Fast as Dilu, loud as thunder – Advances in THz spintronics

In the age of the Three Kingdoms, Liu Bei's steed was named Dilu. Its unaesthetic appearance once led people to believe that the horse was cursed, and would bring misfortune to people who rided it. Bei had for sure heard about the rumor, but never thought about abandoning the horse, even during his most difficult times. Once Bei was attending an ill-intentioned feast in Jingzhou, where a local warlord arranged a plot to hunt him down at the scene. Not long before the warlord made the move, Bei was informed and he fled, riding Dilu. In a fluster, he got lost and trapped in the middle of a river called Tanxi. No horse had ever been able to travel through Tanxi because it was wide and had strong undercurrent. The enemy pursuers were getting really close and Bei had nowhere to hide. In despair, he said, "Dilu, Dilu, you bring me misfortune after all," and planned to give up.


Dilu rose in a flash, leaped for an astonishing height, and landed to the other side of the bank, bringing Bei to safety. The "cursed" horse ended up saving Bei's life in a heroic act.


In quantum mechanics, there is a subject in a similar situation to Dilu, and that is the electron spin. Around 1920s, physicists Stern and Gerlach reported a surprising discovery, that is, in addition to having the degree of freedom of the 3D orbital, electron has an additional degree of freedom called spin. Spin is an intrinsic physical quantity, and therefore does not have a classical analog; it cannot be viewed as self-rotation of an object albeit its name.


Such a nonintuitive object brought considerable difficulty to the initial formulation of quantum mechanics. It was found that the Schrodinger equation, which is the most fundamental equation of quantum mechanics, cannot independently infer the existence of spins. Ironically, the Stern-Gerlach experiment dictated that spins must exist. This pushed Pauli made a generalization to the Schrodinger equation, modifying it in such a way that spin is artificially introduced by a two by two matrix. He knew the modification was unjustified but somehow it seemed to work for a wide variety of occations. This issue wasn't clarified until the development of the relativistic quantum mechanics.


Recent years, it has become clear to researchers that spins not only represent a "troublesome" concept that pushes people to perfect the theoretical framework, but can be used an alternative information carrier and boost the performance of household electronic devices as well.


Why is it so? Transistors are the building blocks of modern electronic devices. To put it simply, it is a switch of electrical current. Current off represents number 0, and on represents number 1. Each transistor is controlled to switch current with a designed sequence and duration, outputing a string of numbers consisting of 0's and 1's, which is the primitive form of information. Information transmits through transistors, modulated by gates, functioning as basic computation procedures. Any physical observable that can represent numbers 0 and 1 is called a bit. Just as how current switches can be used as bits, spins can be perfect bits as well. Stern-Gerlach experiment demonstrated that spin projections can take two discrete states, spin up and spin down, which happens to correspond to the numbers 0 and 1.


The most significant advantage of using spin bits is that they are considerably faster. The information processing speed of a transistor is limited by the rate as which current can be switched. Traditional transistors use electrical gates to modulate current. Limited by fundamental physics, the process cannot surpass the GHz range (109 times per sec). This is exactly the reason why the clock rate of even the most up-to-date single-core CPU has ceased to increase since many years ago. On the contrary, spin bits can break the GHz limit with ease; spin dynamics in solid-state matter typically locates in the THz frequency range (1012 times per sec), which is three orders of magnitude faster than the GHz range.


Spin dynamics being in the THz regime is an advantage for ultrafast spintronic devices, but it again brought difficulty to researchers who attempt to understand their fundamental physics. Since the frequency of spin dynamics far exceeds those of traditional circuits, microwave, and radio-frequency technologies, traditional approaches do not have enough time resolution to see spins in action.


Xin Qi Ji of the Song Dynasty wrote: "Horses are as fast as Dilu, arrows are as loud as thunder." This vivid depiction of ancient Chinese battlefield may imply interesting physics as well. For those wanting to strike an enemy horse as fast as Dilu, they resort to arrows traveling so fast that their aerodynamics would produce the sound of thunder. For those wanting to resolve spin dynamics, they must use a paradigm-shifting toolkit that has unprecedented time resolution. The only tool that satisfies this condition is the ultrafast optical spectroscopy technique.


In an invited review article titled "THz spin dynamics of rare-earth orthoferrites" in the second issue of Photonics Insights, Dr. Xinwei Li (researcher at Caltech) and Prof. Junichiro Kono (chair professor at Rice University) introduced the application of ultrafast optical spectroscopy in spintronics. The article focused on rare-earth orthoferrites (RFeO3), the most crucial material system for THz spintronics.


The article pointed out that there are two major reasons for the explosive advancement of ultrafast optical investigation of THz spintronics in recent years. First is that high-power femtosecond lasers have recently become widely available. One femtosecond is 10-15 sec, whose characteristic frequency is 1015 Hz, which is another three orders of magnitudes higher than the THz regime. Current laboratory lasers readily outputs pulses with femtosecond pulse durations and mJ-level pulse energy, thus paving the way for resolving spin dynamics in the time domain. The second reason is the optimization of theoretical methodology. In solids, spins will not evolve in isolation. Their dynamics must be strongly coupled with the other degrees of freedom in the same material, such as lattice, charge, and orbital. With the aim to provide guidance to experiments, theoretical tools have to take into account the complex many-body correlations within realistic systems, and in addition, their manifestations in the out-of-equilibrium scenario. Current tools such as time-domain density functional theory, dynamical mean-field theory, renormalization group, and tensor networks are important in this context.


The article consists of two broad topics, and four major chapters, as shown in Fig. 1.


Figure 1. The four central problems of interest in THz spintronics.


First, optical detection of spin dynamics was discussed. As mentioned above, spins are intrinsic properties of solids, and so would exhibit collective excitations with defined eigenfrequencies and dispersion relations. In quasi-equilibrium, researchers consider optical excitation as perturbations, which deviates spins from their equilibrium positions. Once the optical field was withdrawn, spins would relax to equilibrium mediated by precession modes, called spin waves. If a probe pulse arrives and interacts with the material, the probe pulse would be encoded with the spin information. This type of pump-probe technique is the foundation of optical detection of spin dynamics. This technique also nurtured time-domain THz spectroscopy technique. THz radiation generated from optical pulses resonantly couple to spin waves, directly interrogating the spin precession frequency and decoherence processes.


The targeted questions are: 1. what type of configurations spins will take in different magnetic phases of solids in equilibrium, and 2. which external factors will affect decoherence processes of spins. Optical detection of THz spin dynamics is the cornerstone for future development of spintronic transistors, and is starting to become one of the most important characterization tools for magnetic condensed matter systems.


The second broad topic is concerned with cases where spins are nontrivially deviated from equilibrium. This happens when light field is in the nonperturbative parameter regime and drives the materials far from equilibrium. In this case, light selectively excites certain degrees of freedom, such as charge and lattice, which in turn drastically modifies the microscopic free energy potential.


Within the modified landscape, spins can take completely different configurations. This is the mechanism of light induced magnetic phase transitions. Research on ultrafast laser control of spins first started from Europe, and now has become the focus of the field of spintronics research, since it reveals the ultimate speed limit of spin motion. What's more is that coherent spin waves can show nonlinearity in the optically excited nonequilibrium scenario. Spin waves strongly couple with one another, enabling researchers to control one spin wave with another spin wave, paving the way for all-magnon logical gates.


THz spintronics is an area full of energy and enthusiasm. Interdisciplinary efforts are needed in the future to develop this field to the extent where it can be useful for real-life applications. Ultrafast lasers indeed are the arrows mentioned by Xin Qi Ji. Hopefully, in this era where Moore's law is ending and the clock rates of CPU are saturating, spintronics can help us break limitations and expand frontiers, just as how Dilu helped Bei escape from enemy forces at Tanxi.