Recovery and nonrecovery of the untrained state in an exchange-coupled system

We report depth sensitive investigations of the magnetic interaction between exchange-coupled stacked CoO and ferromagnetic Co bilayers (separated by thick Au layers) as we explore the degree of recovery of the untrained state after the first two field cycles. Such a recovery is expected by field cycling a reorientation field $\left(H_{\mathrm{RE}}\right)$ along a direction (${\mathrm{\Omega }}_{\mathrm{RE}}$) away from the initial field cooling direction. Measurements as a function of ${\mathrm{\Omega }}_{\mathrm{RE}}$ and the strength of $H_{\mathrm{RE}}$ (along each direction) map the influence of ${\mathrm{\Omega }}_{\mathrm{RE}}$ on the reversal mechanism in the layers and thereby the degree of recovery. Our results are consistent with the earlier observations in similar systems that was realized with ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$. We ascribe these partial and/or significant recoveries to the unchanged sense of rotation after initial field cooling of the ferromagnetic magnetization upon each field cycling. Furthermore, in our system, we find that this recovery can be regulated by choosing various other $H_{\mathrm{RE}}$ and ${\mathrm{\Omega }}_{\mathrm{RE}}$ values without changing the rotational sense. The best recipe for recovery is identified for ${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$, that can be achieved partially with $H_{\mathrm{RE}}=3.0$ kOe and remain significant even with $H_{\mathrm{RE}}=10.0$ kOe. In this study we not only understand the fundamental mechanism in the recovery of training, but also instigate its technological prospects by lifting the directional restrictions of the reorientation field.

Figure 1

Illustration of the neutron scattering geometry. $H_{\mathrm{a}}$ along the $+y$ axis is shown to be antiparallel to $H_{\mathrm{FC}}$. $M_{\mathrm{FM}}$ is the FM magnetization making an angle ${\mathrm{\Phi }}_A$ with respect to the field axis. The reorientation field $H_{\mathrm{RE}}$ along the $-x$ axis (for ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$) is also shown along with two other orientations (${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$ and ${135}^{\circ }$) in the sample plane.

Figure 2

XTEM micrographs of the ${\left[\text{Co/CoO/Au}\right]}_{16}$ multilayer.

Figure 3

SQUID magnetization hysteresis loops for different field cycles measured at 10 K and for various reorientation fields $H_{\mathrm{RE}}$ along ${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$ in the sample plane. The black, red, and blue circles mark the applied field values $H_{\mathrm{a}}$ for the neutron measurements along the respective branch of the loops.

Figure 4

SQUID magnetization hysteresis loops for different field cycles measured at 10 K and for various reorientation fields $H_{\mathrm{RE}}$ along ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$ in the sample plane. The blue circles mark the applied field values $H_{\mathrm{a}}$ for the neutron measurements along the respective branch of the loops.

Figure 5

SQUID magnetization hysteresis loops for different field cycles measured at 10 K and for various reorientation fields $H_{\mathrm{RE}}$ along ${\mathrm{\Omega }}_{\mathrm{RE}}={135}^{\circ }$ in the sample plane.

Figure 6

The field derivative of magnetization ${\chi }_{\text{mag}}$ as a function of field measured at a reorientation field $H_{\mathrm{RE}}=0.5$ kOe and along different orientations ${\mathrm{\Omega }}_{\mathrm{RE}}$ in the sample plane. The Gaussian fits to the peaks are shown in lines.

Figure 7

The normalized integrated area ratios $\text{C}1n=\text{X}1/\text{X}n$ ($n=2,4,5$) with respect to the initial training for various reorientation field $H_{\mathrm{RE}}$ and along different orientations ${\mathrm{\Omega }}_{\mathrm{RE}}$ in the sample plane. Here $n$ is the number of loop cycle. The symbol sizes are typical of their error bars.

Figure 8

The ratio of normalized integrated area corresponding to the fourth field cycle with respect to the trained state during the fourth field cycle (C14/C12) for various reorientation field $H_{\mathrm{RE}}$ and along different directions ${\mathrm{\Omega }}_{\mathrm{RE}}$ in the sample plane. The symbol sizes are typical of their error bars.

Figure 9

Specular reflectivity patterns (solid symbols) along with their best fits (open symbols) as a function of $Q_{\mathrm{z}}$ for the NSF $[R_{--}$ (black) and $R_{++}$ (red)] and SF $[R_{-+}$ (blue)] channels measured at (a) close to the coercive field $H_{\mathrm{a}}=-2.0$ kOe, (b) a slightly higher field $H_{\mathrm{a}}=-2.07$ kOe, (c) a saturation field of $H_{\mathrm{a}}=-10.0$ kOe during the first field cycle, and (d) at $H_{\mathrm{a}}=-1.55$ kOe during the second field cycle.

Figure 10

FM layer switching sequence during the first field cycle at $H_{\mathrm{a}}=-2.07$ kOe and during the second field cycle at $H_{\mathrm{a}}=-1.55$ kOe. The arrows indicate the ${\mathbf{M}}_{\mathbf{FM}}$ orientations in the respective layers. The applied field $H_{\mathrm{a}}$ is along the $-y$ axis.

Figure 11

(a) SF specular reflectivity $\left[R_{-+}\right]$ patterns as a function of $Q_{\mathrm{z}}$ measured during the first field cycle at $H_{\mathrm{a}}=-2.07$ and $-10.0$ kOe and during the second field cycle at $H_{\mathrm{a}}=-1.55$ kOe. (b) Plot of the corresponding corrected SF signals as a function of $Q_{\mathrm{z}}$.

Figure 12

Specular reflectivity patterns (solid symbols) along with their best fits (open symbols) as a function of $Q_{\mathrm{z}}$ for the NSF $[R_{--}$ (black) and $R_{++}$ (red)] and SF $[R_{-+}$ (blue)] channels measured at (a) $H_{\mathrm{a}}=-1.43$ kOe, (b) $H_{\mathrm{a}}=-1.67$ kOe, and (c) $H_{\mathrm{a}}=-1.73$ kOe during the fourth field cycle for different $H_{\mathrm{RE}}$ ($=0.5$, 3.0, and 10.0 kOe, respectively) values when ${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$.

Figure 13

FM layer switching sequence during the different fourth field cycles at $H_{\mathrm{a}}=-1.44$ kOe ($H_{\mathrm{RE}}=0.5$ kOe), $-1.67$ kOe ($H_{\mathrm{RE}}=3.0$ kOe), and $-1.73$ kOe ($H_{\mathrm{RE}}=10.0$ kOe) when ${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$. The arrows indicate the ${\mathbf{M}}_{\mathbf{FM}}$ orientations in the respective layers. The applied field $H_{\mathrm{a}}$ is along the $-y$ axis.

Figure 14

(a) SF specular reflectivity $\left[R_{-+}\right]$ patterns as a function of $Q_{\mathrm{z}}$ measured during the fourth field cycle for ${\mathrm{\Omega }}_{\mathrm{RE}}={45}^{\circ }$ at $H_{\mathrm{a}}=-1.44, -1.67$, and $-1.73$ kOe for $H_{\mathrm{RE}}=0.5$, 3.0, and 10.0 kOe, respectively. (b) Plot of the corresponding corrected SF signals as a function of $Q_{\mathrm{z}}$.

Figure 15

Specular reflectivity patterns (solid symbols) along with their best fits (open symbols) as a function of $Q_{\mathrm{z}}$ for the NSF $[R_{--}$ (black) and $R_{++}$ (red)] and SF $[R_{-+}$ (blue)] channels measured at (a) $H_{\mathrm{a}}=-1.73$ kOe and (b) $H_{\mathrm{a}}=-1.65$ kOe during the fourth field cycle for different $H_{\mathrm{RE}}$ ($=2.0$ and 10.0 kOe, respectively) values when ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$.

Figure 16

FM layer switching sequence during the different fourth field cycles at $H_{\mathrm{a}}=-1.73$ kOe ($H_{\mathrm{RE}}=2.0$ kOe) and $-1.65$ kOe ($H_{\mathrm{RE}}=10.0$ kOe) when ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$. The arrows indicate the ${\mathbf{M}}_{\mathbf{FM}}$ orientations in the respective layers. The applied field $H_{\mathrm{a}}$ is along the $-y$ axis.

Figure 17

SF specular reflectivity $\left[{\mathrm{R}}_{-+}\right]$ patterns as a function of $Q_{\mathrm{z}}$ measured during the fourth field cycle for ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$ at $H_{\mathrm{a}}=-1.73$ kOe, and $-1.65$ kOe for $H_{\mathrm{RE}}=2.0$ kOe and 10.0 kOe, respectively. (b) Plot of the corresponding corrected SF signals as a function of $Q_{\mathrm{z}}$.

Figure 18

Sketch showing the rotational sense of ${\mathbf{M}}_{\mathbf{FM}}$ under different conditions as ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$ lies in the sample plane. The reorientation field $H_{\mathrm{RE}}$ can be either along the $+x$ axis (a) and (b) when the ${\mathbf{M}}_{\mathbf{FM}}$ rotational senses are sensitive to the strength of $H_{\mathrm{RE}}$ or along the $-x$ axis (c) when they are insensitive.

Figure 19

Sketch showing the rotational sense of ${\mathbf{M}}_{\mathbf{FM}}$ in the present geometry as ${\mathrm{\Omega }}_{\mathrm{RE}}={90}^{\circ }$ lies in the sample plane. The reorientation field $H_{\mathrm{RE}}$ is along the $-x$ axis when the ${\mathbf{M}}_{\mathbf{FM}}$ rotational sense is insensitive to the $H_{\mathrm{RE}}$ strength.