Spin-orbit quantum impurity in a topological magnet


Engineered atomic impurity

Co3Sn2S2 has a layered crystal structure and a ferromagnetic ground state (Curie temperature, TC = 170 K) with the c-axis magnetization arising from the Co kagome lattice. Cleaving preferentially breaks its S-Sn bond, which leads to the S and Sn terminated surfaces. Previous STM studies have dominantly observed two surfaces, one with largely vacancy defects and the other with adatom defects11,13,14. Several factors challenge their assignation, as the two surfaces have identical lattice symmetries, their interlayer distance is sub-Å in scale, and STM topographic image convolutes the spatial variation of the integrated local density of states and the geometrical corrugations23. Decisive experimental evidence for surface identification can be found by imaging the symmetry-dictated surface boundary and the layer-selective chemical dopants23,24,25. In previous work11, we have determined that the vacancy surface is the Sn layer and the adatom surface is the S layer by imaging their surface boundary determined by the crystalline symmetry. We further conclude this assignation by doping the bulk Co3Sn2S2 single crystals with 1% In impurities and imaging the layer-selective In-dopants. The In impurities preferentially replace the Sn atoms according to previous experimental and theoretical studies20,21, as well as our recent systematic single-crystal growth22. Indeed, on the vacancy surface identified11 to be Sn, we observe dilute substitutional atoms with consistent concentration (Fig. 1a), suggesting these impurities to be In atoms.

Fig. 1: Engineered atomic impurity state in a topological magnet.

a Atomically-resolved topographic image of Sn layer of 1% In doped Co3Sn2S2. b Differential conductance spectrums taken on the Sn lattice (blue) and at the In impurity (red), respectively. c First-principles calculation13 of the spin-resolved local density of states of the Sn lattice (blue) and an In impurity (red), which shows a magnetic impurity resonance. The inset shows the spin-down states of the Co atom closest to the In impurity. d Topographic image of an isolated impurity. e Corresponding differential conductance map taken at E = −270 meV (resonance energy). f Correlation between the atomic structure and the pattern in the differential conductance map. g Differential conductance spectra taken across the surface with spatial variation from the center of the In impurity (dark red) to far away (blue). The inset shows the exponential fit to the spatial decay of the impurity resonance.

Spatial feature of single impurity resonance

By performing an extensive study on the electronic properties of the In impurities, we find that each impurity repeatedly features a sharp state at the negative energy as shown in Fig. 1b. First-principles calculations show that each In impurity is almost nonmagnetic but introduces a strong resonance (Fig. 1c), similar to the experimental data. The calculations further reveal that the impurity resonance arises from a spin-down state (opposite to the bulk magnetization direction) and resides in the spin-down bandgap. Thus, the magnetic resonance state likely arises from the local impurity perturbation of the spin-polarized band structure. As the low-energy band structure is dominated by Co 3d orbitals, the resonant impurity state of the In atom also implies that there a strong local impact on the Co kagome lattice in real-space. To explore the detailed real-space feature, we probe the local electronic structure for an isolated In impurity, as shown in Fig. 1d. The corresponding dI/dV map at the impurity resonance energy in Fig. 1e shows a localized pattern bound to the impurity site (Fig. 1e). The bound state couples with three nearby Co atoms in the underlying kagome lattice, as illustrated in Fig. 1f. This is consistent with the first-principles calculation that the nearby magnetic Co atoms also feature such resonance state (inset of Fig. 1c), supporting the Co-In coupling (See Supplementary Note 1). Figure 1g shows the representative dI/dV curves measured with increasing distance from the impurity, demonstrating the bound state decaying in intensity without detectable energy dispersion or splitting. An exponential fit to the decay yields a characteristic length scale of 2.8 Å (inset of Fig. 1g). Therefore, these systematic characterizations reveal that the nonmagnetic In impurity couples with the underlying magnetic kagome lattice to introduce a striking localized bound state.

Magnetic nature of single impurity resonance

To probe the magnetic nature of the impurity bound state, we perform tunneling experiments with a spin-polarized Ni tip under weak magnetic fields26,27,28,29. The bulk crystal has a coercive field BC ~ 0.3 T, and Ni tip is a soft magnet with a BC 0.1 T that can be easily flipped by reversing the magnetic field29. We measure the tunneling signal of the impurity state while sequentially applying fields along the c-axis of +0.5 T, + 0.1 T, −0.1 T, −0.5 T, −0.1 T, and +0.1 T to systematically flip the magnetization of the tip and sample (Fig. 2a). This sequence allows us to perform spin-polarized measurements of the impurity. The +0.5 T field polarizes both the sample and tip, aligning the spin of the tip and anti-aligning the spin of the impurity state, due to the spin-down nature of the impurity state. A + 0.1 T field does not change the polarization of either the tip or impurity state. Flipping the field to −0.1 T also flips the spin of the tip, leaving the spin of the impurity state unchanged (down). Here, with both tip and impurity state spins aligned down, we observe an intensity increment of the tunneling signal. Next, we further decrease the field to −0.5 T, which flips up the spin of the impurity state with a corresponding reduction of the tunneling signal. Last, by sequentially changing the field to −0.1 T and +0.1 T, we flip the spin of the tip (down) and again observe an increase in the intensity. Our progressive field manipulation strongly supports that impurity state features spin-down polarization tied to the bistable magnetic bulk, consistent with the first-principles calculation.

Fig. 2: Magnetic nature of the impurity bound state.
figure2

a Dependence of the impurity state with Ni tip under a weak magnetic field. We apply +0.5 T, + 0.1 T, −0.1 T, −0.5 T, −0.1 T, + 0.1 T fields to systematically flip the magnetization of the tip and sample. The inset schematics illustrate the respective spins of the tip and the impurity state that is anti-aligned with bulk magnetization direction. b Dependence of the impurity state with a strong magnetic field. Under both +8 T and −8T, the peak exhibits a magnetization-polarized Zeeman energy shift of 2.2 meV, which amounts to an effective moment of −5µB. The inset data shows the energy shift for different magnetic field magnitudes. Inset schematic illustrates the magnetization-polarized Zeeman effect. The applied field aligns the spins of the impurity state in the same orientation, hence +z and –z orientation fields lead the energy to shift in the same direction.

To further determine the effective moment of this magnetic polarized state, we probe the state by applying a strong external magnetic field (|B | BC) along the c-axis with a nonmagnetic tip. Under the field, a spin-up/spin-down band hosting an intrinsic magnetic moment of +1/−1 Bohr magneton will exhibit a Zeeman shift to lower/higher energies in a rate of 0.058 meVT−1. Moreover, when the magnetism of the system is polarized with an applied field, the spin-polarized state will always shift to the same energy direction regardless of the relative field orientation11 (top inset schematic in Fig. 2b), which was also experimentally observed for the 8 T and −8T data (Fig. 2b). The positive energy shift indicates the state has a negative magnetic moment, calculated to be −5μB (or a Landé g factor of 10) based on a shift rate of 0.275 meVT−1 (right inset of Fig. 2b). This large value is beyond the spin Zeeman effects (~−1μB) and indicates the additional negatively polarized orbital magnetization. The anomalous Zeeman effect with an unusual moment or g factor has been observed in the electronic bands of kagome magnets9,11,17, which is often linked to the Berry phase physics associated with magnetism and spin-orbit coupling9,11,30,31. Since the In impurity couples with the Co atoms in the kagome lattice, the higher orbital angular momentum of the hybridized In-Co orbital can contribute to the large effective moment. We note that the effective moment of −5μB represents the diamagnetic response induced by the In impurity, and should not be thought as the local magnetic moment of the impurity atom.

Interacting impurity states induced quantized orbitals

Having characterized magnetic resonance state from the isolated impurity, we further probe the coupled impurity states to understand how they interact with each other through extensive imaging and spectroscopy investigation with a nonmagnetic tip. In Fig. 3a, we present the evolution of the impurity bound state with increasing perturbation strength caused by a second nearby impurity. We find that with decreasing spatial separation, the bound state progressively decreases in intensity and finally splits into two subpeaks. Figure 3b further compares three cases with one isolated impurity, two neighboring impurities, and three neighboring impurities, respectively. We find the quantized number of split impurity states matches with the coupled impurity number, highlighting their atomic-scale quantum-level coupling. Differential conductance maps at these corresponding splitting energies demonstrate their distinct orbital hybridizations (Fig. 3c). For two neighboring impurities, the dI/dV maps show a bonding (σ) and antibonding (σ*) orbital formation4, consistent with the quantum coupling of doubly degenerate states. For three impurities, the dI/dV maps show the formation of one bonding (σ) and two antibonding (σ1*, σ2*) orbitals, an unusual situation in which we discuss below.

Fig. 3: Interacting impurity states induced quantized orbitals.
figure3

a Differential conductance spectra taken at the central impurity with perturbations of varying strengths from a second impurity. Inset: respective topographic images for impurity configurations. Note the images are acquired by finding different surface locations. b Local impurity state with coupling to different numbers of impurities. The arrows highlight the quantized splitting with additional interacting impurity numbers. Note the images are acquired by finding different surface locations. c dI/dV maps at the respective bound state energies in (b). dI/dV maps taken at V = −270 mV for a single impurity; −315 mV (bonding state σ) and −240 mV (antibonding state σ) for a double impurity, respectively; −310 mV (bonding state σ), −220 mV (antibonding state σ1*) and −170 mV (antibonding state σ2*) for a triple impurity, respectively. The black dots mark the center of impurities.



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