Fluctuations are ubiquitous in nanometer-scale systems, spanning orders of magnitude in space and time. Real-space access to fluctuating states is impeded by a dilemma
between spatial and temporal resolution. Averaging over an extended period of time (or repetitions) is key for the majority of high-resolution imaging experiments, especially in weak
contrast systems. If, by lack of better knowledge, averaging is indiscriminate, it leads to a loss of temporal resolution and to motion-blurred images. We present coherent correlation imaging (CCI) – a high-resolution, full-field imaging technique that realizes multi-shot, time-resolved imaging of stochastic processes. The key of CCI is
the classification of camera frames that correspond to the same physical state (Fig. 1) even at low photon count, where imaging is not possible. CCI combines a correlation-based similarity
metric with powerful classification algorithm developed for genome research [1] realizing informed, non-sequential signal averaging while maintaining single frame temporal resolution. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state. Our material is a Co-based chiral ferromagnetic multilayer with
magnetic pinning low enough to exhibit stochastically recurring dynamics that resemble thermally-induced Barkhausen jumps near room temperature. CCI reconstructs sharp, high-contrast
images of all domain states by phase retrieval [2] and, unlike previous approaches, also tracks the time when these states occur. The spatiotemporal imaging reveals an intrinsic transition
network between the states and unprecedented details of the magnetic pinning landscape (Fig. 2). 
**References** 
[1] G. Sherlock, et. al., Current Opinion in Immunology 12, 201-205 (2000)
[2] Flewett, S. et al., Optics Express 20, 29210–29216, 2012 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/575255bbb0f7b8891a22722531593fa6.png) 
Principle of time-resolved coherent correlation imaging. Top: Sequence of camera frames showing Fourier-space coherent scattering patterns. Coherent correlation imaging classifies
scattering frames by their underlying domain state, as indicated by the colors. Bottom: Real-space images reconstructed from an informed average of same-state frames. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c06609f11a71267f63b9f1a35eff95c7.png) 
Map of attractive (blue dots) and repulsive (red areas) pinning sites. The background shows the position of the domain walls and their relative occurrence observed in the experiment.

Coherent Correlation Imaging: Resolving fluctuating states of matter

Gate voltage control of magnetic order is desirable for spintronic device applications [1], [2], but 180° magnetization switching is not straightforward since electric fields do not break time-reversal symmetry. Ferrimagnets have two sublattices with opposing magnetic moments, and by changing the relative amplitude of the magnetization of the two sublattice, magnetic reversal can be achieved. Here we show that ferrimagnetic order in rare earth-transition metal thin films can be dynamically controlled by voltage through solid-state hydrogen gating. We focus on GdCo ferrimagnetic structures with perpendicular magnetic anisotropy, and show that the dominant lattice of GdCo ferrimagnetic thin films at room temperature can be reversibly toggled by hydrogen loading/unloading into the material controlled using a solid-state hydrogen pump [3]. The loading/unloading of hydrogen is mediated by a positive gate bias applied to the top electrode generates protons through hydrolysis of ambient moisture in the air, as shown previously [3]. We find that hydrogen injection into the GdCo leads to a significant decrease in the compensation temperature. With a fixed perpendicular bias field, we show that a gate voltage can induce 180° magnetic switching of the sublattices by shifting the magnetic compensation temperature above and below room temperature. The localized nature of the hydrogen gating effect allows for gate-voltage generation of ferrimagnetic spin textures such as chiral domain walls in racetrack devices. The work provides a means to tune ferrimagnetic spin textures and dynamics, and provides a new direction in magnetoionic control of magnetism for data storage and computing.

**References:**

[1] F. Matsukura, Y. Tokura, and H. Ohno, “Control of magnetism by electric fields,” Nat. Nanotechnol., vol. 10, no. 3, pp. 209–220, 2015. [2] E. Y. Tsymbal, “Electric toggling of magnets,” Nat. Mater., vol. 11, no. 1, pp. 12–13, 2011. [3] A. J. Tan et al., “Magneto-ionic control of magnetism using a solid-state proton pump,” Nat. Mater., vol. 18, no. 1, pp. 35–41, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a025e553f973e3a2bdc508401f7c457e.jpg)
Coercivity (Hc) versus temperature showing compensation temperature change of GdCo by solid-state ionic gating.

![](https://assets.underline.io/uploads/markdown_image/1/image/e240923efec7bf678cdf53c00f3dffa0.jpg)
Reversed domain generator based on hydrogen gating: a sequence of wide field MOKE contrast images showing the movement of the generated reversed domain.

 Voltage control of ferrimagnetic order and voltage-assisted spin texture writing by solid-state hydrogen gating

Exchange bias is a well-known and very useful effect that occurs due to an interfacial coupling between adjacent thin films of an antiferromagnet and a ferro(ferri)magnet [1]. Controlling exchange bias in an antiferromagnet/ferro(ferri)magnet thin film system by application of a gate voltage is much sought-after for spintronic applications. However, since the exchange bias effect is related to the ordering of spins in both the antiferromagnet and the ferro(ferri)magnet, and electric fields have little influence over the spin order, electrical control of exchange bias is very hard to achieve practically. Recently, ionic gating of magnetic heterostructures, where a gate voltage is used to drive ions (O2-, H+ etc.) in or out of the active layers, has yielded very interesting and promising results. Due to the size of the H+ ion, protonic gating is potentially faster and more reversible compared to gating with other ions and is also able to cause large changes in magnetic properties in the underlying active layers, such as modulation of perpendicular magnetic anisotropy in ultra-thin Co films [2]. The utility of protonic gating was further demonstrated when it was shown that ferrimagnetic order in GdCo metal thin films can be dynamically controlled by this method [3]. GdCo is comprised of two sub-lattices, one made up of Gd atoms and one of Co atoms, and the magnetic moments in each sub-lattice point in opposite directions, hence resulting in ferrimagnetic order. Experimental and theoretical analyses show that the protons being inserted into the GdCo reduce the effective magnetic moment of the Gd atoms, and by starting from a Gd-dominated magnetic state, the overall magnetization can be switched 180 degrees through proton gating. Harnessing this functionality, we have shown, in this work, that exchange bias toggling is possible when we incorporate the GdCo ferrimagnet in an exchange biased heterostructure with NiO serving as the antiferromagnet. Using sputter deposition we have engineered a stack with the structure NiO(33)/Pd(1)/GdCo(10)/Pd(10)/GdOx(30)/Au(3) on thermalized Si, which has fully shifted loops, i.e. the exchange bias field is larger than the coercive field (HEB&gt;HC), as depicted in Fig. 1(a). When a sufficiently high (&gt;1.5V) positive voltage is applied to the Au top electrode (Pd serves as the bottom electrode), atmospheric water is split and the proton is transported through the GdOx electrolyte, into the GdCo(10)/Pd(10) layers. Starting from a Gd-dominated state of the GdCo, upon enough insertion of hydron ions after applying +1.8V, the dominant sublattice of GdCo switches from Gd to Co, as expected from previous work, but is now also accompanied by a toggling of the exchange bias direction, as shown in Fig. 1(b). The effect is fully reversible, as shown in Fig. 1(c). We can understand this phenomena when we realize that although the gating does nothing to the relative spin orientation in either the ferrimagnet or the antiferromagnet, the ferrimagnet’s magnetization direction depends not only on the spin orientation of the sublattices but also on the relative magnitude. The magnetization direction flips 180 degrees during gating but the relative spin orientation across the interface remains the same. Essentially, if initially the pinned magnetization is +Mz (meaning HEB is -ve) then after gating the pinned magnetization will be -Mz necessarily making HEB +ve. To the best of our knowledge, this is the simplest demonstration of exchange bias toggling to date, since our system does not rely on any complex materials or growth processes and works at room temperature, as opposed to some previous works [4,5]. Due to the small size of the proton, our method is highly reversible, and initially we have shown full cycling toggling of the exchange bias up to 10 times, where the hysteresis loop remains fully shifted throughout the process (Fig. 2) as evidenced by HEB/HC being over 1. We believe our simple but robust method to toggle exchange bias can serve as a platform for demonstrating more functionalities and/or devices and can have broad implications for spintronics in general. This work is supported in part by SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST).

**References:**

[1]. Y. Fan et al., Nature Nanotechnology, Vol. 8, p. 438 (2013) [2]. A.J. Tan et al., Nature Materials, Vol. 18, p. 35 (2019) [3]. M. Huang et al., manuscript under review [4]. S. Wu et al., Physical Review Letters, Vol. 110, p. 067202 (2013) [5]. X. He et al., Nature Materials, Vol 9, p. 579 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/36bc1892deb385267892bf4aee4bb5dd.jpg)
Fig. 1. MOKE hysteresis loops of the structures described in the text in the (a) initial state, (b) after applying +1.8V for 180s and (c) after applying 0V for 80s. The MOKE signal follows the Co magnetic moments, which is why in the Gd dominated state (a) and (c) the loops are inverted

![](https://assets.underline.io/uploads/markdown_image/1/image/ee59777b4e38f83110d076127ab1a339.jpg)
Fig. 2. Reversible toggling of exchange bias in sample with fully shifted loops, where the voltage was toggled between +1.8V and 0V with period of 40s. Note that the erratic oscillations in EB towards the latter cycles are due to noise during measurement of individual hysteresis loops

 Exchange Bias Toggling in GdCo/NiO Thin Film System by Solid-State Hydrogen Gating

HOA: Magnetic Imaging and Magnetization Dynamics

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Coherent Correlation Imaging: Resolving fluctuating states of matter

Voltage control of ferrimagnetic order and voltage-assisted spin texture writing by solid-state hydrogen gating

Exchange Bias Toggling in GdCo/NiO Thin Film System by Solid-State Hydrogen Gating

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