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Recent work in spin caloritronics4,5 aimed at spin-dependent thermoelectric effects led to the discovery of thermally driven spin sources6,7,8,9,10, cooling/heating by spin currents11,12, the magneto Seebeck13,14,15,16 and Seebeck rectification17 in magnetic tunnel junctions. Ref. 18 predicted spin-dependent temperatures in spin valve structures for sufficiently weak inter-spin heat exchange. The spin heat relaxation by inelastic scattering leads to a breakdown of the Wiedemann–Franz relation19 between the charge and electronic heat conductance of the spin valve18,20. Earlier experiments on the magnetic field dependence of the in-plane thermal conductance of magnetic multilayers21,22,23,24 focused on determining whether the giant magnetoresistance effect is dominated by either elastic or inelastic scattering. In these devices the change in heat resistance was found to be proportional to the (charge) magnetoresistance change because both are caused by (spin-dependent) interface scattering but no spin accumulations or spin-dependent temperatures build up.

A spin-dependent temperature builds up in spin valves when the thermal conductivity (κ) in the ferromagnet (κ↑≠κ↓) is spin polarized and the spin flip and inelastic scattering are sufficiently weak18,20. The Wiedemann–Franz relation tells us that the electronic part of the heat conductance in metals (κe) is proportional to the electrical conductivity (σ), with a polarization Pκ = (κe↑−κe↓)/κe that should be equal to Pσ = (σ↑−σ↓)/σ. A heat current through a ferromagnetic metal (F) will therefore be spin polarized, creating a spin heat accumulation (SHA) by the spin-heat coupling at an interface with a non-magnetic metal (N; Fig. 1). If there would be no inelastic scattering of the electrons this SHA decays with the same spin relaxation length (λs) as the spin accumulation, that is, the difference in the local chemical potential of the spin species. In real physical systems though, the ever-present inelastic phonon and electron–electron scattering leads to the exchange of heat between the two spin channels, thereby equilibrating the spin-up and spin-down temperatures T↑ and T↓ to the same average temperature (Fig. 1). Spin temperatures equilibrate over the spin heat relaxation length (λQ), which at lower temperatures is limited by spin flip scattering (λQ = λs) and at high temperatures by inelastic scattering (when λQ<λs). The thermal equivalent for the diffusion equation for the spin accumulation reads:

where Ts = T↑−T↓ is the SHA. The temperature drop that builds up at the F/N interface (Fig. 1) then becomes (Supplementary Section SA):

In regular current-perpendicular-to-plane spin valve devices inelastic scattering is caused by electron–phonon and electron–electron interactions20. Time-domain thermoreflectance25 and ballistic-electron emission microscopy studies26 on inelastic scattering of hot electrons in copper found an inelastic (charge) equilibration length of the order of 60 nm, which is more than five times smaller than λs = 350 nm at room temperature27. As long as the copper spacer layer in a spin valve is comparable to λQ the SHA should be detectable by the second ferromagnetic layer. In Fig. 2, the spin-dependent temperatures T↑ and T↓ are plotted for the parallel (P) and antiparallel (AP) alignment of the magnetic layers in such a current-perpendicular-to-plane spin valve. For the P configuration the SHAs at both F/N interfaces have opposite sign and sum up to be negligibly small. On the other hand, in the AP configuration both interfaces contribute constructively to generate a large SHA leading to a significant temperature drop ΔT (equation (1)) at both F/N interfaces. If λQ = λs the Wiedemann–Franz relation holds, that is, the relative thermal conductance ratio (κP−κAP)/κp equals the giant magnetoresistance ratio (σP−σAP)/σp of the nanopillar. However, in the presence of inter-spin and spin-conserving inelastic scattering λQ<λs and we may expect the Wiedemann–Franz relation to break down, because heat exchange short-circuits the spin channels, thereby decreasing κP−κAP but not σP−σAP.

Figure 1: SHA at an F/N interface.
figure 1

The spin polarized heat current in a ferromagnetic metal (F; blue shading) creates an SHA at the interface with a non-magnetic metal (N; red shading), because the heat currents have to be equally distributed over the spin channels in N. Inelastic scattering equilibrates the spin channel temperatures on the scale of the spin heat relaxation length λQ.

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Figure 2: SHA in an F/N/F spin valve.
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Temperature profiles over the stack in the P and AP configuration in the presence of a heat current (Q). a, In the P configuration the SHAs at both F/N interfaces have opposite signs, leading to a negligibly small SHA. b, For the AP configuration the SHAs at the F/N interfaces have the same sign, creating a large SHA and a corresponding temperature drop between the F/N interfaces and the bulk of the F layers. c, A temperature drop between the P and AP configuration builds up owing to the spin heat valve effect.

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To observe the SHA, we use a nanopillar spin valve (Ni80Fe20/Cu/Ni80Fe20 stack with dimensions 150×80 nm2 and a thickness of each layer of 15 nm) as shown in Fig. 3. We measure the temperature of the bottom contact using a Pt-Constantan (Ni45Cu55) thermocouple (contacts 3 and 4) while sending a charge current through the Pt-heater (contact 1 to 2). Both the thermocouple and the heater are electrically isolated from the bottom contact by an Al2O3 barrier (∼8 nm thick). All samples were initially characterized by electrical measurements of the four-probe electrical resistance of the nanopillar using contacts 6 and 8 while sending a charge current from contact 5 to contact 7. Using a standard lock-in technique9,12,28 with low excitation frequency (Methods), we separate the second harmonic voltage component V 2fI2 from the first harmonic voltage response V 1fI (Methods). Measurements are carried out at room temperature as well as 77 K.

Figure 3: Device geometry.
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a, Schematics of the measured device showing an F/N/F pillar spin valve sandwiched between Au top and Pt bottom contacts. A charge current I through the Pt-heater (contact 1 and 2) increases the temperature of the bottom contact, which is simultaneously measured by a Pt-Constantan (Ni45Cu55) thermocouple. Both the heater and thermocouple are electrically isolated from the bottom contact by an Al2O3 barrier (green; 8 nm thick) to avoid any charge-related spurious signals. b, Coloured 3D scanning electron microscope image of the measured device. The nanopillar sits half way between the Pt–Ni45Cu55 thermocouple (contacts 3 and 4) and the Pt-Joule heater (contacts 1 and 2). Crosslinked polymethyl methacrylate (blue) electrically isolates the bottom contact (grey contacts 5 and 6) from the top contact (contacts 7 and 8).

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To prove the existence of an SHA, we measure the thermovoltage V 2f by the Pt–Ni45Cu55 thermocouple as a function of an in-plane magnetic field, shown in Fig. 4a at room temperature. The second harmonic resistance R2f = V 2f/I2 is characterized by four abrupt changes corresponding to the switching from P to AP configurations and vice versa. On the right y axis the difference between the thermocouple (TTC) and reference temperature (T0 = 300 K) is plotted. The spin heat valve signal Rs2f = RP2f−RAP2f of −0.04 V A−2 corresponds to a temperature difference of −6 mK. At 77 K (Fig. 4b), the spin heat valve signal is −0.06 V A−2, corresponding to a temperature change of −17 mK between P and AP configurations. The background resistance, Rb2f = (RP2f+RAP2f)/2, is lower at 77 K (21.15 V A−2) than at room temperature (29.13 V A−2) owing to the reduced resistance of the heater. Similar values are found for two other samples from the same batch (Supplementary Section SB).

Figure 4: Measured spin heat and conventional spin valve effects.
figure 4

a,b, Second harmonic response R2f = V 2f/I2 measured at the thermocouple, at room temperature (a) and at 77 K (b), both for an r.m.s. current of 2 mA through the heater. Red and blue curves show forward (−H→H) and backward (H→−H) traces of the applied magnetic field. On the right axes the second harmonic r.m.s. value of the temperature differences are shown at the Pt–Ni45Cu55 thermocouple TTC relative to the reference room temperature T0 as TTC−T0 = V 2f/SNiCu−SPt, where SNiCu (SPt) is the Seebeck coefficient for Ni45Cu55(Pt) (Supplementary Table SI) and T0 is taken as 300 K in a and 77 K in b. The heat resistance RQ,pillar R2f of the nanopillar and therefore the temperature is larger in the AP than the P configuration. c,d, Four-probe electrical resistances R1f = V 1f/I as a function of magnetic field measured using contacts 6 and 8 while current flows from contact 5 to contact 7 for room temperature (c) and 77 K (d).

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In Fig. 4c we show the four-probe electrical resistance of the nanopillar at room temperature as a function of the external magnetic field measured using contacts 6 and 8 while a charge current flows from contact 5 to contact 7. A spin valve signal of −80 mΩ is observed on a background resistance of 2.27 Ω. By using the three-dimensional finite element model (3D-FEM) to fit the spin valve signals, we obtain a spin polarization Pσ of 0.52, typical of the bulk spin polarization for Permalloy12,28,29. As a consistency check, the spin-dependent Seebeck9,28 and Peltier effects12 are also measured in the same device (see Supplementary Section SC).

Fitting the measured spin heat valve signal of −0.04 V A−2 to the spin heat diffusion model under the assumption of equal polarizations Pκ and Pσ (Supplementary Sections SA and SE) leads to a spin heat relaxation length λQ,Py of 1 nm in Permalloy, which is one-fifth of its spin relaxation length of 5 nm (ref. 30). Taking the same scaling for the copper layer we obtain a λQ,Cu of 70 nm as one-fifth of λs,Cu = 350 nm (ref. 27). In another set of samples, we measured the SHA for varying thickness of the Cu layer (tN = 5, 15 and 60 nm). This allows us to obtain λQ,Cu of 45 nm in close agreement with the value obtained above (Supplementary Section SI). The fact that we observe SHA up to 60 nm and that λQ,C u>tN shows that inter-spin and electron–phonon inelastic scattering is surprisingly weak in nanopillar devices even at room temperature.

Most material-dependent transport parameters at 77 K can be found in the literature (Supplementary Table S1). To fit the measured spin valve signal at 77 K of −160 mΩ (Fig. 4d), we require a slightly higher spin polarization Pσ of 0.59, in agreement with earlier reports25. From the measured spin heat valve signal of −0.06 V A−2 and Pκ = Pσ = 0.59, we obtain a λQ,Cu of 150 nm, more than two times longer than the λQ,Cu at room temperature, demonstrating the reduced inelastic scattering.

From the 3D-FEM and the above experimental results we can now estimate the difference in the effective temperatures of the spin-up and the spin-down channels in the copper layer. We find T↑−T↓ = 120 mK (at room temperature) and 350 mK (at 77 K), up to 10% of the temperature bias of 4 K across the nanopillar for a root-mean-square (r.m.s.) current of 2 mA through the heater. Here, the temperature bias is defined as the temperature difference between the bottom Pt/Py and the top Py/Au interface. In addition to the vertical temperature difference over the nanopillar a horizontal temperature gradient exists, parallel to the Py/Cu interface. The horizontal temperature gradient is only 6% of the vertical temperature gradient (Supplementary Section SF) and does not lead to any SHA. In our modelling we do not take into account electrical or heat interface resistances30. We would like to emphasize that those would not modify the extracted values of the SHA (Supplementary Section SH).

The SHA is a unique concept that deserves more study. Our results indicate that the spin heat relaxation length in copper is close to the recently measured charge heat relaxation length25,26. Indeed, at higher temperatures the inelastic scattering is thought to be dominated by phonons and is not spin selective. We should therefore interpret the results not as a temperature difference of thermalized spin channels. The SHA is rather a measure of the difference between non-thermalized spin distributions that can be parameterized by the effective temperature parameter20.

We measured the difference between the effective temperatures for spin-up and spin-down electrons in heat current-biased nanopillar spin valves. Modulating the heat conductance of the nanopillar by the magnetization configurations allows control of the flow of heat across the nanopillar, opening up possibilities for room-temperature magnetic thermal switches. Whereas optical pump and probe techniques and hot-electron transistors can access spin-dependent relaxation processes only at high energies, conventional transport experiments are limited to very low temperatures. The spin heat valve measurement, on the contrary, offers a unique possibility to estimate inelastic scattering lengths at the Fermi energy both at low and elevated temperatures.

Methods

Fabrication.

One optical lithography step followed by eleven electron-beam lithography steps were employed to make the device. For each step, materials were electron-beam evaporated except for the Ni45Cu55 alloy, which was sputtered to maintain the bulk stoichiometry. First, a 40-nm-thick Pt Joule heater was deposited on a thermally oxidized Si substrate. Then, the Pt-Constantan (Ni45Cu55) thermocouple was realized on top of a 10-nm-thick Au layer. This is followed by a deposition of an 8-nm-thick Al2O3 layer over the Pt-Joule heater and the thermocouple to electrically isolate them from the bottom contact of the nanopillar. The insulating layer prevents the pick-up of any charge-related effects. A Pt bottom contact (60 nm thick) is then deposited on top of the heater and thermocouple. In the next step, Ni80Fe20 (15)/Cu(tCu = 5, 15 and 60)/Ni80Fe20 (15)/Au(10), where the numbers in parentheses are the thicknesses in nanometres, was deposited without breaking the vacuum of the deposition chamber. Crosslinked polymethyl methacrylate around the nanopillar prevents short-circuiting between the bottom and the top contact (130-nm-thick Au).

Measurements and modelling.

All measurements were done using a standard lock-in technique at low frequency (f<20 Hz) such that a quasi-steady-state condition is reached and at the same time capacitive and inductive coupling are suppressed. As a measured signal V has both linear and nonlinear contributions given as V = I R1f+I2R2f, we used a multiple lock-in measurement to distinguish the first harmonic resistance R1f = V 1f/I from the second harmonic resistance R2f = V 2f/I2. To fully characterize the samples, four different measurements were performed. First, in the spin valve measurements, the four-probe resistance of the nanopillar was measured as a function of magnetic field from which the bulk conductivity polarization (Pσ) was obtained. Then we measure the spin-dependent Seebeck and spin-dependent Peltier effect in the same device. From these measurements, the spin polarizations of the Seebeck (PS) and Peltier coefficients (PΠ) are obtained. By using the 3D-FEM (Supplementary Section SE) together with the extracted values for Pσ, PS and PΠ, we determine the spin heat relaxation length. Measurements were taken both at room temperature and 77 K.