The Spin Hall Effect (SHE) utilizes spin-orbit coupling to convert electrical current into pure spin current or vice versa, which can subsequently be employed to drive magnetization reversal or precessional dynamics, manifesting as the spin-orbit torque (SOT) effect. This phenomenon underpins the third-generation Spin Orbit Torque Magnetic Random Access Memory (SOT-MRAM) in the spintronics. In 2009, the Institute of Physics Chinese Academy of Sciences and Beijing National Laboratory for Condensed Matter Physics pioneered and obtained the first original patent in the SOT-MRAM field [Junyang Chen, Xiufeng Han, et al., Patent No. CN200910076048.X], introducing two core structures like the spin current generation layer/magnetic metal bilayer and spin current generation layer/magnetic tunnel junction (SOT-MTJ) for the field. Since them, these structures have become central in subsequent SOT effect studies and SOT-MRAM device development. Over the past decade, efforts have been made to optimize the spin current generation layer for higher current-to-spin conversion efficiency - spin Hall angle (SHA), zero-field ultrafast pulse SOT-driven magnetization switching capability, enhanced conductivity, etc., ultimately endowing SOT-MRAM with superior performances in terms of low energy consumption (1pJ~1fJ), high speed (< 1 ns), and extended endurance (>10¹²).

The SHE originates from intrinsic spin-orbit coupling in materials, manifesting through three microscopic mechanisms: the intrinsic mechanism dependent on band structure, the extrinsic side jump and skew scattering mechanisms. The latter broadens the design space for enhancing SHE beyond preferred heavy metals, including various elements, alloys, and compounds. Efforts to enhance SHE have included alloying light and heavy metals or periodically stacking ultrathin multilayers, grounded in the principle of introducing more spin-orbit coupling-related impurity scattering centers in composite materials. Spin-orbit-coupling-related scattering encompasses not only electronic impurity scattering but also interactions between electrons and magnetic structures, such as magnon scattering or spin fluctuation scattering. These interactions open new possibilities for establishing a correlation between SHE and magnetic order structures and their phase transitions.

Although researchers have recognized the potential of linking SHE with magnetic structures to amplify the former and have experimentally tried to explore this relationship in magnetically ordered systems like ferromagnets and antiferromagnets, physically elucidating this connection remains challenging. In classical SOT effect studies involving spin current generation layer/magnetic thin film bilayers, the SOT effect is influenced not only by the current-to-spin conversion efficiency of the bulk phase of the spin generation layer but also by its spin transmission efficiency at the bilayer interface. Both are related to the magnetic structure of the spin generation layer, necessitating the decoupling of bulk and interface effects, an intractable task complicated by their co-dependent relationship with magnetic structure.

This research, motivated and sparked by the rich physical correlations and challenges in studying the SHE in magnetically ordered systems, leverages a spin current generation layer/tunnel junction/magnetic metal trilayer structure and Spin Hall Tunneling spectroscopy (SHTS) to investigate the "strong correlation" between SHE and magnetic order in the antiferromagnetic material chromium (Cr). This tunnel junction structure circumvents direct contact between the spin current generation layer and the magnetic metal layer, effectively bypassing the aforementioned interface effects and highlighting bulk phase effects. Spin Hall Tunneling spectroscopy can measure both direct spin Hall effect (DSHE) and inverse spin Hall effect (ISHE), with this complementary measurement approach enhancing the reliability of experimental data. The chosen Cr material, an antiferromagnetic material, can be integrated into Cr/MgO/Fe full single-crystal magnetic tunnel junctions via molecular beam epitaxy. The single-crystal system can reduce the impact of impurity scattering on SHE, favoring the purity and prominence of the magnetic-order-relevant effects.

As shown in Figure 2, when current is applied between electrodes 1 and 3, spin-polarized current is injected into Cr. The spin current part, due to the presence of ISHE, generates a transverse current between electrodes 2 and 4. Due to the open-circuit condition between electrodes 2 and 4, a voltage generated by ISHE can be detected there. The polarity of this voltage can be altered by reversing the magnetization direction of Fe, serving as evidence for the ISHE signal. Conversely, when current is applied between electrodes 2 and 4, the DSHE in Cr leads to the accumulation of non-equilibrium spins at the Cr/MgO interface, creating a spin chemical potential there. This spin chemical potential can be read out through the MgO/Fe tunnel, generating a voltage between electrodes 1 and 3. The detected voltage polarity is also related to the magnetization direction of the Fe detection electrode, serving as a marker for DSHE. This measurement method has elucidated the temperature-dependent relationship of SHA or current-to-spin conversion efficiency, revealing a significant peak near the Néel temperature of Cr, the antiferromagnetic-to-paramagnetic phase transition point.

This experimental outcome clearly displays the strong correlation between the SHE in bulk antiferromagnetic Cr and its magnetic order structure, confirming the feasibility of enhancing SHE through spin fluctuations near the phase transition temperature. Combined with relatively higher conductivity and longer spin diffusion length of Cr compared to traditional heavy metals, the discovery of spin fluctuation-enhanced SHE in magnetically ordered Cr offers a new material option for developing low-energy and low-cost SOT-MRAM devices. This work has been published in “Nano Letters”. The research was conceptualized and guided by Prof. Xiufeng Han from the Institute of Physics, Chinese Academy of Sciences, Associate Prof. Caihua Wan, and Prof. Yuan Lu from the University of Lorraine, France. Dr. Chi Fang (Ph.D. graduate from the Institute of Physics, CAS, currently a postdoctoral researcher at the Max Planck Institute of Microstructure Physics) is the first author of the paper. Prof. Stuart S. P. Parkin, the director of the Max Planck Institute of Microstructure Physics, provided guidance on data analysis. Prof. Ning Tang from Peking University and Dr. Zhenchao Wen from the National Institute for Materials Science, Japan, supported the thin film preparation for the study. Dr. Satoshi Okamoto from Oak Ridge National Laboratory, USA, and Prof. Naoto Nagaosa from RIKEN Center, Japan, provided theoretical guidance. Other contributing authors helped to analysis data or deposit thin films or writing.

This study entitled "Observation of the Fluctuation Spin Hall Effect in a Low-Resistivity Antiferromagnet" was published on Nano Letters.

The work was funded by Chinese Academy of Sciences and the key research and development projects from the Ministry of Science and Technology and key grants from the National Natural Science Foundation of China.