Materials with new or improved properties are crucial for technological development. To provide the foundation for future successful products, it is important to prepare and characterise new chemical compounds that could show unusual properties. The properties of magnetic materials are closely related to their crystal, magnetic and electronic structures. This thesis focuses on the novel synthesis and structural characterisation of a number of new ternary or pseudo-ternary silicides and germanides of manganese with iridium, cobalt or palladium. To provide a more complete picture of the complex magnetic properties, crystal and magnetic structure refinements by the Rietveld method of X-ray and neutron powder diffraction data are complemented by single-crystal X-ray diffraction, electron diffraction, magnetisation measurements and Reverse Monte Carlo simulations of magnetic short-range order. The experimental results are corroborated by first-principles electronic structure and total energy calculations.

A commensurate non-collinear antiferromagnetic structure is found for most compounds of the solid solution Mn₃Ir_1-yCo_ySi_1-xGe_x. The non-collinearity is a result of geometric frustration in a crystal structure with magnetic Mn atoms located on a three-dimensional network of triangles. The close structural similarity to the β-modification of elemental manganese, which does not order magnetically, inspired a closer theoretical comparison of the Mn₃Ir_1-yCo_ySi_1-xGe_x properties with β-Mn.

Magnetic frustration is also observed for Mn₄Ir_7-xMn_xGe₆, and is an important factor underlying the dramatic change from commensurate antiferromagnetic order to spin glass properties induced by a small variation in Mn concentration. Magnetic short-range order with dominant antiferromagnetic correlation is observed for Mn₈Pd₁₅Si₇, and results from a random distribution of Mn atoms in-between the geometrically frustrated magnetic moments on the Mn octahedra.

An incommensurate cycloidal magnetic structure, observed for IrMnSi, is stabilised by an electronic structure effect, which also accounts for the non-collinearity of the Mn₃IrSi type magnetic structure.