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In the community of magnetism, it has been generally assumed that spin glass transitions occur due to frustration from random interactions, so-called quenched disorder. However, disorder-free spin glass transitions are observed experimentally in a geometrically frustrated pyrochlore magnet. So far, there are no convincing theoretical explanations for the mechanism of this spin glass transition without quenched disorder.

A recent experiment suggested that lattice distortions play important roles in the spin glass transition on the prototypical geometrically frustrated spin glass Y2Mo2O7[1]. This lattice distortion results from the selection of the electron orbitals[2], i.e., Jahn-Teller distortion. Being motivated by the experiment, we introduced a model which includes not only the spin degrees of freedom but also the lattice distortions as dynamical variables. This model doesn’t include any quenched disorder, but both spins and lattice distortions are geometrically frustrated. We performed extensive numerical simulations for the model and analyzed a mean-field model which can be solved exactly in the infinite dimension.

In the numerical simulations[3], we found that spins and lattice distortions simultaneously freeze at a common finite temperature. Both degrees of freedom do not exhibit any long range order below the freezing temperature. In the mean-field analysis in the spherical limit using the replica method[4], we found that replica symmetry breaking appears only in the phase where both spins and lattice distortions are frozen, implying that a complex free-energy landscape is induced by the spin-lattice coupling

 

[1]P. M. Thygesen, et al., Phys. Rev. Lett. 118, 067201 (2017)

[2]KM, C. Hotta and H. Yoshino, Phys. Rev. Research 4, 033157 (2022)

[3]KM, C. Hotta and H. Yoshino, Phys. Rev. Lett. 124, 087201 (2020)

[4]KM and H. Yoshino, Phys. Rev. B 107, 054412 (2023)

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