Hall detection of a ppm spin polarization

Hall effects have been employed as sensitive detectors of magnetic fields and magnetizations. In spintronics, exotic phenomena often emerge from a non-equilibrium spin polarization or magnetization, that is very difficult to measure directly. The challenge is due to the tiny total moment, which is out of reach of superconducting quantum interference devices and vibrating sample magnetometers or spectroscopic methods such as X-ray magnetic circular dichroism. The Kerr effect is sufficiently sensitive only in direct gap semiconductors, in which the Kerr angle can be resonantly enhanced. Here we demonstrate that even one excess spin in a million can be detected by a Hall effect at room temperature. The novel Hall effect is not governed by the spin Hall conductivity but by its energy derivative thereby related to the spin Nernst effect.


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In principle, a non-equilibrium magnetization ( m) should induce an electromotive force E AHE perpendicular to an applied current density j c analogous to the anomalous Hall effect (AHE) 2,9 in ferromagnets as illustrated in Fig. 1: Since Hall measurements do not require specific structures or sample sizes, they may serve as a more flexible electrical probe of m than the contact voltage to ferromagnetic electrodes [10][11][12] .
However, such a non-equilibrium anomalous Hall effect has only been observed in a few semiconductors in which the optically excited spin polarization P , i.e. the ratio of the spin polarized to the total density, is very high [13][14][15] (P > 10 %). In conventional metals the spin polarization due to the non-equilibrium magnetization is far below 0.1% 16 , which appears to have discouraged researchers to attempt detection by a Hall voltage.
In this paper we show that a non-equilibrium magnetization causes a detectable Hall voltage even in a metal and at room temperature owing to a novel mechanism formulated below. Figure 2a is a schematic illustration of our measurement setup. The sample is a bilayer of nonmagnetic iridium-doped copper (Cu 95 Ir 5 ) and a ferrimagnetic insulator yttrium iron garnet (YIG). A non-equilibrium magnetization m is injected into the Cu 95 Ir 5 layer via the spin pumping from the YIG layer 5,17 , the orientation of which is antiparallel to the YIG magnetization. We apply a magnetic field normal to the sample surface so that the YIG magnetization is aligned perpendicular to the interface. In this out-of-plane magnetization  For vanishing currents (the black curve at the bottom in Fig. 2d), the Hall voltage is almost zero even at the FMR, which confirms that the ISHE is forbidden in the out-of-plane magnetization configuration 18 .
Surprisingly, when the microwave and electric currents are simultaneously applied, a conspicuous Hall voltage emerges at the ferromagnetic resonance field H FMR , as shown in  We phenomenologically describe the observations using a diffusion theory of the spin Hall effect (SHE). The non-equilibrium magnetization in Cu 95 Ir 5 can be considered due to a spin accumulation as sketched in Fig. 1, of which the magnitude is defined as the difference between chemical potentials of spin-up and spin-down electrons: Here we define the up-spin direction is antiparallel to m.
where − m/| m| denotes the spin polarization vector of the more populated sub-band. According to Eq. (2), the non-equilibrium AHE in the linear response in µ s is proportional to the energy derivative of the spin Hall conductivity (∂σ SHE /∂ε), while the conventional spin Hall effect (anomalous Hall effect) scales with σ SHE (σ AHE ). Figure 4 shows the Cu 95 Ir 5thickness dependence of the non-equilibrium AHE resistance measured at 50 mW microwave excitation; the decay trend is well explained by Equation (2)  ∂σ SHE /∂ε can be decomposed into two terms: where we define the spin Hall angle as θ SHE = σ SHE /σ and σ is the conductivity of the In conclusion, the Hall detection of ppm-order spin polarization offers a straightforward approach to detect tiny non-equilibrium magnetizations electrically and non-invasively using simple sample structures without ferromagnetic electrodes. This measurement also manages to determine the energy dependence of the spin Hall conductivity around the Fermi energy without carrier doping or thermal gradients and is applicable to a wide range of materials.
Our method should help setting up an extensive database of spin Hall and spin Nernst coefficients for conductors that are potentially relevant for spin Hall devices.

Method
The single-crystal yttrium iron garnet (YIG) films used in the present work were prepared by liquid phase epitaxy (LPE) on a gallium gadolinium garnet substrate. All samples were cut from a single 4.5 µm LPE YIG film. To achieve good-YIG/Cu 95 Ir 5 interfaces, the YIG films underwent an acid pickling process before being transferred into high vacuum under which they were annealed in-situ for three hours at 500 • C before the Cu 95 Ir 5 layer was sputtered at room temperature. The Cu 95 Ir 5 thickness was calibrated by X-ray reflectometry using control samples. The crystallographic properties of the YIG/Cu 95 Ir 5 device were 7 characterized by transmission electron microscopy (TEM) and x-ray diffractometry, to confirm that the YIG films were high quality single crystals with a lattice constant of 12.376Å, while the Cu 95 Ir 5 layers showed multi-crystalline structures without a preferred orientation.
During electric measurement the sample is placed at the center of a TE 011 microwave cavity with the resonance frequency of 9.45 GHz and the microwave field is along the x axis as defined in Fig. 2a.  Charge current is applied along the x axis and the Hall voltage is measured in the y direction.
The magnetic field is applied normal to the sample surface which is a 2 mm×3 mm rectangle.