Fig. 3: Insights into the critical behavior captured by the topological Hall effect (THE). | Nature Communications

Fig. 3: Insights into the critical behavior captured by the topological Hall effect (THE).

From: Colossal topological Hall effect at the transition between isolated and lattice-phase interfacial skyrmions

Fig. 3

a Power-law behavior of Δρ/M ≡ nsk(THE)/nsk(MFM) with effective temperature \({T}^{\prime}=T\cdot \kappa\), and a critical point at \({T}_{\mathrm{c}}^{\prime}=110\pm 15\,{\mathrm{K}}\). Insets show the estimation of critical exponents, γ for \({T}^{\prime} \, < \, {T}_{\mathrm{c}}^{\prime}\) and γ + 2β for \({T}^{\prime} \, > \, {T}_{\mathrm{c}}^{\prime}\). b Evolution of nsk(MFM) with \({T}^{\prime}\), showing a power-law behavior for \({T}^{\prime} \, > \, {T}_{\mathrm{c}}^{\prime}\) and the estimation of the critical exponent 2β. c Identification of the critical region Tc(κ) using three different approaches, namely, the local maximum in ρTHE with T and κ, the power-law rise in Δρ/M and the transition region (from isolated skyrmions to a disordered skyrmion lattice) indicated by MFM. The error bar in the estimated exponents reflects the error in the slope of the linear fits shown in the insets to (a and b). The same error bar is reflected through the shaded regions in the power-law fits. Error bars on \({\rho }_{\mathrm{max}}^{\mathrm{THE}}\) in (c) reflect the variation in the peak position of ρTHE between Fig. 2b, c. The shaded region for Tc(κ) from Δρ/M in (c) reflects a conservative estimate of ±35% variation in κ, resulting from an upper bound in the estimation of the exchange (A) and DMI(D) constants as well as Keff from magnetization measurements5.

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