Single-crystal growth and magnetic, magnetoelectric, and optical properties of ferroaxial-type SrMn$_2$Ni$_6$Te$_3$O$_{18}$

1. Problem Statement and Motivation

• Context: Ferroic orders (ferroelectricity, ferromagnetism) and more exotic orders like ferrotoroidal (FT) and ferroaxial (FA) orders are crucial for advanced electromagnetic technologies. FA order involves rotational distortions of structural units that break rotational symmetry while preserving spatial inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries.
• Gap in Knowledge: While the $AB_2C_6Te_3O_{18}$ family of oxides (where $A$=Pb, Sr; $B$=Mn, Cd; $C$=Ni, Co) is known to host FA-type structural distortions, the interplay between this FA distortion and magnetic ordering remains poorly understood. Specifically, the magnetic properties of SrMn$_2$Ni$_6$Te$_3$O$_{18}$ (SrMNTO) had not been investigated despite the presence of magnetic Mn$^{2+}$ and Ni$^{2+}$ ions.
• Objective: To synthesize high-quality single crystals of SrMNTO, characterize their FA domain structure, determine the magnetic ground state, and systematically investigate the resulting magnetoelectric (ME) and optical responses to understand the coupling between FA structural distortion and magnetism.

2. Methodology

The study employed a comprehensive suite of experimental techniques:

• Synthesis:
  • Polycrystals: Synthesized via solid-state reaction of SrCO$_3$, MnCO$_3$, NiO, and TeO$_2$ at 1123 K.
  • Single Crystals: Grown using a TeO$_2$ self-flux method (molar ratio Sr:Mn:Ni:Te = 1:3:5:5) with slow cooling from 1323 K to 1223 K.
• Structural Characterization:
  • X-ray Diffraction (XRD): Used for phase purity and crystallographic orientation (identifying the long axis as [001]).
  • FA Domain Imaging: Utilized a linear electrogyration (EG) imaging technique. By applying an electric field ($E$) and measuring the induced optical rotation ($\Delta I/I$), the spatial distribution of FA domains (clockwise vs. counter-clockwise rotation) was mapped.
• Magnetic & Neutron Measurements:
  • Magnetization: Measured using a MPMS3 system to determine susceptibility ($\chi_m$) and transition temperatures.
  • Neutron Powder Diffraction (NPD): Performed at JRR-3 (HERMES diffractometer) to determine the magnetic structure and propagation vector. Rietveld refinement was conducted using FullProf and SARAh.
• Magnetoelectric (ME) & Optical Measurements:
  • ME Effect: Measured electric polarization ($P$) induced by magnetic fields ($H$) after "ME cooling" (cooling through $T_N$ under applied $E_c$ and $H_c$ fields) to control domain states.
  • Nonreciprocal Directional Dichroism (NDD): Measured optical absorption differences ($\Delta \alpha$) for light propagating parallel and anti-parallel to the $c$-axis to detect antisymmetric ME components.
• Comparative Study: Limited measurements were also performed on the isostructural compound PbMn$_2$Ni$_6$Te$_3$O$_{18}$ (PbMNTO) to assess the robustness of these properties against A-site substitution (Sr vs. Pb).

3. Key Results

A. Crystal Growth and FA Domains

• High-quality, dark green, translucent single crystals (up to a few mm) were successfully grown.
• FA Domain Imaging: The EG imaging revealed that the single crystals preferentially form single ferroaxial (FA) domains. The signal ($\Delta I/I$) was uniform across the sample and reversed sign linearly with the applied electric field, confirming a single-domain state without structural phase transitions to non-FA phases.
• PbMNTO also exhibited single FA domains, suggesting this is a robust feature of the $AB_2C_6Te_3O_{18}$ family.

B. Magnetic Structure

• Transition Temperature: An antiferromagnetic (AFM) transition occurs at $T_N = 83$ K.
• Magnetic Moments: Mn$^{2+}$ and Ni$^{2+}$ moments order antiferromagnetically. The effective moment ($\mu_{eff} \approx 11.7 \mu_B$/f.u.) suggests orbital moments are largely quenched.
• Magnetic Configuration: Neutron diffraction and Rietveld refinement determined a c-axis collinear bidirector-type antiferromagnetic structure.
  • Moments are aligned parallel to the $c$-axis.
  • Within pairs of ions related by a mirror plane, moments are antiparallel.
  • The magnetic propagation vector is $q = (0,0,0)$.
• Symmetry: The magnetic point group is $6/m'$, which breaks both $\mathcal{P}$ and $\mathcal{T}$ symmetries, allowing for a linear magnetoelectric effect and a ferrotoroidal (FT) state.

C. Magnetoelectric (ME) Properties

• All three independent ME tensor components allowed by the $6/m'$ symmetry were detected:
  • Diagonal components: $\chi_{11}$ (and $\chi_{22}$) and $\chi_{33}$.
  • Antisymmetric off-diagonal component: $\chi_{12} = -\chi_{21}$.
• Anomaly in $\chi_{33}$: The component parallel to the $c$-axis ($\chi_{33}$) exhibits a unique temperature dependence:
  • It shows a peak around 75 K.
  • It undergoes a sign reversal around 50 K.
  • This behavior mirrors that of the prototypical ME material Cr$_2$O$_3$, suggesting a mechanism driven by Heisenberg exchange and spin fluctuations. The sign reversal origin is complex due to the two distinct magnetic ions (Ni and Mn) and requires further theoretical study.
• PbMNTO showed identical $\chi_{33}$ behavior, confirming the robustness of this phenomenon against Sr/Pb substitution.

D. Optical Properties (NDD)

• NDD Observation: A nonreciprocal directional dichroism ($\Delta \alpha$) was observed in the antiferromagnetic phase.
• Significance: The observation of NDD confirms the presence of the antisymmetric ME component ($\chi_{12} = -\chi_{21}$), which is a hallmark of the ferrotoroidal (FT) state. This directly links the FA structural distortion and the bidirector magnetic order to unconventional electromagnetic responses.

4. Significance and Conclusions

• Material Platform: The study establishes SrMNTO (and PbMNTO) as a robust platform for studying the interplay between ferroaxial structural distortions and magnetic order. The properties are insensitive to the A-site cation (Sr vs. Pb).
• Domain Control: The preferential formation of single FA domains in these crystals simplifies the study of symmetry-dependent phenomena, as domain averaging effects are minimized.
• Symmetry Breaking: The work confirms that the combination of FA structural rotation and bidirector-type AFM order creates a ferrotoroidal state that breaks both $\mathcal{P}$ and $\mathcal{T}$ symmetries.
• Novel Physics: The discovery of the sign reversal in $\chi_{33}$ and the observation of NDD provide experimental evidence for complex exchange-driven mechanisms in multicomponent magnetic oxides.
• Future Directions: The findings suggest that extending this research to other members of the $AB_2C_6Te_3O_{18}$ family (e.g., with Cd or Co) could yield further insights into symmetry-controlled physical phenomena.

In summary, this paper successfully bridges the gap between structural ferroaxiality and magnetic ordering in the $AB_2C_6Te_3O_{18}$ family, demonstrating that these materials host robust ferrotoroidal states with rich magnetoelectric and optical responses.