Antiferromagnetic domain size and exchange bias

Using neutron diffraction, we measured the sizes of antiferromagnetic domains in three ferromagnet/antiferromagnet bilayer samples as a function of the magnitude and sign of exchange bias, temperature, and antiferromagnet composition. Neutron-scattering techniques were applied to thin films with masses less than $10\mu \text{g}$. We found the antiferromagnetic domain size to be consistently small regardless of the exchange bias. For a Co/untwinned single crystalline antiferromagnet (AF)-fluoride bilayer, the antiferromagnetic domain size is comparable to the crystallographic domain size of the AF. For one sample the highest temperature at which the exchange bias was nonzero (i.e., the blocking temperature) was suppressed by $\sim 3\text{K}$ compared to the Néel temperature of the antiferromagnet.

Figure 1

(Color online) Exchange bias $H_E$ ($\square$) as a function of temperature for the $\text{Co}/{\text{Zn}}_{0.30}{\text{Fe}}_{0.70}{\text{F}}_2$ sample. The temperature dependence of the integrated intensity of the (100) Bragg reflection are shown ($●$). The solid curves are fits to a model discussed in the text.

Figure 2

Schematics of (a) specular reflectometry, (b) off-specular reflectometry, and (c) glancing incidence (x-ray) diffraction. These geometries were used for the x-ray diffraction experiments. Insets: Diagrams showing typical values for the wave vector transfer for the experiments.

Figure 3

(Color online) (Upper panels) Off-specular and specular x-ray intensity maps and (lower panels) reflectivities normalized to the Fresnel reflectivity $\left(R_F=16{\pi }^2/Q_z^4\right)$ for the three samples (a) $\text{Co}/{\text{Ni}}_{0.55}{\text{Fe}}_{0.45}{\text{F}}_2$, (b) $\text{Co}/{\text{Zn}}_{0.30}{\text{Fe}}_{0.70}{\text{F}}_2$, and (c) $\text{Co}/{\text{FeF}}_2$. The solid curves are the best-fitting reflectivities calculated using the chemical model shown in the inset.

Figure 4

(Color online) (a) X-ray intensity map measured under conditions of glancing incidence diffraction for the (110)-type Bragg reflection from the ${\text{FeF}}_2$ film. (b) X-ray intensity profile of the $\left(\overline{1}10\right)$ Bragg reflection vs ${\alpha }_f$. (c) X-ray intensity profile integrated over a region corresponding to ${\alpha }_f/{\alpha }_c=1.0\pm 0.5\text{vs}$ $\varphi$. (d) Solid symbols: Width (FWHM) of the $\left(hh0\right)$ Bragg reflections for ${\text{FeF}}_2$ film (and for select Bragg reflections from the ${\text{LaFeO}}_3$ film and a GaAs perfect crystal, open symbols). The line is the best fit of Eq. (1) to the ${\text{FeF}}_2$ data.

Figure 5

(Color online) (a) Unit cell of the AF color coded to show the two spin sublattices. (b) Three-dimensional perspective of the incident neutron wave vector $k_i$ illuminating the sample’s surface [the (110) plane] from behind the figure and the diffracted wave vector $k_f$ exiting the figure at right. (c) Schematic of the neutron-scattering experiment as viewed from above (b). A neutron beam (tan) with width $w$ illuminates the sample. A position sensitive detector measures the neutron intensity as a function of $2\theta$ and wavelength. An AF domain with dimension $\Delta$ parallel to the wave vector transfer $Q$ is shown. The sample’s surface normal is rotated from the incident neutron beam by an angle $\omega$.

Figure 6

(Color online) Neutron intensity image (neutrons counted in a bin with dimensions $0.005\text{Å}$ by $0.066°$, scale at right) vs $2\theta$ and $\lambda$. $\left(h00\right)$-type Bragg reflections are labeled. The intensity within the dashed box was integrated along contours of constant $d$ spacing to form the diffraction pattern in Fig. 7. A contour of constant $d$ spacing $\left(d=4.66\text{Å}\right)$ is shown by the yellow line.

Figure 7

(Color online) (a) $\left(h00\right)$-type diffraction pattern at 6 K. (b) The (100) ${\text{Zn}}_{0.30}{\text{Fe}}_{0.70}{\text{F}}_2$ AF Bragg reflection profile for $T=6$, 20, 30, and 300 K. The solid curves are Gaussian functions fitted to the scans. Note that the bottom 6 K measurement was taken with $H_{\text{FC}}$ applied perpendicular to the easy axis of the AF.

Figure 8

The (002) graphite Bragg reflection measured as a function of neutron time of flight. The solid curve is the intensity profile of a function proportional to $e^{-\left|t-t_0\right|/{\sigma }_m}$ (for $t>t_0$) where $t$ is the time of flight and ${\sigma }_m$ is the moderator time constant (emission time of the moderator after $t_0$).

Figure 9

(Color online) The (100) AF Bragg reflection profile for AF films with different alloy compositions. Profiles are displaced for the sake of clarity, and only a portion of the data for $d$ spacing ranging from 0.2 to $8\text{Å}$ are shown. Approximately 2 h were required for each measurement.

Figure 10

(Color online) The (100) ${\text{Zn}}_{0.30}{\text{Fe}}_{0.70}{\text{F}}_2$ AF Bragg reflection profile at 6 K showing the intensities (blue squares) and fitted background (green curve) whose difference is the integrated intensity of the reflection.