Thermal spin transfer in Fe-MgO-Fe tunnel junctions

Magneto-Seebeck effect in Co2FeAl/MgO/Co2FeAl: first-principles calculations

The magneto-Seebeck effect has recently attracted considerable attention because of its novel fundamental physics and future potential application in spintronics. Herein, employing first-principles calculations and the spin-resolved Boltzmann transport theory, we have systematically investigated the electronic structures and spin-related transport properties of Co2FeAl/MgO/Co2FeAl multilayers with parallel (P) and anti-parallel (AP) magnetic alignment. Our results indicate that the sign of tunneling magneto-Seebeck (TMS) value with Co2/O termination is consistent with that of the measured experimental result although its value (-221%) at room temperature is smaller than the experimental one (-95%). The calculated spin-Seebeck coefficients of the Co2/O termination with P and AP states and the FeAl/O termination with the AP state are all larger than other typical Co2MnSi/MgO/Co2MnSi heterostructures. By analyzing the geometries, electronic structures, and magnetic behaviors of two different terminations (Co2/O and FeAl/O terminations), we find that the two terminations in the interface region form anti-bonding and bonding states, reconstructing the energy gap, changing the magnetic moment of O atoms, and improving the spin-polarization (-82%). This phenomenon can be ascribed to the charge transfer and hybridization between Co/Fe 3d and O 2p states, which also results in a bowknot orbital shape of Co atoms with Co2/O termination and an ankle shape of Co atoms with FeAl/O termination far away from the interface. Moreover, there are spin-splitting transmission gaps with the Co2/O-termination around the Fermi level, while the transmission gaps with the FeAl/O-termination are closed and thus show a typical metallic character. Our findings will guide the experimental design of magneto-Seebeck devices for future spintronic applications.

Magnetic tunnel junctions with integrated thermometers for magnetothermopower measurements

Magnetic tunnel junction (MTJ) micropillars were fabricated with integrated thermometers and a heater line (HL) for thermovoltage measurements. This novel thermometer configuration enabled a direct measurement of ΔT across the MTJ micropillar. The MTJ devices were patterned from a CoFeB/MgO/CoFeB stack, with a 1.2 nm to 1.6 nm MgO wedge across the wafer, resulting in resistance area products in the range of 0.7 kΩ · µm²  <  R  ×  A  <  55 kΩ · µm². This allowed the measurement of thermoelectric properties as a function of the tunnel barrier thickness. The thermometers showed a homogeneous heating behavior for all devices across the wafer. Combining the in-stack temperature measurements and finite element simulations the thermal profile across the MTJ structure and the thermopower were estimated with a noticeable improvement of the measurement accuracy. The studied MTJ structures showed tunneling magnetoresistance (TMR) ratios up to 125%, and tunneling magnetothermopower (TMTP) up to 35%.

Enhancement of thermal spin transfer torque by double-barrier magnetic tunnel junctions with a nonmagnetic metal spacer

Enhancement of thermal spin transfer torque in a double-barrier magnetic tunnel junction with a nonmagnetic-metal spacer is proposed in this study. The results indicate that, given the same temperature difference, thermal spin transfer torque and charge current density for the proposed double barrier magnetic tunnel junction configuration can be approximately twice as much as that of the traditional single-barrier magnetic tunnel junctions. This enhancement can be attributed to the resonant tunneling mechanism in the double-barrier structure.

The inverse thermal spin-orbit torque and the relation of the Dzyaloshinskii-Moriya interaction to ground-state energy currents

Using the Kubo linear-response formalism we derive expressions to calculate the electronic contribution to the heat current generated by magnetization dynamics in ferromagnetic metals with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e. the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from the Kubo linear response of the energy current in order to extract the heat current. We show that the expressions of the DMI coefficient can be derived elegantly from the DMI energy current. Guided by formal analogies between the Berry phase theory of DMI on the one hand and the modern theory of orbital magnetization on the other hand we are led to an interpretation of the latter in terms of energy currents as well. Based on ab initio calculations we investigate the electronic contribution to the heat current driven by magnetization dynamics in Mn/W(0 0 1) magnetic bilayers. We predict that fast domain walls drive strong heat currents.

Magnetic coherent tunnel junctions with periodic grating barrier

A new spintronic theory has been developed for the magnetic tunnel junction (MTJ) with single-crystal barrier. The barrier will be treated as a diffraction grating with intralayer periodicity, the diffracted waves of tunneling electrons thus contain strong coherence, both in charge and especially in spin. The theory can answer the two basic problems present in MgO-based MTJs: (1) Why does the tunneling magnetoresistance (TMR) oscillate with the barrier thickness? (2) Why is the TMR still far away from infinity when the two electrodes are both half-metallic? Other principal features of TMR can also be explained and reproduced by the present work. It also provides possible ways to modulate the oscillation of TMR, and to enhance TMR so that it can tend to infinity. Within the theory, the barrier, as a periodic diffraction grating, can get rid of the confinement in width, it can vary from nanoscale to microscale. Based on those results, a future-generation MTJ is proposed where the three pieces can be fabricated separately and then assembled together, it is especially appropriate for the layered materials, e.g., MoS₂ and graphite, and most feasible for industries.

Thermal Transport and Nonequilibrium Temperature Drop Across a Magnetic Tunnel Junction

In the field of spin caloritronics, spin-dependent transport phenomena are observed in a number of current experiments where a temperature gradient across a nanostructured interface is applied. The interpretation of these experiments is not clear as both phonons and electrons may contribute to thermal transport. Therefore, it still remains an open question how the temperature drop across a magnetic nanostructured interface arises microscopically. We answer this question for the case of a magnetic tunnel junction (MTJ) where the tunneling magneto-Seebeck effect occurs. Our explanation may be extended to other types of nanostructured interfaces. We explicitly calculate phonon and electron thermal conductance across Fe/MgO/Fe MTJs in an ab initio approach using a Green function method. Furthermore, we are able to calculate the electron and phonon temperature profile across the Fe/MgO/Fe MTJ by estimating the electron-phonon interaction in the Fe leads. Our results show that there is an electron-phonon temperature imbalance at the Fe-MgO interfaces. As a consequence, a revision of the interpretation of current experimental measurements may be necessary.

Giant thermal spin-torque-assisted magnetic tunnel junction switching

Spin-polarized charge currents induce magnetic tunnel junction (MTJ) switching by virtue of spin-transfer torque (STT). Recently, by taking advantage of the spin-dependent thermoelectric properties of magnetic materials, novel means of generating spin currents from temperature gradients, and their associated thermal-spin torques (TSTs), have been proposed, but so far these TSTs have not been large enough to influence MTJ switching. Here we demonstrate significant TSTs in MTJs by generating large temperature gradients across ultrathin MgO tunnel barriers that considerably affect the switching fields of the MTJ. We attribute the origin of the TST to an asymmetry of the tunneling conductance across the zero-bias voltage of the MTJ. Remarkably, we estimate through magneto-Seebeck voltage measurements that the charge currents that would be generated due to the temperature gradient would give rise to STT that is a thousand times too small to account for the changes in switching fields that we observe.

Voltage tuning of thermal spin current in ferromagnetic tunnel contacts to semiconductors

Spin currents are paramount to manipulate the magnetization of ferromagnetic elements in spin-based memory, logic and microwave devices, and to induce spin polarization in non-magnetic materials. A unique approach to create spin currents employs thermal gradients and heat flow. Here we demonstrate that a thermal spin current can be tuned conveniently by a voltage. In magnetic tunnel contacts to semiconductors (silicon and germanium), it is shown that a modest voltage (~200 mV) changes the thermal spin current induced by Seebeck spin tunnelling by a factor of five, because it modifies the relevant tunnelling states and thereby the spin-dependent thermoelectric parameters. The magnitude and direction of the spin current is also modulated by combining electrical and thermal spin currents with equal or opposite sign. The results demonstrate that spin-dependent thermoelectric properties away from the Fermi energy are accessible, and open the way towards tailoring thermal spin currents and torques by voltage, rather than material design.

Time-resolved measurement of the tunnel magneto-Seebeck effect in a single magnetic tunnel junction

Recently, several groups have reported spin-dependent thermoelectric effects in magnetic tunnel junctions. In this paper, we present a setup for time-resolved measurements of thermovoltages and thermocurrents of a single micro- to nanometer-scaled tunnel junction. An electrically modulated diode laser is used to create a temperature gradient across the tunnel junction layer stack. This laser modulation technique enables the recording of time-dependent thermovoltage signals with a temporal resolution only limited by the preamplifier for the thermovoltage. So far, time-dependent thermovoltage could not be interpreted. Now, with the setup presented in this paper, it is possible to distinguish different Seebeck voltage contributions to the overall measured voltage signal in the μs time regime. A model circuit is developed that explains those voltage contributions on different sample types. Further, it will be shown that a voltage signal arising from the magnetic tunnel junction can only be observed when the laser spot is directly centered on top of the magnetic tunnel junction, which allows a lateral separation of the effects.

Direct imaging of thermally driven domain wall motion in magnetic insulators

Thermally induced domain wall motion in a magnetic insulator was observed using spatiotemporally resolved polar magneto-optical Kerr effect microscopy. The following results were found: (i) the domain wall moves towards hot regime; (ii) a threshold temperature gradient (5  K/mm), i.e., a minimal temperature gradient required to induce domain wall motion; (iii) a finite domain wall velocity outside of the region with a temperature gradient, slowly decreasing as a function of distance, which is interpreted to result from the penetration of a magnonic current into the constant temperature region; and (iv) a linear dependence of the average domain wall velocity on temperature gradient, beyond a threshold thermal bias. Our observations can be qualitatively explained using a magnonic spin transfer torque mechanism, which suggests the utility of magnonic spin transfer torque for controlling magnetization dynamics.

Theory of the spin Seebeck effect

The spin Seebeck effect refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimeters. The inverse spin Hall effect converts the injected spin current into a transverse charge voltage, thereby producing electromotive force as in the conventional charge Seebeck device. Recent theoretical and experimental efforts have shown that the magnon and phonon degrees of freedom play crucial roles in the spin Seebeck effect. In this paper, we present the theoretical basis for understanding the spin Seebeck effect and briefly discuss other thermal spin effects.

Spin-dependent thermoelectric effects in graphene-based spin valves

Using first-principles calculations combined with non-equilibrium Green's function (NEGF), we investigate spin-dependent thermoelectric effects in a spin valve which consists of zigzag graphene nanoribbon (ZGNR) electrodes with different magnetic configurations. We find that electron transport properties in the ZGNR-based spin valve are strongly dependent on the magnetic configurations. As a result, with a temperature bias, thermally-induced currents can be controlled by switching the magnetic configurations, indicating a thermal magnetoresistance (MR) effect. Moreover, based on the linear response assumption, our study shows that the remarkably different Seebeck coefficients in the various magnetic configurations lead to a very large and controllable magneto Seebeck ratio. In addition, we evaluate thermoelectric properties, such as the power factor, electron thermal conductance and figure of merit (ZT), of the ZGNR-based spin valve. Our results indicate that the power factor and the electron thermal conductance are strongly related to the transmission gap and electron-hole symmetry of the transmission spectrum. Moreover, the value of ZT can reach 0.15 at room temperature without considering phonon scattering. In addition, we investigate the thermally-controlled magnetic distributions in the ZGNR-based spin valve and find that the magnetic distribution, especially the local magnetic moment around the Ni atom, is strongly related to the thermal bias. The very large, multi-valued and controllable thermal magnetoresistance and Seebeck effects indicate the strong potential of ZGNR-based spin valves for extremely low-power consuming spin caloritronics applications. The thermally-controlled magnetic moment in the ZGNR-based spin valve indicates its possible applications for information storage.

Seebeck rectification enabled by intrinsic thermoelectrical coupling in magnetic tunneling junctions

An intrinsic thermoelectric coupling effect in the linear response regime of magnetic tunneling junctions (MTJ) is reported. In the dc response, it leads to a nonlinear correction to Ohm's law. Dynamically, it enables a novel Seebeck rectification and second harmonic generation, which apply for a broad frequency range and can be magnetically controlled. A phenomenological model on the footing of the Onsager reciprocal relation and the principle of energy conservation explains very well the experimental results obtained from both dc and frequency-dependent transport measurements performed up to GHz frequencies. Our work refines previous understanding of magnetotransport and microwave rectification in MTJs. It forms a new foundation for utilizing spin caloritronics in high-frequency applications.

Spin caloritronics

Spintronics is about the coupled electron spin and charge transport in condensed-matter structures and devices. The recently invigorated field of spin caloritronics focuses on the interaction of spins with heat currents, motivated by newly discovered physical effects and strategies to improve existing thermoelectric devices. Here we give an overview of our understanding and the experimental state-of-the-art concerning the coupling of spin, charge and heat currents in magnetic thin films and nanostructures. Known phenomena are classified either as independent electron (such as spin-dependent Seebeck) effects in metals that can be understood by a model of two parallel spin-transport channels with different thermoelectric properties, or as collective (such as spin Seebeck) effects, caused by spin waves, that also exist in insulating ferromagnets. The search to find applications--for example heat sensors and waste heat recyclers--is on.