According to basic principles of thermodynamics, heat will flow from a warmer to a colder region. The precise way in which the heat flows depends on the nature of the excitations in the system that transports the energy. One well-known example is the thermoelectric effect, which couples heat flow with charge currents. Thermoelectric materials have wide applications in thermometers and thermoelectric generators. Spin caloritronics (from ‘calor’, the Latin word for heat) is another example that combines the flow of heat with spintronics. In spin caloritronic systems heat currents coincide with spin currents carried by electrons or magnons (spin-waves), which expands the study of transport theory from conductors to a wide variety of insulating magnetic materials. The figure below describes the relationship between charge, spin, and heat flow.
Our group’s research is mainly focused on the theoretical study of the magnon contribution to spin caloritronics, such as the longitudinal spin Seebeck effect (LSSE) and the magnon Nernst effects (MNE). In the spin Seebeck effect, an analog of the Seebeck effect, a voltage results from a temperature gradient (orange arrow below) applied to the system that drives a spin current, Js. The spin current, Js, in turn generates a charge flow (blue arrow below) that produces a voltage. In the LSSE a temperature gradient drives a parallel (as opposed to a transverse) magnon current in a magnetic insulator. When a conductor with atoms of large atomic mass (so the spin-orbit coupling is large) is supported on the magnetic material, the interfacial coupling between the conductor and the insulator can transfer the angular momenta from magnons to a spin current of electrons in the conductor, which in turn produces an electrical voltage, V, via the Inverse Spin Hall Effect (ISHE), as shown in the figure on the right just below.
The LSSE is of increasing importance in spin caloritronics, since it enables direct generation of a spin current from heat and provides a novel route to thermoelectric generation induced by the ISHE. Following the first experimental observation of the LSSE in the YIG/Pt system, the phenomenological Landau-Lifshitz-Gilbert (LLG) equation has been used to describe the physics of LSSE. However, the microscopic description of the magnon-electron interaction at the interface is not fully understood, and remains a topic of investigation, including theoretical efforts by our group [1].
Another way to generate a spin current with heat flow is via the magnon Nernst effect (MNE), a magnonic version of anomalous Nernst effect, where a temperature gradient generates a transverse magnon current in a magnetic insulator. (See figure below.) The key ingredient for this Hall-like spin transport is the asymmetric Dzyaloshinskii-Moriya interaction (DMI), which can lead to a net momentum space Berry curvature in the magnon wavefunctions when summing over all magnon modes and hence can cause a non-zero transverse spin current. This effect therefore provides a probe of the magnon band topology due to its sensitivity to the Berry curvature. On the other hand, MNE does not depend on the net moment of the insulator but the topological nature of the material, which suggests that antiferromagnets with zero net moment can serve as effective spin generators and provide a promising platform to explore novel caloritronic effects.
From the discussion and figures above it is clear that a detailed description of the spin transport across the interface of the magnet/metal in the LSSE is of crucial importance for generating the ISHE from the temperature gradient applied to the magnetic system. The majority of the theoretical studies conducted so far have assume an isotropic (Heisenberg-type) magnetic exchange interaction at the interface. However, this ignores spin-orbit coupling at the interface, which will generally lead to an anisotropic magnetic exchange. This magnetic anisotropy has important implications for the spin current transport across the interface. Moreover, the crystalline cut of the interfacial layer of the magnetic also has important implications for the spin injection when the magnetic order is non-collinear. In the figure below, a color scale plot of the injection spin-current density, iz, is shown for crystals with surface orientation [111] (left) and [100] (right). Here, kBTM=5J/8, kBTI=J/2, Jij=J, |DM/J| is the coupling ratio in the bulk, and |DM/J| is the coupling ratio at the interface. S=1/2 is the magnitude of the local spin. The results were recently published by group members [2].
Besides the theoretical study on magnon-based spin caloritronics, we also collaborate with experimental groups on using spin-caloritronic probes to detect magnetic properties of insulating quantum materials and exploring possible materials for the application of spintronic devices. Two of our key collaborators are the groups of Professor Chia-Ling Chien and Professor Jianshi Zhou.
We have recently reported the electrical detection of room-temperature magnetization switching in the canted antiferromagnetic insulator LaFeO3, capped with a Pt or W overlayer. The observation of a large magneto-thermovoltage with an in-plane temperature gradient suggests that the mechanism is the swapping of spin currents in the antiferromagnet. This effect provides a sensitive electrical probe of the tiny net magnetization in the insulator, which can be manipulated by a magnetic field on the order of 10 mT. Our results highlight a new material class of insulating canted antiferromagnets for spintronics and spin caloritronics and suggests a method for the electrical readout of magnetic signals in an antiferromagnetic insulator. More details of this work can be found in the Nature Physics article we recently published.
This work was recently covered in the Northeastern News.
We gratefully acknowledge financial support from the National Science Foundation via grant DMR-1949701.
