  Since the energy momentum tensor of a magnetic field always contains a spin-2
component in its anisotropic stress, stochastic primordial magnetic field (PMF)
in the early universe must generate stochastic gravitational wave (GW)
background. This process will greatly affect the relic gravitational wave
(RGW), which is one of major scientific goals of the laser interferometer GW
detections. Recently, the fifth science (S5) run of laser interferometer
gravitational-wave observatory (LIGO) gave a latest upper limit
$\Omega_{GW}<6.9\times10^{-6}$ on the RGW background. Utilizing this upper
limit, we derive new PMF Limits: for a scale of galactic cluster $\lambda=1$
Mpc, the amplitude of PMF, that produced by the electroweak phase transition
(EPT), has to be weaker than $B_{\lambda} \leq 4\times 10^{-7}$ Gauss; for a
scale of supercluster $\lambda=100$ Mpc, the amplitude of PMF has to be weaker
than $B_{\lambda} \leq 9\times 10^{-11}$ Gauss. In this manner, GW observation
has potential to make interesting contributions to the study of primordial
magnetic field.
