Magnetic states of coupled spin tubes with frustrated geometry in CsCrF4

Abstract

Abstract When a theoretical model is realized in nature, small perturbation terms play important roles in the selection of the ground state in geometrically frustrated magnets. In case of a triangular spin tube, the two-dimensional network of the inter-tube interaction forms characteristic lattices. Among them Kagome-Triangular (KT) lattice is known to exhibit an enriched phase diagram including various types of non-trivial structures: non-coplanar cuboc structure, coplanar 120° structure with the two-dimensional propagation vector of $${\boldsymbol{k}}_{2\mathrm{D}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:math> = (0, 0), $$\sqrt 3 \times \sqrt 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> <mml:mo>×</mml:mo> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> </mml:mrow> </mml:math> structure with $${\boldsymbol{k}}_{2{\mathrm{D}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mstyle> <mml:mi>D</mml:mi> </mml:mstyle> </mml:mrow> </mml:msub> </mml:math> = (1/3, 1/3), and incommensurate structure. We investigate the magnetic state in the model material CsCrF 4 by using neutron diffraction technique. Combination of representation analysis and Rietveld refinement reveals that a very rare structure, i.e., a quasi-120° structure with $${\boldsymbol{k}}_{2{\mathrm{D}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mstyle> <mml:mi>D</mml:mi> </mml:mstyle> </mml:mrow> </mml:msub> </mml:math> = (1/2, 0), is realized at the base temperature. The classical calculation of the phase diagram elucidates that CsCrF 4 is the first experimental realization of the KT lattice having ferromagnetic Kagome bond. A single-ion anisotropy and Dzyaloshinskii-Moriya interaction play key roles in the selection of the ground state. Furthermore, a successive phase transition having an intermediate state represented by $${\boldsymbol{k}}_{2{\mathrm{D}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mstyle> <mml:mi>D</mml:mi> </mml:mstyle> </mml:mrow> </mml:msub> </mml:math> = (1/3, 1/3) is observed. The intermediate state is a partially ordered 120° structure which is induced by thermal fluctuation.