Revealing defect-induced spin disorder in nanocrystalline Ni

We combine magnetometry and magnetic small-angle neutron scattering to study the influence of the microstructure on the macroscopic magnetic properties of a nanocrystalline Ni bulk sample, which was prepared by straining via high-pressure torsion (HPT). As seen by magnetometry, the mechanical deformation leads to a significant increase of the coercivity compared with nondeformed polycrystalline Ni. The neutron data reveal a significant spin-misalignment scattering caused by the high density of crystal defects inside the sample, which were created by the severe plastic deformation during the sample preparation. The corresponding magnetic correlation length, which characterizes the spatial magnetization fluctuations in real space, indicates an average defect size of 11 nm, which is smaller than the average crystallite size of 60 nm. In the remanent state, the strain fields around the defects cause spin disorder in the surrounding ferromagnetic bulk, with a penetration depth of ∼22 nm. The range and amplitude of the disorder is systematically suppressed by an increasing external magnetic field. Our findings are supported and illustrated by micromagnetic simulations, which for the case of nonmagnetic defects (holes) embedded in a ferromagnetic Ni phase, further highlight the role of localized spin perturbations for the magnetic microstructure of defect-rich magnets such as HPT materials.

Figure 1

(a) X-ray diffractogram of high-pressure torsion (HPT) Ni (black solid line) and of nondeformed (nd) Ni (blue dashed line; $\mathrm{Cu}{K}_{\alpha }$ radiation). Red solid line: x-ray diffraction (XRD) data refinement using the Le Bail fit method implemented in the Fullprof software. The bottom orange solid line represents the difference between the calculated and observed intensities. (b) Room-temperature magnetization curves of HPT Ni and of nd Ni. Inset in (b): zoom of the magnetization curves between ±20 mT. (c) Semilogarithmic plot of the upper right branch of the magnetization curves plotted in (b). The large data points in (c) correspond to the field values (see inset) where the small-angle neutron scattering (SANS) measurements have been carried out. Horizontal dashed line: saturation magnetization $M_s=55.5{\mathrm{Am}}^2/\mathrm{kg}$ of bulk Ni [39].

Figure 2

(a) Magnetic-field dependence of the (over 2π) azimuthally averaged total (nuclear + magnetic) small-angle neutron scattering (SANS) cross-section $d\mathrm{\Sigma }\left(q,H_0\right)/d\mathrm{\Omega }$ and (b) of the purely magnetic SANS cross-section $d{\mathrm{\Sigma }}_{\mathrm{mag}}\left(q,H_0\right)/d\mathrm{\Omega }$ (log-log scale). Dashed lines in (b): Extrapolation of $d{\mathrm{\Sigma }}_{\mathrm{mag}}\left(q,H_0\right)/d\mathrm{\Omega }\propto 1/q^n$ from $q_{\max }$ to infinity and of $d{\mathrm{\Sigma }}_{\mathrm{mag}}\left(q,H_0\right)/d\mathrm{\Omega }\propto a+b{q}^2$ from $q_{\min }$ to $q=0$. Inset in (b): Field dependence of the asymptotic power-law exponent $n$ of the magnetic SANS cross-section $d{\mathrm{\Sigma }}_{\mathrm{mag}}\left(q,H_0\right)/d\mathrm{\Omega }$ on a semilogarithmic scale.

Figure 3

Magnetic-field dependence of the normalized magnetic correlation function $C\left(r,H_0\right)$. The correlation functions were numerically computed by a direct Fourier transformation [Eq. (3)] of $d{\mathrm{\Sigma }}_{\mathrm{mag}}\left(q,H_0\right)/d\mathrm{\Omega }$ shown in Fig. 2. Inset: Plot of $C\left(r,H_0\right)$ on a semilogarithmic scale, emphasizing the nonexponential decay of the correlations.

Figure 4

Field dependence of the magnetic correlation length $l_c\left(H_0\right)$ determined from the computed $C\left(r,H_0\right)$ data shown in Fig. 3 (log-log scale). Dashed line: Fit of the $l_c\left(H_0\right)$ data using Eq. (5).

Figure 5

Illustration of the spin-misalignment correlations around defects. Shown are the results of micromagnetic simulations for a spherical defect (magnetic hole) embedded in a uniform Ni matrix. Applied-field values (${\mathit{H}}_0$ is parallel to the $z$ direction): (a) 0.05 T and (b) 2 T. Top panel: projections of the three-dimensional magnetization distribution $\mathit{M}\left(\mathit{r}\right)$ into the $y-z$ plane. Bottom panel: perpendicular magnetization component $M_y$. The black arrows and color bars in (b) indicate the strength and orientation of $M_y$ (arbitrary units). Materials parameters of Ni were used (Ref. [40]).