Exchange spring switching in Er-doped ${\mathrm{DyFe}}_2/{\mathrm{YFe}}_2$ magnetic thin films

Reversible magnetic exchange springs can be formed in multilayer films, grown by molecular beam epitaxy. Here we demonstrate that small amounts of anisotropic ${\mathrm{ErFe}}_2$, placed in the middle of the ${\mathrm{YFe}}_2$ magnetic exchange springs, can bring about substantial changes. Results are presented for an Er-doped (110)-oriented multilayer film, at 100 K in fields of up to $\pm 14$ T. Using both Er and Dy-specific soft x-ray magnetic circular dichroism and micromagnetic modeling, it is demonstrated that Er doping gives rise to (i) noncollinear exchange spring states in zero field, (ii) magnetic exchange spring collapse, (iii) a marked increase in the number of different exchange spring states available to the system, and (iv) strikingly different Er and Dy magnetization loops. Full and partial loops are presented for both the in-plane hard and easy axes. The magnetization loops for Dy sublattice show that at least ten different exchange spring states are accessed during magnetic reversal. Magnetic switching scenarios, involving mixtures of Néel-like and Bloch-like domain walls, are presented and discussed.

Figure 1

Anisotropy energy surfaces for ${\mathrm{Er}}^{3+}$ and ${\mathrm{Dy}}^{3+}$ ions in the cubic Laves R${\mathrm{Fe}}_2$ compounds at 100 K. Note that the Er moments can easily change direction, between easy $\langle 111\rangle$ directions, by sliding over low energy saddle $\langle 110\rangle$ points. By contrast, the Dy moments have to jump over quite a large energy barrier.

Figure 2

Schematic representations of two stable exchange spring states in zero field. The blue (red) arrows represent the Dy (Er) moments, respectively, while the yellow arrows represent the Fe moments. We denote these two spin configurations as ${\mathrm{Dy}}_{\mathrm{B}}\left[001\right]/{\mathrm{Er}}_{\mathrm{S}}\left[111\right]$ (left) and ${\mathrm{Dy}}_{\mathrm{B}}\left[001\right]/{\mathrm{Er}}_{\mathrm{S}}\left[\overline{1}11\right]$ (right), respectively. Here the ${\mathrm{Dy}}_{\mathrm{B}} \left({\mathrm{Er}}_{\mathrm{S}}\right)$ stands for the bulk Dy (Er in the spring), respectively. Note that the precise direction of the Er moments will be modified by the presence of exchange springs.

Figure 3

Schematic representations of two stable exchange spring states in zero field. Notation and color scheme as per Fig. 2. We denote these two exchange spring states as ${\mathrm{Dy}}_{\mathrm{B}}\left[010\right]/{\mathrm{Er}}_{\mathrm{S}}\left[\overline{1}11\right]$ (left) and ${\mathrm{Dy}}_{\mathrm{B}}\left[010\right]/{\mathrm{Er}}_{\mathrm{S}}\left[11\overline{1}\right]$ (right), respectively.

Figure 4

Geometry used in the XMCD experiments. In (a) and (b) the x-ray beam is directed along an easy $\left[001\right]$ and hard $\left[\overline{1}10\right]$ axis, respectively. The magnetic field and the x-ray beam are collinear, and the film can be rotated either way about the vertical (support) axis.

Figure 5

Dy- and Er-XMCD signals measured using fluorescence yield.

Figure 6

(a) Dy (blue) and Er (red) element-specific XMCD-magnetization loops for magnetic fields applied along an in-plane $\left[001\right]$ axis. (b) First derivative $\partial M_{\mathrm{Dy}}/\partial B_{\mathrm{a}}$ for decreasing applied field. The derivative for increasing field is essentially the same, but inverted in signal and field.

Figure 7

(a) Dy (blue) and Er (red) element-specific XMCD-magnetization loops for magnetic fields applied along an in-plane $\left[\overline{1}10\right]$ axis. (b) First derivative $\partial M_{\mathrm{Dy}}/\partial B_{\mathrm{a}}$ for decreasing applied field.

Figure 8

Plausible four-step magnetic reversal process in an Er-doped ${\mathrm{DyFe}}_2/{\mathrm{YFe}}_2$ multilayer, for fields directed along an in-plane easy $\left[00\overline{1}\right]$ axis. The proposed spin state sequence is only valid starting from a large positive field state (A1) and reducing to a large negative field state (A5).

Figure 9

Partial loop (green) obtained by sweeping the field from (a) $10\to -2.84\to 10$ T and (b) from $10\to -3.6\to 10$ T, for a magnetic field applied along an in-plane $\left[001\right]$ axis.

Figure 10

Calculated Dy and Er loops at 100 K for a two-step magnetic reversal: ${\mathrm{Dy}}_{\mathrm{B}}\left[00\overline{1}\right]/{\mathrm{Er}}_{\mathrm{S}}\left[\overline{1}11\right]\to {\mathrm{Dy}}_{\mathrm{B}}\left[00\overline{1}\right]/{\mathrm{Er}}_{\mathrm{S}}\left[\overline{1}1\overline{1}\right]\to {\mathrm{Dy}}_{\mathrm{B}}\left[001\right]/{\mathrm{Er}}_{\mathrm{S}}\left[\overline{1}1\overline{1}\right]$. Red curve Er; blue curve Dy.

Figure 11

Comparison between the (a) Er- and (b) Dy-doped ${\mathrm{DyFe}}_2/{\mathrm{YFe}}_2$ multilayers at 100 K for fields applied along a hard in-plane $\left[\overline{1}10\right]$ axis.

Figure 12

(a) Average energy per formula unit vs magnetic field, (b) average moment per formula unit vs magnetic field, (c) average Dy moment vs magnetic field, and (d) average Er moment vs magnetic field for the first four states (A1) $\to$ (A4) of Fig. 8.

Figure 13

Plausible four-step magnetic reversal process in a Er-doped ${\mathrm{DyFe}}_2/{\mathrm{YFe}}_2$ multilayer, for fields directed along a hard in-plane $\left[\overline{1}10\right]$ axis. The proposed spin state sequence is only valid starting from a large positive field state (B1), reducing to a large negative field state (B5).

Figure 14

Partial loop (green) obtained by sweeping the field from (a) $10\to -2.75\to 10$ T and (b) from $10\to -5\to 10$ T, for a magnetic field applied along an in-plane $\left[\overline{1}10\right]$ axis.

Figure 15

(a) Average energy per formula unit vs magnetic field, (b) average magnetic moment per formula unit vs magnetic field, (c) average Dy moment vs magnetic field, and (d) average Er moment vs magnetic field for the first four states (B1) $\to$ (B4) of Fig. 13.