Stress‐Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex

Abstract Domain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single‐crystal X‐ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry‐breaking phase transitions in the mononuclear Mn3+ compound [Mn(3,5‐diBr‐sal2(323))]BPh4, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress‐induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc‐P1 transition


Introduction
Domain walls (DWs) in ferroic materials-ferromagnets, ferroelectrics,f erroelastics-represent the regions where there is ac hange in order parameter. [1] Thed imensions, mobility,a nd internal structure of domain walls continue to yield useful functionality such as magnetic racetrack memory, [2] in which the supersonic motion [3] of magnetic DWsi s driven by spin-polarized currents.Inthe last decade,work on ferroelectric oxides has unexpectedly revealed that electrical conductivity, [4] or even superconductivity, [5] is possible within ferroelectric DWs, despite the fact that ferroelectrics should be good insulators.T hus,f ar from being an inert barrier between functional ordered regions,t he DW in both ferro-magnets and ferroelectrics is instead recognized as af unctional entity in itself,and is being investigated for applications in which "the wall is the device". [1] In this context, it is of interest to examine other types of ordered materials to probe the nature of DW structure and to look for new functionality.
Whilst most reports on ferroic properties focus on inorganic oxides,m olecular systems also offer ar ich playground for structural and electronic ordering. Forexample,in molecular crystals both intramolecular and intermolecular degrees of freedom can be modulated to induce changes in either local point-group and/or global translational symmetry, as has been demonstrated in organic ferroelectric materials. [6] Thevibronic phenomenon of thermal spin state switching [7] is also well known to cause significant structural reorganization in both small-molecule transition-metal complexes [8] and solid-state oxides. [9] In spin crossover (SCO) materials,t he switching is usually strongly coupled to structural degrees of freedom, with local bond-length changes of up to 0.2 in each metal-donor distance due to depopulation/population of anti-bonding orbitals during the electron pairing/unpairing process.T hese local distortions at the molecular scale propagate macroscopically through elastic coupling,resulting in macroscopic changes in lattice parameters. [10] Thevariety of SCO phenomena can be understood in terms of the evolution of the totally symmetric HS fraction order parameter, g, which may couple to as ymmetry-breaking order parameter driving spin state ordering, h,o rt ov olume and shear strains. [11] Such coupling,i nt urn, can give rise to large anomalies in elastic properties. [12] In some SCO crystals,t his drives cooperative phase transitions to produce multiple structural phases with spin state ordering over atemperature gradient. [13] Such ordering phenomena have been the focus of sustained experimental [14] and theoretical [11,15] investigations over the last decade but little is known about the DW architecture in the ordered phases,asinmost systems studied so far,s pin state ordering results in antiphase boundaries. Herein, we report magnetic,structural, and elastic properties of an ew Mn 3+ SCO complex,[Mn(3,)]BPh 4 , 1,and show that the ferroelastic DWsinone of two spin state ordered phases are mobile in response to shear stress.T he DWsd etected in complex 1 are distinct from the high-spin/ low-spin (HS/LS) phase boundary,which develops in crystalline SCO materials across at hermal gradient, and in which spatiotemporal effects can be very effectively followed by optical microscopy. [16] Such examples of an isostructural phase transition between LS and HS phases do not correspond to DW formation, rather to ap hase boundary.I nt he isostructural case both HS and LS phases have the same symmetry,so the symmetry-breaking order parameter is 0a nd the HS/LS interface is not aDW. In contrast, in the case of complex 1,the spin state and ferroelastic order parameters are both coupled with strain, making it inevitable that the DWsw ill contain local variations in spin state,thus realizing anew class of DW architecture.

Results and Discussion
[Mn(3,5-diBr-sal 2 (323))]BPh 4 , 1,b elongs to the [Mn(Rsal 2 (323))] + series of Schiff base complexes,m any of which exhibit thermal SCO or stabilization of the rare S = 1 state. [14f,17] Dark red crystals of complex 1 were prepared in aone-pot synthesis,Scheme 1, and magnetic susceptibility in heating and cooling modes over the temperature range 4-300 Kwas recorded on aSQUID magnetometer in an applied field of 0.1 T, Figure 1a and Figure S1.
Plots of c M T versus T, Figure 1a,indicate that complex 1 is in its spin quintet form at room temperature.A9.3 %increase in c M T was observed on cooling from 300 K (2.49 cm 3 mol À1 K) to 95 K( 2.72 cm 3 mol À1 K), whereupon an abrupt drop to a c M T value of 2.1 cm 3 mol À1 Kw as observed with aT 1 = 2 fl value of 82 K, Figure S2. This represents a50:50 ratio of spin quintet and triplet forms.Afurther decrease on cooling below circa 20 Ki so bserved, which is attributed to zero-field splitting. On heating, an abrupt and hysteretic transition was observed with T 1 = 2 › = 90 K.
Thus,w ei dentify af irst-order phase transition related to spin state switching centred at 86 Kwith athermal hysteresis window of 8K.T he width of the hysteresis is of the same order of magnitude as reported for other Mn 3+ SCO complexes with an N 4 O 2 2À ligand donor set. [14f, 17c] The transition at circa 86 Kw as accompanied by ac hange in entropy of circa 8Jmol À1 K À1 ,o btained by integration of the peak from heat capacity measurements,F igure 1b.S uch alarge entropy change suggests that asignificant component of the thermodynamic driving force is configurational, which involves both structural and electronic reorganizations accompanying the SCO behaviour.N oi nfluence of magnetic field on the heating branch was observed and only as light upward shift in the cooling branch by 1.5 Kw as observed when applying fields of 1Tand 5T ,F igure S3.
Resonant ultrasound spectroscopy (RUS) revealed that three structural phases emerge over the temperature interval of the SCO,i ncluding as tructural state that contains ferroelastic twin domains (see below). Single-crystal diffrac-  and heating (red curve) modes between 4and 300 Km easured at 0.1 T. Inset:8Kwide hysteretic transition. b) Heat capacity, Cp,v ersus T of asingle crystal of complex 1 measured by two methods, the relaxation method (black circles) and the temperature sweep method (red line, warming;blue line, cooling).T he temperature sweep method is sensitive to sharp changes such as first order phase transitions, whereas the relaxation method more accuratelyd etermines the magnitude of the heat capacity where it is smoothlyv arying with temperature. Inset:E ntropy change DS determined from integration of the peak in the heat capacity:7 .90 Jmol À1 K À1 on cooling and 8.46 Jmol À1 K À1 on heating.
tion was used to elucidate the structure in each phase and the full transition sequence is Cc!Pc!P1.
At room temperature,c omplex 1 crystallises in the monoclinic polar space group Cc and data in this high temperature (HT) phase was collected at 293 Kand at 250 K, Table S4. Thea symmetric unit comprises one full occupancy [Mn III L] + cation, which is chelated by ah exadentate trans-N 4 O 2 -ligand, Figure 2a and Figure S5. By symmetry,t he global polarization in the Cc space group lies on the (a,c) plane.The geometry around the Mn 3+ centre can be described as ad istorted octahedron even though the bonds involve different atoms,M n ÀN amine/imine and MnÀO phen ,w ith bond lengths in the equatorial plane showing significant elongation, Figure S4 and Table S5. This is consistent with population of the d x 2 Ày 2 orbital of the anti-bonding e g *orbitals in the Jahn-Te ller distorted S = 2state.The asymmetric unit also contains one disordered BPh 4 À counteranion, Figure 2aand  Thel attice parameters show as teep decrease in a and increases in b and c below the transition at circa 90 K, Figures S30 and S31. Ad ifferent set of superstructure reflections,characteristic of the loss of the c glide plane,w as observed in afull data set collected at 83 Kand 25 K, the lowtemperature (LT) phase,i ndicating that it has ad ifferent symmetry from the higher temperature phases.The symmetry decrease requires refining the structure in the space group P1, which is chiral and polar. Theu nit cell contains four independent [Mn III L] + cations and four BPh 4 À counteranions, the latter now in afully ordered configuration, Figure 2a and Figures S9 and S10. Tw oo ft he four Mn 3+ cations are in the S = 1s tate and two are in the S = 2s tate.T here is no indication of ageometric Jahn-Teller effect in the S = 1Mn 3+ cations.The MnÀN imine and MnÀN amine bond lengths in all the measured structures are similar to those of other related Mn 3+ S = 1a nd S = 2c omplexes,T able S5. [14f,17] Va lues of SMn, F,a nd z, [18] which define the degree of octahedral distortion in relation to spin state changes,are also higher, as expected, for the S = 2Mn 3+ cations in the HT and INT phases (293 K, 250 K, 150 K, 110 K) than for the LT S = 1 Mn 3+ cations observed at 83 Ka nd 25 K, Table S6.
Only weak hydrogen-bonding interactions between the Mn 3+ complex cation(s) and the BPh 4 À counteranion(s) were found in HT (250 K), INT (110 K) and LT (83 K) phases, Figures S20-S25. Af ull Hirshfeld surface analysis,m apped over d norm ,o fc omplex 1,F igures S26-S28, shows that the three main contributions to the intermolecular interactions are H···H, H···Br and H···C with an increase in H···Br and adecrease in H···H interactions in the LT phase compared to the INT and HT phase,F igure S29. Thes light changes in intermolecular interactions may generate ac ritical elastic energy,w hich directly affects the spin state causing the hysteretic response between the INT and LT phases.The spin state distribution across the three phases is summarized in Tables S5 and S6 and in the structure diagrams in Figure 2b,c and Figures S12-S19 in which the striped spin state order of the Mn 3+ complex cations in the low-temperature regime is apparent.
Thet hermal evolution of complex 1 is unambiguously associated with the two phase transitions in the sequence Cc!Pc!P1. Given the group-subgroup relationship between the Cc and Pc space groups,w hich have the same translation symmetry (a,b,c), [19] the Cc!Pc transition is allowed to be second order.T he related order parameter, q, describing the associated structural order,h as the symmetry of irreducible representation (irrep) at the border of the Brillouin zone, Y 1 . This is not the case for the transition between the Pc and P1p hases because there is no groupsubgroup relationship;s ome translation symmetry operator exists in the Pc phase and not in the P1phase and vice versa, Figure 2. Such ar econstructive phase transition must be first order.
Lattice distortions associated with structural, magnetic, electronic or any other phase transition between structures that have agroup-subgroup relationship depend formally on coupling between at hermodynamic order parameter, q,a nd components of asecond rank strain tensor, [e i ]. [20] Thelowest order coupling terms permitted by symmetry are l i e i q 2 , i = 1,2,3,5, and l i e i 2 q 2 , i = 4,6, for Cc!Pc. Coupling of the form l i e i q 2 gives e i / q 2 . [20] Strain variations calculated from lattice parameter data in Figure S36 reveal unambiguously that q 2 for the Cc!Pc transition varies continuously through the transition temperature, T c ,a nd has an on-linear dependence on temperature in the stability field of the Pc structure, Figure 3a.
Theprecise form of the non-linearity is highly sensitive to the choice of baseline for the reference states.Analternative approach is to follow by X-ray diffraction the temperature dependence of the intensity I k of superlattice reflections associated with the Cc!Pc transition, corresponding to Bragg peaks (hkl)with h + k odd. Figure 3c shows that below T c it appears that the fit of I k 2 has linear dependence so I k 2 / (T c ÀT)and, hence the order parameter scales as, q 4 / (T c ÀT), indicating that the transition is close to being Landau tricritical in character with T c = 247 AE 2K.Byway of contrast, the Pc!P1t ransition is very obviously first order,w ith alarge discontinuity at circa 90 K, Figure 3a-c.
Thetwo phase transitions are also evident in variations in elastic properties obtained by RUSfrom asmall single crystal. This technique is commonly used to investigate phase transitions, [21] and has been used once previously for an onsymmetry-breaking SCO material. [22] Thes quare of the frequencies, f,o fm echanical resonance peaks of as ingle crystal scales with different combinations of elastic moduli. Thep eak widths at half maximum height provide am easure of acoustic dissipation in the form of the inverse mechanical quality factor, Q À1 .Astack of spectra collected from asingle crystal during cooling from 295 to 4K,F igure 4a,r evealed as mall shift in the frequency trends of all resonance peaks below circa 250 K. There was then am ore marked shift in resonance frequencies below circa 85 K. Thew idths of individual peaks also increased abruptly below circa 85 K. On heating back up to room temperature from 7K,F igure 4d,the resonance peaks returned to the same positions as in the cooling sequence,c onfirming that the crystal survived the two phase transitions without cracking.
It is well understood that changes in the elastic constants of single crystals at phase transitions depend primarily on the form and strength of the coupling between the driving order parameter and strain. [23] Coupling of the form l i e i q 2 is expected to give rise to discontinuous softening as the crystal is cooled through the transition temperature of ac lassical displacive transition, with the magnitude of the effect depending sensitively on l i 2 .However,the Cc!Pc transition is marked by aslight minimum in f 2 followed by an increase in the slope of the stiffening trend with falling temperature.The Pc!P1t ransition is marked by as mall discontinuity and alarger increase in slope of the stiffening trend, Figure 4b,e. Such stiffening occurs either when the values of l i are negligibly small, which is not the case here,orwhen the time required for relaxation of the order parameter in response to astrain induced by some external stress is short in comparison with the timescale of the applied stress.Changes in the elastic constants during the Pc!P1t ransition can be attributed to the partial spin state conversion due to the stronger bonding nature of the LS state.
As shown in Figure 5, variations of f 2 for the Pc phase with respect to values extrapolated linearly from the stability field of the Cc structure,e xpressed as Df 2 ,h ave nonlinear form similar to variations of the strains,t hat is, e i / Df 2 / q 2 .T his confirms that relaxation of the order parameter requires times greater than circa 10 À6 s, given that the observed resonance frequencies are circa 10 5 -10 6 Hz. Thep attern of acoustic loss also adds insights into the nature of the phase transitions.Anormal expectation for displacive transitions is that Q À1 values,F igure 4c,f,a re low in the high-symmetry phase,w ith the possibility of ap eak at the transition point marking ac ritical slowing down of the atomic motions responsible for the transitions,and high in the low-symmetry Figure 3. a, b) Temperatured ependence of strain components for the Pc and P1s tructures, as defined with respect to the parent Cc structure. All the strains vary continuously through the Cc !Pc transition at circa 247 Kand discontinuously through the Pc!P1transition at circa 90 K. c) Variations of the square of the intensity, I k ,ofthe superstructure reflection with hk1 = À181, which appears in diffraction patterns from the Pc phase. The data show I k 2 / (T c ÀT), within experimental uncertainty,and T c = 247 AE 2K.
phase if there is aloss mechanism involving atransformation microstructure such as ferroelastic twin walls. [21] Instead, the steep reduction in values of Q À1 as the Cc! Pc transition point is approached from above is more reminiscent of the magnetic ordering transition in YMnO 3 , [24] as well as structural transitions involving hydrogen bonding in ametal-organic framework [25] and in the mineral lawsonite. [26] In each of these cases,t he transitions were interpreted as having as ignificant component of order-disorder character, and this was confirmed by calorimetric measurements in the case of lawsonite. [27] Dynamical clustering of ordered regions ahead of the transition contributes to relatively high acoustic losses by coupling with local strains and this disappears below the transition when the ordering is static.
By way of contrast with the Cc!Pc transition, there is as teep increase in Q À1 immediately below the Pc!P1 transition, as would be typical of af erroelastic transition in which the loss is due to mobility of ferroelastic twin walls in response to an applied stress.T ypical examples are (Ca,Sr)-TiO 3 and Sr(Zr,Ti)O 3 perovskites at temperatures below the cubic-tetragonal transition. [28] TheR US evidence of acoustic loss is thus that crystals with P1symmetry contain ferroelastic twins even when they developed by af irst-order transition from the Pc structure,F igure S16, and that the twin walls are at least partially mobile under the influence of external stress. Given that there is coupling between the ferroelastic and spin state order parameters,itisinevitable that these domain walls will contain local variations in the degree of spin state order that also must respond to the external stress.
As described in the introduction, the discovery of mobile ferroelastic DWsi nc omplex 1 is quite distinct from the motion of the HS/LS boundary in isostructural single-crystal SCO samples [16] and instead represents anew phenomenon. It will now be important to establish amethod to determine the velocity of DW motion in ferroelastic SCO systems,which will enable meaningful comparison with their ferromagnetic and ferroelectric counterparts.I nt hese latter materials there are Figure 4. a,d) RUS spectra as afunction of frequency for asingle crystal of complex 1,stacked up the y-axis in proportion to the temperature at which they were collected. The y-axis is really amplitude in volts but has been relabelled as temperature. Spectra were collected during (a) cooling and (d) heating between circa 295 Ka nd circa 4K.The highlighted red lines (cooling) and blue lines (heating)i ndicate the expected location of the transitions at circa 255 Ka nd circa 85 K. b,e) f 2 and c,f) Q À1 data from fitting of selected resonancesw ith an asymmetric Lorentzian function, showing the continuousstructural phase transition at circa 255 Kand the discontinuoustransition at circa 85 K. marked differences between the magnetic-field induced supersonic speeds of 750-1000 ms À1 achievable in ferromagnetic thin films [29] and nanowires, [30] and the much slower motion of ferroelectric DWs, in which velocities are also much more sensitive to sample preparation and orientation. [31] Internal DW structure is also typically complex in ferroic materials;i nf erromagnets,i nw hich the magnitude of the quantized spins cannot change across the wall, the magnetization is inverted by chiral out-of-plane (NØel) or in-plane (Bloch) rotation of the spins. [1] In contrast, ferroelectric DWs are Ising-like as the non-quantized polarization axis can vary in size and gradually reverse its sign. [1] It will therefore be of interest to further probe the internal structure of ferroelastic DWsi nS CO crystals,n anomaterials [7a] and films [32] using advanced imaging techniques suitable for different physical scales. [8]

Conclusion
In summary,w eh ave demonstrated formation of mobile ferroelastic twin walls in aM n 3+ SCO crystal with strong coupling between spin state and elastic order parameters.The spin quintet form of Mn 3+ SCO compounds exhibits ap ronounced Jahn-Teller effect, which can be easily injected into or removed from the lattice by changing the spin state via thermal or other perturbations.This large change in structural distortion is likely to have contributed to the considerable elastic strain in the Pc!P1transition. As spin state switching results in achange in both magnetization, through achange in the overall spin state of the transition metal ion, and large atomic displacements,s uch compounds are ideal for magnetoelectric applications.T hese include,f or example,d ata storage devices with an electrical input and magnetic readout, which would avoid the problems of reading ferroelectric random access memory (FeRAM). [33] In the case of complex 1,a ll three structural phases are polar and therefore potentially ferroelectric.T hus,i ti so fi nterest to explore these aspects and to investigate the potential for ferroelectric ordering and DW conductivity in our ongoing studies on this and related materials.