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Magneto-Seebeck tunneling on the atomic scale

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Science  08 Mar 2019:
Vol. 363, Issue 6431, pp. 1065-1067
DOI: 10.1126/science.aat7234

Mapping out the magneto-Seebeck coefficient

In the Seebeck effect, a temperature difference across a device generates voltage. If the thermal gradient is imposed across a magnetic tunnel junction—with two magnetized layers separated by an insulating tunnel barrier—the magnitude of the generated voltage depends on the relative orientation of the magnetization in the two layers. Transport measurements of this so-called magneto-Seebeck tunneling typically reveal only the signal averaged over the device. Friesen et al. created an atomic-scale version of this experiment by using a scanning tunneling microscope with a spin-polarized tip that they scanned across the surface of a magnetic sample. By heating the tip, they were able to map out the spatial dependence of the spin-resolved Seebeck coefficient.

Science, this issue p. 1065

Abstract

The tunneling of spin-polarized electrons across a magnetic tunnel junction driven by a temperature gradient is a fundamental process for the thermal control of electron spin transport. We experimentally investigated the atomic-scale details of this magneto-Seebeck tunneling by placing a magnetic probe tip in close proximity to a magnetic sample at cryogenic temperature, with a vacuum as the tunneling barrier. Heating the tip and measuring the thermopower of the junction while scanning across the spin texture of the sample lead to spin-resolved Seebeck coefficients that can be mapped at atomic-scale lateral resolution. We propose a spin detector for spintronics applications that is driven solely by waste heat, using magneto-Seebeck tunneling to convert spin information into a voltage that can be used for further data processing.

Active elements in spintronics devices must be scaled down to smaller and smaller dimensions, leading to higher charge and spin current densities and the subsequent generation of nontrivial heat fluxes. These have been considered unwanted side effects, but they have gained renewed interest recently because of experimental and theoretical studies showing that the relationship between spin and heat can be useful for future energy-efficient devices (13)—for example, by using waste heat for power generation, sensing, or computing applications. However, a detailed understanding of these effects at an atomic scale is missing.

Magneto-Seebeck tunneling is a spin-dependent generalization of the purely thermoelectric tunneling Seebeck effect (4). Its basis is the temperature-driven spin-polarized tunneling of electrons in a magnetic tunnel junction (MTJ) where the temperature T drops by ∆T across the junction. In each magnetic lead, the density of electrons follows a Fermi distribution around the chemical potential μ (Fig. 1A). For finite ∆T, a net tunneling of spin-polarized electrons is generated, resulting in a thermovoltage Uth = S · ∆T, with S being the Seebeck coefficient that depends on the relative orientation between the MTJ leads’ magnetizations. As has been shown in a theoretical study for the spin-averaged case, and assuming ∆T to be much smaller than the sample temperature Ts, S is given by (5)

S=π23kB2e2TsΣσ(1)
Fig. 1 Experimental approach.

(A) Schematic depiction of magneto-Seebeck tunneling between a hot and a cold magnet. A temperature-dependent filling (dark shading) of the spin-dependent DOS results in a net spin-polarized (sp) tunnel current. E, energy. (B) Schematics of a single-atom MTJ between a magnetic probe tip heated by a laser and a cold magnetic sample. The spin-resolved thermovoltage Uth arising from the temperature drop ∆T between the tip (at temperature Tt) and sample (at temperature Ts) is measured.

Here, σ = dI/dU and Σ = d2I/dU2 (where I is the current) are the first- and second-order differential conductances that are proportional to the density of states (DOS) and its first derivative in energy at μ, respectively (5), and kB is the Boltzmann constant. Consequently, a large thermally induced voltage is expected for MTJs with substantial nonlinearity, as expressed by a high Σ/σ ratio. To date, experimental studies of magneto-Seebeck tunneling have been performed in planar MTJ structures by using insulating tunneling barriers, formed by oxide layers between thin-film metal electrodes (611). In these structures, direct measurement and control of ∆T at the MTJ appears to be challenging. In addition, although the overall chemical composition of the MTJ can be controlled, atomic-scale local variations in the thin-metal films and the tunnel barrier of the fabricated MTJ are still prevalent. The measurements on planar junctions are averaged over the whole MTJ, preventing an experimental investigation of magneto-Seebeck tunneling between well-defined magnetic interfaces across a well-defined tunnel barrier.

We studied such tunneling by producing an MTJ consisting of an atomically sharp magnetic tip that is in tunneling contact with an ultrathin magnetic film (Fig. 1B). We thereby realized a single-atom point contact MTJ, with a vacuum serving as the tunnel barrier.

The ultrathin magnetic film is realized by evaporating Fe onto a clean W(110) single-crystal surface. Figure 2A shows the resulting magnetic structure of our sample schematically, depicting the system of combined Fe monolayer (ML) and double-layer (DL) areas. Whereas the ML is known to be in-plane ferromagnetic with domains that extend over large areas (12), the DL exhibits an easy magnetization axis pointing out of the surface plane (13). Performing spin-polarized scanning tunneling microscopy (SP-STM) with a magnetic probe tip that is magnetized out of the surface plane results in a spin-resolved tunnel conductance σ that resolves the out-of-plane component of the sample spin texture on the local scale (14). In Fig. 2B, such a Fe/W(110) ultrathin magnetic film surface is shown, as imaged by SP-STM with a bulk antiferromagnetic Cr tip that exhibits out-of-plane spin sensitivity (15). The topography is colored with σ as measured via lock-in technique by applying a small modulation bias [Umod = 3 mV root mean square (RMS); frequency f = 4 kHz] to the MTJ (14). Whereas the ML does not exhibit out-of-plane spin contrast, a nanometer-scale magnetic domain pattern with chiral Néel-type domain walls (16) is revealed by SP-STM, in agreement with the model depicted in Fig. 2A. Within the DL, a dislocation line releases the stress in the pseudomorphically grown film and locally interrupts the domain pattern (17). The spin-resolved map in Fig. 2C shows a DL zoom-in to four domains and four domain walls. The detailed spin configuration on the DL is revealed by fitting an established model of chiral 180° domain walls to a line section of σ (1821). Within the model, both the tunneling magnetoresistance (TMR), resulting from spin-polarized tunneling (21), and tunneling anisotropic magnetoresistance (TAMR), arising from relativistic spin-orbit coupling (SOC) (22), are taken into account. Additionally, a finite tunnel current spin polarization angle θt with respect to the easy axis of the DL is implemented in the model. As can be seen from the fit results in Fig. 2C, TMR and TAMR contributions are substantial for the MTJ, and the tip magnetization is canted by 17° with respect to the surface normal.

Fig. 2 Imaging atomic-scale magnetic spin structures.

(A) Schematics of the magnetic structure of the Fe/W(110) sample. Spin-polarized tunneling from an out-of-plane magnetized probe tip results in a magnetic contrast on the DL of Fe. (B) SP-STM image of the Fe/W(110) sample surface. The topography is colored with the magnetic map. U = 250 mV; I = 1 nA; Ts = 50 K. (C) SP-STM magnetic map and corresponding line profile perpendicular to the domain walls in the DL, where x is the lateral position on the sample. The spin texture on the surface is determined by fitting a model of four domain walls (red) that accounts for the TMR and TAMR of the MTJ.

To directly investigate magneto-Seebeck tunneling, the voltage UMTJ generated at the MTJ has been recorded on the ferromagnetic domains of the DL while heating the tip with a laser. The tip height is adjusted for constant σ, and experiments have been performed with compensated tunneling conditions, meaning that a dc countervoltage Uc has been applied such that σ·(Uc + UMTJ) = 0 (23). The laser heating causes an expansion of the tip, requiring a retraction of the tip position to maintain tunnel contact. From this, the temperature drop of ∆T at the MTJ has been quantified by fitting the thermally induced retraction of the tip with a model of linear expansion at a given laser power (20, 24). The results for the spin-resolved Uc as a function of ∆T are shown in Fig. 3A for the parallel and antiparallel alignments of the tip and sample magnetization as determined from SP-STM on the same area. The data indicate a linear relation between Uc and ∆T, suggesting Seebeck tunneling at the MTJ that follows Uth = ST, even in the limit of a single-atom point tunnel contact. Additionally, a spin dependence is observed, as revealed by the two distinct slopes of Uc (∆T), which can be explained via a two-channel model of elastic spin-polarized tunneling. S is determined for both domain types, yielding Sap = (15 ± 1) μV K−1 for the antiparallel and Sp = (11 ± 1) μV K−1 for the parallel MTJ spin configurations, corresponding to a tunneling magneto-Seebeck (TMS) ratio of −36%, which is defined as (Sp Sap) divided by min(|Sp|, |Sap|) (10).

Fig. 3 Determination of magneto-Seebeck tunneling coefficients.

(A) Uc recorded on magnetic domains corresponding to the parallel or antiparallel magnetic alignment of the tip to the sample. When tip heating is applied, a linear increase in Uc is observed with increasing ∆T. (B) Map of local compensation bias Uc for zero tunneling current, with no tip heating, as generated on the same area as in Fig. 2B. σ = 4 nS; Umod = 3 mV RMS; Ts = 50 K. (C) Map of magneto-Seebeck coefficients S on the DL magnetic domain pattern, as calculated from Uc from the image in (B). Fitting the profile with a model of magneto-Seebeck tunneling results in the determination of contributions to S arising from TMS and TAMS thermopower. (D) Angularly and (E) component-resolved decomposition of the experimentally observed contributions to Seebeck tunneling: spin-averaged, TMS, and TAMS thermopower.

On the same area as that shown in Fig. 2A, Uc has been recorded with no tip heating (∆T = 0). In Fig. 3B, the map of Uc is used to color the topography, being in the range of several hundred microvolts. In this case, a slightly different tip was used, resulting in Sap = (7 ± 1) μV K−1 and Sp = (4 ± 1) μV K−1, as revealed by a corresponding tip heating experiment. The TMS ratio is calculated to be −75% and is substantially larger than that in the experiment shown in Fig. 3A. The observed pattern in Uc corresponds to the spin texture shown in Fig. 2C. The finite Uc is explained by the MTJ acting as a fast-switching diode for current rectification (2427), generating a dc bias Urect from Umod:

Urect=Umod24Σσ(2)

The nonlinearity of the MTJ in terms of Σ/σ gives rise to considerable Urect that is also actively compensated for zero net tunnel current in our experiment by applying Uc. As both Uc and S depend critically on Σ/σ, the measured finite TMS ratio implies that this rectified voltage will also be spin polarized. This approach of compensated conditions allows for magnetic imaging at μ, by using a spin-polarized ac tunnel current while compensating for dc components. Combining Eq. 1 with Eq. 2 results in S being a linear function of Urect:

S=4π23kB2e2TsUmod2Urect(3)

Consequently, the scanning probe capability of STM together with spin-resolved tunnel current rectification experiments allows for direct mapping of S on the atomic scale, even at ∆T = 0 (20). Figure 3C shows such a magneto-Seebeck map, as generated from Urect in Fig. 3B, under compensated conditions. As can be seen from the map and the corresponding line profile, a clear contrast is visible between the magnetic domains. A cosine dependency of S on the angle enclosed by the magnetizations of the leads has been found in lithographically fabricated MTJs, which is attributed to the TMS effect (11). Additionally, S varies with the relative orientation of the sample magnetization with respect to the fixed tunnel current direction. This tunneling anisotropic magneto-Seebeck (TAMS) thermopower results from SOC and scales with sin2 of the angle enclosed by the tunnel current direction and the sample magnetization (28, 29). In our experimental data, small enhancements in S are observed whenever the tip is positioned above a domain wall. The magnetic moment on the sample passes through the perpendicular configuration with respect to the tunnel current direction. Consequently, we attribute the local enhancement in S to TAMS thermopower arising from a local SOC-induced modification of the band structure at the domain walls. Taking spin-averaged, TMS, and TAMS tunneling into account, S as a function of sample magnetization phase θs is given byS=Savg+STMScos(θtθs)+STAMSsin2(θs)(4)with Savg, STMS, and STAMS being the spin-averaged, TMS, and TAMS contributions to thermal tunneling, respectively, and where θs is related to the lateral position by a standard Bloch wall profile (20, 21). The model also accounts for a canted tip magnetization θt with respect to the magnetic easy axis of the sample. As can be seen from the fit results in Fig. 3C, the model reproduces the experimental data. It allows for the angle-resolved decomposition of spin-averaged, TMS, and TAMS contributions to thermal tunneling (Fig. 3D). TMS tunneling becomes important for the parallel and antiparallel alignments of tip and sample magnetization, whereas TAMS generates a considerable modification of S on the domain walls. The three main contributions are summarized in Fig. 3E. The spin-averaged Seebeck tunneling generates a considerable thermopower of (5.43 ± 0.01) μV K−1 in our experiments. It is accompanied by a TMS contribution of up to ±(1.48 ± 0.02) μV K−1, and a TAMS thermopower of up to (1.6 ± 0.1) μV K−1 is generated.

Combining the scanning probe capability of SP-STM together with sensitive spin-resolved tunnel current rectification experiments in compensated conditions allows for the determination of S at high lateral resolution, without the need for tip heating. In Fig. 4A, the magnetic map of a single atomic layer of Fe/Ir(111) is shown, exhibiting a magnetic nanoskyrmion square lattice with a periodicity of 1 nm. This chiral noncollinear spin texture is stabilized by interfacial Dzyaloshinskii-Moriya interactions (30, 31). The simultaneously recorded map of S as obtained from Eq. 3 by using spin-polarized tunnel current rectification is shown in Fig. 4B. Both images show a very regular magnetic lattice with only local screening by individual defect atoms. The corrugation in S across the nanoskyrmion lattice is shown by the line profile in Fig. 4C. Here, S varies between −2.1 and −2.6 μV K−1 on a lateral scale of 0.5 nm. Thus, a TMS ratio of approximately −24% has been observed on the nanoskyrmion lattice, indicating a substantial change of thermally induced spin-polarized tunneling when moving the magnetic tip across the spin texture.

Fig. 4 Mapping the magneto-Seebeck tunneling coefficients on a nanoskyrmion lattice.

(A) Spin-resolved map of the Fe/Ir(111) nanoskyrmion lattice, taken at compensated tunneling conditions. σ = 4.5 nS; Umod = 12 mV RMS; Ts = 25.3 K. (B) Magneto-Seebeck map of the same area (the same scale bar applies) as in (A), revealing a considerable variation of S on the nanoskyrmion lattice. (C) Line profile along the line in (B). (D) Potential application in a spintronic device. Bit information is decoded from the thermovoltage generated by a heat-driven MTJ element that is placed on a racetrack for magnetic skyrmions.

Our study may enable high-efficiency spintronics applications that recover waste heat to drive atomic-scale read elements for the detection of individual magnetic domains, domain walls, or skyrmions. Such a potential application is depicted in Fig. 4D for a skyrmion-based magnetic racetrack memory. Bit information is encoded by the presence or absence of a skyrmion, and trains of skyrmions are moved along the track with electric currents. An MTJ fabricated on the racetrack allows for the decoding of the magnetic information in terms of magneto-Seebeck tunneling. The readout element is driven purely by waste heat from the device, and the spin information is converted into a voltage that is used for further processing. Such a readout element has no need for an electric power supply and can be deeply embedded into an atomic-scale, three-dimensional integrated circuit, using waste heat rather than generating it.

Supplementary Materials

www.sciencemag.org/content/363/6431/1065/suppl/DC1

Materials and Methods

Supplementary Text

Fig. S1

References (3348)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: Funding: We acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG), via the following projects: SPP1538 Spin Caloric Transport, project KR3771/1-1; SFB668 Magnetism from Single Atoms to Nanostructures, part project B04; and SCHL2096/1-1/2. Author contributions: C.F. and H.O. performed the experiments. C.F. analyzed the data. C.F., J.F., A.S., and S.K. were involved in the technical realization of the experiments. C.F., S.K., and R.W. wrote the manuscript. All authors discussed and commented on the experiments and the manuscript. S.K. leads the project. Competing interests: The authors declare no competing financial interests. Data and materials availability: All data shown in the paper are available in tabulated form in the Zenodo public repository (32).

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