetic susceptibility fitting yields an effective moment per Yb$_4$1 (4.78 $_4$2/Yb) consistent with the free-ion value, and a negative Curie-Weiss temperature ($_4$3 K) indicative of dominant AFM correlations. CEF analysis demonstrates a well-isolated $_4$4 Kramers doublet ground state, separated via cubic CEF from excited multiplets, confirming the effective spin-1/2 character at low temperature with an expected saturation moment of $_4$5/Yb.

Frustration Signatures in Specific Heat and Magnetic Entropy

Specific heat $_4$6 reveals a sharp peak at $_4$7 K, signaling a magnetic phase transition, with the accompanying magnetic entropy $_4$8 constituting only 27\% of $_4$9. This strong suppression relative to the expected doublet entropy highlights substantial frustration and partial entropy release well above $^{3+}$0. Under applied magnetic fields, the transition peak broadens and shifts to higher temperature, consistent with suppression of frustration by external fields.

Isothermal Magnetization and Hysteresis

At $^{3+}$1 K ($^{3+}$2), $^{3+}$3 exhibits clear hysteresis for $^{3+}$4 T, reflective of ferromagnetic ordering, but the spontaneous magnetization (0.1 $^{3+}$5/Yb) is an order of magnitude smaller than the CEF-predicted value. For $^{3+}$6 T, $^{3+}$7 increases monotonically, saturating at 1.1 $^{3+}$8/Yb at 9 T. Notably, no 1/2 magnetization plateau—theoretically anticipated for AFM sawtooth chains—is observed, suggesting deviations from classical sawtooth models attributable to severe frustration or additional exchange couplings.

Neutron Diffraction and Magnetic Structure

Powder neutron diffraction patterns at $^{3+}$9, $J_1$0, and $J_1$1 K display no superlattice reflections characteristic of AFM ordering for $J_1$2. Instead, a slight enhancement at select Bragg peaks and absence of significant lattice modulations point to ferromagnetic alignment with substantially reduced moment amplitudes. The limited intensity is compatible with uniform ferromagnetic arrangements, but unambiguous magnetic structure determination remains hampered by powder averaging and signal limitations.

Interpretation: Frustrated Ferromagnetic Ground State

The ground state of ZnYb$J_1$3S$J_1$4 is thus characterized by ferromagnetically aligned Yb moments within the sawtooth chain, yet their magnitude is strongly reduced by frustration. This distinguishes ZnYb$J_1$5S$J_1$6 phenomenology from predicted AFM, spin-dimer, or plateau states for the pure sawtooth chain. The reduction of moment amplitude and entropy suppression underscores the complexity of frustration effects, likely involving inter-chain couplings or beyond nearest-neighbor interactions absent from idealized models. Observations parallel the reduced moment formation in frustrated zigzag chain systems (e.g., YbCuS$J_1$7) but exhibit distinct uniform ferromagnetic order.

Implications and Future Directions

Practically, the findings establish ZnYb$J_1$8S$J_1$9 as a unique platform for exploring quantum frustration in $J_2$0-electron sawtooth chains. Theoretically, the reduced ferromagnetic order juxtaposed with AFM correlations challenges conventional interpretations of sawtooth chain physics and suggests reevaluation of model Hamiltonians to incorporate anisotropic exchange, multi-chain effects, and CEF-driven spin-orbit coupling. The absence of anticipated magnetization plateaus further motivates refinement in frustrated spin chain theory. Future research should pursue single-crystal neutron diffraction, ESR, and NMR studies to resolve microscopic spin correlations, anisotropy, and excitation spectra, enabling precise mapping of the exchange landscape and ground-state wavefunctions.

Conclusion

ZnYb$J_2$1S$J_2$2 exemplifies a frustrated sawtooth chain system wherein strong spin-orbit coupling and CEF isolation yield ferromagnetic order of markedly reduced Yb$J_2$3 moments. Enhanced thermodynamic and magnetic characterization demonstrates entropy suppression, hysteretic magnetization, and absence of conventional AFM order—each a signature of acute frustration effects. The results underscore the necessity for advanced theoretical models and further experimental scrutiny to fully elucidate the interplay between geometric frustration and quantum magnetism in $J_2$4-electron lattices.