Bias asymmetry in the conductance profile of magnetic ions on surfaces probed by scanning tunneling microscopy

The conductance profiles of magnetic transition-metal atoms, such as Fe, Co, and Mn, deposited on surfaces and probed by a scanning tunneling microscope (STM), provide detailed information on the magnetic excitations of such nanomagnets. In general, the profiles are symmetric with respect to the applied bias. However, a set of recent experiments has shown evidence for inherent asymmetries when either a normal or a spin-polarized STM tip is used. In order to explain such asymmetries, here we expand our previously developed perturbative approach to electron-spin scattering to the spin-polarized case and to the inclusion of out of equilibrium spin populations. In the case of a magnetic STM tip, we demonstrate that the asymmetries are driven by the nonequilibrium occupation of the various atomic spin levels, an effect that is reminiscent of electron spin transfer. In contrast, when the tip is not spin polarized, such a nonequilibrium population cannot be built up. In this circumstance, we propose that the asymmetry simply originates from the transition metal ion density of states and from the uneven electronic coupling between the scattering magnetic atoms and both the tip and the substrate. These effects are included in the formalism as a nonvanishing real component to the spin-scattering self-energy.

Figure 1

Cartoon describing the transport processes, where an atom deposited on a substrate is probed by a STM tip. Here, we assume that the atom is in its ground state with spin-up orientation. In (a), the tip is non-spin-polarized and inelastic steps in the conductance appear for both bias polarities. In (b) and (c), the tip is fully spin polarized with polarization respectively up (b) or down (c). This leads to a conductance step only for one of the two bias polarities.

Figure 2

Excitation spectrum for an antiferromagnetically exchanged coupled Mn dimer deposited on CuN. The ground state is a $S=0$ spin singlet. The first three excited state multiplets have respectively spin $S=1$, 2, and 3. In the figure, we also indicate the energy separation between the various spin multiplets in units of the exchange parameter $J_{dd}$.

Figure 3

Normalized conductance spectra for the Mn dimer calculated at different tip to sample distance, i.e., for different ${\Gamma }_{\mathrm{tip}-\mathrm{S}}$ coupling strengths. We notice that the stronger is the coupling, the more the system is driven out of equilibrium. This results in the appearance of additional spin transitions, which manifest themselves as steps or drops of the conductance as a function of bias.

Figure 4

Nonequilibrium population of the Mn dimer singlet ($S=0$), triplet ($S=1$), and quintuplet ($S=2$) states. The inset shows a magnified view of the population of the $S=2$ state as it start to get populated at approximately 12 mV.

Figure 5

Normalized conductance spectra for a single Mn atom explored by a non spin-polarized STM tip at different tip to sample electronic couplings ${\Gamma }_{\mathrm{tip}}-\mathrm{S}$. Here, a magnetic field of 3 T is applied along the $z$ axis. Comparison is made between second- and third-order calculations.

Figure 6

Nonequilibrium population of the various spin states of Mn on CuN as a function of bias for non-spin-polarized tip.

Figure 7

Normalized conductance spectra for a single Mn atom explored by spin-polarized STM tip at different tip to sample electronic couplings ${\Gamma }_{\mathrm{tip}}-\mathrm{S}$. Here, a magnetic field of 3 T is applied along the $z$ axis. The asymmetry in the conductance profile is is due to the spin-polarization of the tip. Such an asymmetry is more pronounced as the system is driven further away from equilibrium. Comparison is made between second- and third-order calculations.

Figure 8

(a) Nonequilibrium population of the various spin states of Mn on CuN as a function of bias for spin-polarized tip and (b) the resulting average magnetization. These have been calculated for a magnetic field of 7 T aligned along the $z$ axis and for strong tip to sample electronic coupling ${\Gamma }_{\mathrm{tip}-\mathrm{S}}=200$ meV. We notice that as the spin is driven far away from its equilibrium ground state the magnetization flips its direction.

Figure 9

(a) Second- and third-order conductance spectra for the Fe atom with spin polarization $\eta =0.35$. The magnetic field of 3 T is applied both parallel and perpendicular to the easy axis of the Fe atom. (b) Second derivative of the current for the same spectra shown in (a).

Figure 10

Normalized conductance spectra for a single Mn single calculated by including the real contribution to the interacting electron-spin self-energy for different on-site energies ${\varepsilon }_0$. Note that the conductance asymmetry increases with decreasing ${\varepsilon }_0$, i.e., as the onsite energy moves closer to the Fermi level.

Figure 11

Comparison between the experimental (red) and theoretical (black) conductance spectra for a Mn trimer on CuN probed by a nonmagnetic STM tip. In the calculation, we have included the real part of the interacting electron-spin self-energy. This provides the conductance asymmetry with bias.