Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Summary

Here, we combine polarization-variable 7-eV laser with spin- and angle-resolved photoemission technique to visualize the spin-orbital coupling effect in solid states.

Abstract

The goal of this protocol is to present how to perform spin- and angle-resolved photoemission spectroscopy combined with polarization-variable 7-eV laser (laser-SARPES), and demonstrate a power of this technique for studying solid state physics. Laser-SARPES achieves two great capabilities. Firstly, by examining orbital selection rule of linearly polarized lasers, orbital selective excitation can be carried out in SAPRES experiment. Secondly, the technique can show full information of a variation of the spin quantum axis as a function of the light polarization. To demonstrate the power of the collaboration of these capabilities in laser-SARPES, we apply this technique for the investigations of spin-orbit coupled surface states of Bi₂Se₃. This technique affords to decompose spin and orbital components from the spin-orbit coupled wavefunctions. Moreover, as a representative advantage of using the direct spin detection collaborated with the polarization-variable laser, the technique unambiguously visualizes the light polarization dependence of the spin quantum axis in three-dimension. Laser-SARPES dramatically increases a capability of photoemission technique.

Introduction

Angle-resolved photoemission spectroscopy (ARPES) technique has developed into one of the most powerful tool to investigate quasiparticle band structures in solid states¹. The most of attractive feature of ARPES is the capability for band mapping to characterize electronic states in energy and momentum space. Spin-resolved ARPES (SARPES), which is here equipped with spin-detectors, e.g. Mott detector^2,3, further enables us to resolve the spin character of the observed band structures⁴. Since the Mott detector can measure the spin with two axes (x and z, or y and z), the combination of the two Mott detectors further allows one to obtain the spin orientation in three dimension^4,5. For several decades, however, the SARPES experiments were suffered from their low efficiency (typically 1/10000 compared to that for spin-integrated ARPES measurement)^3,4,5,6,7, which had limited the energy and angular-resolutions. Recently, the energy resolution of SARPES has been increased with a high-efficient spin detector based on exchange scattering, the so-called very-low-energy electron-diffraction (VLEED) detector^7,8,9,10. With this detector, the data quality has been significantly improved and the data acquisition time has been shortened. Recently, SARPES has succeeded greatly to address spin-polarized electronic states and particularly spin-orbit coupling effect resulting in the spin texture of the surface bands⁷.

Here, we employ SARPES measurements with a polarization-variable vacuum ultraviolet laser light (laser-SARPES) and demonstrate the great advantages of this combined technique. Through the investigation on the spin-orbit coupled surface states in Bi₂Se₃, we present two capabilities of laser-SARPES. Firstly, due to the orbital selection rule of linearly polarized lasers in dipole transition regime, p- and s-polarized lights selectively excite a part of eigen-wavefunctions with different orbital symmetry. Such an orbital selective excitation is thereby available in SARPES, namely, orbital-selective SARPES. Secondly, three-dimensional (3D) spin-detection in SARPES shows the direction of the spin quantum axis and directly displays full information of the light-polarization dependence. In this protocol, we briefly describe a methodology to perform this state-of-the-art laser-SARPES technique to study the strong spin-orbit coupling effects.

Our laser-SARPES system is located at The Institute for Solid State Physics, The University of Tokyo¹¹. The schematic drawing of our laser-SAPRES machine is shown in Figure 1. The polarization-variable 7-eV laser light¹² illuminates the sample surface and the photoelectrons are emitted from the sample. The polarization of laser is automatically controlled by MgF₂-based λ/2- and λ/4-waveplates to selectively use linear and circular polarizations. A hemispherical electron analyzer corrects the photoelectrons, and analyzes their kinetic energy (E_kin) and emission angle (θ_x and θ_y). The photoelectron intensities are mapped on the E_kin-θ_x screen monitored by a CCD camera. This image is directly transformed into the energy band structure in reciprocal space.

For SARPES measurement, the photoelectrons with a specific emission angle and kinetic energy analyzed by the electron analyzer are guided to two VLEED-type spin detectors with a 90-degree photoelectron deflector and the photoelectron beams are focused onto two different targets of Fe(001)-p(1×1) films terminated by oxygen. The photoelectrons reflected by the targets are detected in single channel detection by using a channeltron placed in each spin detector. The VLEED targets can be magnetized with Helmholtz-type electric coils which are arranged with orthogonal geometry with respect to each other. The magnetization direction is controlled by the bipolar condenser bank. The double VLEED spin detectors thereby enable us to analyze the spin-polarization vector of the photoelectron in three dimensions.

Protocol

1. Sample Mount and Installation

1. Cut single-crystal samples of Bi₂Se₃¹³ in an approximate size of 1 × 1 × 0.5 mm³ and use sliver-based epoxy to glue the sample to the sample holder.
2. Paste the scotch tape on the sample surface.
   NOTE: The scotch tape is used to cleave the sample in ultrahigh vacuum (UHV) chamber to obtain an atomically clean surface.
3. Install the sample into the sample magazine in the load lock, and start the pump until the pressure of the load lock is lower than 1×10^-5 Pa.

2. Sample Cleaving

1. Open the UHV valve between the load lock and the UHV preparation chamber.
2. Move the sample magazine from the load rock to the preparation chamber by using the linear/rotary feedthrough which is attached to the load lock chamber.
3. Pick up the sample from the sample magazine by the transfer rod attached to the preparation chamber.
4. Put back the sample magazine into the load lock and close the UHV valve.
5. Wait until the pressure of the preparation chamber is below 5×10^-7 Pa.
6. Peel the scotch tape by using wobble stick in the preparation chamber and cleave the sample under the UHV condition.

3. Sample Transfer to The Measurement Position

1. Transfer the sample to the UHV measurement chamber, and fix the sample to the main gonio-stage by the screw driver equipped with the measurement chamber.
2. Move the gonio-stage to the measurement position and use the micrometer stage to precisely move the sample position onto the focus of the spectrometer.

4. 7eV-laser Setup

1. Turn on the Nd:YVO4 laser.
   NOTE: The laser generates 355 nm laser light with a high repetition rate of 120 MHz.
2. Open the laser beam shutter, and make sure that the laser passes through the KBBF crystal and a second-harmonic wave of 177 nm (6.994 eV) is generated.
3. Optimize the power of the 7eV-laser by changing the power of the 355-nm laser with the variable attenuator.

5. ARPES Data Acquisition

1. Open the analyzer control software on the desktop computer.
   NOTE: We use "SES software" which is a general program for controlling ScientaOmicron analyzer with an electron deflector.
2. Select Setup… below Sequence on the menu bar (Figure 2, step i.2-1).
3. Choose ARPES configuration (Figure 3, step i.3-1) and ARPES Mapping in the list (Figure 3, step i.3-2) to perform Fermi surface mapping with the photoelectron deflector.
4. Click Edit (Figure 3, step i.3-3) and configure Fermi surface mapping ranging from -12° to 12° of an emission angle θ_y with step size of 0.5° (Figure 3, step i.3-4).
   NOTE: The hemispherical analyzer with an electron deflector enables us to map the Fermi surface without the sample rotations.
5. Click Run (Figure 2, step i.2-3).

6. SARPES Data Acquisition

1. Manually change the machine set-up for SARPES measurement including the analyzer entrance slit and the aperture size (Figure 1).
2. Select Setup… below Sequence on the menu bar (Figure 2, step i.2-2).
3. Choose Spin configuration (Figure 4, step i.4-1) and Normal in the list (Figure 4, step i.4-2), and click OK (Figure 4, step i.4-3).
4. Select DA30 (Figure 5, step i.5-1) on the menu bar and Control Theta… (Figure 5, step i.5-2) to open the setting panel for the DA30 angle (θ_x, θ_y) configuration.
5. Choose the emission angle (θ_x, θ_y) = (-6°, 0°) to take SARPES spectra (Figure 5, step i.5-3).
6. Apply magnetic field by controlling the bipolar condenser bank to magnetize the VLEED target in positive direction along the particular axis (α: x, y, or z).
   NOTE: In our system, this process can be done through command prompt [Figure 6 (a)].
7. Click Run to take intensity spectrum (Figure 2, step i.2-3).
8. Apply magnetic field to magnetize the VLEED target in negative direction along α and start scan to take intensity spectrum.
9. Calculate the spin-polarization and the spin-resolved spectra.

7. Scanning the light polarization dependence

1. Change the angle of the λ/2-waveplate precisely controlled by the stepping motor to tune the light polarization of the 7 eV-laser.
   NOTE: In our system, this process can be done through command prompt [Figure 6 (b)].
2. Take the spin-resolved spectra for x, y and z axes.
3. Scan the spin-resolved spectra as a function of the light polarization with varying the half waveplate angle from 0° to 102° with step size of 3°.

Results

Before starting SARPES experiments, k positions need to be accurately determined for taking spin-resolved spectrum by using high statistic spin-integrated ARPES results with high energy- and angular-resolutions (protocol 5.1-5.5). This is demonstrated in Figure 7 where the ARPES results for a Bi₂Se₃ single crystal are presented. This material is known as a prototypical topological insulator with a spin-polarized surface states

Discussion

ARPES and SARPES techniques have been commonly used for studying electronic band structures through the band mapping and spin-detection^1,2. In addition to these general advantages shown above, laser-SARPES based on orbital selection rule in optical dipole excitation can be employed as a novel technique for visualizing the spin-orbital coupling effect in the wavefunction and quantum spin interference. As demonstrated in Figure 9

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
DA30-L hemispherical analyzer	ScientaOmicron		http://www.scientaomicron.com/en/products/353/1170
Silver-based epoxy	Epoxy Technology	H20E
Sctoch tape	3M	801-1-18C
UHV valve	VAT	01034-KE01
linear/rotary feedthrough	Ferrovac	MD40
transfer rod	UHV design	PP series
wobble stick	Ferrovac	WM40
Paladin compact 355	Coherent
half waveplate	Kogakugiken		order made
Bipolar condenser bank	Tsuji electronics