Probing exchange bias at the surface of a doped ferrimagnetic insulator

With the realization of stress-induced perpendicular magnetic anisotropy, efficient spin-orbit torque switching, and room temperature topological Hall effect, interest in rare earth iron garnets has been revived in recent years for their potential in spintronic applications. In this study, we investigate the magnetic properties of micrometer-thick Bi and Ga substituted thulium iron garnets (BiGa:TmIG) grown by the liquid-phase epitaxy method. Above the magnetization compensation (MC) temperature, anomalous triple hysteresis is observed in BiGa:TmIG/Pt heterostructures by anomalous Hall effect measurements. X-ray magnetic circular dichroism and energy dispersive spectroscopy measurements reveal its origin as an internal exchange bias (EB) effect arising from inhomogeneities localized at the surface of the film. Possibly depending on the difference in thickness and defect realization of the EB layer, two types of magnetization reversal mechanisms, namely, the Stoner-Wohlfarth type and the reversible domain-wall motion type, are observed. Our results show that rich meta-magnetic phases exist in garnets close to MC, which can be robustly tuned by chemical composition engineering and conveniently probed by electrical transport measurements.

Figure 1

(a) Illustration of a unit cell of ${\mathrm{Tm}}_3{\mathrm{Fe}}_5\mathrm{O}$ drawn with VESTA [26]. (b) Schematic of the structure of the LPE-grown BiGa:TmIG films. (c) XRD scans taken on both sides of the $14.1\mu \mathrm{m}$ thick BiGa:TmIG film. (d) $MH$ loops measured by a VSM with IP and OP field scans. (e) Saturation magnetization (solid symbols) and coercivity (open symbols) as a function of temperature for Sample 1 (${\mathrm{Bi}}_{0.63}{\mathrm{Tm}}_{2.36}{\mathrm{Ga}}_{1.15}{\mathrm{Fe}}_{3.85}{\mathrm{O}}_{12}$, solid and open red circles) and Sample 2 (${\mathrm{Bi}}_{0.5}{\mathrm{Tm}}_{2.5}{\mathrm{Ga}}_{1.3}{\mathrm{Fe}}_{3.7}{\mathrm{O}}_{12}$, solid and open blue stars).

Figure 2

(a) Schematic of the SH-AHE magnetometry. (b) AHE in the $\mathrm{BiGa}:\mathrm{TmIG}\left(14.1\mu \mathrm{m}\right)/\mathrm{Pt}\left(10\mathrm{nm}\right)$ Device 1. Field is applied in the OP direction and a linear background from the ordinary Hall effect is removed. (c) The temperature dependence of AHE resistance $R_{yx}$ and coercivity $H_{\text{c}}$. Blue and red arrows represent the Tm and Fe sublattice magnetization, respectively.

Figure 3

(a) Representative XMCD energy scans at the Fe ${\mathrm{L}}_3$ and Tm ${\mathrm{M}}_5$ edges with a fixed external field. (b) and (c) Fe and Tm sublattice hysteresis were obtained by fixing energy at ${\mathrm{L}}_3$ and ${\mathrm{M}}_5$ peaks while scanning the external field applied normal to the sample surface. (d) Tm/Fe atomic ratio depth profile obtained by cross-sectional EDS measurement.

Figure 4

(Top) AHE of Device A at 140 K as shown in Fig. 5. (Bottom) Illustration of the internal EB effect. Blue and red arrows represent the Tm and Fe magnetization, respectively. MC denotes the magnetization compensation boundary between surface and bulk. Only part of the bulk is drawn. In regime (i) $H<H_{\text{b}}$, exchange energy aligns the surface moments with those of the bulk, while in regime (ii), an external field larger than $H_{\text{b}}+H_{\text{bc}}$ reverts the surface magnetization and a domain wall is formed beneath the MC boundary.

Figure 5

AHE results of Hall bar Device A and B fabricated on Sides A and B, respectively, on a BiGa:TmIG film. Both devices share the same $\mathrm{BiGa}:\mathrm{TmIG}\left(14.1\mu \mathrm{m}\right)/\mathrm{Pt}\left(5\mathrm{nm}\right)$ structure and Hall bar geometry, and the measurements were done simultaneously. The inset is a cross-sectional AFM scan across the border between Sides A and B.

Figure 6

(a) The 200–250 K AHE results of the same Device 1 shown in Fig. 2. (Inset) Schematic of the composition-gradient-caused $T_{\text{MC}}$ gradient and the effective EB layer thickness. (b) Fe sublattice hysteresis measured by XMCD on the back side of the $\mathrm{BiGa}:\mathrm{TmIG}\left(14.1\mu \mathrm{m}\right)$ sample. (c) (Top) Fe sublattice hysteresis at 140 K. (Bottom) Illustration of the proposed domain-wall motion model. At regime (i) $H=H_{\text{i}}$, the domain wall starts to enter the XMCD probing region which has a thickness of $d_{\text{XMCD}}$. In regime (ii) $H_{\text{i}}<H<H_{\text{f}}$, the partial domain wall is formed and probed by XMCD. At (iii) $H=H_{\text{f}}$, the wall leaves the XMCD probing region. And finally, when $H>H_{\text{f}}$ [regime (iv)], the wall is pushed below the MC boundary by the external field.

Figure 7

(a) $MH$ loops of a $\mathrm{BiGa}:\mathrm{TmIG}\left(14.1\mu \mathrm{m}\right)$ sample with IP field scans. A linear paramagnetic background from GGG substrate is removed. (b) Calculated uniaxial anisotropy energy density as a function of temperature.

Figure 8

(a) and (b) Saturation magnetization as a function of temperature for Sample 1 (${\mathrm{Bi}}_{0.63}{\mathrm{Tm}}_{2.36}{\mathrm{Ga}}_{1.15}{\mathrm{Fe}}_{3.85}{\mathrm{O}}_{12}, 14.1\mu \mathrm{m}$) and Sample 2 (${\mathrm{Bi}}_{0.5}{\mathrm{Tm}}_{2.5}{\mathrm{Ga}}_{1.3}{\mathrm{Fe}}_{3.7}{\mathrm{O}}_{12}, 2\mu \mathrm{m}$).

Figure 9

(a) Saturation magnetization as a function of temperature for Sample 1 and Sample 2. A positive $M_{\text{s}}$ value means Tm dominant and negative Fe dominant. (b) $M_{\text{s}}$ vs $T$ between 135 and 200 K. (c) $\sqrt{K_{\text{u}}}/H_{\text{b}}$ as a function of temperature. The inset is an illustration of the composition gradient in the EB layer.