Peter M. Gehring

The unexpected discovery of ordered magnetism in two-dimensional van der Waals materials at the monolayer limit [B. Huang , ] challenges the Mermin-Wagner theorem [N. D. Mermin and H. Wagner, ], which forbids spontaneous breaking of continuous symmetries in two dimensions at finite temperatures. The persistence of static magnetism in low dimensions is fundamentally influenced by magnetic anisotropy which is tied to the local single-ion crystalline electric field. Crucially, spin-orbit coupling connects the structural properties with spin degrees of freedom. We investigate the magnetic single-ion properties in the two-dimensional van der Waals magnet VI 3 . Utilizing neutron and x-ray diffraction, we map out the symmetry breaking phase transitions in VI 3 and argue for the presence of a single structural transition at T S ∼ 80 K, driven by an orbital degeneracy, followed by a ferromagnetic transition at a lower temperature, T C ∼ 50 K. Through a comparative analysis of samples prepared under varying conditions, we suggest that lower temperature transitions reported near ∼ 30 K are not intrinsic to VI 3 . A group theoretical analysis suggests a structural transition from rhombohedral R 3 ¯ to triclinic P 1 ¯ or P 1 . This transition is significant as it suggests the formation of two distinct crystallographically inequivalent V 3 + sites on the honeycomb lattice, each with distinct spin-orbital properties. Neutron spectroscopy provides evidence for dominant magnetic exchange coupling only between symmetry-equivalent sites in the triclinic unit cell. We suggest this breaks up the low-temperature two-dimensional honeycomb VI 3 lattice into two interpenetrating approximately hexagonal planes resulting in a fragmentated honeycomb. Our findings highlight the critical role of magnetoelastic coupling in determining the magnetic and structural phases in two-dimensional van der Waals magnets.

Single crystal spinel CoFe ₂ O ₄ exhibits the largest room‐temperature saturation magnetostriction among non‐rare‐earth compounds and a high Curie temperature ( K), properties that are critical to a wide range of industrial and medical applications. Neutron spectroscopy reveals a large band splitting (∼60 meV) between two ferrimagnetic magnon branches, which is driven by site mixing between Co ²⁺ and Fe ³⁺ cations, and a significantly weaker magnetocrystalline anisotropy (∼3 meV). Central to this behavior is the competition between vast mismatched molecular fields on the tetrahedral A ‐site and octahedral B ‐site sublattices and the single‐ion anisotropy on the B ‐site. This creates a strong, energetic anisotropy that locks the magnetic moment within each structural domain in place. As a result of these differing energy scales, switching structural domains is energetically favored over a global spin reorientation under applied magnetic fields, and this is what amplifies the magnetostrictive nature of CoFe ₂ O ₄ .

Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of ∼100 μ m whereas usual surface layers only extend over a few unit cells (or ∼nm). We present a muon spectroscopy study of Pb(Fe _{1/2} Nb _{1/2} )O₃ (PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe³⁺ ( S = 5 / 2 , L ≈ 0) ions, PFN has been characterized as a unique example of a ‘cluster spin-glass’. We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm³ crystal of PFN. Zero-field positive muon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe³⁺ spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe³⁺ relaxation rates as a function of muon implantation depth in our single crystal. Using negative muon elemental analysis, we find small-to-no measurable change in the Fe³⁺/Nb⁵⁺ concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics.

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting t...

Manley et al. (Science Advances, 16 September 2016, p. e1501814) report the splitting of a transverse acoustic phonon branch below T_C in the relaxor ferroelectric Pb[(Mg_1/3Nb_2/3)_1−xTi_x]O₃ with x = 0.30 using neutron scattering methods. Manley et al. argue that this splitting occurs because these phonons hybridize with local, harmonic lattice vibrations associated with polar nanoregions. We show that splitting is absent when the measurement is made using a different neutron wavelength, and we suggest an alternative interpretation.