Spin Nernst Conductivities Research Articles

Conflux of spin Nernst and spin Hall effect in ZnCu2SnSe4 Topological Insulator

A comprehensive exploration of the intriguing phenomena known as the spin Nernst effect (SNE) and the spin Hall effect (SHE) within the context of nonmagnetic strong topological insulatorZnCu2SnSe4, has been carried out employing first-principles calculations. Our theoretical calculations unveil significantly large intrinsic spin Nernst conductivity (SNC) and spin Hall conductivity (SHC) in the bulk topological insulatorZnCu2SnSe4. Delving deeper into the intricacies of our findings, we elucidate how the inverted band order in the topological materials drastically influences the spin Berry curvature, consequently exerting a profound impact on SHC and SNC. Detailed analyses reveal that the contribution from the bulk to the generation of pure spin current in a topological insulator is comparable to that of a surface. This underscores the potential role of topological insulators in the development of spin-switching devices. We present compelling evidence thatZnCu2SnSe4holds immense promise as an optimal candidate for the generation of pure spin currents, achieved through the application of both thermal gradients and electric fields. This, in turn, opens up exciting avenues for its utilization in the realms of spin-caloritronics, spin-orbitronics, and spintronics.

Anisotropic spin Hall and spin Nernst effects in bismuth semimetal

Bismuth is an archetypal semimetal with gigantic spin–orbit coupling and it has been a major source material for the discovery of seminal phenomena in solid state physics for more than a century. In recent years, spin current transports in bismuth have also attracted considerable attention. In this paper, we theoretically study both spin Hall effect (SHE) and spin Nernst effect (SNE) in bismuth, based on relativistic band structure calculations. First, we find that there are three independent tensor elements of spin Hall conductivity (SHC) (σijs) and spin Nernst conductivity (SNC) (αijs), namely, Zyxz, Zxzy, and Zzyx, where Z=σ or α. We calculate all the elements as a function of the Fermi energy. Second, we find that all SHC elements are large, being ∼1000 (ħ/e)(S/cm). Furthermore, because of its low electrical conductivity, the spin Hall angles are gigantic, being ∼20 %. Third, all the calculated SNC elements are also pronounced, being comparable to that [∼0.13 (ħ/e)(A/m-K)] of gold. Finally, in contrast to Pt and Au where Zyxz=Zxzy=Zzyx, the SHE and SNE in bismuth are anisotropic, i.e., Zyxz≠Zxzy≠Zzyx. In particular, SNC is highly anisotropic, and αyxz, αxzy and αzyx differ even in sign. Also, such anisotropy in SHE can be significantly enhanced by either electron or hole doping. Consequently, the Hall voltages due to the inverse SHE and inverse SNE from the different conductivity elements could cancel each other and thus result in a small spin Hall angle if polycrystalline samples are used, which may explain why the measured spin Hall angles ranging from nearly 0 to 25 % have been reported. We hope that these interesting findings would stimulate further experiments on bismuth using highly oriented single crystal specimens.

Tunable large spin Nernst effect in a two-dimensional magnetic bilayer

We theoretically investigate topological spin transport of the magnon polarons in a bilayer magnet with two-dimensional square lattices. Our theory is motivated by recent reports on the van der Waals magnets which show the reversible electrical switching of the interlayer magnetic order between antiferromagnetic and ferromagnetic orders. The magnetoelastic interaction opens band gaps and allows the interband transition between different excitation states. In the layered antiferromagnet, due to the interband transition between the magnon-polaron states, the spin Berry curvature which allows the topological spin transport occurs even if the time-reversal symmetry is preserved. We find that the spin Berry curvature in the layered antiferromagnet is very large due to the small energy spacing between two magnonlike states. As a result, the spin Nernst conductivity shows a sudden increase (or decrease) at the phase transition point between ferromagnetic and antiferromagnetic phases. Our results suggest that the ubiquity of tunable topological spin transports in two-dimensional magnetic systems.

Low-temperature suppression of the spin Nernst angle in Pt

The coupling between electrical, thermal, and spin transport results in a plethora of novel transport phenomena. However, disentangling different effects is experimentally very challenging. We demonstrate that bilayers consisting of the antiferromagnetic insulator hematite ($\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$) and Pt allow one to precisely measure the transverse spin Nernst magnetothermopower (TSNM) and observe the low-temperature suppression of the platinum (Pt) spin Nernst angle. We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the N\'eel vector of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$, rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing one to unambiguously distinguish the TSNM from thermally excited magnon transport, which usually dominates in ferri/ferromagnets due to their nonzero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below $\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. We compare these results with theoretical calculations of the temperature-dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect.

Tunable spin Hall and spin Nernst effects in Dirac line-node semimetals XCuYAs ( X=Zr,Hf ; Y=Si,Ge )

The quaternary arsenide compounds XCuYAs (X=Zr, Hf; Y= Si, Ge) belong to the vast family of the 1111-type quaternary compounds, which possess outstanding physical properties ranging from $p$-type transparent semiconductors to high-temperature Fe-based superconductors. In this paper, we study the electronic structure topology, spin Hall effect (SHE) and spin Nernst effect (SNE) in these compounds based on density functional theory calculations. First we find that the four considered compounds are Dirac semimetals with the nonsymmorphic symmetry-protected Dirac line nodes along the Brillouin zone boundary $A$-$M$ and $X$-$R$ and low density of states (DOS) near the Fermi level ($E_F$). Second, the intrinsic SHE and SNE in some of these considered compounds are found to be large. In particular, the calculated spin Hall conductivity (SHC) of HfCuGeAs is as large as -514 ($\hbar$/e)(S/cm). The spin Nernst conductivity (SNC) of HfCuGeAs at room temperature is also large, being -0.73 ($\hbar$/e)(A/m-K). Moreover, both the magnitude and sign of the SHC and SNC in these compounds can be manipulated by varying either the applied electric field direction or spin current direction. The SHE and SNE in these compounds can also be enhanced by tuning the Fermi level via chemical doping or electric gating. Finally, a detailed analysis of the band-decomposed and $k$-resolved spin Berry curvatures reveals that these large SHC and SNC as well as their notable tunabilities originate largely from the presence of a large number of spin-orbit coupling-gapped Dirac points near the Fermi level as well as the gapless Dirac line-nodes, which give rise to large spin Berry curvatures. Our findings thus suggest that the four XCuYAs compounds not only provide a valuable platform for exploring the interplay between SHE, SNE and band topology but also have promising applications in spintronics and spin caloritronics.

Spin Nernst effect in a p-band semimetal InBi

Since spin currents can be generated, detected, and manipulated via the spin Hall effect (SHE), the design of strong SHE materials has become a focus in the field of spintronics. Because of the recent experimental progress also the spin Nernst effect (SNE), the thermoelectrical counterpart of the SHE, has attracted much interest. Empirically strong SHEs and SNEs are associated with d-band compounds, such as transition metals and their alloys—the largest spin Hall conductivity (SHC) in a p-band material is for a Bi–Sb alloy, which is only about a fifth of platinum. This raises the question whether either the SHE and SNE are naturally suppressed in p-bands compounds, or favourable p-band systems were just not identified yet. Here we consider the p-band semimetal InBi, and predict it has a record SHC which is due to the presence of nodal lines in its band structure. Also the spin-Nernst conductivity is very large, but our analysis shows its origin is different as the maximum appears in a different tensor element compared to that in SHC. This insight gained on InBi provides guiding principles to obtain a strong SHE and SNE in p-band materials and establishes a more comprehensive understanding of the relationship between the SHE and SNE.

Tunable large spin Hall and spin Nernst effects in the Dirac semimetals ZrXY (X=Si,Ge;Y=S,Se,Te)

The ZrSiS-type compounds are Dirac semimetals and have been attracting considerable interest in recent years due to their topological electronic properties and possible applications. In particular, gapped Dirac nodes can possess large spin Berry curvatures and thus give rise to large spin Hall effect (SHE) and spin Nernst effect (SNE), which may be used to generate pure spin current for spintronics and spin caloritronics without applied magnetic field or magnetic material. In this paper we study both SHE and SNE in ZrXY (X = Si, Ge; Y = S, Se, Te) based on \textit{ab initio} relativistic band structure calculations. Our theoretical calculations reveal that some of these compounds exhibit large intrinsic spin Hall conductivity (SHC) and spin Nernst conductivity (SNC). The calculated SHC of ZrSiTe is as large as -755 ($\hbar$/e)(S/cm). Since the electric conductivity of these Dirac semimetals are much smaller than that of platinum which has the largest intrinsic SHC of $\sim$2200 ($\hbar$/e)(S/cm), this indicates that they will have a larger spin Hall angle than that of platinum. Remarkably, we find that both the magnitude and sign of the SHE and SNE in these compounds can be significantly tuned by changing either the electric field direction or spin current direction and may also be optimized by slightly varying the Fermi level via chemical doping. Analysis of the calculated band- and $k$-resolved spin Berry curvatures show that the large SHE and SNE as well as their remarkable tunabilities originate from the presence of many slightly spin-orbit coupling-gapped Dirac nodal lines near the Fermi level in these Dirac semimetals. Our findings suggest that the ZrSiS-type compounds are promising candidates for spintronic and spin caloritronic devices, and will certainly stimulate further experiments on these Dirac semimetals.

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.

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-resolved orbital magnetization in Rashba two-dimensional electron gas

We calculate orbital spin-dependent magnetization in a two-dimensional electron gas with spin-orbit interaction of Rashba type. Such an orbital magnetization is admitted by the time-reversal symmetry of the system, and gives rise to spin currents when the system is not in thermal equilibrium. The theoretical approach is based on the linear response theory and the Matsubara Green's function formalism. To account for the spin-resolved orbital magnetization a spin-dependent vector potential has been introduced. The spin currents which appear in thermal nonequilibrium due to the spin-resolved orbital magnetization play an important role in the spin Nernst effect, and have to be included in order to correctly describe the low-temperature spin Nernst conductivity.

Chirality-induced magnon transport in AA-stacked bilayer honeycomb chiral magnets

In this Letter, we study the magnetic transport in AA-stacked bilayer honeycomb chiral magnets coupled either ferromagnetically or antiferromagnetically. For both couplings, we observe chirality-induced gaps, chiral protected edge states, magnon Hall and magnon spin Nernst effects of magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall and spin Nernst conductivities do not change sign as function of magnetic field or temperature similar to single-layer honeycomb ferromagnetic insulator. In contrast, for antiferromagnetically coupled layers, we observe a sign change in the thermal Hall and spin Nernst conductivities as the magnetic field is reversed. We discuss possible experimental accessible honeycomb bilayer quantum materials in which these effects can be observed.

Topological hardcore bosons on the honeycomb lattice

This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.

Spin Hall and spin Nernst effects in a two-dimensional electron gas with Rashba spin-orbit interaction: Temperature dependence

Using the Matsubara Green's function formalism we calculate the temperature dependence of spin Hall and spin Nernst conductivities of a two-dimensional electron gas with Rashba spin-orbit interaction in the linear response regime. In the case of the spin Nernst effect we also include the contribution from spin-resolved orbital magnetization, which assures correct behavior of the spin Nernst conductivity in the zero-temperature limit. Analytical formulas for the spin Hall and spin Nernst conductivities are derived in some specific situations. Using the Ioffe-Regel localization criterion, we have also estimated the range of parameters where the calculated results for the spin Hall and spin Nernst conductivities are applicable. Analytical results show that the vertex correction totally suppresses the spin Hall conductivity at arbitrary temperature. The spin Nernst conductivity, in turn, vanishes at $T=0$ when the orbital contribution is taken into account, but generally is nonzero at finite temperatures.

Detecting topological phases in silicene by anomalous Nernst effect

Silicene undergoes various topological phases under the interplay of intrinsic spin-orbit coupling, perpendicular electric field, and off-resonant light. We propose that the abundant topological phases can be distinguished by measuring the Nernst conductivity even at room temperature, and their phase boundaries can be determined by differentiating the charge and spin Nernst conductivities. By modulating the electric and light fields, pure spin polarized, valley polarized, and even spin-valley polarized Nernst currents can be generated. As Nernst conductivity is zero for linear polarized light, silicene can act as an optically controlled spin and valley field-effect transistor. Similar investigations can be extended from silicene to germanene and stanene, and a comparison is made for the anomalous thermomagnetic figure of merits between them. These results will facilitate potential applications in spin and valley caloritronics.

Hall and Nernst effects in monolayer MoS2

We study Hall and Nernst transports in monolayer MoS2based on Green’s function formalism. We have derived analytical results for spin and valley Hall conductivities in the zero temperature and spin and valley Nernst conductivities in the low temperature. We found that tuning of the band gap and spin-orbit splitting can drive system transition from spin Hall insulator (SHI) to valley Hall insulator (VHI). When the system is subjected to a temperature gradient, the spin and valley Nernst conductivities are dependent on Berry curvature.

Room-temperature spin thermoelectrics in metallic films

Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects which takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to two novel processes, namely a dynamical Elliott-Yafet spin relaxation and a dynamical side-jump mechanism. Both are the high-temperature counterparts of the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current understanding of the spin Hall, spin Nernst and Edelstein effects at low $T$. We consider the experimentally relevant regime $T > T_D$, with $T_D$ the Debye temperature, as the latter is lower than room temperature in transition metals such as Pt, Au and Ta typically employed in spin injection/extraction experiments. We show that the interplay between intrinsic (Bychkov-Rashba type) and extrinsic (dynamical) spin-orbit coupling yields a nonlinear $T$- dependence of the spin Nernst and spin Hall conductivities.

Spin Hall and Spin Nernst Effects Due to Intrinsic Spin-Orbit Coupling in Monolayer and Bilayer Graphene

We consider intrinsic contributions to the spin Hall and spin Nernst effects in monolayer and bilayer graphene. The spin Hall (Nernst) effect consists in the generation of transverse spin current by longitudinal electric field (temperature gradient). The relevant electronic spectrum for monolayer and bilayer graphene has been obtained from the corresponding effective Hamiltonians. Both spin Hall and spin Nernst conductivities have been determined within the linear response theory and Green function formalism. The influence of an external vertical voltage between the two atomic sheets in the case of a bilayer graphene is also analyzed and discussed. This voltage can generally lead to a phase transition between the topological insulator phase and conventional insulator. In the case of bilayer graphene, the main focuss is on an asymmetrical case, with different spin-orbit parameters in the two atomic sheets. Such a difference may be generated by different atomic planes adjacent to bilayer graphene on its both sides.

Spin Hall and spin Nernst effects in graphene with intrinsic and Rashba spin—orbit interactions

The spin Hall and spin Nernst effects in graphene are studied based on Green's function formalism. We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in the Kane—Mele model with various structures. When both intrinsic and Rashba spin—orbit interactions are present, their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level. When the Rashba spin—orbit interaction is smaller than intrinsic spin—orbit coupling, a weak kink in the conductance appears. The kink disappears and a divergence appears when the Rashba spin—orbit interaction enhances. When the Rashba spin—orbit interaction approaches and is stronger than intrinsic spin—orbit coupling, the divergence becomes more obvious.

Intrinsic contribution to spin Hall and spin Nernst effects in a bilayer graphene

We consider intrinsic contributions to the spin Hall and spin Nernst effects in a bilayer graphene. The relevant electronic spectrum is obtained from the tight binding Hamiltonian, which also includes the intrinsic spin–orbit interaction. The corresponding spin Hall and spin Nernst conductivities are compared with those obtained from effective low-energy k ⋅p and reduced Hamiltonians, which are appropriate for states in the vicinity of the Fermi level of a neutral bilayer graphene. Both conductivities are determined within the linear response theory and Green function formalism. The influence of an external voltage between the two atomic sheets is also considered. The results reveal a transition from the topological spin Hall insulator phase at low voltages to conventional insulator phase at larger voltages.