Spin Nernst Effect Research Articles

Laser control of magnonic topological phases in antiferromagnets

We study the laser control of magnon topological phases induced by the Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser electric field can be considered as a time-periodic perturbation, we apply the Floquet theory and perform the inverse frequency expansion by focusing on the high frequency region. Using the obtained effective Floquet Hamiltonian, we study nonequilibrium magnon dynamics away from the adiabatic limit and its effect on topological phenomena. We show that a linearly polarized laser can generate helical edge magnon states and induce the magnonic spin Nernst effect, whereas a circularly polarized laser can generate chiral edge magnon states and induce the magnonic thermal Hall effect. In particular, in the latter, we find that the direction of the magnon chiral edge modes and the resulting thermal Hall effect can be controlled by the chirality of the circularly polarized laser through the change from the left-circular to the right-circular polarization. Our results thus provide a handle to control and design magnon topological properties in the insulating AF.

Recent advances in the spin Nernst effect

We welcome the spin Nernst effect to the royal family of Hall/Nernst effects with the recent experimental observations. Spin Nernst effect is the thermal analog of spin Hall effect which produces pure spin current in non-magnet through the interplay between the relativistically originated spin-orbit coupling and the thermodynamic forces. When a thermal gradient is created across a non-magnet, which has high spin-orbit coupling, a pure spin current is generated in a transverse direction by virtue of the spin Nernst effect. This effect can be useful for manipulating the magnetization of neighboring ferromagnet and hence it can provide an opportunity to write memory bits. In this article we briefly review the recent experimental evidences of spin Nernst effect and its possible application.

Magnonic Floquet Quantum Spin Hall Insulator in Bilayer Collinear Antiferromagnets

We study irradiated two-dimensional insulating bilayer honeycomb ferromagnets and antiferromagnets coupled antiferromagnetically with a zero net magnetization. The former is realized in the recently synthesized bilayer honeycomb chromium triiodide CrI3. In both systems, we show that circularly-polarized electric field breaks time-reversal symmetry and induces a dynamical Dzyaloshinskii-Moriya interaction in each honeycomb layer. However, the resulting bilayer antiferromagnetic system still preserves a combination of time-reversal and space-inversion ({bf{P}}{bf{T}}) symmetry. We show that the magnon topology of the bilayer antiferromagnetic system is characterized by a {{bf{Z}}}_{{bf{2}}} Floquet topological invariant. Therefore, the system realizes a magnonic Floquet quantum spin Hall insulator with spin filtered magnon edge states. This leads to a non-vanishing Floquet magnon spin Nernst effect, whereas the Floquet magnon thermal Hall effect vanishes due to {bf{P}}{bf{T}} symmetry. We study the rich {{bf{Z}}}_{{bf{2}}} Floquet topological magnon phase diagram of the system as a function of the light amplitudes and polarizations. We further discuss the great impact of the results on future experimental realizations.

Topological magnon nodal lines and absence of magnon spin Nernst effect in layered collinear antiferromagnets

We propose the existence of a symmetry-protected topological Dirac nodal-line (DNL) magnonic phase in layered honeycomb collinear antiferromagnets even in the presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that the magnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D) honeycomb collinear antiferromagnets cancels out in the layered honeycomb collinear antiferromagnets. In other words, the magnon spin Nernst effect in each 2D antiferromagnetic layer cancels out the succeeding layer. Hence, the Berry curvature vanishes in the entire Brillouin zone due to the combination of time-reversal and space-inversion symmetry. However, upon symmetry breaking by an external magnetic field, we show that a non-vanishing Berry curvature and Chern number protected topological magnon bands are induced in the non-collinear spin structure. This leads to an experimentally accessible magnon thermal Hall effect in the symmetry-broken topological DNL magnonic phase of layered honeycomb antiferromagnets. We propose that the current predicted results can be experimentally investigated in the layered honeycomb antiferromagnets CaMn2Sb2, BaNi2V2O8, and Bi3Mn4O12(NO3).

Control of magnetization dynamics by spin-Nernst torque

Control of magnetization dynamics is one of the primary goals in spintronics. It has been demonstrated using spin Hall effect i.e charge current to spin current conversion in non-magnetic metal which has large spin-orbit coupling such as Pt, W etc. Recently different groups have shown generation of spin current in Pt, W while thermal gradient is created by virtue of spin Nernst effect. In this work we show the evidence of magnetization control by spin Nernst torque in Pt/Py bi-layer. We compared relative strength of spin Nernst Torque and spin Hall torque by measuring the systematic variation of magnetic linewidth on application of constant heat or charge current. Spin-torque ferromagnetic resonance (ST-FMR) technique is adopted to excite the magnet and to measure line-width precisely from the symmetric and anti-symmetric voltage component. Control of magnetization dynamics by spin Nernst torque will emerge as an alternative way to manipulate nano-magnets.

Spin and charge Nernst effect in a four-terminal double-dot interferometer

We investigate the spin and charge Nernst effect of a four-terminal Aharonov–Bohm interferometer with Rashba spin–orbit interaction (RSOI). It is shown that a pure spin Nernst effect or a fully spin-polarized Nernst effect can be obtained by modulating the magnetic flux phase ϕ and the RSOI induced phase φ. It is also demonstrated that some windows of ϕ (or φ) for maintaining an almost fully spin-polarized Nernst effect exist and their width is under the control of the other phase. Moreover, for the charge Nernst coefficient Nc and spin Nernst coefficient Ns the relationship Nc(ϕ,φ)=−Ns(φ,ϕ) always holds. These results suggest that our proposal may act as a controllable thermospin generator.

Generalized Fourier law and anomalous Righi–Leduc effect in a ferromagnet

Spin caloritronics brings us new spin-thermal related effects, such as spin Seebeck effect, spin Nernst effect and their inverse effects. It is time to revisit the thermoelectric effects in ferromagnets by considering them. In this paper, a generalized Fourier law is derived and an anomalous Righi–Leduc effect is proposed for a ferromagnet when a temperature gradient is applied. A full description including particle current, spin current and heat current is necessarily taken into account and gives rise to novel contributions to the Righi–Leduc coefficient. This may shed more light on the spin caloritronics in ferromagnets.

Conserved spin current for the Mott relation

The conserved bulk spin current [Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], defined as the time derivative of the spin displacement operator, ensures automatically the Onsager relation between the spin Hall effect (SHE) and the inverse SHE. Here, we reveal another desirable property of this conserved spin current: the Mott relation linking the SHE and its thermal counterpart, the spin Nernst effect (SNE). According to the Mott relation, the SNE is known once the SHE is understood. In a two-dimensional Dirac-Rashba system with a smooth scalar disorder potential, we find a sign change of the spin Nernst conductivity when tuning the chemical potential.

Spin-Nernst effect in the paramagnetic regime of an antiferromagnetic insulator

We theoretically investigate a pure spin Hall current driven by a longitudinal temperature gradient, i.e., the spin Nernst effect (SNE), in a paramagnetic state of a collinear antiferromagnetic insulator with the Dzyaloshinskii-Moriya interaction. The SNE in a magnetic ordered state in such an insulator was proposed by Cheng et al. [R. Cheng, S. Okamoto, and D. Xiao, Phys. Rev. Lett. 117, 217202 (2016)]. Here we show that the Dzyaloshinskii-Moriya interaction can generate a pure spin Hall current even without magnetic ordering. By using a Schwinger boson mean-field theory, we calculate the temperature dependence of SNE in a disordered phase. We also discuss the implication of our results to experimental realizations.

Rashba-driven anomalous Nernst conductivity of high spin-orbit-coupled lead chalcogenide films

The presence of a finite Berry curvature $\left(\Omega\left(k\right)\right)$ leads to anomalous thermal effects. In this letter, we compute the coefficients for the anomalous Nernst effect $\left(ANE\right) $ and its spin analogue, the spin Nernst effect $\left(SNE\right)$ in lead chalcogenide (\textit{PbX}; \textit{X} = S, Se, Te) films. The narrow gapped \textit{PbX} films with a large spin-orbit coupling (\textit{soc}) offer a significant Rashba interaction that gives rise to $ \Omega\left(k\right) $ and the attendant anomalous thermal behaviour. In presence of a temperature gradient, the $ ANE $ and $ SNE $ establish a thermal and spin current and are characterized by their respective coefficients which acquire higher values for a stronger Rashba interaction. We further show that an extrinsic \textit{soc} generated by an in-plane electric field offers a gate-like mechanism to control (and turn-off) the anomalous thermal currents. Finally, we conclude by deriving the efficiency of an $ ANE $-driven low-temperature Carnot heat engine and demonstrate that it can be gainfully optimized in systems with a robust intrinsic \textit{soc} resulting in low carrier effective masses.

Spin Hall and Nernst effects of Weyl magnons

In this paper, we present a simple model of a three-dimensional insulating magnetic structure which represents a magnonic analog of the layered electronic system described in [Phys. Rev. Lett. {\bf 107}, 127205 (2011)]. In particular, our model realizes Weyl magnons as well as surface states with a Dirac spectrum. In this model, the Dzyaloshinskii-Moriya interaction is responsible for the separation of opposite Weyl points in momentum space. We calculate the intrinsic (due to the Berry curvature) transport properties of Weyl and so-called anomalous Hall effect (AHE) magnons. The results are compared with fermionic analogs.

Magnonic quantum spin Hall state in the zigzag and stripe phases of the antiferromagnetic honeycomb lattice

We investigated the topological property of magnon bands in the collinear magnetic orders of zigzag and stripy phases for the antiferromagnetic honeycomb lattice and identified Berry curvature and symmetry constraints on the magnon band structure. Different symmetries of both zigzag and stripy phases lead to different topological properties, in particular, the magnon bands of the stripy phase being disentangled with a finite Dzyaloshinskii-Moriya (DM) term with non-zero spin Chern number. This is corroborated by calculating the spin Nernst effect. Our study establishes the existence of the non-trivial magnon band topology for all observed collinear antiferromagnetic honeycomb lattice in the presence of the DM term.

Direct detection of spin Nernst effect in platinum

Generation of spin current lies at the heart of spintronic research. The spin Hall effect and the spin Seebeck effect have drawn considerable attention in the last few years to create pure spin current by heavy metals and ferromagnets, respectively. In this work, we show the direct evidence of heat current to spin current conversion in non-magnetic Platinum by the spin Nernst effect (SNE) at room temperature. This is the thermal analogue of the spin Hall effect in non-magnets. We have shown that the 8 K/μm thermal gradient in Pt can lead to the generation of pure spin current density of the order of 108 A/m2 by virtue of SNE. This opens up an additional possibility to couple the relativistic spin-orbit interaction with the thermal gradient for spintronic applications.

Spin and Charge Nernst Effects in Four-Terminal Ferromagnetic Graphene

The spin and charge Nernst effects in a four-terminal ferromagnetic graphene are theoretically investigated by using the nonequilibrium Green’s function method. The results of this study reveal that (1) when the four leads are normal graphene, the pure charge Nernst effect can be obtained under the assistance of magnetic field, (2) when the ferromagnetic graphene leads are in a parallel configuration of the magnetizations, both the spin and charge Nernst effects can be generated simultaneously, it is worth noting that, for the first two cases, the Nernst effect cannot be obtained without the [Formula: see text] direction magnetic field, and (3) the pure spin Nernst effect (without charge Nernst effect) emerged only by the temperature difference for the antiparallel configuration. In addition, the magnitude of the spin and charge Nernst coefficients can be tuned by adjusting the strength of magnetic flux and exchange field. All the results indicate that the proposed multi-terminal graphene nanosystem is a promising candidate for spin caloritronics devices.

Large anomalous Nernst and spin Nernst effects in the noncollinear antiferromagnets Mn3X ( X=Sn,Ge,Ga )

Noncollinear antiferromagnets have recently been attracting considerable interest partly due to recent surprising discoveries of the anomalous Hall effect (AHE) in them and partly because they have promising applications in antiferromagnetic spintronics. Here we study the anomalous Nernst effect (ANE), a phenomenon having the same origin as the AHE, and also the spin Nernst effect (SNE) as well as AHE and the spin Hall effect (SHE) in noncollinear antiferromagnetic Mn$_3X$ ($X$ = Sn, Ge, Ga) within the Berry phase formalism based on {\it ab initio} relativistic band structure calculations. For comparison, we also calculate the anomalous Nernst conductivity (ANC) and anomalous Hall conductivity (AHC) of ferromagnetic iron as well as the spin Nernst conductivity (SNC) of platinum metal. Remarkably, the calculated ANC at room temperature (300 K) for all three alloys is huge, being up to 5 times larger than that of iron. Moreover, the calculated SNC for Mn$_3$Sn and Mn$_3$Ga is also large, being as large as that of platinum. This suggests that these anitferromagnets would be useful materials for thermoelectronic devices and spin caloritronic devices. The calculated ANC of Mn$_3$Sn and iron are in reasonably good agreement with the very recent experiments. The calculated SNC of platinum also agrees with the very recent experiments in both sign and magnitude. The calculated thermoelectric and thermomagnetic properties are analyzed in terms of the band structures as well as the energy-dependent AHC, ANC, SNC and spin Hall conductivity via the Mott relations.

Spin-Caloritronic Batteries

The thermoelectric performance of a topological energy converter is analyzed. The H-shaped device is based on a combination of transverse topological effects involving the spin: the inverse spin Hall effect and the spin Nernst effect. The device can convert a temperature drop in one arm into an electric power output in the other arm. Analytical expressions for the output voltage, the figure-of-merit (ZT) and energy converting efficiency are reported. We show that the output voltage and the ZT can be tuned by the geometry of the device and the physical properties of the material. Importantly, contrary to a conventional thermoelectric device, here a low electric conductivity may in fact enhance the ZT value, thereby opening a path to new strategies in optimizing the figure-of-merit.

Observation of transverse spin Nernst magnetoresistance induced by thermal spin current in ferromagnet/non-magnet bilayers

Electric generation of spin current via spin Hall effect is of great interest as it allows an efficient manipulation of magnetization in spintronic devices. Theoretically, pure spin current can be also created by a temperature gradient, which is known as spin Nernst effect. Here, we report spin Nernst effect-induced transverse magnetoresistance in ferromagnet/non-magnetic heavy metal bilayers. We observe that the magnitude of transverse magnetoresistance in the bilayers is significantly modified by heavy metal and its thickness. This strong dependence of transverse magnetoresistance on heavy metal evidences the generation of thermally induced pure spin current in heavy metal. Our analysis shows that spin Nernst angles of W and Pt have the opposite sign to their spin Hall angles. Moreover, our estimate implies that the magnitude of spin Nernst angle would be comparable to that of spin Hall angle, suggesting an efficient generation of spin current by the spin Nernst effect.

The spin Nernst effect in tungsten.

The spin Hall effect allows the generation of spin current when charge current is passed along materials with large spin-orbit coupling. It has been recently predicted that heat current in a nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. We report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field dependence of the voltage resembles that of the spin Hall magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Spin thermal effects: A new member of the Hall family.

The spin Nernst effect — a spin accumulation in a ferromagnet in the direction normal to an applied thermal gradient and external magnetic field — has been experimentally demonstrated.

Observation of the spin Nernst effect.

The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, which so far has been discussed only on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent yttrium iron garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal and transverse thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.