In geometrically frustrated magnets, macroscopically degenerated ground-states in low-energy regime can be solved by small perturbations. This tells us that magnetic states at low temperatures highlights small effects such as magnetic anisotropy, exchange randomness, and site dilution. These thus play key roles in determining ground states in frustrated magnets. The equilateral triangular spin tube antiferromagnet CsCrF₄ [1,2] is a candidate for realizing a ground state sensitive to small perturbations. Magnetic Cr³⁺ ions having S = 3/2 form triangular spin tubes along the crystallographic c axis, as illustrated in Fig. 1. The tubes couple magnetically with one another and form the kagome-triangular lattice in the ab plane [3]. Neutron powder diffraction study conducted by our group identified long-range magnetic order below 2.8 K [4]. The magnetic moments form a quasi-120° structure in the ab plane. It is unique that the 120° structure propagates antiferromagnetically along the a and c axes with a magnetic propagation vector k_mag = (1/2, 0, 1/2). Discussion of ground states in the kagome-triangular lattice model suggested that the ground state of CsCrF₄ is close to the boundary on the magnetic phase diagram in the kagome-triangular lattice model [4]. This proposes that small perturbations may induce various types of magnetic states in CsCrF₄.

Fig. 1. Schematic view of the crystal structure of CsCrF₄. Red lines a indicate the nearest-neighbor interaction along the c axis. Blue and yellow lines indicate the nearest- and second-neighbor interactions in the ab plane.

To introduce small perturbations into CsCrF₄, we investigate chemical substitution effect. A magnetic Fe-substituted CsCr_1-xFe_xF₄ showed long-range magnetic order and enhancement of magnetic anisotropy [5]. In a nonmagnetic Al-substituted CsCr_1-xAl_xF₄, a weak feature of magnetic ordering was observed [5]. Hereby, we report chemical substitution effects on the magnetic ground state in CsCrF₄ [6].

We carried out neutron powder diffraction experiments on CsCr_0.94Fe_0.06F₄ and CsCr_0.98Al_0.02F₄. In both compounds, magnetic Bragg peaks indicative of the long-range magnetic order are clearly observed, as shown in Fig. 2. Most strikingly, the magnetic peaks in CsCr_0.94Fe_0.06F₄ are indexed by a propagation vector k_mag = (0, 0, 1/2), which is different symmetry from k_mag = (1/2, 0, 1/2) in the parent CsCrF₄. Magnetic structure analysis identifies that the 120° structure does not alternate in the ab plane, whereas the intratube structure is the same as in CsCrF₄. Based on the Goodenough-Kanamori rule on superexchange interactions [7,8], it is predicted that ferromagnetic (antiferromagnetic) interactions between the Cr³⁺ ions via the F^- ions turn into antiferromagnetic (ferromagnetic) interactions by the Fe³⁺ ion substitution, namely bond substitution. The identified magnetic structure, thus, means that the bond substitution by the magnetic Fe³⁺ ion modifies the intertube structure, but the intratube structure is intact.

Fig. 2. Neutron diffraction profiles for (a) CsCr_0.94Fe_0.06F₄ and (b) CsCr_0.98Al_0.02F₄ at 1.5 K. Red circles and black curves show the experimental data and simulations, respectively. Vertical bars and triangles indicate the position of the nuclear and magnetic Bragg peaks. Blue curves show the difference between the data and simulations. Insets are the determined magnetic structures.

On the contrary, in CsCr_0.98Al_0.02F₄ the observed magnetic peaks are indexed by the same propagation vector as in the parent CsCrF₄. Analyzing the magnetic structure, we find that the spin configuration in CsCr_0.98Al_0.02 is not changed drastically, even though a relative angle between three spins in the 120° structure deviates more from 120° than that in CsCrF₄. Since substituting the Cr³⁺ ion with the Al³⁺ ion creates a spin vacancy, trigonal symmetry of the 120° structure is locally broken. However, the spin vacancy only produces a small effect on the ground state of CsCrF₄, and therefore the quasi-120° structure is still realized globally in CsCr_0.98Al_0.02F₄.

In conclusion, we have studied magnetic orders in magnetic Fe- and nonmagnetic Al-substituted CsCrF₄ through the neutron powder diffraction experiment. The magnetic structure analysis reveals that the Fe-substituted sample exhibits a 120° structure having k_mag = (0, 0, 1/2), and the Al-substituted one has a quasi-120° structure having k_mag = (1/2, 0, 1/2). Importantly, the magnetic structure in CsCr_0.94Fe_0.06F₄ differs from that in the parent CsCrF₄. This result concludes that the ground state in CsCrF₄ is more sensitive to magnetic substitution rather than nonmagnetic one on the Cr site.

References

• [1] H. Manaka et al., J. Phys. Soc. Jpn. 78, 093701 (2009).
• [2] H. Manaka et al., J. Phys. Soc. Jpn. 80, 084714 (2011).
• [3] K. Seki and K. Okunishi, Phys. Rev. B 91, 224403 (2015).
• [4] M. Hagihala et al., npj Quantum Mater. 4, 13 (2019).
• [5] H. Manaka et al., J. Phys. Soc. Jpn. 88, 114703 (2019).
• [6] S. Hayashida, M. Hagihala, M. Avdeev, Y. Miura, H. Manaka, and T. Masuda, Phys. Rev. B 102, 174440 (2020).
• [7] J. B. Goodenough, Phys. Rev. 100, 564 (1955).
• [8] J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959).

Authors

• S. Hayashida, M. Hagihala^a, M. Avdeev^b, Y. Miura^c, H. Manaka^d, and T. Masuda
• ^aHigh Energy Accelerator Research Organization (KEK)
• ^bAustralian Nuclear Science and Technology Organisation (ANSTO)
• ^cSuzuka National College of Technology
• ^dKagoshima University