Phase diagram for the first peak in torque curves of YBa2Cu4O8 crystals up to 15 T

Torque measurements on single crystals of YBa2Cu4O8 show multiple peaks as a function of angle θ ca between the c-axis and the magnetic field H in the c-a plane. We propose that the first peaks at θ ca (90 - 10) deg. and (90 + 10) deg. arise from a long-range spiral spin density wave through the matching pinning between vortices and spins. We construct a contour map for a competing order parameter in YBa2Cu4O8 which starts at a finite magnetic field and is located far from the upper critical field line. We extended our torque measurements up to 15 T. The regime of the proposed spin density wave goes to higher temperatures when field increases. The first peak does not appear when the field direction is scanned in the c-b plane. We interpret that the origin of the first peak is due to the Zeeman effect between spiral spins and vortices. The NMR line width of the c-axis aligned YBa2Cu4O8 powders in H perpendicular c shows broadening at temperatures below 30 K, and may be caused by the proposed spin density wave. We consider that these features are able to be observed only for the cleanest underdoped cuprate