Spin Hall Magnetoresistance as a Probe for Surface Magnetization in $\mathrm{Pt}/\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ Bilayers

We study the spin Hall magnetoresistance (SMR) in Pt grown in situ on ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ (CFO) ferrimagnetic insulating films. A careful analysis of the angle-dependent and field-dependent longitudinal magnetoresistance indicates that the SMR contains a contribution that does not follow the bulk magnetization of CFO, but it is a fingerprint of the complex magnetism at the surface of the CFO layer, thus signaling SMR as a tool for mapping surface magnetization. A systematic study of the SMR for different temperatures and CFO thicknesses gives us information impossible to obtain with any standard magnetometry technique. On one hand, the surface magnetization behaves independently of the CFO thickness and does not saturate up to high fields, evidencing that the surface has its own anisotropy. On the other hand, characteristic zero-field magnetization steps are not present at the surface while they are relevant in the bulk, strongly suggesting that antiphase boundaries are responsible for such intriguing features. In addition, a contribution from the ordinary magnetoresistance of Pt is identified, which is distinguishable only due to the low resistivity of the in situ grown Pt.

Figure 1

Angle-dependent magnetoresistance measurements at 9 T and 300 K for the $\mathrm{Pt}(6.5\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$ sample along (a) $\gamma$, (b) $\beta$, and (c) $\alpha$ rotation planes. $R_L$ is the measured longitudinal resistance and $R_{L0}$ the subtracted background. The sketches in the right define the Hall bar geometry, the longitudinal measurement setup, and the angles $\alpha$, $\beta$, and $\gamma$.

Figure 2

The amplitude of ADMR at 9 T as a function of the temperature, for the three different angles $\alpha$ (green circles), $\beta$ (blue squares), and $\gamma$ (red triangles), for (a) $\mathrm{Pt}(6.5\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$, (b) $\mathrm{Pt}(4\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$, and (c) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$ samples.

Figure 3

Longitudinal resistance $R_L$ for (a) $\mathrm{Pt}(6.5\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$, (b) $\mathrm{Pt}(4\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$, and (c) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$ samples, as a function of $H$ applied along $\mathbf{t}$ (red curves), $\mathbf{j}$ (blue curves), and $\mathbf{n}$ (black curves). $R_{L0}$ is the subtracted background. The orientations of the applied field and the measurement configuration are sketched in the inset. All measurements are done at 50 K.

Figure 4

Orange, blue, and green curves are the additional magnetoresistance observed for out-of-plane $H$, $[R_L(\mathbf{H}||\mathbf{n})-R_L(\mathbf{H}||\mathbf{j})]/R_{L0}$, as a function of $H/\rho$ for the three $\mathrm{Pt}/\mathrm{CFO}(40\mathrm{nm})$ samples with different Pt thicknesses at 50 K. The red curve is the longitudinal magnetoresistance $[R_L(\gamma )-R_{L0}]/R_{L0}$ as a function of $H\cos (\gamma )/\rho$, where $H\cos (\gamma )$ is the out-of-plane component of the field for the 6.5-nm-thick Pt, at 300 K. The dashed black line is a guide for the eye.

Figure 5

(a) Magnetic hysteresis loops for the $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(40\mathrm{nm})$ sample measured by VSM at 50 K. $H$ is applied along $\mathbf{t}$ (red curve) and $\mathbf{n}$ (black curve), as defined in the inset. A diamagnetic background has been subtracted. (b) Comparison of normalized hysteresis loops with $H$ applied along $\mathbf{t}$ for the same sample. The red curve is the one in (a), normalized to the maximum value. The blue curve is computed from the longitudinal resistance $R_L$ at 50 K as a function of $H$ applied along $\mathbf{t}$, which is shown in Fig. 3. The green curve is the difference between the two hysteresis loops.

Figure 6

Longitudinal resistance $R_L$ for (a)–(c) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(20\mathrm{nm})$ and (d)–(f) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(60\mathrm{nm})$ samples, as a function of $H$ applied along $\mathbf{t}$ (red curves) and $\mathbf{n}$ (black curves). Measurements are done at 50 (a),(d), 150 (b),(e), and 300 K (c),(f).

Figure 7

Comparison of normalized magnetic hysteresis loops with $H$ applied along $\mathbf{t}$ for (a),(b) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(20\mathrm{nm})$ and (c),(d) $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(60\mathrm{nm})$ samples at 50 (a),(c) and 300 K (b),(d). The red curve is measured by VSM magnetometry and normalized to the maximum value after diamagnetic background subtraction. The blue curve is computed from the longitudinal resistance $R_L$ as a function of $H$ applied along $\mathbf{t}$, which is shown in Fig. 6.

Figure 8

Comparison of normalized hysteresis loops for $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(20\mathrm{nm})$ (black curves) and $\mathrm{Pt}(2\mathrm{nm})/\mathrm{CFO}(60\mathrm{nm})$ (red curves) samples, computed from the longitudinal resistance $R_L$ at (a) 50, (b) 150, and (c) 300 K, as a function of $H$ applied along $\mathbf{t}$ (shown in Fig. 6).