Exchange bias in multigranular noncollinear ${\mathrm{IrMn}}_3/\mathrm{CoFe}$ thin films

Antiferromagnetic spintronic devices have the potential to greatly outperform conventional ferromagnetic devices due to their ultrafast dynamics and high data density. A challenge in designing these devices is the control and detection of the orientation of the antiferromagnet. One of the most promising ways to achieve this is through the exchange bias effect. This is of particular importance in large-scale multigranular devices. Previously, due to the large system sizes, only micromagnetic simulations have been possible, with an assumed distribution of antiferromagnetic anisotropy directions and grain size. Here, we use an atomistic model where the distribution of antiferromagnetic anisotropy directions occurs naturally and where the exchange bias occurs due to the intrinsic disorder in the antiferromagnet. We perform large-scale simulations of exchange bias, generating realistic values of exchange bias. We find a strong temperature dependence of the exchange bias, in agreement with experimental observations, approaching zero at the blocking temperature of the antiferromagnet. We find that the experimentally observed increase in the coercivity at the blocking temperature occurs due to the superparamagnetic flipping of the antiferromagnet during the hysteresis loop cycle. We find a large discrepancy between the exchange bias predicted from a geometric model of the antiferromagnetic interface, indicating the importance of grain edge effects in multigranular exchange biased systems. The grain size dependence shows the expected peak due to a competition between the superparamagnetic nature of small grains and reduction in the statistical imbalance in the number of interfacial spins for larger grain sizes. Our simulations confirm the existence of single antiferromagnetic domains within each grain. The model gives insights into the physical origin of exchange bias and provides a route to developing optimized nanoscale antiferromagnetic spintronic devices.

Figure 1

Visualization of the multigranular IrMn/CoFe bilayer structure. The CoFe is represented by gold spheres and lifted 5 nm above the IrMn to show the multigranular structure below. The Ir is represented as black spheres and the Mn is dark blue. The system is $50\times 50$ nm in size.

Figure 2

The granular structure generated from the Poisson distribution. The grain size distribution, the input median, and standard deviation nearly match the output distribution. Inset: The generated granular structure. The grain shapes look realistic, as do the distribution of grain sizes.

Figure 3

The magnetization direction throughout the equilibration stage of the simulation and direction of the net interface exchange field. (a) The direction of the net magnetization of the FM throughout the equilibration stage. The simulated magnetization has remained along the (1,0,0) direction. (b) During the equilibration step, the FM relaxes to its minimum energy position; as there is no applied field, the minimum energy occurs when the FM aligns with the interface moment of the AFM. In this simulation, the FM also has a granular structure so each FM grain will follow the magnetization of the interface field of the AFM below it. The angle of rotation away from the setting field direction is plotted on the histogram in (b) and shown schematically in the inset. The inset shows the color in the diagram represents the angle to the setting field direction at the end of the equilibration simulation. While most of the grains are have only canted $10\text{−}{60}^{\circ }$ away from the setting field direction, some of the grains are almost ${150}^{\circ }$ away.

Figure 4

The motion of the FM throughout the equilibration stage of the simulation. During the equilibration stage, all external fields are removed and the only force the FM feels is from the AFM below. (a) The motion of the FM throughout the simulation. The FM cants slightly away from the setting field direction and into the direction of the interface moment from the AFM below. The direction of the interface field is only slightly away from the setting field direction. (b) The interface layer of the FM shows canting of up to 20 degrees and imprinting from the grains below.

Figure 5

Simulated hysteresis loop for a granular AFM. The hysteresis loop exhibits 0.12 T of exchange bias.

Figure 6

Magnetization along the $x$ direction for sublattice 1 throughout the hysteresis loop for three different grains. Every grain of the AFM rotates at the same time, and the shaded rectangles show the points where the FM reverses magnetization.

Figure 7

Temperature dependence of exchange bias simulated hysteresis loop for a granular AFM at (a) 50, (b) 100, (c) 300, (d) 400, (e) 500, and (f) 700 K. (g) The simulated temperature dependence of the exchange bias and (h) the coercivity, compared with the experimental results of Ali et al. [31]. The simulated exchange bias decreases with temperature, as does the experimental result.

Figure 8

Magnetization along $x$ of one AFM sublattice in one grain; it can be seen to rotate at negative saturation of the FM. (a) The magnetization rotates between the positive and negative exchange bias directions. The points at which the FM flips are outlined by the gold dashed lines. (b) The magnetization length remains constant, suggesting the grain flips coherently and does not form domains.

Figure 9

The simulated grain size dependence of the exchange bias and coercivity at $T=0\mathrm{K}$ compared to experimental results [12]. (a) The exchange bias has a maximum value in 4 nm grains, in contradiction with the experiments. The experimental results were measured at $T=300\mathrm{K}$, explaining the difference in magnitude between the two datasets. The fit to the experimental data is taken from [12]. (b) The coercivity of the hysteresis loop seems to be unrelated to the grain diameter, as shown by the linear fit with a gradient of only 0.0005 T.

Figure 10

Predicted exchange bias in the multigranular system for different grain sizes. The exchange bias decreases with the grain diameter as observed in our simulations.

Figure 11

The simulated grain size dependence of the exchange bias and coercivity at $T=300\mathrm{K}$ compared to experimental results [12]. The dependence of the exchange bias with grain size at 300 K. The experimental results for AFM thicknesses of 6 and 12 nm are shown; our simulation behaves more like a 12 nm system than a 6 nm system, even though our AFM thickness was only 5 nm.