Ultrafast generation of hidden phases via energy-tuned electronic photoexcitation in magnetite B. Truc P. Usai F. Pennacchio G. Berruto R.Claude I. Madan

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Ultrafast generation of hidden phases

via energy-tuned electronic photoexcitation in magnetite

B. Truc, P. Usai, F. Pennacchio, G. Berruto, R.Claude, I. Madan,

T. LaGrange, G. M. Vanacore,∗S. Benhabib,†and F. Carbone‡

Institute of Physics, LUMES, ´

Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne CH-1015, Switzerland

V. Sala

Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy

(Dated: October 4, 2022)

Metal-insulator transitions (MIT) occurring in non-adiabatic conditions can evolve through high-

energy intermediate states that are diﬃcult to observe and control via static methods. By monitoring

the out-of-equilibrium structural dynamics of a magnetite (Fe3O4) crystal via ultrafast electron

diﬀraction, we show that MITs can evolve through diﬀerent pathways by properly selecting the

electronic excitation with light. Near-infrared (800 nm) photons inducing d-d electronic transitions

is found to favor the destruction of the long-range zigzag network of the trimerons and to generate

a phase separation between cubic-metallic and monoclinic-insulating regions. Instead, visible light

(400 nm) further promotes the long-range order of the trimerons by stabilizing the charge density

wave ﬂuctuations through the excitation of the oxygen 2p to iron 3d charge transfer and, thus, fosters

a reinforcement of the monoclinic insulating phase. Our experiments demonstrate that tailored light

pulses can drive strongly correlated materials into diﬀerent hidden phases, inﬂuencing the lifetime

and emergent properties of the intermediate states.

I. INTRODUCTION

The physical properties of strongly correlated materi-

als are mainly deﬁned by the complex interplay among

the electronic, orbital, spin, and atomic degrees of free-

dom. At equilibrium, phase transitions follow an ergodic

pathway within the material free-energy landscape, and

the transition is characterized by a succession of thermo-

dynamic equilibrium states between two global minima.

Instead, using ultrashort laser pulses drive the transi-

tion out-of-equilibrium and induce a distinct pathway by

transiently changing the coupling between the relevant

degrees of freedom. Light-driven phase transitions reveal

the presence of new intermediate (hidden) states of mat-

ter [1–9]. Such hidden phases are not only of interest

from a fundamental point of view but also bear potential

for ultrafast technological devices [9, 10].

Magnetite (Fe3O4) is a prototypical strongly-correlated

system. It exhibits a complex interplay between the

crystal structure [11], charge [12–15] and orbital or-

ders [16, 17], which leads to the emergence of an

atypical thermodynamic MIT in the vicinity of 125 K,

known as the Verwey transition (VT) [18]. It is found

that the structural changes play a key role in VT

[19, 20]. Above Verwey temperature (TV), magnetite has

a cubic inverse spinel F d¯

3mstructure formally written

Fe+3[Fe+2Fe+3 ]O4, the ﬁrst Fe+3 (A-type) occupied the

tetrahedral sites, whereas the [Fe+2Fe+3] (B-type) occu-

pied the octahedral sites. Below the TV, the symmetry

∗Currently at Department of Materials Science, LUMiNaD, Uni-

versity of Milano-Bicocca, Via Cozzi 55, 20125 Milan, Italy

†siham.benhabib@epﬂ.ch

‡fabrizio.carbone@epﬂ.ch

changes from the cubic F d¯

3mto the monoclinic Cc phase

[11].

In the low-temperature (LT) phase, a new kind of bond

dimerized state, the so-called trimeron, has been dis-

covered and shown to form a long-range order [21, 22].

The trimeron unit results from multiple cooperative ef-

fects, including charge, t2gorbital orderings, and strong

electron-phonon coupling [23]. Therefore, trimerons are

deemed to be the key actor of VT, which has been

recently described microscopically as an order-disorder

transition from a trimeron liquid with incommensurate

ﬂuctuations to a commensurate crystal below TV[24–

26]. Optical experiments have shown that light oﬀers

the intriguing possibility to manipulate such charge ﬂuc-

tuations resulting in tuning the electron-phonon cou-

pling [26] and suggesting that the light-induced transition

can be very orbital-selective. Here, we directly visual-

ize the out-of-equilibrium structural dynamics of a mag-

netite single crystal employing ultrafast electron diﬀrac-

tion (UED).

UED allows us to track the lattice evolution of magnetite

across the photoinduced MIT. We show that, depending

on the photon energy of the femtosecond optical excita-

tion used in the experiment (1.55 eV vs. 3.10 eV), we trig-

ger diﬀerent electronic excitations, consequently leading

to distinct nonequilibrium metastable structural states.

II. EXPERIMENTAL METHODS

The UED experiments were performed in reﬂection ge-

ometry [27, 28] with a grazing angle of 0.5◦to 5◦. The

light source is a Ti:sapphire laser ampliﬁer with a central

wavelength of 800 nm with a pulse duration of 45 fs at a

repetition rate of 20 kHz.

arXiv:2210.00070v1 [cond-mat.str-el] 30 Sep 2022

FIG. 1. Static diﬀraction pattern of magnetite in the cubic

phase F d¯

3mabove TV, T=150 K (a) and in the monoclinic

phase Cc below TVat T=40 K (b). (c) Cubic face-centered

structure oriented along the [110] direction reﬂecting the cubic

unit cell of magnetite above TV. (d) The elongated unit cell

of magnetite below TV. (e) Peak proﬁle of the (660) Bragg

peak above and below TV, its parameters are extracted from

a Voigt proﬁle ﬁt. (f) Temperature dependence of the in-

terplanar atomic change (expansion/compression) along [110]

extracted from the (660) Bragg peak position (see SI). (h)

Evolution of the integrated area under the (660) Bragg peak

across the transition.

High-quality magnetite with TV≈117 K exposing the

ﬂat and optically polished (110) surface was ﬁxed on a

cold ﬁnger attached to a ﬁve-axis manipulator with silver

conductive paste and placed inside an ultrahigh vacuum

chamber (≤10−9mbar). The temperature range is con-

trolled using an open cycle cryostat with helium liquid

ﬂow (see the SI).

III. RESULTS

We have ﬁrst monitored the quasi-adiabatic transi-

tion induced by varying the temperature of magnetite

(without photoexcitation). We investigate the structural

changes by decreasing the temperature from 150 K down

to 40 K and simultaneously following the quasi-static

change of the diﬀraction pattern along the [110] direc-

tion where anomalies attributed to the trimerons have

been recently observed [29].

In Fig.1(a) and (b), we show the static diﬀraction pat-

terns of magnetite measured above and below TV, re-

spectively. Speciﬁcally, we monitor the changes of the

(660) Bragg peak of the cubic phase and observe a sig-

niﬁcant modiﬁcation of the peak position from which we

extract the atomic interplanar expansion or compression

(see SI) shown in Fig.1(f). This is accompanied by a drop

in the diﬀraction intensity as illustrated in Fig.1(g). Such

intensity drop results from the combination of two con-

comitant factors: i) the lowering of the structure factor

when transitioning from a high-symmetry cubic phase

to a lower symmetry monoclinic structure, and ii) the

incoherent electron scattering process through multiple

micro-sized structural domains (twins) that emerge in

LT phase [30]. Across VT, at 117 K, the cubic lattice

transforms into the monoclinic phase, which is evidenced

by the expansion of the lattice along the [110] direction,

as sketched in Fig.1(d). This speciﬁc expansion signiﬁ-

cantly changes the shear strain εxy (see SI). In addition,

it causes a signiﬁcant softening in the shear elastic con-

stant c44 , as reported in ultrasound measurements [31].

Although our technique is moderately surface sensitive

(5-10 nm), the agreement between the monitored position

shift of the Bragg peak from our data and the reported

softening in the elastic constant c44 demonstrates that

our observations are representative of bulk dynamics.

Ginzburg-Landau’s (GL) theory of phase transition such

as VT in magnetite correlates transformation shear

strains to an order parameter. Hence, we ascribe the

measured shear strain (εxy) being strongly coupled to

the order parameter (OP) ∆, and retrieve its symmetry

based on the framework of GL [32] and a fundamental

group theory analysis (see SI). We found that ∆ has T2g

symmetry with one nonzero component, i.e., ∆ = (∆xy ,

0, 0).

Using detailed group theory calculations, several authors

have identiﬁed the set of phonons, including ∆5,X3, and

Γ+5 (T2g), as the structural OPs [33–35]. Furthermore,

ab initio calculations have demonstrated the strong cou-

pling between these structural OPs and the T2gorbital

ordering within a trimeron [33]. Therefore, we conclude

that the trimerons arrangement along the [110] direction

is a conceivable OP candidate with T2grepresentation.

The OP with T2grepresentation was suggested recently

by electron diﬀraction measurements, where the authors

consider an anomalous electronic nematic phase above

Tv with a T2grepresentation which involves a diﬀerent

set of rotational symmetry breaking than the usual ones

[36].

We obtain insights into the non-adiabatic MIT in mag-

netite by investigating the out-of-equilibrium response of

the lattice, initially kept at 80 K (below TV), after pho-

toexcitation. In Fig.2, we present the evolution of the

(660) Bragg peak following ultrashort laser pulses at two

diﬀerent wavelengths, 800 nm and 400 nm at 2.9 mJ/cm2

and 1.2 mJ/cm2incident ﬂuence, respectively. The ﬂu-

ence used for 800 nm corresponds to the intermediate ﬂu-

ence regime [37].

Fig.2(a) shows the structural dynamics following

800 nm photoexcitation. The (660) atomic planes un-

dergo a maximum compression of around -0.06 %. Based

on our static data shown above (Fig.1), the compres-

sion of the monoclinic lattice along the [110] direction

denotes the transformation toward a cubic structure, con-

sistent with ref.[37]. Their recent out-of-equilibrium opti-

cal measurements have shown a photoinduced phase sep-

aration between insulating regions and metallic islands

at LT through 800 nm laser pulses in a similar ﬂuence

regime. This observation is supported by pump-probe

x-ray diﬀraction measurements [38], where the authors

attribute the insulating state to the monoclinic regions

and the metallic state to the cubic islands. Expanding

the investigation range of previous measurements that

were limited to the ﬁrst 10 ps [36–38], our data unveil

the complex establishment of the hidden phase which

lasts approximately 50 ps and interestingly follows three

compression stages. First, during the ﬁrst 22 ps (N°1),

an abrupt compression of -0.03 % occurs. In the second

stage (N°2) between 22 ps and 27 ps, the lattice under-

goes a minor contraction. Finally, the third step (N°3)

emerges and adds an extra -0.03 % to the lattice com-

pression. This multi-step process is characteristic of the

presence of distinct dynamic processes, such as electron-

phonon coupling and phonon-phonon interaction [36, 39].

Note that the electron-electron interaction is expected to

occur on a faster timescale <300 fs [38], beyond the tem-

poral resolution in these experiments. The relaxation

process also evolves with multiple timescales. Qualita-

tively, the ﬁrst recovery stage (N°4) occurs from 50 ps

to 126 ps and reaches an intermediate compressed state

close to -0.03 %, which interestingly corresponds to the

value of the process N°3. Then, a second long process oc-

curs towards the total recovery (N°5) to the equilibrium

phase, which is still not reached after 1.3 ns (see SI). In

a second data set with a slightly higher ﬂuence (see SI),

we conﬁrm the multiple compression stage process and

show that each stage’s duration and amplitude depend

on the ﬂuence used.

In Fig.2(c), the response of the Bragg peak intensity

after the 800 nm photoexcitation shows a drop. Taking

only into account the recovery towards the higher symme-

try cubic high temperature phase after the 800 nm pho-

toexcitation, we expect an increase in the intensity, which

we do not observe. This observation suggests that the

dominant process is the structural disorder caused by the

motion of the atoms induced by the rise in the lattice tem-

perature by ultrashort laser pulses [40], known as the in-

duced Debye-Waller eﬀect (see SI). Similarly to the peak

position shift response, the Bragg peak intensity does not

fully recover to its initial state after 1.3 ns (see SI). The

long dynamics revealed by our data indicate the metasta-

bility of the induced 800 nm phase illustrating the com-

plexity of the thermalization process in magnetite, in-

volving multiple interplays of electron-electron, electron-

phonon, and phonon-phonon scattering. Such lifetime is

a signature of a hidden out-of-equilibrium phase which is

supported by the unusual structural dynamics and the

decrease in the intensity due to the phase separation

between cubic and monoclinic islands, which is not an

equilibrium state but rather a local minimum within the

energy landscape of the excited conﬁguration.

We extend our investigation for hidden phases in mag-

netite by changing the energy of the optical excitation to

3.10 eV (400 nm). In Fig.2(b), diﬀerent from the 800 nm

case, we observe that the 400 nm laser pulses induce a

0.4 % expansion of the lattice along the [110] direction

(instead of a contraction), indicating a reinforcement of

the monoclinic distortion. At 90 K, before excitation, the

crystalline structure has a monoclinic angle βM= 90.236◦

[21]. The 400 nm induced expansion is mainly related to

the variation of the tilting angle βM, where we expect

a value βM400 nm >90.236◦. A quantitative value for

the tilting angle can only be retrieved when monitoring

the behavior of multiple Bragg peaks along diﬀerent zone

axes. Nevertheless, our data clearly show that the 400 nm

optical excitation induces a lattice change that is oppo-

site to the quasi-adiabatic lattice response from our equi-

librium data presented above (Fig.1(f)), where the stabi-

lization of the structure from 90 K down to 40 K shows no

modiﬁcation of the lattice parameters expected thermo-

dynamically. Since the generated structure is not acces-

sible thermally but only induced optically, we associate it

with the emergence of a new hidden phase characterized

by a monoclinic lattice with a tilting angle larger than the

equilibrium value of 90.236◦. The 400 nm hidden phase

is also completely diﬀerent from the one established by

the 800 nm light. The ﬁrst is ﬁrmly monoclinic, whereas

the second is a mixture of monoclinic and cubic sepa-

rated regions. The 400 nm structural hidden phase takes

around 50 ps to emerge with only one direct expansion

process, as presented in Fig.2(b), which we relate mainly

to electron-phonon interaction. This new state lasts up

to 300 ps without any recovery to the initial state giving

it a metastable character. We observe a signiﬁcant drop

in the intensity response (Fig.2(d)). For the 800 nm case,

thermal eﬀects and multiple scatterings from the mixed

phase are the origins of the intensity drop. Although

the decrease in intensity is consistent with the reduction

of the structure factor for the (660) Bragg peak, it is

surprising to observe a shrinking of the FWHM, indicat-

ing a higher homogeneity in the atomic planes, which

we cannot associate with a thermal-like behavior. This

suggests that the new hidden structural state possesses

a larger structural long-range order related to a larger

monoclinic angle.

IV. DISCUSSION

The formation of distinct metastable hidden phases

through two diﬀerent photon energies demonstrates the

critical role played by electronic excitations in estab-

lishing such nonequilibrium phases in magnetite. At

LT, magnetite is thermodynamically stabilized in the

insulating phase, resulting from a commensurate long-

range order along the [001] direction [21, 38] of the

trimerons zigzag network [22, 41] with a coherent length

of (385±10) nm [14]. Each trimeron unit couples lin-

early three FeBsites in the form Fe3+

B- Fe2+

B- Fe3+

B, in

which the minority spin t2gelectron is delocalized from

FIG. 2. Evolution of the lattice change compression/expansion along the [110] direction (a) under 800 nm and (b) 400 nm

photoexcitation. In (a), the shaded areas show multiple compression stages. (c) and (d) evolution of the normalized intensity

under 800 nm and 400 nm photoexcitation, respectively. (e) and (f) time dependence of the FWHM (full width at half maximum)

under 800 nm and 400 nm photoexcitation, respectively. Solid lines are guides to the eye.

the central Fe2+

Bsite into the nearest neighbors Fe3+

and each Fe3+

Bsite is shared between three trimerons.

In addition to the Jahn-Teller distortion caused by the

orbital ordering [42], the electron localization within a

trimeron unit produces a structural distortion in the FeB

sites, where the distance between the central Fe2+

Band

its two Fe3+

Bnearest neighbors gets shorter, leading to

a monoclinic distortion [21]. This distortion has been

conﬁrmed by high-accuracy synchrotron x-ray structure

reﬁnements [43], where it is found that fourteen over the

sixteen nonequivalent trimerons have shown a shorter

FeB- FeBdistance. When we excite magnetite using pho-

ton pulses with an energy of 1.55 eV (800 nm), LDA+U

calculations [16] and optical conductivity measurements

[37, 44] both agree in predicting the triggering of elec-

tronic d-d excitations. They correspond to an electron

delocalization from an occupied t2gof Fe2+

Bto an un-

occupied t2gorbital of Fe3+

Bfollowing the conﬁguration

3d6

i3d5

j→3d5

i3d6

j. The d-d excitations encompass an-

other inter-site excitation corresponding to the transi-

tion from an occupied t2gof Fe2+

Bto an unoccupied egof

Fe3+

B[16]. However, this excitation is only possible at an

energy higher than 2 eV. Triggering the d-d excitation re-

stores the mobility of the minority spin t2gelectrons and

causes the valency to change for both Fe2+

Band Fe3+

Band,

hence, alternates their sites inside the trimeron (see SI).

The direct consequence of this local electronic ﬂuctuation

is the destruction of the trimeron. According to out-of-

equilibrium x-rays measurements, this destruction occurs

in an ultrashort timescale <300 fs [38]. The destruc-

tion of trimerons yields the suppression of the long-range

zigzag order connected at Fe3+

Bsites. When the trimeron

breaks, the FeB- FeBdistance returns to its initial value.

Hence, the structure relaxes, giving rise to the emergence

of cubic phase islands inside the remaining monoclinic

regions forming a phase separation that we qualify as

an 800 nm metastable hidden phase. Following the elec-

tronic excitation, the relaxation process back to the equi-

librium conﬁguration continues via electron-phonon and

phonon-phonon scattering mechanisms. Electrons pri-

marily interact with high-energy optical phonons, which

then anharmonically decay toward acoustic modes via a

three-phonon scattering process [45–48]. For magnetite,

we can interpret the newly observed two steps in the re-

laxation process as the strong electron-phonon coupling

involving the conduction electrons coupling with the X3-

driven mode (TO) for the ﬁrst stage and the phonon-

phonon coupling between X3(TO) and ∆5(TA) modes

for the second. This scenario is supported by recent

UED data that have shown under similar photoexcitation

(800 nm) that the X3(TO) mode is preferably triggered

via the electron-phonon coupling [36] in the ﬁrst few pi-

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Ultrafastgenerationofhiddenphasesviaenergy-tunedelectronicphotoexcitationinmagnetiteB.Truc,P.Usai,F.Pennacchio,G.Berruto,R.Claude,I.Madan,T.LaGrange,G.M.Vanacore,S.Benhabib,yandF.CarbonezInstituteofPhysics,LUMES,EcolePolytechniqueFederaledeLausanne(EPFL),LausanneCH-1015,SwitzerlandV.SalaDipartim...

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Ultrafast generation of hidden phases via energy-tuned electronic photoexcitation in magnetite B. Truc P. Usai F. Pennacchio G. Berruto R.Claude I. Madan

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