Sign Change of the Spin Hall Effect Due to Electron Correlation in CuIr Alloys
Z. Xu1), B. Gu1), M. Mori1), T. Ziman2, 3) and S. Maekawa1)
1)
R. G. for Spin-Energy Transfer Materials, ASRC, JAEA
2)
Institut Laue Langevin 3) Univ. Grenoble

Spintronics is a rich research field, not only for the wide
applications of low energy consumption and energy
transformation devices, but also for the new physics with theinterplays among charge, spin, orbital, heat and so on. The spin
Hall effect (SHE), which converts the injected longitudinalcharge current into the transverse spin current via the spin-orbit
interactions, is crucial for the development of spintronic devices.
The SHE is characterized by the ratio between the transverse
and the longitudinal resistivities, called spin Hall angle (SHA).
The magnitude of SHA describes conversion efficiency between
the charge current and the spin current, while the signdistinguishes the scattering direction of electrons, i.e., clockwiseor anticlockwise into the transverse direction.
In the experiment of the CuIr alloys, the dominant
contribution to the SHE was verified to be an extrinsic skew
scattering mechanism and the SHA was measured to be positive
2.1% [1].
The skew scattering arises from the interference between thescatterings of the d-wave and the p-wave described by the phaseshifts. The phase shift of p orbitals is calculated to be -0.05 by
the density functional theory (DFT), which means the electron
number of the partially filled p orbitals of the Ir impurity isslightly smaller than that of the Cu host. Since the phase shift ofp orbitals is small, the SHA is approximately proportional to it,
and it gives SHA=-1.0% [2].
Such a negative SHA is opposite in sign with the experiment.
We argue that such a discrepancy is highly non-trivial, which
inspires us to find out the key physics decisive on the sign ofSHA. Based on the Anderson model [3], it indicates that thelocal correlation effects in the 5d orbitals will raise the 5d stateof the Ir impurities, so that the electron number of the 5dorbitals of Ir will decrease, as sketched in Fig. 1 [2]. In a metal
the net charge of the impurity must vanish, thus the decrease of
5d electrons is partially balanced by the increase of 6p electronsof Ir. This may change the phase shift of p orbitals from small
negative to positive, and the sign of SHA from negative topositive correspondingly, which sheds light on removing thediscrepancy between theory and experiment in sign.
To simulate the local correlation effects numerically, wedevelop two specific combined methods of DFT+QMC(quantum Monte Carlo algorithm) and DFT+HF (Hartree-Fockapproximation) [2, 4]. By both of the two methods, as the local
correlation parameter U increases from 0, the sign of SHAchanges from negative to positive as expected, giving a positive
SHA at the realistic value of U=0.5 eV, as shown in Fig. 2 [2].
These theoretical results are consistent with the experiment inquality, revealing the key physics that the local correlation
effects are decisive on the sign of SHA in the CuIr alloys.
Furthermore, such a sign of SHA of CuIr is sensitive toperturbation of the local correlations, which is favorable toprospects of controlling the sign of the transverse spin Hall
voltage, as illustrated in Fig. 3. This may open up a way todevise a spin current switch or a spin current diode.
References[1] Y. Niimi et al., Phys. Rev. Lett. 106, 126601 (2011).

[2] Z. Xu et al., Phys. Rev. Lett. 114, 017202 (2015).

Fig. 1 Schematic picture of the density of states (DOS) of thenonmagnetic CuIr alloys with the 5d orbitals of Ir including the local
correlation U, based on the Anderson model [2, 3].

Fig. 2 SHA of the CuIr alloys by DFT under U=0 (red dot), by
quantum Monte Carlo (black circles) and Hartree-Fockapproximation (black line) under U>0 for the 5d orbitals of Ir [2].

Fig. 3 Schematic picture about the external control of the sign of
SHE in CuIr alloys.

[3] P. W. Anderson, Phys. Rev. 124, 41 (1961).
[4] Z. Xu et al., J. Appl. Phys. 117, 17D510 (2015).