Research articlesInfluence of spin Nernst effect on continuum spin conductivity in antiferromagnets in the checkerboard lattice
Introduction
The spin separation caused by the thermal flow of electrons in condensed matter or spin Nernst effect is a phenomenon that has been experimentally observed since 2016 where both spin-up and spin-down electrons are separated with the application of an external magnetic field [1], [2]. This effect is similar to the spin Hall effect where an electrical current leads to a spin separation. The interest in magnon spintronics as well as in the utilization of magnons to transport of information has increased a lot recently due to the fact that magnons allow the transport of information through spins without Joule effect [3], [4], [5], [6], [7], [8], [9], [10], [11]. The detection of the spin Nernst effect by applying a longitudinal temperature gradient has been performed in a Platinum thin film, where the spin Nernst effect and the quantum spin Hall effect are of comparable intensities however, differing in sign [2].
In the collinear easy-axis anisotropic antiferromagnet, the symmetry guarantees that the spin wave modes are doubly degenerate. The two modes may carry opposite spin angular momentum and therefore, exhibit opposite chirality. So, in a two-dimensional antiferromagnet in the honeycomb lattice the presence of a Dzyaloshinskii-Moriya interaction, a longitudinal temperature gradient may drive to two modes of opposite transverse directions, realizing a spin Nernst effect of magnons with the vanishing of thermal Hall current. Thus, the magnons around the and K points of the first Brillouin zone contribute oppositely to transverse spin conductivity and the competition between them leads to a sign change of the spin Nernst coefficient at finite temperature.
The transmission of magnons through the antiferromagnetic and ferromagnetic chains can be altered by the Berry curvature generated by the Dzyaloshinskii-Moriya interaction (DM) which acts like an effective magnetic field leading so, to chiral magnons with nontrivial topological properties [12], [13], [14], [15]. This different kind of Hall effect arises naturally due to the coupling between spin-orbit interaction and the lattice being different from the Hall effect induced by the Lorentz force [16]. One of the firsts experimental studies of the magnon Hall effect were performed in the ferromagnetic insulator Lu2V2O7, Ho2V2O7, In2Mn2O7 [17], [18]. Moreover, the magnon Hall effect has been observed in magnets Cu as well [19], [20]. In general, these studies display that the topology of the system leads to a sign change in the Hall spin conductivity as function of the temperature and magnetic field [14].
In general, the spin transport in two-dimensional antiferromagnetic materials have many applications in nano-devices where the spin transport by magnons has been experimentally and theoretically studied in [9], [10], [11], [21], [22], [23], [24], [25], [26]. The aim of this paper is to study the effect of not opening of the gap in the honeycomb lattice in the presence of DM interaction on spin transport or verify the influence of the magnon Nernst effect on longitudinal spin conductivity . This work is divided in the following way: In Section 2, we discuss about the spin Hall effect. In Section 3, we present results for longitudinal spin conductivity. In the last Section 4, ene presents our conclusions and final remarks.
We analyze the influence of the spin Nernst effect on spin transport in the model given bywhere is an anisotropy parameter and . and are antiferromagnetic exchange interactions. The checkerboard lattice present two inequivalent sites where the symbols and in sums mean respectively nearest and next-nearest-neighbors interactions.
Section snippets
Spin wave approach and spin Nernst effect
The Holstein-Primakoff representation expanded in first order is employed to calculate the magnetic spin excitations with aim to determine the spin conductivity: , and for sublattice A and , and for sublattice B. In this representation, the Hamiltonian is described aswhere andwithandIn following,
Longitudinal spin current
The spin current operator (in x direction) is obtained from the discrete version of the continuity equation asIn terms of spin waves operators, one writes the spin current asIn following, by performing the discrete Fourier transformone obtainswhere is a matrix is the
Final remarks
In summary, we analyse the influence of the spin Nernst effect on the longitudinal spin conductivity in the two-dimensional antiferromagnetic model in the checkerboard lattice in the presence of Dzyaloshinskii-Moriya interaction, employing spin waves. One obtains a large spin conductivity at , at limit (DC limit). The effect of the spin Nernst effect obtained on conductivity is very small due to the fact that the DM interaction presents a very small influence on conductivity since that
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was partially supported by National Council for Scientific and Technological Development.
References (31)
- et al.
Phys. Rep.
(2011) - et al.
Physica C
(2019) - et al.
Eur. Phys. J. B
(2013) - et al.
J. Magn. Magn. Mater.
(2014) Phys. Lett. A
(2019)- et al.
Sci. Adv.
(2017) - et al.
Nat. Mater.
(2017) - et al.
Nature (London)
(2010) - et al.
J. Phys. D
(2010) - et al.
Nat. Mater.
(2012)