Near complete laser-induced modulation of the ferromagnetic-antiferromagnetic phase fraction in FeRh films

TL;DR

This work probes the AF-FM first-order transition in FeRh by combining quasi-static and laser-modulated thermoreflectance to resolve phase coexistence at the micrometer scale. A large, laser-driven modulation of the FM fraction is observed within the phase-coexistence interval, enabling quantitative tracking of FM content up to ~90% and distinguishing thermoreflectance from phase-fraction effects. A rate-independent Preisach RPM model with quenched disorder reproduces the DC and AC responses and minor-loop behavior, linking the observed modulation to the extrema of the temperature history under periodic driving. The results demonstrate the persistence of RPM-guided hysteresis under high-frequency, non-equilibrium conditions and suggest potential uses in memory and patterning of FeRh phase domains.

Abstract

With its huge entropy change and a strong interplay between magnetic order, structural and electrical properties, the first-order antiferromagnetic/ferromagnetic phase transition is a paradigmatic example of the multicaloric effect. The unraveling of the physics underlying the phase transition needs a better understanding of the thermal hysteresis of FeRh within the AF-FM phase coexistence region. In this work, we compare the effect of two very different types of thermal cycling on the hysteresis of the magnetic order: quasi-static heating, and cooling of the entire 195 nm thick film, and a f =100 kHz modulated heating driven by a laser focused down to a spot of about ten microns squared at the film surface. Taking advantage of the reflectivity difference between both phases to probe optically their respective fraction, we show that whereas only temperature-driven reflectivity variations ($dR/dT$, thermoreflectance) are detected in the pure phases, a huge modulation of the phase-dependent reflectance at the driving frequency $f$ is detected in the phase coexistence temperature range. This is quantitatively described as resulting from a substantial modulation of the FM fraction (up to 90% with increasing laser power. A simplified rate-independent hysteresis model with return-point-memory (RPM), represented in terms of bistable units that undergo a temperature excursion corresponding to a given laser power, reproduces very well the optically measured FM phase modulation characteristics for a broad range of temperature excursions. This offers an insight into the leading role of quenched disorder in defining thermal hysteresis in FeRh under high excitation frequency, when the material is periodically driven out-of-equilibrium.

Figures (14)

• Figure 1: (a) Scheme of the modulated reflectance experiment. (b) Magnetization (black curve) and reflectance of the FeRh/MgO sample normalized to the AF phase level at $\lambda_b = 488$ nm on an area of diameter $4~\upmu$m (smoothed signal), acquired from the ADC channel of the lock-in amplifier, with pump laser off, along a heating (red curve), and cooling (blue curve) ramp driven by the heating stage within the quasi-static regime. (c) Quasi-static major hysteresis loop with a set of first-order return curves measured without pump laser. The return curves are measured over the cooling branch starting from $T_{start} = 120$° C, and heating back to $T_{start}$ at a reversal point $T_{rev} = 89, 86, 85, 84$° C; (d) a set of nested minor loops starting from the cooling branch verifying the return point memory (RPM). The inset shows a set of nested minor loops starting from the heating branch. A detailed description of the protocol followed for measuring the nested minor loops is given in the main text.
• Figure 2: (a) to (e): Reflectance thermal hysteresis curves acquired from the lock-in ADC channel as a function of heating stage temperature for increasing pump power. A progressive closing of the cycle and global down-shift in temperature are apparent. (f) to (n): Modulated reflectance in-phase signal for up (down) temperature ramp in red (blue) colour. For higher pump powers the modulated reflectance is similar to (j,n) albeit wider and with the transition starting at a lower temperature. The dashed black curves represent the calculated contribution of the thermoreflectance to the signal (see text).
• Figure 3: Modulated reflectance amplitude for overlaying pump and probe laser spots versus pump power $P$: (a) measured at a temperature where the sample is either in the pure AF ($T$=50$^{\circ}$C (40$^{\circ}$C) for $P<$13 mW ($>$13 mW)), or in the pure FM phase (110 $^{\circ}$C), and (b) in the phase coexistence interval, at the temperature where $V_{\rm{f}}$ is maximum (the full curve is a guide for the eye). Note the factor 10 between $y$-scales in (a) and (b).
• Figure 4: (a) Time dependent surface temperature (red curve) induced by the square-modulated (green curve) laser pump (see Appendix \ref{['App:TemperatureIncrease']}). (b) Schematics of the modulated FM fraction $x\left(t\right)$ (red curve) at pump frequency $f=100$ kHz (green curve) showing the in-phase component with amplitude $\Delta x^p_f$ (black curve), the maximum, and average values $\Delta x_{\rm{max}}$, $\Delta x_{\rm{av}}$, respectively, and the non-modulated fraction $x_0$.
• Figure 5: Dashed curves: AF fraction obtained from the DC reflectance without pump. Schematics of the major thermal hysteresis loop with two first-order minor loops that take place under heating (red curve) and cooling (blue curve) of the heating stage (i.e. loops with one vertex lying on the major cycle). The relationship between the quantities $\Delta x_{av}$, $\Delta x_{max}$ measured with the lock-in amplifier under laser pumping when the pump induces periodic $\Delta T = T_{peak} - T_{base}$, and the shape, and the location of the minor loop swept by $\Delta T$ are shown. While the amplitude of the AC signal measured at a given $T_{base}$ is strictly related to the shape of the minor loop, the value of the DC signal depends on the location of the minor loop centre at $(1 - x_0) - \Delta x_{av}$.