Spin Seebeck effect at low temperatures in the nominally paramagnetic insulating state of vanadium dioxide

Vanadium dioxide is an archetypal strongly correlated transition metal oxide, with a phase transition at ∼345 K in bulk between a high temperature, rutile metallic phase with 1D vanadium chains, and a low temperature, monoclinic insulating phase with dimerized vanadium atoms. The vanadium dimers are thought to form singlets, greatly reducing the magnetic response of the VO₂ at low temperatures.^1–3 

The spin Seebeck effect (SSE) has proven useful in characterizing angular momentum transport in magnetic insulators.^4,5 In measurements of the nonlocal spin Seebeck effect (nlSSE), the current flowing through a heater wire on the surface of a material of interest is driven at angular frequency ω, leading to a temperature gradient with a DC offset and an AC component at 2ω. A properly oriented angular momentum current is driven by the temperature gradient (e.g., a flux of magnons in a ferrimagnet⁶ or antiferromagnet⁷), and a voltage at 2ω is detected at nearby inverse spin Hall detector made from a strong spin–orbit metal (e.g., Pt). The nlSSE was first observed in the ferrimagnetic insulator Y₃Fe₅O₁₂ (YIG), where the magnon spin diffusion length is found to be several micrometers at room temperature.⁸ This nonlocal approach to examining the SSE has been applied to different magnetic systems, including antiferromagnets (NiO,⁷ α-Fe₂O₃,⁹ and α-Cr₂O₃¹⁰). The local SSE has been observed in paramagnets (Gd₃Ga₅O₁₂ ≡ GGG, DyScO₃;¹¹ La₂NiMnO₆ above its ferromagnetic ordering temperature;¹² the quantum spin chain compound Sr₂CuO₃¹³). In GGG, while there is no long-range magnetic order, there are short-range order¹⁴ and field-induced long-range order that are thought to play a role in the transport of angular momentum as detected by the local SSE.¹⁵ Thus far, there are no reports of the nlSSE in paramagnets.

In this work, we report a nonlocal spin Seebeck response in VO₂ films at low temperatures deep in the insulating regime. Given the expected nature of paramagnetism in this material, this observation is surprising. For a fully spin dimerized system, paramagnetic response is expected to be suppressed at low temperatures, unlike, e.g., a classical spin liquid (such as GGG). The “local” paramagnetism, as in the van Vleck mechanism, is expected to be temperature independent, not expected to transport angular momentum and, thus, should not contribute to the SSE response. The SSE is nonhysteretic as a function of B and has the expected dependence on orientation of magnetic field in-plane. With the field in-plane, the SSE signal grows in magnitude with the decrease in temperature below an onset of detectability at approximately 30 K, with a sign inversion between 15 and 10 K.

The ∼100 nm thick epitaxial VO₂ film was grown by reactive sputtering on top of an Al₂O₃ substrate (r-cut). A 4-mTorr argon/oxygen mix (8% O₂) was used during deposition, and the substrate was kept at 520 °C during the growth and later cooled down at a rate of 12 °C min⁻¹. X-ray diffraction measurements confirmed single-phase growth, textured along (100) for VO₂. Transport measurements were carried out on a TTPX Lakeshore cryogenic probe station, using a Keithley 6221 current source and a Keithley 2182A nanovoltmeter. Electron beam lithography and magnetron sputtering are used to prepare Pt nanowires (100 μm long, 20 nm thick, 200 nm wide, separated by 400 nm) on the VO₂ surface for the nonlocal SSE measurements, shown in Fig. 1(b). Typical resistance of each wire is 18–20 kΩ. The films exhibit a large, hysteretic metal–insulator transition [Fig. 1(c)], as expected for high quality films. Measurements are performed as a function of temperature and field in a Quantum Design Physical Property Measurement System equipped with a rotation stage.

As shown in Fig. 1(a), an AC heater current at angular frequency ω = 2π × (7.7 Hz) is driven through a Pt wire, while the voltage across the other wire is measured at ω and 2ω using a lock-in amplifier. The dominant signal at ω is due to capacitive coupling between the wires. Even in the absence of VO₂ (e.g., Pt wires fabricated on SiO₂/Si or sapphire substrates), there is a temperature-dependent, magnetic field-independent parasitic background signal at 2ω in this electrode and wiring geometry (see supplementary material Fig. S2).

Below 30 K, a magnetic field-dependent 2ω signal becomes detectable, as shown in Figs. 2(a) and 2(b) for in-plane field oriented along α = 0°. The signal magnitude increases with the increase in field, linearly near B = 0 T, and saturates at high fields, with no indication of hysteresis as a function of B. As the temperature decreases, the magnitude of the signal increases, with a change in sign between 10 and 15 K. The signal grows rapidly with further decreases in temperature, and the saturation at large B is readily apparent.

To confirm that this 2ω signal results from the spin Seebeck effect, it is important to consider the field dependence of the signal on the orientation of B in the plane of the film. As shown in Fig. 3(a), at each temperature and fixed field B = 3 T, the signal is fit well by a cos α dependence, as expected for the SSE and required for the generation of an inverse spin Hall signal in the Pt associated with transport of angular momentum from magnetization oriented along the y-axis in the geometry of Fig. 1(a). The 2ω voltage signal likewise depends linearly on heater power at fixed B oriented at α = 0°, as expected for a signal of spin Seebeck origin [Fig. 3(b)]. A possible confounding effect could be the Nernst response of Pt but that is expected to be temperature independent¹¹ and would require a vertical temperature gradient at the VO₂/Pt detector interface and in the Pt detector. Instead, the temperature dependence of the signal is qualitatively similar to the paramagnetic response reported in the susceptibility,^3,16 supporting that the measured signal originates from the SSE. In addition to Nernst response, another possible contribution to a 2ω signal in the detector would be local SSE at the detector due to a local temperature gradient.¹⁷ However, our temperature profile simulations (see the supplementary material) show that the vertical temperature difference between detector Pt and underlying VO₂ film is on the order of 10⁻⁴ mK (Fig. S9), far too small to lead to any measurable Nernst or local spin Seebeck effects.

Extensive additional control experiments are shown in the supplementary material. Concerns about charge leakage, unintended capacitive couplings, and other artifacts have been raised in nonlocal spin transport experiments in conducting samples.¹⁸ We examined the 2ω signal present in the identical Pt electrode geometry, fabricated directly on a sapphire substrate, and found no magnetic field dependence for in-plane fields (Fig. S1). We performed a temperature-dependent study of this background as a function of wiring configuration on a SiO₂/Si substrate (Fig. S2), and again we found that it is field independent. Measurements on VO₂ devices with a Au wire and a Pt wire show a field-dependent 2ω SSE response when the Pt wire is used as the detector, and no temperature/field-dependent response when the Au wire is used as the detector (Fig. S5). Possible charge leakage between heater and detector is expected to lead to a 1ω signal rather than a 2ω signal; the 1ω signal is dominated by capacitive effects (out of phase response larger than the in-phase response) and shows no clear field dependence at 5 K (Fig. S6). These controls as well as the systematic dependence of the measured signal on temperature, power, field magnitude and direction, and device geometry are consistent with nlSSE response as the signal origin.

The growth of the SSE signal magnitude with a decrease in temperature is consistent with observations of local SSE response in other paramagnets.¹¹ In these experiments, the local SSE response as a function of B resembles the experimentally determined M vs B polarization. Deviations in the SSE vs B in GGG from a simple Brillouin function-like dependence become apparent below 4 K and are thought to be related to short-range magnetic order.¹⁵ Because of the small volume of VO₂ material relative to the volume of sapphire substrate and paramagnetic impurities contained within the sapphire,¹⁹ it has not been possible to isolate directly M vs B for the VO₂ films in our samples. The low temperature magnetization M in bulk VO₂ crystals³ does not saturate at high fields.

The sign reversal in the measured SSE between 10 and 15 K is qualitatively similar to a sign reversal observed in nlSSE measurements on YIG films.⁶ In that system, spin transport takes place via magnons, with regions of elevated magnon chemical potential building up in proximity to the injecting and collecting Pt wires.²⁰ The SSE sign reversal in that case is a consequence of a crossover of length scales between Pt electrode spacing and magnon chemical potential spatial scale, affected strongly by the thickness of the magnon-bearing YIG film on the GGG substrate. In the present experiment, the sign reversal in SSE response moves to lower temperatures with the increase in electrode spacing (see supplementary material Fig. S3), though a detailed study has not been performed. Sign reversal of the SSE response as a function of temperature can also take place due to other mechanisms. In antiferromagnets and compensated ferrimagnets, competing responses of two magnon branches can cause a crossover in SSE sign as a function of temperature.²¹ Similarly, in an antiferromagnet, the presence of multiple magnon branches can lead to a field-dependent precession of the magnon pseudospin.²² Both of these possibilities would require the presence of long-range magnetic order and multiple magnon branches in the material, which are believed absent in VO₂.

Repeated measurements of devices, after cycling back to room temperature and sample aging on the timescale of days or weeks, show much reduced signal magnitudes, though identical field dependences. The nlSSE signal depends critically on interfacial exchange coupling between the oxide and the Pt conduction electrons and, hence, is extremely sensitive to the Pt/oxide interface quality. The observed signal reduction upon sample aging likely indicates degradation of the Pt/VO₂ interface.

The presence of a strong spin Seebeck response that grows at low temperatures in VO₂ calls into question the nature of the angular momentum-carrying excitations. In prior examinations of paramagnets, the argument was advanced that SSE response can originate from short-range magnetic order¹⁵ or field-supported paramagnons at temperatures above a low ordering temperature.¹¹ The magnetic state of monoclinic VO₂ is thought to be a singlet-dimer state,¹ rather than a traditionally ordered state. One picture for the phase is that the dominant spin-carrying excitations are thermally excited triplets (“triplons”), and the increase in susceptibility at low temperatures in the material is due to the Curie-like response of the temperature-dependent effective spin of the dimers.^3,16 This picture does not have long-ranged order nor well-defined magnons. The sign inversion of the SSE as a function of temperature suggests that it may be related to the spatial distribution of the local chemical potential of spin-carrying excitations.

A triplon SSE has been reported in the local measurement configuration in the spin-Peierls system CuGeO₃,²³ where Cu atoms form one-dimensional spin-1/2 chains with antiferromagnetic exchange interactions. The most important feature of the triplon SSE is that it has the opposite sign of voltage to the magnon SSE in ferromagnetic insulators. This is because triplon spin current is carried by an excitation with spin direction parallel to the external field, while magnons carry angular momentum antiparallel to the field. Another feature of the triplon local SSE is that its magnitude does not scale with the $M(H)$ response and does not saturate at high fields, similar to what is observed in the VO₂ nlSSE. Based on this phenomenology, VO₂ is another candidate for the observation of the triplon SSE, though the sign reversal as a function of temperature in the nlSSE measurement complicates interpretation.

We note one report in the literature²⁴ in which muon spin rotation implies the onset of an internal magnetic field within monoclinic VO₂ below a sharp transition near 35 K. This is interpreted as originating from the “disruption of the V–V dimers,” which produce a “nonzero net spin” below 35 K. This suggests that there may indeed be some magnetic ordering taking place that is not readily observed in the susceptibility yet may lead to well-defined magnon excitations. While high temperature defect-mediated ferromagnetism is possible in VO₂ films deposited on sapphire,²⁵ there is no evidence of any ferromagnetic order in the present or other materials grown by the authors, nor is the observed field dependence compatible with ferromagnetism.

To summarize, we have detected a spin Seebeck response in insulating VO₂ films below 30 K that grows in magnitude with the decrease in temperature. This response is nonhysteretic in B, has the expected SSE dependence on field orientation in the plane, and saturates at large B and low temperatures. Given the singlet-dimer nature expected of the monoclinic VO₂ ground state, a detailed examination of angular momentum transport in this system is needed to explain these observations, and whether such an effect is a consequence of the transport of triplet excitations or a sign of the emergence of magnon-like excitations in a magnetically ordered phase below 35 K.

See the supplementary material for additional control experiments and thermal modeling.

The authors thank Shusen Liao for his assistance with finite element modeling. X.Z., D.N., R.L., and T.J.L. acknowledge support from Nos. DMR-1704264 and DMR-2102028 for spin Seebeck measurements. D.N. and L.C. acknowledge support from DOE BES Award No. DE-FG02-06ER46337 for data acquisition and development for spin transport in VO₂. Synthesis, characterization, joint design of the experiments, extensive discussions, and joint writing of the manuscript were funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-FG02-87ER45332.