Noncollinear magnetism at interfaces in iron-chromium alloys: The ground states and finite-temperature configurations

Noncollinear configurations of local magnetic moments at Fe/Cr interfaces in Fe-Cr alloys are explored using a combination of density functional theory (DFT) and magnetic cluster expansion (MCE) simulations. We show that magnetic frustration at Fe/Cr interfaces can be partially resolved through the formation of noncollinear magnetic structures, which occur not only at stepped but also at smooth interfaces, for example at the (110) interface where magnetic noncollinearity predicted by simulations is observed experimentally. Both DFT and MCE simulations predict that the magnetically frustrated (110) interface has the highest formation energy in the low-temperature limit. Using MCE and kinetic Monte Carlo simulations, we investigate the effect of temperature on magnetic order at interfaces and on interface energies. We find that while the low-temperature noncollinear bulk magnetic configurations of Cr remain stable up to the Néel temperature, the chromium atomic layers close to the interfaces retain their magnetic order well above this temperature. We also show that above the Curie temperature the (110) interface is the lowest energy interface, in agreement with DFT simulations of interfaces separating ferromagnetic Fe and nonmagnetic Cr.

Figure 1

Schematic representation of the DFT magnetic structure of the (110) Fe/Cr interfaces with collinear (left) and noncollinear (right) magnetic order, showing Fe (black) and Cr (green) atoms near the interface. The magnitude and orientation of local magnetic moments are indicated by arrows.

Figure 2

Schematic representation of the DFT magnetic structure of the (100) Fe/Cr interfaces with collinear (left) and noncollinear (right) magnetic order, showing Fe (black) and Cr (green) atoms near the interface. The magnitude and orientation of local magnetic moments are indicated by arrows.

Figure 3

Schematic representation of the DFT magnetic structure of the (111) Fe/Cr interfaces with collinear (left) and noncollinear (right) magnetic order, showing Fe (black) and Cr (green) atoms near the interface. The magnitude and orientation of local magnetic moments are indicated by arrows.

Figure 4

Variation of the magnitude of Cr and Fe DFT local moments (in ${\mu }_B$) in the vicinity of the (100), (110), and (111) interfaces, in relation to their bulk values. Converged values are found for both collinear (Coll) and noncollinear (NColl) magnetic structures for the same supercells as those noted in Table . For the (110) interfaces, only the values corresponding to Cr atoms situated in one of the two columns in the Fig. 1 are shown.

Figure 5

Noncollinear DFT magnetic structures near Fe/Cr interfaces: absolute values of the angle between the local moments of various atoms and the moments of the inner bulklike Fe atoms. For the (110) interface, only the values corresponding to Cr atoms in one of the two columns in Fig. 1 are shown.

Figure 6

The MCE magnetic structure of the (100) Fe/Cr interface. Fe atoms are shown as black spheres, Cr atoms are green spheres.

Figure 7

The MCE magnetic moments diagram for the (100) Fe/Cr interface. Fe moments are shown as dark-gray dots, Cr moments as green dots. Arrows represent directions of total magnetic moments for Fe and Cr subsystems.

Figure 8

Angle between the average Cr MCE magnetic moments in an atomic layer and the average Fe moment shown as a function of the number of the Cr layer. For the (110) Fe/Cr interface, two angles are shown for the Cr subsystem, corresponding to the two Cr columns with antiparallel (in the bulk) orientation of magnetic moments.

Figure 9

The MCE magnetic structure across the (110) Fe/Cr interface. Fe atoms are shown as black spheres, Cr atoms are green spheres.

Figure 10

Magnitude (in ${\mu }_B$) of Cr magnetic moment shown as a function of atomic layer for the (100) Fe/Cr interface simulated using MCE for several temperatures (a), and the temperature dependence of the average MCE Cr magnetic moment near the Cr-Fe interface and in the bulk (b).

Figure 11

Magnitude (in ${\mu }_B$) of Fe magnetic moment vs atomic layer index at the (100) interface simulated using MCE for several temperatures.

Figure 12

Temperature dependence of the MCE interface formation energies.

Figure 13

Regions in the space of the second-nearest-neighbor interaction parameters where the collinear magnetic structure at the (100) Fe/Cr interface is stable (shaded). The star sign indicates the actual values of these parameters in the MCE model.