Symmetry and magnetic field driven transitions in the 2D triangular lattice compound RbFe(MoO4)2

Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups

A magnetic superspace group (MSSG) simultaneously constrains both the magnetic and non-magnetic (e.g. displacive, occupational, rotation and strain) degrees of freedom of an incommensurately modulated magnetic crystal. We present the first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent incommensurate modulations, along with a number, symbol and reference setting for each group. We explain the process for generating an exhaustive set of inequivalent magnetic superspace groups, describe several examples, and show how the tables can be accessed via the ISO(3+d)D interface within the ISOTROPY Software Suite. We recommend that published incommensurate magnetic structures indicate a magnetic superspace-group number and symbol from these tables, as well as the transformation matrix from the published group setting to the reference setting used in these tables.

Magnetic Ground State Crossover in a Series of Glaserite Systems with Triangular Magnetic Lattices

The magnetic properties are reported for three members of the glaserite series of compounds, Na₂BaM(VO₄)₂, M = Mn, Mn_0.6Co_0.4, and Co. Large single crystals are grown using a high-temperature hydrothermal synthesis method. This structure type exhibits a triangular magnetic lattice in which M²⁺O₆ octahedra are interconnected with nonmagnetic (VO₄)^3- groups. All the structures crystallize at room temperature with rigid trigonal symmetry (space group P3̅ m1); however, at lower temperatures both Na₂BaMn(VO₄)₂ and Na₂BaMn_0.6Co_0.4(VO₄)₂ undergo a structural transition to lower symmetry (monoclinic, C2/ c). The bulk magnetic measurements indicate that Mn- and Co-structures are antiferromagnetic and ferromagnetic, respectively. Na₂BaMn_0.6Co_0.4(VO₄)₂ does not show any long-range ordering down to 0.5 K, although a broad heat capacity anomaly near 1.2 K suggests short-range magnetic order or freezing into a spin-glass-like state related to the chemical disorder and resulting competing magnetic interactions. The magnetic structures of Na₂BaMn(VO₄)₂ and Na₂BaCo(VO₄)₂ were determined using neutron powder diffraction. At zero magnetic field, Na₂BaMn(VO₄)₂ possesses an antiferromagnetic structure with the moments ordered in a Néel-type arrangement and aligned along the C₄ axis of the octahedra. Under applied magnetic field at 0.3 K, the evolution of the magnetic structure toward a fully polarized state is observed. Na₂BaCo(VO₄)₂ represents a ferromagnetic (FM) magnetic structure with Co moments aligned parallel to the c-axis direction. The relationships between these structures and magnetic properties are discussed.

Magnetic superspace groups and symmetry constraints in incommensurate magnetic phases

Superspace symmetry has been for many years the standard approach for the analysis of non-magnetic modulated crystals because of its robust and efficient treatment of the structural constraints present in incommensurate phases. For incommensurate magnetic phases, this generalized symmetry formalism can play a similar role. In this context we review from a practical viewpoint the superspace formalism particularized to magnetic incommensurate phases. We analyse in detail the relation between the description using superspace symmetry and the representation method. Important general rules on the symmetry of magnetic incommensurate modulations with a single propagation vector are derived. The power and efficiency of the method is illustrated with various examples, including some multiferroic materials. We show that the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structural and physical properties of incommensurate magnetic materials. This is especially relevant when the properties of incommensurate multiferroics are investigated.