Lorentz Ultrafast Electron Microscopy

• Lorentz ultrafast electron microscopy is defined by the use of time-synchronized electron pulses that probe transient electromagnetic fields via the Lorentz force.
• Ultrafast Lorentz TEM employs Fresnel contrast imaging to track nanoscale magnetic dynamics with high localization precision.
• The CDEM approach uses energy-resolved spectroscopy to measure THz near fields and reconstruct charge-carrier dynamics in semiconductors.

Searching arXiv for recent and relevant papers on Lorentz ultrafast electron microscopy and closely related UTEM methods. Lorentz ultrafast electron microscopy denotes ultrafast electron-microscopy methods in which synchronized free-electron pulses probe transient electromagnetic fields through the Lorentz interaction. In the reported implementations, this category includes stroboscopic ultrafast Lorentz transmission electron microscopy, where transverse deflections are converted into Fresnel contrast for imaging nanoscale magnetic dynamics, and charge dynamics electron microscopy (CDEM), where inelastic energy shifts induced by terahertz near fields are measured in an ultrafast scanning transmission electron microscope to retrieve field amplitude and phase and reconstruct charge-carrier dynamics in solids (Möller et al., 2019, Yannai et al., 2022).

1. Scope and conceptual position

Lorentz ultrafast electron microscopy is defined by the use of time-synchronized electron pulses as probes of transient electric and magnetic fields. The common element is the Lorentz force acting on the probe electrons, but the measured observable depends on the implementation. In ultrafast Lorentz imaging of magnetic textures, the dominant signature is transverse deflection, which is converted into image-plane intensity contrast by Fresnel defocus. In CDEM, the dominant signature is a net energy change caused primarily by the longitudinal electric field component $E_z$ of a THz near field (Möller et al., 2019, Yannai et al., 2022).

The two realizations occupy different operating regimes. The magnetic-vortex experiment employs a stroboscopic scheme synchronized to a radio-frequency drive and records real-space trajectories of a vortex core in a Permalloy nanoisland. CDEM, by contrast, probes photoinduced charge transport in a semiconductor by measuring the energy distribution of transmitted electrons as a function of lateral position and pump–probe delay. The CDEM work explicitly places this interaction in an intermediate Lorentz-interaction regime distinct from both photon-induced near-field electron microscopy (PINEM), where $T \ll \tau_e$, and standard deflectometry or Lorentz TEM, where $T \gg \tau_{\mathrm{int}}$ (Yannai et al., 2022).

A common misconception is that Lorentz ultrafast electron microscopy is limited to magnetic-domain imaging. The reported semiconductor experiment shows that Lorentz-type ultrafast EM also includes energy-resolved spectroscopy of THz-frequency near fields generated by moving charge carriers, not only deflection-based imaging (Yannai et al., 2022).

2. Interaction physics and governing equations

The fundamental interaction is the Lorentz force. In the CDEM formulation, an electron moving through the transient field generated by photoexcited carriers experiences

$$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$

The corresponding classical energy change is

$$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$

with $\tau \simeq L/v$. For the measured mean energy shift at spatial pixel $(x,y)$ and pump–probe delay $\Delta t$, the experiment uses

$$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$

In the experiment the dominant contribution to the measured signal is from the longitudinal electric field component $E_z$ (Yannai et al., 2022).

In ultrafast Lorentz microscopy of magnetic textures, the same interaction is expressed as a transverse momentum transfer. Each electron moving with velocity $T \ll \tau_e$0 through an in-plane sample field $T \ll \tau_e$1 experiences

$T \ll \tau_e$2

which yields a deflection angle

$T \ll \tau_e$3

In Fresnel mode this angle produces a shift in the image plane, so the observed contrast is proportional to the divergence of the projected deflection field. The resulting bright peak at the vortex core can be localized far more precisely than the magnetic point resolution itself (Möller et al., 2019).

The statistical distinction between point resolution and localization precision is central. The magnetic point resolution is reported as $T \ll \tau_e$4, while the statistical localization precision obeys

$T \ll \tau_e$5

and reaches $T \ll \tau_e$6 in the reported experiment. This directly addresses the frequent confusion between the width of a magnetic contrast feature and the uncertainty with which its center can be tracked (Möller et al., 2019).

3. Instrument architectures and synchronization schemes

The magnetic-vortex study uses an ultrafast Lorentz transmission electron microscope in Fresnel mode. A femtosecond laser with $T \ll \tau_e$7, $T \ll \tau_e$8 pulses at $T \ll \tau_e$9 is frequency-doubled to $T \gg \tau_{\mathrm{int}}$0 and stretched to $T \gg \tau_{\mathrm{int}}$1. These pulses strike a laser-triggered ZrO/W field-emitter tip in the TEM gun, producing ultrashort electron pulses. Electron optics form a near-parallel beam through the sample, while the projector or defocus coils set a controlled overfocus of $T \gg \tau_{\mathrm{int}}$2. The objective lens is nearly off to minimize magnetic field at the sample, and a Gatan Ultrascan camera records the Fresnel images. A fast photodiode on the laser oscillator provides a $T \gg \tau_{\mathrm{int}}$3 reference for a high-bandwidth arbitrary waveform generator, which locks the RF output phase to the laser timing and delivers RF burst or continuous-wave excitation via a custom TEM holder up to GHz. The reported laser-electronic timing jitter is $T \gg \tau_{\mathrm{int}}$4, with overall system jitter $T \gg \tau_{\mathrm{int}}$5 (Möller et al., 2019).

The CDEM implementation uses an ultrafast scanning transmission electron microscope. A laser-driven photocathode generates femtosecond electron pulses at $T \gg \tau_{\mathrm{int}}$6, and a delay stage controls the pump–probe delay $T \gg \tau_{\mathrm{int}}$7 between an IR pump and the electron probe. The sample is an InAs crystal, $T \gg \tau_{\mathrm{int}}$8 thick with a cleaved $T \gg \tau_{\mathrm{int}}$9 facet, operated in STEM mode to allow raster scanning in $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$0 and $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$1. Both pump and probe derive from the same mode-locked Ti:Sapphire laser $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$2, ensuring sub-$$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$3 timing jitter. The present demonstration reports a lateral resolution of $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$4, set by the STEM beam spot size, while noting that nanometer resolution is achievable with standard STEM focusing. The effective time resolution is determined by the electron pulse duration $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$5 and the near-field transit time $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$6, with a few-hundred-femtosecond precision reached by deconvolution (Yannai et al., 2022).

The contrast mechanisms differ correspondingly. In Fresnel-mode ultrafast Lorentz microscopy, contrast arises from the gradient of the in-plane magnetization, such that domain walls appear as black/white lines and the vortex core yields a local intensity peak. In CDEM, contrast is encoded in the electron energy spectrum measured by EELS, with a typical energy resolution of $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$7, sufficient to resolve $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$8 energy shifts induced by THz fields of order $$F(t) = -e \left[ E(r(t),t) + v(t)\times B(r(t),t) \right].$$9 (Möller et al., 2019, Yannai et al., 2022).

4. Measurement protocols and inverse reconstruction

The magnetic-vortex experiment is organized around stroboscopic sampling of a reproducible RF phase. The sample is a polycrystalline Permalloy $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$0 square of $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$1 lateral size and $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$2 thickness, contacted on opposite edges with $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$3-thick Au leads on a $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$4 Si membrane window of $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$5. Under continuous-wave excitation, the drive frequency is swept to find resonance, with maximum orbit observed at $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$6. At that frequency and $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$7, 21 delay steps from $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$8 to $$\Delta E = \int F\cdot v\,dt = -e \int_{t_0}^{t_0+\tau} E(r(t),t)\cdot v(t)\,dt,$$9 in $\tau \simeq L/v$0 increments are acquired; at each delay, 32 images of $\tau \simeq L/v$1 each are recorded and grouped into eight $\tau \simeq L/v$2 subsets. In the burst experiment, $\tau \simeq L/v$3 RF pulses at $\tau \simeq L/v$4 are applied for a total on-time of $\tau \simeq L/v$5, switched off at a zero-crossing, and delays from $\tau \simeq L/v$6 to $\tau \simeq L/v$7 are sampled in $\tau \simeq L/v$8 steps with $\tau \simeq L/v$9 integration per image. Absolute $(x,y)$0 is determined from a small-angle beam deflection near an Au contact, imaged in diffraction mode and fitted in phase versus delay (Möller et al., 2019).

Data reduction in the magnetic case proceeds by median-filtering each Lorentz frame with a $(x,y)$1 pixel filter, thresholding the $(x,y)$2 bright peak, and taking the center of mass of the thresholded region as the vortex-core position. The resulting $(x,y)$3 and $(x,y)$4 are then analyzed with a harmonic-orbit model and, for the free decay, with moving-window fits. The underlying collective-coordinate description is the Thiele equation,

$(x,y)$5

where $(x,y)$6 is the core position, $(x,y)$7 the gyrovector magnitude, $(x,y)$8 the viscous damping parameter, and $(x,y)$9 the restoring-force constant (Möller et al., 2019).

The CDEM acquisition protocol samples the full electron energy spectrum $\Delta t$0 at each spatial pixel over pump–probe delays from $\Delta t$1 to $\Delta t$2, producing a $\Delta t$3 dataset $\Delta t$4. In practice, $\Delta t$5 is fitted with the theoretical inelastic-scattering probability to extract the local THz field amplitude $\Delta t$6 and phase $\Delta t$7. In the Fourier domain, the retrieval is expressed as

$\Delta t$8

where $\Delta t$9 encodes the known transit-time window function (Yannai et al., 2022).

Reconstruction of the underlying charge dynamics then requires a microscopic model. The reported workflow follows Reklaitis by solving coupled drift-diffusion equations for electrons and holes under the pump profile, obtaining transient current densities $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$0 and $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$1. A Poisson solver is then applied through $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$2 with $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$3, and the time-dependent Schrödinger equation for the electron wavefunction under the potential $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$4 is solved in the classical limit to recover $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$5. Four global fitting parameters, including carrier mobility ratio, surface recombination rate, pump spot size, and overall amplitude, are adjusted to obtain agreement between simulation and measurement, after which the full $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$6 charge density $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$7 is obtained (Yannai et al., 2022).

5. Demonstrated physical regimes

Magnetic vortex dynamics

The magnetic-vortex experiment examines the current-driven gyration of a vortex core in a $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$8-sized magnetic nanoisland. Under continuous-wave excitation, the reported peak-to-peak orbit diameter along the long axis is $$\Delta \mathcal{E}(x,y,\Delta t) = -e \int E_z[r(t;x,y),t+\Delta t]\,v_z\,dt.$$9. A best-fit harmonic-oscillator analysis of 42 data points yields $E_z$0 and $E_z$1, while the localization precision is $E_z$2 in both $E_z$3 and $E_z$4 (Möller et al., 2019).

After switch-off in the burst experiment, the vortex gyrates with decaying amplitude, and the trajectory is extracted up to $E_z$5. A moving-window fit of $E_z$6 width shows that the orbit diameter decays nearly linearly rather than purely exponentially, that the instantaneous damping $E_z$7 increases with decreasing diameter, and that the instantaneous free frequency $E_z$8 hardens from $E_z$9 to $T \ll \tau_e$00 at intermediate diameter. The mean center of gyration shifts by $T \ll \tau_e$01, indicating pinning in a disorder potential. The measurements therefore do not support an interpretation based on intrinsic damping alone; the reported attribution is to local disorder in the vortex potential, and comparison with micromagnetic models by Min et al. suggests additional dissipation via internal-structure deformations under spatial disorder (Möller et al., 2019).

Nanoscale charge dynamics in semiconductors

The CDEM experiment addresses photoexcited carrier transport in a semiconductor, exemplified with InAs. An IR pump pulse of $T \ll \tau_e$02 duration and $T \ll \tau_e$03 center wavelength creates a nonuniform distribution of electrons and holes via the photo-Dember effect. Because $T \ll \tau_e$04, electrons diffuse into the bulk while holes remain near the surface, launching a single-cycle THz-frequency electromagnetic pulse into the surrounding vacuum. A time-delayed electron pulse of $T \ll \tau_e$05 and duration $T \ll \tau_e$06 traverses the near-field region at a lateral impact parameter of order $T \ll \tau_e$07, and its measured free-electron energy provides direct access to the THz near-field amplitude and phase (Yannai et al., 2022).

From these field maps and the microscopic inversion procedure, the experiment reconstructs movies of the generated charges. The reported snapshots reveal annular and dipolar patterns on $T \ll \tau_e$08 length scales and $T \ll \tau_e$09 timescales, and the work reports oscillations of photo-generated electron-hole distributions inside the semiconductor. This establishes that Lorentz-type ultrafast EM can access non-equilibrium transport phenomena on nanometer–femtosecond scales through an external near-field measurement combined with model-based inversion (Yannai et al., 2022).

6. Capabilities, limitations, and projected extensions

The demonstrated capabilities are complementary. In the magnetic implementation, the temporal resolution is limited by the electron-pulse duration $T \ll \tau_e$10 and synchronization jitter of order $T \ll \tau_e$11, which is sufficient for $T \ll \tau_e$12 dynamics but challenging for $T \ll \tau_e$13. Signal-to-noise requires minutes of integration per frame, and the magnetic point resolution is about $T \ll \tau_e$14, although localization reaches $T \ll \tau_e$15 through high counts. In the CDEM implementation, the present demonstration achieves $T \ll \tau_e$16 lateral resolution and a few-hundred-femtosecond temporal precision after deconvolution, while explicitly noting that nanometer resolution is achievable with standard STEM focusing (Möller et al., 2019, Yannai et al., 2022).

The sensitivity limits are also stated differently in the two modalities. For CDEM, the current setup is reported to detect local current of order $T \ll \tau_e$17, corresponding to field of order $T \ll \tau_e$18 and $T \ll \tau_e$19. With state-of-the-art monochromated EELS of $T \ll \tau_e$20 resolution, that limit can drop by two orders of magnitude. This suggests that low-density plasmas or even single-electron regimes may become accessible within the same Lorentz-interaction framework (Yannai et al., 2022).

The reported future directions span both charge and spin phenomena. For magnetic dynamics, the cited extensions include ultrafast imaging of domain-wall motion, skyrmion gyration, spin-wave propagation, ultrafast switching in multiferroics, and phase transitions in correlated oxides under electrical or optical drive. For CDEM, the proposed targets include light-induced phase transitions such as superconductivity onset, insulator-to-metal switching, and charge-density-wave melting, as well as Floquet engineering, ultrafast Hall effects, and nonlinear near fields in metasurfaces and nanocavities at mid-IR to THz frequencies. The CDEM work further states that, by tuning electron velocity, interaction length, or employing attosecond pulse trains, the time window can span $T \ll \tau_e$21 to $T \ll \tau_e$22 (Möller et al., 2019, Yannai et al., 2022).

Taken together, these results define Lorentz ultrafast electron microscopy as a family of UTEM methodologies that couple nanometer-scale electron probing with direct Lorentz interaction spectroscopy or deflection imaging. The experimental record presently spans few-nm tracking of magnetic vortex orbits and model-based reconstruction of femtosecond semiconductor charge transport, indicating that both electric and magnetic ultrafast near fields can be mapped in real space and time within a single conceptual framework (Möller et al., 2019, Yannai et al., 2022).