Shear Viscosity of Superfluid3Heup to 15 Tesla

We present the first measurements of the viscosity of superfluid {sup 3}He in magnetic fields up to 15 T , at temperatures down to 2 mK along the melting curve, using an assumption for the temperature dependence of the normal density. At fields higher than 4 T , the viscosity shows a minimum in the A{sub 1} phase, and reaches a local maximum at the A{sub 2} transition which becomes global at 14.6 T . The sharp decrease just below the A{sub 1} transition can be understood within the Ginzburg-Landau framework and is consistent with both theory and experiments in lower fields. At temperatures below the minimum, the viscosity in the A{sub 1} phase is dominated by a term with T{sup {minus}2} dependence. Additionally, we have calculated the temperature dependence of the viscosity tensor in the low temperature limit using the method of temperature asymptotes. {copyright} {ital 1997} {ital The American Physical Society}