This PDF file includes:

• Section S1. Determination of the magnetic phase diagram for MnSi thin plates
• Section S2. Relationship between the nonreciprocal nonlinear Hall effect and second-harmonic resistivity
• Section S3. Current dependence of the nonlinear Hall effect measured by using square-wave current
• Section S4. Frequency dependence of skyrmion velocity
• Section S5. Calculation of nonreciprocal nonlinear Hall responses to AC
• Section S6. Calculation of current-induced dynamics of a single skyrmion string
• Fig. S1. Functional forms of the dimensionless functions f_b(λ) and f_e(λ).
• Fig. S2. Temperature dependence of longitudinal resistivity and magnetic field dependence of planar Hall resistivity.
• Fig. S3. Current dependence of the nonreciprocal nonlinear Hall effect measured by using square-wave current.
• Fig. S4. Frequency dependence of skyrmion velocity.
• References (32–34)

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