# Spin ARPES

Electron spin plays a significant role in shaping the properties of quantum materials. How do we observe the spin texture of electronic bands in momentum space? How does this further our understanding of solids beyond that which can be learnt from conventional ARPES? We answer these questions by developing a high resolution spin-resolved ARPES setup that has the ability to visualize spin texture in electronic band structures.

### Contents

## Our Motivation

Electron spin interactions play key roles in determining the electronic structure of quantum materials. These specific roles, however, are not always well understood and cannot be answered by conventional ARPES.

### Topological materials

Topological materials with strong spin-orbit coupling host topologically nontrivial surface states with characteristic spin-momentum locking features. There is a variety of families of topological material, each possessing interesting systems. Examples include the topological insulator Bi_{2}Te_{3}, Kondo insulator SmB_{6}, crystalline insulator PbSnTe, magnetic Weyl semimetal Co_{3}Sn_{2}S_{2}, and candidate topological superconductor FeTe_{1-x}Se* _{x}*. The topological property of many of these materials are still under debate, hence spin texture in the surface state of such materials would serve as evidence for revealing the role of spin-orbit coupling and determining whether the materials are actually topological.

### Noncentrosymmetric materials

Broken inversion symmetry, together with strong spin-orbit coupling (SOC), can give rise to spin-splitting effects, as commonly seen on the surface of materials like Antimony. Noncentrosymmetric materials with strong spin-orbit coupling, such as BiTeX (X = Cl, I, Br), are less common and are associated with novel Rashba spin-splitting in the bulk. Rashba spin-splitting is closely related to a wide variety of novel physical phenomena, such as anisotropic magnetoresistance, Majorana fermions, Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states in superconductors, and even spintronic applications in the absence of a magnetic field. The study of the spin textures in these materials is thus crucial.

### Strongly correlated materials

Electrons in strongly correlated materials are described by dynamics which cannot be considered individually and separately. Their spins can also interact with charge, orbital, and lattice degrees-of-freedom to give rise to a variety of phases. Examples include high *T*_{c} superconductors in the copper- and iron-based families, as well as manganites that host colossal magnetoresistance. These phenomena cannot be fully understood without a complete picture of the spin degree-of-freedom.

### Low-dimensional magnetic materials

Due to their reduced dimensionality, low dimensional magnets *usually* exhibit weak magnetic ordering compared to conventional bulk magnets. However, magnetic materials with dimensions less than 3 have shown unconventional magnetic behavior. One example is the study of Cr-based chalcogenides, where intrinsic ferromagnetic order has been found. Observing the spin-resolved quantum phase transition from paramagnetic to ferromagnetic ordering in 2D magnetic materials is therefore desired for understanding exchange interactions in lower dimensions that give rise to magnetic ordering.

In addition to equilibrium studies of quantum materials, the need for advanced spintronic applications requires us to understand and manipulate spin interactions in a variety of materials in the time domain.

## Our Approach

Our spin ARPES system uses a 6 eV laser for excitation. We are working on integrating an 11 eV laser. The system is completely home-built and is based on the **Time of Flight** (TOF) technique. Unlike conventional ARPES systems, which use a hemisphere deflector for obtaining energy distributions, the TOF system measures photoelectrons' velocity distributions. The TOF technique gives us higher sensitivity and efficiency compared to a conventional Mott polarimeter attached to a hemisphere deflector.

The basic schematic is straightforward. Angular resolution is constrained by the system's finite angular acceptance of the photoelectrons from the sample. Energy resolution is determined by the time *t* between pulse excitation and detection by the Multichannel Plate. Thus, the relation between kinetic energy and flight time *t* is:

where *L* is the length of the electron flight path.

Our spin-resolved capability is based on electron exchange scattering polarimetry. Scattering cross-section is, crucially, spin-dependent. We scatter emitted photoelectrons from a polarized magnetic scattering target, and collect intensity data (*I*_{up} and *I*_{down}) for up and down polarized magnetic targets independently. As scattered intensity is proportional to cross-section, the resulting polarization *P* of photoelectrons emitted is:

Our spin-TOF follows the approach developed in collaboration with Chris Jozwiak, Zahid Hussain, and Alessandra Lanzara at Lawrence Berkeley National Lab [1].

## Our Results

The figure shows the spin-polarized surface states of Bi_{2}Se_{3}. Red and blue colors indicate opposite in-plane spin polarization. Spin-momentum locking of the topological surface state is apparent from opposite momenta possessing opposite spin polarizations.

## Publications

[1] C. Jozwiak et al. Spin-polarized surface resonances accompanying topological surface state formation. *Nat. Commun.* **7**,13143 (2016)