Electric-Field Adjustable Time-Dependent Magnetoelectric Response in Martensitic FeRh Alloy

Steady or dynamic magnetoelectric response, selectable and adjustable by only varying the amplitude of the applied electric field, is found in a multiferroic FeRh/PMN-PT device. In-operando time-dependent structural, ferroelectric, and magnetoelectric characterizations provide evidence that, as in magnetic shape memory martensitic alloys, the observed distinctive magnetoelectric responses are related to the time-dependent relative abundance of antiferromagnetic-ferromagnetic phases in FeRh, unbalanced by voltage-controlled strain. This flexible magnetoelectric response can be exploited not only for energy-efficient memory operations but also in other applications, where multilevel and/or transient responses are required.


Introduction
During the last decades, a flurry of research in spintronics has focused on finding a system where the net magnetization can be controlled by electric field without the need of electric current, hence largely overcoming power dissipation by Joule heating. 1 Multiferroic oxides and related heterostructures have been pivotal in this race, 2-5 by exploiting the steady magnetoelectric (SME) coupling among distinct ferroic orders. On the other hand, dynamic magnetoelectric (DME) coupling effects, those showing time dependence magnetic response to the electric field, have been observed in a few multiferroic single-phase systems only at low temperatures [6][7][8][9][10][11] . DME effects in single phase multiferroic systems, can be broadly categorized depending on its origin as arising from: i) coexistence of competing multiferroic domain structures, 6-9 ii) multiferroic domain walls, 10 or iii) electric excitation of magnetic waves. [10][11] Heterostructures with possible appearance of room-temperature DME coupling have been theoretically suggested but not experimentally realized yet. 12 Here we explore a radically different approach to obtain a DME above room temperature.
Inspired by the physics underneath shape-memory martensitic alloys, we take advantage of the '-FeRh first order transition, from antiferromagnetic (AFM) to ferromagnetic (FM) states, that occurs at the Néel temperature (T N ≈ 75-105 °C). A coexistence of AFM and FM nanoregions near T N , together with thermal hysteresis, have been documented in this system. [13][14] The unit cell volume expansion (~1%) 15 of FeRh at the transition point has been exploited to achieve SME by electric modulation of the relative concentration of FM and AFM phases using piezoelectric substrates. [16][17] Importantly, FeRh alloys are known to display remarkably large magnetocaloric and elastocaloric effects, 18 both associated to the martensitic nature of the AFM-FM phase transition. The martensitic character of the FeRh phase transition anticipates a particular DME response to electric/strain stimuli, which has not been explored yet.
In the present work, either SME or DME responses, adjustable by modifying the amplitude of an applied electric field, are found in a FeRh/piezoelectric device. Time-dependent structural and magnetoelectric characterizations as well as direct magnetic domain imaging using X-ray magnetic circular dichroism (XMCD), under in-operando conditions have shown that the DME effect arises from the time-dependent evolution of the relative abundance of AFM and FM phases obtained after suitable electric field poling.

Results and Discussion
The central result of our work is shown in Figure 1. We measured the time dependence of the magnetoelectric effect of a 50 nm thick FeRh film grown on top of a ferroelectric (0.72)[PbMg 1/3 Nb 2/3 O 3 ]-(0.28)[PbTiO 3 ] (PMNPT) (001)-oriented single-crystal substrate.
Isothermal measurements were performed at 110 °C (i.e., near the AFM-FM phase transition with coexistence of both phases) and at magnetic remanence ( 0 H = 0, see detailed explanation on sample preparation in Supporting Information Figure S1). The time-dependent in-plane magnetic moment [m(t,V)] was recorded while applying voltage pulse V(t) trains (using Vibrating Sample Magnetometer platform from MicroSense Co) as illustrated in Figure 1a using the electric configuration shown in Figure 1b. First, the PMNPT substrate was poled by a voltage large enough to saturate its polar state, applied for 10 s (from -10 s to 0 s in Figure 1a).
Subsequently, longer voltage pulse (0 s -80 s in Figure 1a [25][26] Therefore, the obvious time-dependent position of the 2(110) must be related to the dynamics of the FM to AFM phase transition. Hence, it can be concluded that the AFM to FM phase transition takes place when certain bias-V is applied, more efficiently at V ≈ V C , but it partially reverses after a certain time for sufficiently high voltages (V > V C ), leading to the observed decrease of magnetization and thus giving rise to a transient magnetoelectric response (Figure 1c).
To rationalize the experimental observation, we will refer to the sketches shown in Figure 3.  Figure 3e). Therefore, the magnetic moment shall decrease and eventually recover its initial value (Figure 3f), which results in the observation of the m(t) peak. The AFM to FM to AFM phase-transformation is, to some extent, slowed down by the inherent viscosity of the martensitic phase transformations (see Supporting Information Figure S7). 27 Dynamic responses have also been reported in multiferroic composites, due to electromechanical resonances 28 or due to Maxwell-Wagner relaxation; 29 however, none of these situations apply in the system explored here.
A direct evidence of the presented scenario can be obtained by imaging the electric field dependence of the magnetic domains. With this purpose, X-Ray Magnetic Circular Dichroism combined with Photoelectron Emission Microscopy (XMCD-PEEM) experiments were performed (see Supporting Information Figure S8). 30 Experimental protocol for setting the initial state of the sample is described in Supporting Information Figure S1. Figures 4a,b show the 2x2