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Unidirectional surface waves in nonreciprocal plasmonic platforms with nonlocal effects have been a topic of significant interest and some controversy. In this study, we present a scheme to achieve unidirectional surface magnetoplasmons (USMPs) with large modal areas at terahertz frequencies. Such large-area USMPs (LUSMPs) exist in a metal-UENZ (uniaxial- ε -near-zero)-Si-InSb structure under external magnetic field, where the effect of nonlocality is included. The field of the LUSMP extends almost uniformly in the UENZ layer with a thickness of wavelength scale, thus its modal size can be represented by the UENZ-layer thickness. Due to the modal energy primarily distributed in the thick UENZ layer, the nonlocality-induced leakage of the LUSMP is significantly reduced by an order of magnitude, compared to previous USMP existing at interface between InSb and opaque isotropic medium. Due to their large modal sizes, such LUSMPs can be efficiently excited by terahertz radiations directly from free space. In addition, LUSMPs offer high degree of freedom for manipulating terahertz waves, such as energy squeezing and trapping. Based on LUSMPs, a terahertz free-space isolator is also developed. Our findings have important implications to the development of innovative plasmonic devices in terahertz regime. [ABSTRACT FROM AUTHOR]