Quantitative Radiography of Magnetic Fields Using Neutron Spin Phase Imaging

We report on a novel neutron radiography technique that uses the Ramsey principle, a method similar to neutron spin echo. For the first time quantitative imaging measurements of magnetic objects and fields could be performed. The strength of the spin-dependent magnetic interaction is detected by a change in the Larmor precession frequency of the neutron spins. Hence, one obtains in addition to the normal attenuation radiography image a so-called neutron spin phase image, which provides a two-dimensional projection of the magnetic field integrated over the neutron flight path.

Figure 1

Radiography images of ferromagnetic steel foils using neutrons of ${\lambda }_0=0.6\mathrm{nm}$ at different $\pi /2$-spin flipper frequencies: (a) 547 kHz, (b) 549 kHz, (c) 551 kHz, and (d) 553 kHz. Each image has a size of $165\times 165$ pixels, which corresponds to about $21.5\times 21.5{\mathrm{mm}}^2$. The vertical stripes with lowered intensity result from the geometry of the transmission spin analyzer. (e) Intensity modulation in three different areas (averaged over $12\times 12$ pixels) of the images as a function of the spin flipper frequency and sinusoidal fits: gap (circle), $20\mu \mathrm{m}$ foil (square), and $40\mu \mathrm{m}$ foil (triangle).

Figure 2

Resulting NSPI image of the two different ferromagnetic steel foils and plot of a horizontal cut.

Figure 3

(a) Phase shift of three different areas (averaged over $12\times 12$ pixels) of the NSPI images as a function of the neutron wavelength ${\lambda }_0$: gap (circle), $20\mu \mathrm{m}$ foil (square), and $40\mu \mathrm{m}$ foil (triangle). The black curves are the linear fits through the data points. (b) Hysteresis curves of the two different ferromagnetic steel foil materials measured with a PPMS.

Figure 4

(a) Radiography image of the 9 mm long steel rod normalized with an empty beam image, taken at a $\pi /2$-spin flipper frequency of 550 kHz with neutrons of ${\lambda }_0=0.5\mathrm{nm}$. The size of the image is $21.5\times 21.5{\mathrm{mm}}^2$. (b) NSPI image generated from a set of 11 individual images. The dashed lines mark the vertical magnetic field direction and the axis along which the spin phase shift is zero due to the vanishing dipolar field under the angle of $52°\pm 2°$.

Figure 5

Scheme of the neutron spin phase imaging setup. The spins of the incoming polarized neutron beam are primarily oriented in $z$ direction along the steady magnetic field ${\overrightarrow{B}}_0$. They pass two phase-locked $\pi /2$-spin flipper coils, which produce a oscillating field in $x$ direction with an angular frequency $\omega$. A sample with a spin-dependent potential produces additional neutron spin precession, causing dephasing of the neutron spins. The spin analyzer lets pass only neutrons of one spin state, which get detected by the two-dimensional image detector.