Demonstration of Ru as the 4th ferromagnetic element at room temperature

Development of novel magnetic materials is of interest for fundamental studies and applications such as spintronics, permanent magnetics, and sensors. We report on the first experimental realization of single element ferromagnetism, since Fe, Co, and Ni, in metastable tetragonal Ru, which has been predicted. Body-centered tetragonal Ru phase is realized by use of strain via seed layer engineering. X-ray diffraction and electron microscopy confirm the epitaxial mechanism to obtain tetragonal phase Ru. We observed a saturation magnetization of 148 and 160 emu cm−3 at room temperature and 10 K, respectively. Control samples ensure the ferromagnetism we report on is from tetragonal Ru and not from magnetic contamination. The effect of thickness on the magnetic properties is also studied, and it is observed that increasing thickness results in strain relaxation, and thus diluting the magnetization. Anomalous Hall measurements are used to confirm its ferromagnetic behavior.


Supplementary Note 1. Additional thin film characterization
The surface profile, as measured by AFM (Supplemental Fig. 1) shows each sample is smooth, with all having a roughness (RMS) less than 3 Å, which in addition, confirms the validity of the results obtained from XRR fitting. Additional cross section STEM images of 2.5 and 12 nm Ru samples were collected (Supplemental Fig. 2). The 2.5 nm Ru shows consistent BCT Ru phase.
In the 12 nm Ru sample there is a distinct BCT Ru region, but also a region that cannot be definitively identified by high resolution STEM because it contains overlapping BCT and HCP phases. Regions with no distinct phase, such as in the 12 nm sample, are also found in the 2.5 and 6 nm Ru films, but the frequency of these regions increases with thickness. This shift to a greater amount of HCP grains with increased thickness is further supported by XRD scans (Fig 1c) showing a zoom in of the boxed region (scale bar is 5 nm and inset is 2 nm) (b) 12 nm Ru (scale bar is 2 nm). In the 12 nm Ru sample, two regions with differing crystallographic structure can be seen, as denoted by regions 1 and 2. Region 2 shows BCT structure akin to that shown in Fig. 2, however, region 1 is not clearly a tetragonal or hexagonal structure, but instead an overlap of both phases.

. Magnetic control measurements
It has been confirmed that the ferromagnetic properties observed were not due to contamination from the VSM sample holder or impurities in the sputtering target. This was accomplished by measuring the moment vs field curve for the holder used for each Ru after acquiring the sample hysteresis curve, a typical observed curve for the holder is shown in Fig. S3a, which clearly shows only diamagnetism from the sample holder. Contamination in the film as a source of ferromagnetism was ruled out by measuring moment vs. field for a 2.5 nm Ru film, with identical Mo seed layer and substrate, but with no texture, as confirmed in Fig. 1c The total number of samples fabricated (top row) are displayed in the '# Made' row and the number of these samples that display ferromagnetic (FM) behavior, such as in Fig. 4, are counted in the #FM row. Finally, the total number of ferromagnetic hysteresis loops measured across multiple measurements of the combined samples of the same thickness is counted in the '#FM M vs. H' row.

The most obvious difference between the M-H and RHall-H measurements is the resulting
Ms calculated. As mentioned in the main text, this is due to the inherit difference in calculating Moment vs field for (a) VSM sample rod, r (b) non-textured Ru (black) and textured (110) Mo with no Ru (blue) control samples. Both curves show no ferromagnetism, and correspond to the 2.5 nm sample. The 6 and 12 nm sample holder show similar non-ferromagnetic behavior.

Supplementary Fig. 3: Magnetic control measurements
Ms between the two measurement methods. In the case of M-H, Ms is calculated by dividing the measured magnetic moment by the appropriate magnetic volume. This calculation relies on the assumption that the Ru thin film is uniformly magnetic, which from XRD and STEM results, we know to be an invalid assumption. Due to this error in the volume, it is not surprising that a smaller than predicted Ms has been calculated from the M-H measurements. Determination of Ms from RHall-H measurements instead relies on the assumption of the shape anisotropy for a thin film as that of an infinite plane, which is a valid assumption given the low surface roughness and uniformity of the Ru thin films observed.
Additionally, it should not be expected for the M-H and RHall-H measurements to have the same shape. In ferromagnets, RHall = RO + RAHE, and so in the switching field region, RAHE is expected to depend linearly on the field since RAHE is directly dependent on Mz, which is proportional to Hz. Thus, RHall will linearly increase with the field until the magnetization is fully saturated; which in the case of a thin film with no easy axis, and a field applied perpendicular to the surface, will occur at H = 4πMs. The switching region of the M-H curve, however, is not linearly dependent on the field since the field is not being applied along a hard anisotropy axis. Finally, it should be noted that in the saturated region of the RHall-H measurement a linear background with negative slope has been subtracted. This negative slope is due to the ordinary Hall effect of Mo and Ru layers, which are electron carrier dominant since the layers are metallic; this same negative linear dependence on field can be seen in the non-textured RHall-H control measurement.