Dimensional reduction by pressure in the magnetic framework materialCuF2(D2O)2pyz: from spin-wave to spinon excitations

M. Skoulatos,1, 2 M. Mansson,2, 3, 4 C. Fiolka,5 K. W. Kramer,5 J. Schefer,2 J. S. White,2, 3 and Ch. Ruegg2, 6

1Heinz Maier-Leibnitz Zentrum (MLZ) and Physics Department E21,Technische Universitat Munchen, D-85748 Garching, Germany

2Laboratory for Neutron Scattering and Imaging,Paul Scherrer Institute, CH–5232 Villigen, Switzerland

3Laboratory for Quantum Magnetism, Ecole Polytechnique Federale de Lausanne, Station 3, CH-1015 Lausanne, Switzerland4Department of Materials and Nanophysics, KTH Royal Institute of Technology, SE-164 40 Kista, Sweden5Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, 3012 Bern, Switzerland

6Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva 4, Switzerland(Dated: September 5, 2018)

Metal organic magnets have enormous potential to host a variety of electronic and magnetic phasesthat originate from a strong interplay between the spin, orbital and lattice degrees of freedom. Wecontrol this interplay in the quantum magnet CuF2(D2O)2pyz by using high pressure to drive thesystem through a structural and magnetic phase transition. Using neutron scattering, we showthat the low pressure state, which hosts a two-dimensional square lattice with spin-wave excitationsand a dominant exchange coupling of 0.89 meV, transforms at high pressure into a one-dimensionalspin-chain hallmarked by a spinon continuum and a reduced exchange interaction of 0.43 meV.This direct microscopic observation of a magnetic dimensional crossover as a function of pressureopens up new possibilities for studying the evolution of fractionalised excitations in low dimensionalquantum magnets and eventually pressure-controlled metal–insulator transitions.

PACS numbers: 64.70.Tg, 62.50.-p, 75.30.Kz, 75.40.Gb, 75.30.Ds, 75.10.Pq, 75.30.Et

Interacting spin systems with strong quantum fluctu-ations are an indispensable platform for exploring con-cepts in quantum many-body theory. For rigorous testsof theory it is often necessary to measure the system re-sponse due to external control parameters such as appliedmagnetic field and pressure (P ). Just modest changes inthese variables afford precise control over the stronglyfluctuating degrees of freedom [1], and provide a directroute towards exotic physics such as magnetic field- andP -driven quantum phase transitions [2–4]. Another wayto tune a system is to modify directly the magnetic su-perexchange, such as by changing the chemistry [5, 6], orby generating a sizeable in-situ modification of the crystallattice. While the latter case proves difficult to achieve,it is much sought-after since it promises the direct controlof magnetic dimensionality. Moreover, such an in-situ di-mensionality change can be independent of the tempera-ture, with such crossovers usually taking place as densityof thermal fluctuations varies.

The different topologies of one-dimensional (1D) andtwo-dimensional (2D) quantum spin systems are well-known to define strongly contrasting ground states anddynamics. In 1D systems such as the half-integer spinchain, fermionic fractional excitations termed unboundspinons give a characteristic excitation continuum thatdisperses only along the chain direction [7]. In contrast,on the 2D magnetic square lattice, Neel-order and spinwaves dispersing within the square lattice plane can beexpected [8]. Exploring an in-situ transformation be-tween 1D and 2D magnetic regimes is experimentallychallenging due to lack of suitable materials, but it can beexpected to provide both a deeper understanding of the

adjacent states, and potentially the discovery of unusualphenomena in the vicinity of the crossover. For example,in recent work on 2D magnetic square lattice systemssuch as Cu(DCOO)2·4D2O and La2CuO4, unusual fea-tures in the excitation spectra of each have been arguedto reflect the existence of fractional excitations analogousto spinons in 1D systems [8, 9]. Clarifying how fractionalexcitations evolve during a continuous 2D to 1D crossovercan motivate new physical concepts, and at the same timeprovide links to related topics such as high-temperaturesuperconductivity [10]. To progress the study of dimen-sional crossovers in quantum spin systems, simple mate-rials with easily tunable structure-property relationshipsare required.

Here, neutron scattering has been used to explore a P -driven change of magnetic dimensionality in the metalorganic compound CuF2(D2O)2pyz, where pyz = D4-pyrazine (Fig. 1). At P = 0 kbar, and in agreementwith a previous report [11], we find a simple antiferro-magnetic (AFM) order below T 0kbar

N = 2.59 K, whereS = 1/2 moments of 0.6 µB/Cu2+ lie in the bc planeand are aligned along [0.7 0 1] in real-space. Withwell-defined spin-wave modes dispersing along (0, Qk, Ql)and no dispersion along Qh, the system displays typi-cal spin-wave dynamics of a 2D magnetic square latticewith J0kbar

2D =0.89(2) meV. Increasing P to 3.6 kbar leadsto a slight reduction in TN (∆T = −0.13(1) K), and asmall softening of the spin-wave modes (J3.6kbar

2D =0.78(3)meV). Further increasing pressure to 6.1 kbar leads toan entirely new phase where both the magnetic orderand spin-wave modes of the 2D state are completelysuppressed. Instead, a spinon continuum is observed

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FIG. 1: CuF2(D2O)2pyz crystal structure. (a) The α-phase(ambient P ) hosts 2D magnetic interactions on a slightly dis-torted square lattice. (b) The magnetic interactions switch to1D in the β-phase (P = 6.1 kbar). The brown rhombi denotethe half-occupied magnetic orbital of Cu2+.

along the Qh direction with J6.1kbar1D =0.43(2) meV, which

is the hallmark of a 1D spin chain. This remarkableP -driven magnetic dimensionality switch between 2Dmagnetic square lattice [Fig. 1(a)] and 1D spin chain[Fig. 1(b)] regimes is argued to be caused by a P -drivenswitch of a Jahn-Teller (JT) distortion characteristic toCuF2(D2O)2pyz.

At ambient P , CuF2(D2O)2pyz has a monoclinic struc-ture (P21/c) with cell parameters of a = 7.6852 A,b = 7.5543 A, c = 6.8907 A and β = 111.25◦ at roomtemperature (RT) [Fig. 1(a)] [14]. The magnetic Cu2+

ions are coordinated by F− ions, O (from D2O), and Natoms (from pyz), all in trans positions of a slightly dis-torted octahedron with bond distances of Cu-F = 1.909A, Cu-O = 1.969 A, and Cu-N = 2.397 A. The Cu-Fand Cu-O bonds are much shorter than the Cu-N bond,indicating that the half occupied magnetic dx2−y2 or-bital is localized in the bc plane and the elongated Jahn-Teller (JT) axis parallel to the a-axis [Fig. 1(a)]. Deu-terium bonds (or hydrogen bonds in the non-deuteratedform [13]) F· · ·D-O provide an efficient superexchangepathway between the Cu2+ ions and result in predom-inantly 2D magnetic interactions J2D on a slightly dis-torted square lattice [14, 15]. Importantly, the differentCu-X (X=F,N,O) bond lengths make the JT axis an ad-ditional and controllable degree of freedom [16].

Recently, CuF2(D2O)2pyz was reported to show aseries of P -driven, first-order structural phase transi-tions [14, 17–19]. The ambient pressure phase, α-CuF2(D2O)2pyz switches to β-CuF2(D2O)2pyz at ∼9 kbar, and γ-CuF2(D2O)2pyz at ∼ 32 kbar. All of thesephases exhibit the same crystal structure and maintainthe monoclinic symmetry with spacegroup P21/c. How-ever, the elongated JT axis changes its orientation withincreasing P from the Cu-N to the Cu-O and Cu-F bond

-1.5 -1 -0.5

(0.5 0 Ql) / (Q

h 0 -0.5) (r.l.u.)

0

1

2

E (

me

V)

a) P = 0 kbar

Ql

Qh

-1.5 -1 -0.5

(0.5 0 Ql) (r.l.u.)

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Ql

Qh

1.5 2 2.5 3 3.5

T (K)

0

100

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nsity (

arb

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nits)

b) P = 0 kbar

TN

= 2.59 K

1.5 2 2.5 3 3.5

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d) P = 3.6 kbar

TN

= 2.46 K

FIG. 2: Spin-wave excitations and magnetic order parameterof CuF2(D2O)2pyz at P = 0 kbar (a)-(b) and at P = 3.6kbar (c)-(d). (a) and (c) show typical 2D spin-wave disper-sions obtained at 1.5 K, with the data fitted using linear spinwave theory. The solid (dashed) line are fits to the Ql (Qh)dispersion. (b) and (d) show the T -dependence of the Braggpeak intensity at Q = (1/2 0 0), with a power-law fit for thelow T region (see text).

for the α, β and γ-phase, respectively. β-CuF2(D2O)2pyzhas cell parameters of a = 6.8607 A, b = 7.6549 A,c = 7.0904 A and β = 114.289◦ at RT and 12.39 kbar[14]. The corresponding bond distances are Cu-F = 1.955A, Cu-O = 2.211 A, and Cu-N = 2.019 A. The elongatedCu-O bond locates the magnetic dx2−y2 orbital in the abplane. The Cu-F···D-O-Cu superexchange paths in the bcplane are broken [Fig. 1(b)]. The switching of the JT axisresults in a dramatic change of the magnetic propertiesbetween the α and β phases. While indeed bulk magneticmeasurements indicate the α-β structural transition toseparate very different magnetic regimes [14, 18], directmicroscopic characterisation of the associated magneticstates has been lacking up to now.

Here we report high-P neutron scattering studies ofthe microscopic magnetism in CuF2(D2O)2pyz as pres-sure moves the system across the structural transi-tion between the α and β phases. Our experimentswere done using two single-crystal pieces of deuteratedCuF2(D2O)2pyz (total mass 0.5 g) coaligned in the(Qh, 0, Ql) plane with a mosaic spread of 0.7◦. For high-P measurements, the sample was loaded inside a piston-cylinder clamp cell. The pressure transmitting mediumwas a 1:1 mix of fluorinerts FC-75:FC-77. The appliedpressure was monitored in-situ by tracking the latticecompression of a NaCl crystal co-mounted with the sam-ple, and using its reported equation of state [20]. Inelas-tic neutron scattering (INS) data were collected usingthe TASP spectrometer at SINQ, PSI [21]. Fixed outgo-ing wave vectors kf = 1.3 A−1 and 1.5 A−1 were used,

3

-1.5 -1 -0.5

(0.5 0 Ql) (r.l.u.)

50

100

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250co

un

ts p

er

~1

0 m

in E=0.5 meVa) 0 kbar

-1.5 -1 -0.5

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50

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150 E=1 meVb) 0 kbar

3.6 kbar

6.1 kbar

-1.5 -1 -0.5

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50

100

co

un

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er

~1

0 m

in c) E=1.5 meV0 kbar

1 1.5 2 2.5

EN (meV)

50

100

150d) Q=(0.5 0 -0.7)0 kbar

3.6 kbar

BG

FIG. 3: INS data from CuF2(D2O)2pyz at all measured pres-sures and 1.5 K. a-c) Q-scans at 0.5 meV, 1 meV and 1.5 meVenergy transfers, respectively. d) shows energy-transfer scansat Q=(0.5 0 -0.7). The sharp spin-wave modes completely dis-appear at P=6.1 kbar (open points in b). Gaussian fits areused throughout (solid lines). The feature denoted as ‘BG’ inpanel (b) for P > 0, is due to background from the pressurecell. It clearly disappears at P = 0, where the cell was notin use. Note that the data of 0 and 3.6 kbar belong to thesame phase (square lattice) and this serves as an independentcriterion for this background.

along with a Be filter placed between the sample and an-alyzer in order to suppress higher-order contamination.All INS data were collected at T = 1.5 K. Further neu-tron diffraction data were collected on the single-crystaldiffractometer TriCS at SINQ, using λ = 2.32 A.

Fig. 2 shows a summary of the spin-wave dispersionand magnetic order in CuF2(D2O)2pyz at P = 0 kbar[Figs. 2(a),(b)] and at P = 3.6 kbar [Figs. 2(c),(d)]. AtP = 0, AFM long-range-order onsets below T 0kbar

N =2.59(1) K [Fig. 2(b)]. The Neel temperature is suppressedat P = 3.6 kbar to T 3.6kbar

N = 2.46(1) K [Fig. 2(d)]. Inboth cases, the magnetic peak intensity has been fittedwith a power-law behavior for the temperature range T >0.7 ∗ TN and with a mean-field critical exponent fixed tothe 3D Heisenberg case [23].

The reduction of TN by ∆T = -0.13(1) K upon increas-ing pressure is accompanied by a softening of the spinwaves, as shown in Figs. 2(a) and (c). At both pressures,the magnetic excitations disperse away from the AFMBragg point Q=(1/2 0 -1), and along Ql in the magneticsquare lattice plane. In contrast, an essentially flat dis-persion is observed along the out-of-plane direction Qh.Figure 3 shows in detail some of the energy-transfer- andQ-scans used to construct the dispersions shown in Fig. 2.

Figs. 3(a)-(c) respectively show well-defined excitationsin Ql scans at fixed energy transfers 0.5 meV, 1 meV and1.5 meV. Fig. 3(d) shows energy scans at fixed Q=(0.5 0 -0.7) for the two pressures. Here the shift down in energyof the peak at P = 3.6 kbar clearly shows a softeningof the dispersion. A comparison between the two scansin Fig. 3(d) also shows a reduced signal-to-noise ratio[see also Fig. 3(b)], as a consequence of introducing thepressure cell.

Despite the slight softening of the excitation band-width at P = 3.6 kbar, the entire dispersion re-mains qualitatively similar. This strongly suggests α-CuF2(D2O)2pyz to host a regime of 2D magnetic inter-actions for all pressures in this structural phase. Usingthe SpinW library [24] we describe the dispersions us-ing linear spin wave theory [see Figs. 2(a) and (c)]. We

find J0kbar2D = 1.05(2) meV and J3.6kbar

2D = 0.92(3) meVfor the 2D exchange coupling at each pressure, whichbecome J0kbar

2D = 0.89(2) meV and J3.6kbar2D = 0.78(3)

meV after taking into account an appropriate quantumrenormalisation factor Zc = 1.18 [11, 22]. The resultobtained at P = 0 kbar agrees well with previous work[11, 18, 19]. Using our results for J and TN , we ex-tract an empirical estimate [25] of the interlayer couplingJ⊥ ∼ 3× 10−4 meV. This makes CuF2(D2O)2pyz an ex-cellent realization of a 2D square lattice AFM.

At the highest P=6.1 kbar, our CuF2(D2O)2pyz sam-ple has transformed into the β phase [26]. In this phaseat 1.5 K, we found no evidence for either magnetic long-range-order or any sharp magnetic inelastic modes. Thisevidences the suppression of the low-P 2D magneticsquare lattice state, which has Qk and Ql as the maindispersion directions. Instead, fundamentally differentbehaviour is observed, since the INS response is mani-fested as a continuum of broad-scattering modes that dis-perse only along Qh, and have no Qk or Ql dependence.The experimental data are summarised as an intensitycolor plot in Fig. 4(b). The constituent energy scansused to construct Fig. 4(b), are shown in Fig. 5 [27].From Figs. 5(a)-(c) the dispersion along Qh is clearlyseen, while data in Fig. 5(d) show no significant disper-sion along Ql.

As can be seen in Fig. 4, the spectrum observed fromCuF2(D2O)2pyz at P = 6.1 kbar [Fig. 4(b)] changes dra-matically and compares well with that expected for aspinon continuum dispersion of a 1D spin chain [Fig. 4(a)][28, 29]. The good agreement between experiment andtheory is further emphasized when i) including the ‘desCloizeaux-Pearson’ analytical result [30] which definesthe lower and upper spinon boundaries (dashed blacklines in Fig. 4), and ii) comparing the experimental datashown in Fig. 5, and the spinon intensities modelled usingthe formalism of Ref. 28 (continuous lines in Fig. 5(a)-(c)). From a simultaneous fit across all of our data, thespinon amplitude and J1D parameters were refined, yield-ing J6.1kbar

1D = 0.43(2) meV. This lies in agreement with

4

FIG. 4: Magnetic INS intensity maps of the spectrum fromCuF2(D2O)2pyz in the high-P phase. (a) shows the theoret-ical spinon dynamic structure factor [28]. (b) shows the ex-perimentally measured spectrum constructed from individualenergy-transfer scans equally spaced in Q. The dashed linescorrespond to the lower and upper spinon boundaries accord-ing to the ‘des Cloizeaux-Pearson’ analytical result [30].

the value ∼ 0.47 meV used in Ref. 18 to describe indi-rect bulk magnetization of the β-CuF2(D2O)2pyz phase.Overall, our results unambiguously unveil the high-Pstate of CuF2(D2O)2pyz to bear the hallmark magneticresponse of a 1D spin chain.

Experimentally we have observed a high-P 1D mag-netic state to be present in β-CuF2(D2O)2pyz atP = 6.1 kbar. This pressure lies below ∼9 kbar reportedin Refs. 14, 18 for the α-β structural phase transition,yet within the range of 5-15 kbar reported in Ref. 19.A possible reason for any absolute pressure variationsacross different studies can be due to the use of differ-ent methods of pressure generation and related inhomo-geneities. Another factor which may be important is ouruse of deuterated CuF2(D2O)2pyz, since differences inproperties could conceivably arise due to subtle changesbetween H and D bonding geometries [15, 31]. Whilewe cannot identify conclusively why the structural tran-sition pressures vary between the different studies, wenevertheless observe directly a marked change in the sys-tem’s magnetic and structural properties to occur over apressure range that is broadly consistent with previouswork [14, 18, 19].

A consistent understanding of the pressure-drivenchange between the low-P and high-P magnetic regimesis achieved if the JT axis of the CuF2O2N2 octahedraswitches from the Cu-N bonds [Fig. 1(a)] to the Cu-Obonds [Fig. 1(b)]. This switch leads to a reorientationof the dx2−y2 orbitals from the bc-plane at low-P to theab-plane at high-P [14]. Without microscopic magneticmeasurements however, two competing scenarios for thehigh-P magnetic state could nevertheless be suggested:i) the system in fact remains 2D, but with interactions ina different plane, or ii) 1D behaviour arises if a particu-

a)

0 0.5 1 1.5EN (meV)

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0 0.5 1 1.5EN (meV)

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0 0.5 1 1.5EN (meV)

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60 Q=(0.75 0 -1.00)Q=(0.75 0 -0.75)Q=(0.75 0 -0.25)Q=(0.75 0 0.00)

BG

Q=(0.5 0 L)L=-0.25L=-0.8

FIG. 5: Excitation spectra of CuF2(D2O)2pyz in the 1D state.(a)-(c) show energy scans along the spin-chain direction Qh.The solid lines are fits according to a theoretical spinon model[28]. (d) shows the spectrum to display no Ql-dependence.The scans in all panels are obtained after subtracting an en-ergy scan at Qh = 0 where no magnetic signal is expected[see Fig. 4]. Despite this background subtraction, the signaldenoted ‘BG’ in (a) for QL = −0.25 is assigned to a par-asitic, temperature-independent scattering process from thepressure cell as explained in the caption of Fig. 3. Panel (a)includes an extra dataset at a different QL value (=-0.8) withbetter conditions achieved, resulting to this background beingabsent.

lar exchange path dominates over all others. Our directneutron scattering measurements reveal the existence ofa spinon continuum [Figs. 4(b) and 5], confirming with-out doubt the 1D S = 1/2 spin chain to be the correctmagnetic model for the high-P state.

Finally, we clarify the picture of the P -driven changein magnetic dimensionality in terms of the crucial ex-change paths. In the 2D state, the Cu-F···D-O-Cu bondsdefine the superexchange pathways. To be effective atmediating superexchange for a 2D square lattice topol-ogy, the near-orthogonal superexchange integrals travers-ing the bc plane must be approximately equal. Oncethis bc-plane connectivity is suppressed, as happens in β-CuF2(D2O)2pyz when the dx2−y2 orbitals reorient to theab-plane, the 1D spin chain state suggests that strongestsuperexchange pathways become those that are linearalong the Cu-pyz-Cu network [Fig. 1(b)]. In this case, theinteraction J1D along the Cu-pyz-Cu bond is expected tobe of the σ-type, and therefore weaker than for the 2Dmagnetic exchange in α-CuF2(D2O)2pyz. This pictureis confirmed quantitatively from our data, since we findthat J6.1 kbar

1D /J0 kbar2D ∼ 0.5.

In summary, our high pressure neutron scatteringstudy of the metal organic magnet CuF2(D2O)2pyz un-veils a dramatic P -driven switch of the system’s magnetic

5

dimensionality. From neutron scattering measurementsof the magnetic excitations, we report that the 2D mag-netic square lattice state at low-P transforms to a 1Dspin chain at high-P . The microscopic mechanism be-hind this behaviour is argued to be a consequence of aP -driven switch of a uniquely sensitive Jahn-Teller axisin this soft material. Here lies the essence of this work:this JT switch across another direction, has a direct con-sequence on the orbital occupancies and in turn to theexchange pathways, which are completely altering themagnetism of the system in a profound way.

More generally, our work provides a reference exam-ple of how dramatic effects on the magnetic states ina 3D coordination material can be generated via mod-est perturbations [17, 19, 31, 32]. Due to both the di-verse range of metal organic materials with different lig-ands and networks that can be synthesized [33], and theirgenerally higher compressibility compared with inorganiccompounds, high-P becomes the effective tool for seek-ing novel quantum states in these materials. In partic-ular, the use of high-P as a precision tuning parameterwill be attractive for studying magnetic dimensionalitychanges across a continuous P -driven structure transi-tion, as opposed to the first-order structural transitionwhich takes place in CuF2(D2O)2pyz. In the formercase, the coupling between strong quantum magnetic andenhanced structural fluctuations in the crossover regionmay lead to exotic quantum magnetic and magnetoelasticstates [34, 35]. An ultimate goal may also be to controla metal-insulator transition in such systems.

Acknowledgements: We are grateful to J.S. Caux forcommunicating his theoretical results on spinon inten-sities, D. Sheptyakov for help during the experiment,and S. Ward for fruitful discussion. MS acknowledgesfunding from the European Community’s Seventh Frame-work Programme (FP7/2007-2013) under Grant Agree-ment No. 290605 (PSI- FELLOW/COFUND) as wellas TRR80 of DFG. The financial support by the SwissNational Science Foundation is gratefully acknowledged(Grant No. 200020-150257). This work is based onexperiments performed at the Swiss spallation neutronsource (SINQ), Paul Scherrer Institute (PSI), Villigen,Switzerland.

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[26] From our neutron experiments at TASP and atT = 1.5 K, the crystal parameters accessible in the hori-zontal [H0L] plane were determined at each P (to ac-curacy 1 in the last digit). For P = 0: a = 7.61 A,c = 6.83 A, β = 112.1◦, for P = 3.6 kbar: a = 7.60 A,

6

c = 6.79 A, β = 113.3◦, and for P = 6.1 kbar: a = 6.87 A,c = 7.09 A, β = 113.4◦. The sharp change in a andc lattice parameters on going from P = 3.6 kbar toP = 6.1 kbar are consistent with the occurrence of the α-β structure transition, reported to take place at ∼ 9 kbarat RT [14, 19].

[27] As a consequence of using the P -cell, various recipro-cal lattice Qk, Ql points were tested in terms of op-timising the signal-to-noise for the measurements. TheQh dependence was optimally conducted at Qk = 0 andQl = −0.25.

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