We have investigated hexagonal YbAgGe down to 70 mK by measuring the magnetic-field and temperature dependence of the resistivity rho of single crystals in fields up to 14 T. Our results extend the H-T phase diagram to the lowest temperatures for H applied in the basal plane and along the c-axis. In particular, critical fields for the suppression of several magnetic phases are determined. The temperature dependence of rho(T) is unusual: whereas at low H, rho(T) reveals a temperature exponent n>=2, we find 1<=n<1.5 and strong enhancement of the temperature dependence of rho(T) close to and beyond the highest critical field for each field direction. For H applied in the basal plane, at high fields a conventional T^2 dependence of rho(T) is reached above 10 T accompanied by an approach to saturation of a strong drop in the residual resistivity. YbAgGe appears to be one of few Yb-based stoichiometric systems, where quantum-critical behaviour may be induced by a magnetic field.
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