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Dimensionality is a critical factor in determining the properties of solidsand is an apparent built-in character of the crystal structure. However, it canbe an emergent and tunable property in geometrically frustrated spin systems.Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet,pharmacosiderite, via muon spin resonance and neutron scattering. We find thatthe spin correlation exhibits a two-dimensional characteristic despite theisotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions inthe three-dimensional cubic crystal, which we ascribe to two-dimensionalisationby geometrical frustration based on spin wave calculations. Moreover, wesuggest that even one-dimensionalisation occurs in the decoupled layers,generating low-energy and one-dimensional excitation modes, causing large spinfluctuation in the classical spin system. Pharmacosiderite facilitates studyingthe emergence of low-dimensionality and manipulating anisotropic responsesarising from the dimensionality using an external magnetic field.

Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clusters