Magnetic shielding and exotic spin-dependent interactions

Experiments searching for exotic spin-dependent interactions typically employ magnetic shielding between the source of the exotic field and the interrogated spins. We explore the question of what effect magnetic shielding has on detectable signals induced by exotic fields. Our general conclusion is that for common experimental geometries and conditions, magnetic shields should not significantly reduce sensitivity to exotic spin-dependent interactions, especially when the technique of comagnetometry is used. However, exotic fields that couple to electron spin can induce magnetic fields in the interior of shields made of a soft ferromagnetic or ferrimagnetic material. This induced magnetic field must be taken into account in the interpretation of experiments searching for new spin-dependent interactions and raises the possibility of using a flux concentrator inside magnetic shields to amplify exotic spin-dependent signals.

Figure 1

Schematic diagram of possible effects of an exotic field $\mathbf{\Upsilon }$ on a magnetic shield. (a) The shield material may interact with $\mathbf{{\rm Y}}$ to generate an induced field ${\mathbf{B}}_{\mathrm{ind}}$ that approximately cancels the effect of $\mathbf{{\rm Y}}$ on electron spins, or (b) the shield material may have no response to $\mathbf{{\rm Y}}$.

Figure 2

Scan of the applied magnetic field within the innermost magnetic shield layer and measured amplitude of nonlinear magneto-optical rotation with frequency modulated light (FM NMOR), centered on the zero-field ($n=0$) resonance [39, 57]. The working region of the magnetometer (width $\approx 6\mu \mathrm{G}$), where the signal is linear in response to the applied field, is designated by the vertical dashed lines. The center of the resonance is offset from zero due to a residual $\sim 20\mu \mathrm{G}$ field from the innermost shield.

Figure 3

The innermost mu-metal magnetic shield and schematic of external field coil.

Figure 4

Estimated shielding factor (ratio of the calculated field without an innermost shield to the measured magnetic field with an innermost shield) as a function of the applied external field. For data with larger external field magnitudes, see Ref. [56]; the upper limit of the field range was defined by the linear working region of the magnetometer (see Fig. 5).

Figure 5

Schematic diagram (not to scale) of a flux concentrator applied to a search for an exotic field $\mathrm{{\rm Y}}$ that couples to electron spins. The magnetic field induced by $\mathrm{{\rm Y}}$ in the gap between the ferrite rods, depending on the choice of ferrite material and the exact geometry, can generate an energy shift of electron spin states over an order of magnitude greater than $\mathrm{{\rm Y}}$ by itself. The induced magnetic field ${\mathbf{B}}_{\mathrm{ind}}$ can be measured with a magnetic sensor such as a SQUID (superconducting quantum interference device).