New Insights into Magnetization Dynamics in Multiferroics: Role of Two-Dimensional Correlations in Three-Dimensional TbMnO₃ and DyMnO₃

In the multiferroic manganites such as TbMnO₃, DyMnO₃and GdMnO₃, frustration, either geometric or that arising from competing microscopic interactions, is known to have a major effect in determining the phase diagram of the material [1,2]. Additionally, the complex incommensurate and cycloidal structures underlying the multiferroicity arise from freezing out of certain dynamical modes. The study of temperature dependence of Electron paramagnetic resonance (EPR) linewidth ΔH(T) provides valuable information about spin dynamics. For example, in TbMnO₃ [3] and DyMnO₃[4] EPR studies showed the presence of frustrated magnetism and strong, short range antiferromagnetic fluctuations much above the antiferromagnetic transition temperature T_N. It turns out that the analysis of ΔH(T) requires fitting the data to an appropriate model. In the EPR studies on TbMnO₃ and DyMnO₃, following reference [5] , the ‘spin freezing model’, where ΔH(T) = A exp[ - (T-T_s)/T₀] + mT + ΔH₀, where A is a proportionality constant, T_S is the critical transition temperature, e.g., T_N, and T₀ is an empirical constant, was used to fit the experimental data. mT and ΔH₀account for linear T-dependence and T-independent value of the line width. However, the fits reported in the papers do not appear to be very good. In a recent detailed study of EPR ΔH(T) in certain doped rare earth perovskite manganites we showed [6] that a more appropriate model to use is the Berezinskii-Kosterlitz-Thouless (BKT) model which takes in to account the possibility that the correlations could be two-dimensional, either due to the nature of the exchange interactions in the material or/and due to the effect of the applied magnetic field. According to this model, ΔH(T) = ΔH_∞exp [3b/√(T/T_BKT -1)] + mT+ ΔH₀, where T_BKT is the BKT transition temperature, ΔH_∞ is a constant, b takes the value of <i>π/</i>2 for a square lattice but has been theoretically shown to take an arbitrary value. This result has been confirmed by a number of recent studies[7]. Following this work, we reanalyse the data on TbMnO₃ and DyMnO₃, the latter in both hexagonal and orthorhombic forms and find that indeed the BKT analysis leads to significantly better fits. We summarize the results below: for TbMnO₃, the spin-freezing model fits with the parameters ΔH₀ = 320.9 (G), A = 7863.5 (G), T_N = 50 K, T₀ = 49.5 and the goodness of the fit factor R² = 0.973; whereas the BKT model fits better. According to this model ΔH_∞= 7.92 (G), m = -0.134, T_BKT = 80.99 K, ΔH₀ = 306.1 (G) and a better fit with R² = 0.996. For hexagonal DyMnO₃the spin freezing model values are ΔH₀ = 975.56 (G). A = 9866.28 (G), T_N = 79.37 K, T₀ = 24.02 and the goodness of the fit factor R² = 0.992. The BKT model fits slightly better. The parameter values are ΔH_∞ = 30.32 (G), m = -0.058, T_BKT = 53.44 K, ΔH₀ = 599.79 (G) and a slightly better fit with R² = 0.999; however, we note that for orthorhombic DyMnO₃ the spin freezing model gives a better fit with parameters ΔH₀ =1477.6 (G). A = 3069.9 (G), T_N = 70 K, T₀ = 189.69 and the goodness of the fit factor R² = 0.997. The parameters for the BKT fit are ΔH_∞ = 185.26 (G), m = -4.88, T_BKT = 16 K ΔH₀= 3263.4 (G) and a slightly poorer fit with R² = 0.994. We discuss the implications of the subtle differences in the spin dynamics as reflected in these numbers.<br/><br/>[1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, Y. Tokura, Nature 426 (2003) 55.<br/>[2] T. Lottermoser et al., Nature 430 (2004) 541.<br/>[3] N O Moreno et al., J. Magn. Magn. Mater. 310 (2007) e364–e366<br/>[4] S Harikrishnan et al., J. Appl. Phys. 104 (2008) 023902<br/>[5] E. Granado, et al., Phys. Rev. Lett. 86 (2001) 5385.<br/>[6] A. Ashoka, K.S. Bhagyashree, S.V. Bhat., Phys. Rev. B 102, (2020) 024429 and<br/>A. Ashoka, K.S. Bhagyashree, S.V. Bhat., MRS Advances, 5, (2020) 2251–2260<br/>[7] S. Chaudhuri et al., Phys. Rev. B<b>106</b>, (2022) 094416 and references cited therein.