You can shield magnetic field by using mu-metal.

You can shield electromagnetic field or radiation of monochromatic or wavelength band by the proper absorbing materials. It depends very much on the wavelength. To shield a magnetic field is more difficult. The difference comes from the fluctuating electromagnetic field and static magnetic field.

You could use nonmagnetic material with high conductivity for shielding of magnetic fields. E.G. it could be superconductor loop around your object. Another variant could be active method of shielding. For this purpose in the loop with usual conductor aroung your object you should insert power supply with some electronic control.

Thanks for answers

You can shield magnetic field by means of a correct arrangement of Helmholtz coils (or similar coil arrangements). By positioning the coils correctly and administrating the correct current you can zeroing the magnetic field in the center of the arrangement.

If the magnetic field is static, you need either a ferromagnetic/ferrimagnetic material or a superconducting shield. Magnetic shielding arises because the ferromagnetic shield generates a field opposite to the one invsting it (creation of free poles). If the field is time dependent, you can additionally exploit the shielding action of eddy currents. At very high frequencies, eddy currents provide for most of the shielding action and a good conducting non ferromagnetic material (e.g. copper) suffices.

For particular configurations of time-invariant magnetic field, a non-ferromagnetic, non superconducting, but only conductive shield (aluminium for example) can be used ! It is possible to use such a shield, shaped as an hollow cylinder, and rotating around an axis perpendicular ro the stationary field. The shielding effet is observed inside the cylinder, it depends on the rotation frequency..

This device allows to create "eddy currents" inside the shield even for a time-invariant magnetic field. It is not transposable to all the configurations.

Fausto,

thanks for answer, but could you explain me shortly, why the superconductor is proper for shielding of static magnetic field, while the ordinary well conducting material (Al, Cu) is not enough.

I think well conducting material (Al, Cu) are able to shield the static magnetic field too.. because H enter a conductor will convert to evanescent current, and dismissed.

The different in supercond is magnetic field-generated-current should "suppose" will stay in the supercond everlasting, and constant magnetic field is allowed by classical theory, but in fact meissner effect is occurring that no magnetic field will be found in the internal of supercond

I think it's better using ferromagnetic materials, such as ferrite or other soft magnets for shielding magnetic field.

The shielding seen by SC materials is mainly due the so called Meisner effect, which is the expulsion of external field from the interior of SC material and special to the SC material. In other well conducting materials, you can even observe diamagnetic like behavior but it will not be effective for the shielding.

Niobium as well as High temperature superconductor work very well to to shield magnetic field. Below critical field (~1200 G for niobium) acts under Meissner effects act as shield and is diamagnetic material.

Artur, for power frequency magnetic field both conductive (Aluminum) and ferromagnetic shields are used. The open conductive shield is more effective than the open ferromagnetic shield. However, the closed ferromagnetic shield is more effective than the closed conductive shield. Generally speaking, the closed ferromagnetic shield is the most effective solution.

Well, well, well.  Static magnetic fields are effectively not present within superconductors.  More precisely, B=0 there (but not H!).  Technically speaking, this is because superconductors are perfect diamagnets. Taking into account that magnetic susceptibility of other diamagnets is 4 to 6 orders of magnitude smaller than for superconductors, one cannot expect any appreciable shielding effect when using normal conductor, even a very good one, gold included.

Things change, when the magnetic field is time-dependent.  Superconductors are no longer perfect,  but ordinary conductors start to work, thanks to eddy currents.  This is however limited to relatively low frequencies because of the skin effect.

I'm interested in very low frequencies, about 1Hz, and the point is to avoid any cross-talking between parallel superconductors.

Artur, you can use an active shield, as Mr. Korobeynikov stated in a previous answer. It consists, in the simplest form, on a wire loop fed by a source of 1 Hz that is controlled both in amplitude and phase. Moreover, you need a magnetic field sensor to measure the 1 Hz field. This way, if the non-mitigated field is higher you have to increase the compensating current, or vice-versa. If you type in Google "active loop" "compensation" "magnetic field" you will see several papers.

If the non-mitigated field is constant you will not need to control the amplitude of the current, but the phase will be always needed.