Coherent ac spin current transmission across an antiferromagnetic CoO insulator

The recent discovery of spin current transmission through antiferromagnetic insulating materials opens up vast opportunities for fundamental physics and spintronics applications. The question currently surrounding this topic is: whether and how could THz antiferromagnetic magnons mediate a GHz spin current? This mismatch of frequencies becomes particularly critical for the case of coherent ac spin current, raising the fundamental question of whether a GHz ac spin current can ever keep its coherence inside an antiferromagnetic insulator and so drive the spin precession of another ferromagnet layer coherently? Utilizing element- and time-resolved x-ray pump-probe measurements on Py/Ag/CoO/Ag/Fe75Co25/MgO(001) heterostructures, here we demonstrate that a coherent GHz ac spin current pumped by the Py ferromagnetic resonance can transmit coherently across an antiferromagnetic CoO insulating layer to drive a coherent spin precession of the Fe75Co25 layer. Further measurement results favor thermal magnons rather than evanescent spin waves as the mediator of the coherent ac spin current in CoO.


Supplementary Note 1. Sample growth
Epitaxial Py/Ag/CoO/Ag/Fe75Co25/MgO(001) and Py/Ag/CoO/MgO(001) samples were grown by molecular beam epitaxy in an ultrahigh-vacuum system with a base pressure of 5x10 -10 Torr. All films were grown at room temperature. Fe75Co25 was grown by evaporation of Fe and Co in a 3:1 ratio. The CoO film was grown by evaporating Co from an e-beam target at an oxygen atmosphere of 2.0x10 -6 Torr. Ag and Py were grown from thermal crucibles. Low-energy electron diffraction (LEED) results show a single-crystalline bcc structure for Fe75Co25 and an fcc structure for the CoO, the NiO, and the Ag layer Supplementary Figure 2b,c show CoO spectra at x-ray polarizations of = 0° and = 90° for a magnetic field applied along the y and z axes. Recalling that the XMLD effect is revealed by the difference between the = 90° and = 0° spectra, observation of opposite CoO XMLD effects for the magnetic field applied along the y and z axes shows that the CoO AFM spins are coupled and rotatable with the Py spins.
Supplementary Figure 2d shows the CoO L3 ratio RL3 (which is defined as the ratio of intensity at a photon energy of 778.2 eV to that at 778.7 eV) as a function of x-ray polarization angle.      Supplementary Figure 3e) shows that the 10nm Ag layer decouples the Py and the Fe75Co25 layers, and that the sample with the 2nm Ag layer retains a temperature-independent Py/Fe75Co25 interlayer coupling, which is consistent with the temperature-independent int value in the main text [ Fig. 2f]. While it was shown recently that AFM magnons can in certain cases mediate an interlayer coupling between two FM layers [5], the weak temperature dependence of the Py/Fe75Co25 interlayer coupling requires additional study. Regarding nature of the coupling between a FM layer and the CoO through a Ag layer, there could be RKKY, pinhole mediation, or dipolar couplings. Our previous work [6] shows that the interlayer coupling between Fe and CoO through Ag oscillates with the Ag thickness with a peak at 2nm Ag and decays to a negligible value for Ag thicker than ~5nm. The oscillatory behavior is a signature of RKKY interaction rather than pinhole mediation or dipolar couplings. In addition, the existence of oscillatory coupling also indicates that the flatness of the Ag spacer layer is better than a fraction of a nanometer.

Supplementary Note 4. Interlayer coupling between Py and FeCo across Ag/CoO/Ag
In fact, our previous x-ray pump-probe measurements of coupling through an insulating MgO layer [3] show that the sample quality is such that there is negligible pinhole and dipolar coupling. Finally, any coupling term should produce a monopolar phase behavior, regardless of the origin of the coupling.
Therefore we conclude that the results obtained from the Py/Ag/CoO/Ag(10nm)/Fe75Co25 sample, particularly the bipolar phase behavior, are due to transmission of a coherent ac spin current through the CoO.

Supplementary Note 5. Uncompensated FM Co spins in CoO
In order to make sure that the observed ac XMCD signal at the Co edge originates solely from the Fe75Co25 layer, we carried out additional ac XMCD measurements of the CoO layer at the Co L3 edge [ Supplementary Figure 4b]. It is well known that oxygen migration at the interface between CoO and a metal layer [7] (e.g. Ag in our case) or the magnetic interaction between the FM and AFM layers across the NM spacer layer [8] can result in a fraction of a monolayer of uncompensated ferromagnetic Co spins at the interface. XMCD and XMLD measurements at the Co edge were used to identify potentially Ac XMCD measurements of the uncompensated FM Co spins were carried out at 4GHz, but did not yield a measurable signal. However, by adjusting the microwave frequency to 2 GHz, we were able to increase the power output of the frequency generator and deliver more rf power to the sample.
However, in this configuration we were limited to exciting the Py FMR at 280K with a resonance field of 80 Oe. We performed ac XMCD measurements on Py(30nm)/Ag(2nm)/CoO(2.5nm)/MgO(001) at 20 Oe, 80 Oe, and 150 Oe. Supplementary Figure 4a surface. The absence of Py FMR at low temperatures (less than ~270K) at 2GHz makes it impossible to make temperature-dependent and field-dependent measurements on the uncompensated FM Co spins. Therefore, we grew a Py(30nm)/Ag(2nm)/Co(1nm)CoO(2.5nm)/MgO(001) sample to simulate the behavior of the FM Co spins at the Ag/CoO interface and performed ac XMCD measurements at 4 GHz (main text). We note that even with the greater microwave power used at 2GHz, the uncompensated FM Co ac XMCD is only a small fraction of the Co ac XMCD signal at 4GHz in Py/Ag/CoO/Ag(10nm)/Fe75Co25 (at least less than 20%) This is strong evidence that the Co ac XMCD signal at 4GHz in the Py/Ag/CoO/Ag/Fe75Co25 system originates mostly from the Fe75Co25 layer.