Journal ArticleThe molecule-based magnet [Ru2(O2CMe)4]3[Cr(CN)6] contains two interpenetrating sublattices with sublattice  moments confined to the cubic diagonals. At ambient pressure, a field of about 850 Oe rotates the antiferromagnetically coupled sublattice moments toward the field direction, producing a wasp-waisted magnetization curve. Up to 7 kbar, the sublattice moments increase with pressure due to the enhanced exchange coupling between the Cr(III) and Ru(II/ III)2 spins on each sublattice. Above 7 kbar, the sublattice moment drops by about half and the parallel linear susceptibility of each sublattice rises dramatically. The phase transition at 7 kbar is most likely caused by a high-to-low-spin transition on each Ru2 complex

Fishman, Randy S.

Miller, Joel Steven

English

The University of Utah: J. Willard Marriott Digital Library

PHYSICAL REVIEW B 81. 172407 (2010)Pressure-induced phase transition in a molecule-based m agnet with interpenetrating sublatticesRandy S. Fishman,1 William W. Shum,2-3 and Joel S. Miller2''Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-607!, USA 1Department o f  Chemistry, University o f  Utah, Salt Lake City Utah 84!12-0850, USA 3Department o f  Chemistry, Cornell University, Ithaca, New York 14853, USA (Received 8 March 2010; revised manuscript received 16 April 2010; published 21 May 2010)The molecule-based magnet [RunfOnCM e^yCriCN^] contains two interpenetrating sublattices with sub­lattice moments confined to the cubic diagonals. At ambient pressure, a field of about 850 Oe rotates the antiferromagnetically coupled sublattice moments toward the field direction, producing a wasp-waisted mag­netization curve. Up to 7 kbar. the sublattice moments increase with pressure due to the enhanced exchange coupling between the Cr(III) and R udl/III); spins on each sublattice. Above 7 kbar. the sublattice moment drops by about half and the parallel linear susceptibility of each sublattice rises dramatically. The phase transition at 7 kbar is most likely caused by a high-to-low-spin transition on each Ru2 complex.DOI: 10.1103/PhysRevB.81.172407 PACS number(s): 75.50.Xx. 75.10.Dg. 75.30.GwMolecule-based materials provide the unprecedented opportunity to tune magnetic properties with choice of cation, guest molecules, or topology and by applying strain or pressure.1 The molecule-based magnet [Ru2(0 2 CMe)4]3[Cr(CN)6] (Cr(Ru?)3) forms a body- centered-cubic structure with two interpenetrating cubic sublattices composed of alternating 5 = 3 /2  [Ru?(0?CMe)4]+ (Ru?) and 5 = 3 /2  [Cr(CN)6]3“ (Cr) ions.2 Due to the ciystal field of the paddle-wheel complex sketched in the lower right of Fig. 1, the spin S of each mixed-valent Ru(II/III)? ion3 experiences an easy-plane anisotropy /)(S -u )2, where D ~  8.6 meV (Ref. 4) and u bisects the paddle wheel along the Ru-Ru axis. The antiferromagnetic (AF) coupling J  between the Cr(III) and Ru(II/III)2 ions within each sublattice is much stronger than the AF coupling K  between sublattices.1600014000oE12000:q3O 10000:Z3E 8000:-S5 6000 15=L 4000 :CM2000:0k 3000H (Oe)FIG. 1. (Color online) The initial magnetization (virgin curve) of polycrystalline Cr(Ru2 ) 3  for 7=8 K (Ref. 6) along with the pre­dicted field dependence (solid curves) for several pressures: 1 bar (squares). 1.84 kbar (circles). 3.46 kbar (diamonds). 5.46 kbar (.v’s). 8.05 kbar (Vs), and 10.22 kbar (triangles). The proposed ground state (Ref. 5) of a single sublattice with classical spins and infinite anisotropy is sketched in the upper left; the Ru2 paddle wheel is sketched in the lower right.To our knowledge, Cr(Ru2)3 is the only material where two three-dimensionally ordered and weakly coupled magnetic sublattices occupy the same volume.Because of the weak AF coupling K  between sublattices, Cr(Ru2)3 undergoes a metamagnetic transition between AF and paramagnetic (PM) states at a critical field H c ~ K / /n B. In ambient pressure, the metamagnetic transition is plotted in Fig. 1 for 7= 8  K. Shum e t al.6 observed that the wasp- waisted magnetization curve of Cr(Ru2)3 sensitively depends on pressure. By 12.8 kbar, the constriction in the virgin curve has disappeared and any signature of the metamagnetic tran­sition has vanished.This Brief Report demonstrates that a phase transition separates a low-pressure (LP) phase below 7 kbar- and a high- pressure (HP) phase above 7 kbar-. In the LP phase, pressure enhances the coupling between sublattices and the sublattice moment grows. But in the HP phase, the sublattice moment falls dramatically and the susceptibility of each sublattice changes form.Because of the easy-plane anisotropy on the Ru? com­plexes, each Cr(Ru2)3 sublattice is magnetically frustrated and a collinear magnetic ground state is not possible. In ear­lier work,5 we constructed the noncollinear magnetic ground state of each sublattice at ambient pressure. For the a , b , and c Ru? spins along the .r, y, or z  axes, the paddle wheels are perpendicular- to the vectors u=x, y, or z. The proposed ground state is sketched in the upper left of Fig. 1: every Cr spin points along one of the eight cubic diagonals (account­ing for orientation) and the sum of the Ru? a , b , and c spins points opposite the Cr spin. For infinite anisotropy and clas­sical spins, the Ru? spins are confined to the easy plane of each paddle wheel; for finite anisotropy and quantum spins, the Ru? spins are canted toward the cubic diagonal but their expectation values are reduced in amplitude. For quantum spins with exchange coupling J = D ! 5 ~ \ . l  meV, the net sublattice spin is M s/= 1.81 per Cr(Ru?)3 unit cell at zero temperature (the net sublattice moment is 2 h bM si=3.62/hb).A model for the field and pressure dependence of the magnetization can be constructed based on the observation that the intersublattice coupling K  ~  1(T3 meV is much smaller than the intrasublattice coupling J  ~  1 meV (positive exchange is defined to be AF).5 At zero temperature, a net1098-0121/2010/8H 17)/172407(4) 172407-1 ©2010 The American Physical SocietyBRIEF REPORTS PHYSICAL REVIEW B 81. 172407 (2010)moment appears above the critical field H C~ K / / . iB— 1000 Oe. Because /nB~  10 T, the magneticground state of each sublattice is only weakly perturbed by an external field up to several thousand Oersted. To a first approximation, the magnetic configuration of each sublattice can be considered to be rigid and the sublattice moment j  = 1 or 2 can be written as 2/t%MJ/(T)n/-, where n ; lies along one of the eight cubic diagonals.Thermal equilibrium between the 64 possible configura­tions {nl5ii2} is achieved by fluctuations of the sublattice moments out of the completely ordered ground state. Below H c, the ground state is AF with sublattice orientations n t = - n 2. Above H, . the sublattice orientations n, and n 2 in the PM state lie along the cubic diagonals that are closest to the field direction m.The energy of a magnetic configuration with sublattice orientations {n1/,n 2/} on cluster i is given byE = Nc£  { -  n1( + n2/) • H + KM2,nu ■ n2,j, (1)iwhere H = //m  is the magnetic field and each cluster contains unit cells. The size £ of a correlated magnetic cluster decreases as magnetic fluctuations are suppressed. Notice that the intrasublattice exchange J  only enters this model implicitly through the sublattice spin which vanishesabove TC*-JS2. Compared to the model introduced in Ref. 5 with coupling energy 3S2Kcn li-n 2j, we now take K =  3S2K C/M ^ .  This scaling removes the dominant tempera­ture dependence from Kc.While this model qualitatively describes C.r(Ru2)3, a quantitative description must also account for the small dis­tortion of the sublattice ground state produced by the mag­netic field. That distortion is responsible for two effects: the weak linear susceptibility 2n BM IH  observed within the AF state at low fields and the even weaker differential suscepti­bility 2/nBd M /d H  observed within the PM state at high fields.In a magnetic field H, we assume that the susceptibility Xsi of each sublattice moment 2/t%MJ/(H ,r )  depends only on the angle 0=arccos(n-m ) between the cubic diagonal n  and the field direction m,2 H, T) = 2 fiBM si( 0 ,7 )n  + Xsii #)H . (2)Expanding Xsi i*1 Legendre polynomials P t(cos 0) up to I = 2 produces the expressionXsi(G) = Xo + Xi sin2(#/2) + _y2 sin4(#/2), (3)which ignores the weak dependence of Xsi on the azimuthal angle (f> about the cubic diagonal.The first term Xo in Eq. (3) is the parallel susceptibility reflecting the induced magnetization along the direction of the sublattice moment n  with 0=0. In our earlier fits at am­bient pressure,5 we took ^ 0= ^ 2=0 and only retained Xi- We now keep all three terms subject to the constraint that Xsl(0 )^ O  for any 0. As shown below, the experimental data is sufficiently discriminating to justify this more refined model and the pressure dependence of the parameters x„ Pro" vides compelling evidence for a phase transition at 7 kbar.With ^ —arccosCiym), the noninteracting susceptibilityFIG. 2. (Color online) Fitting results as a function of pressure or temperature for (a) and (b) the sublattice spin M sh (c) and (d) the intersublattice exchange K  (millielectron volt), and (e) and (f) the number N Ct or Cr ions within a fluctuating magnetic cluster. Dashed vertic;d lines separate the LP and HP regions.of the magnetic configuration {n^n?} is given by Xnim =Xsi(@i)+Xsi(@2) Per Pa'r ° f  Cr atoms. The additional linear term N Cl.x„imH I2  is added to the magnetization and the extra term - N Cl-x„imH 2I4  is added to the energy E  of Eq. (1) for each cluster.This model was used to evaluate the magnetization 2 /nBM av of a polycrystalline sample by averaging over field directions m. For every temperature T , M av depends on six parameters: the three components of the sublattice suscepti­bility Xm the sublattice spin M sh the weak AF interaction K between sublattices, and the number N Cr of Cr(Ru2)3 unit cells within each cluster (half belonging to each sublattice). For T=  8 K, the resulting fits are plotted in Fig. I.7 For tem­peratures up to 30 K and pressures up to 11.7 kbar, M sh K, and N Cr are plotted in Fig. 2.Generally, these fits break down close to Tc and at high fields because the field-induced change Xsi(@)H in each sub­lattice moment becomes a substantial fraction of the zero- field moment 2/hbM si(0 ,T ).1 In other words, the sublattice ground state can no longer be considered to be rigid near Tc or for high fields.The fitting parameters show a marked change at 7 kbar. In the LP phase below 7 kbar, applied pressure has the expected effect of enhancing the intrasublattice exchange J  compared172407-2BRIEF REPORTS PHYSICAL REVIEW B 81, 172407 (2010)T = 8 K2 ./  -1 \LP ' Ik HPP (kbar)FIG. 3. (Color online) The three components x„ («=0, 1, and 2) of the sublattice susceptibility Xst(@) versus pressure at 8 K.to the anisotropy D  of the Ru2 paddle-wheel complex. Con­sequently, the sublattice spin M st plotted in Fig. 2(a) in­creases with pressure in the LP phase. At 8 K, M st increases from 1.8 to 2.2 between ambient pressure and 5.46 kbar. To explain this enhancement, J  must be increased by about 60% and D U  lowered from 5 to 3. The increase in J  is also reflected in the growth of 7C from 33 to 42 K.6 Notice that M S,{T) shows the expected reduction with temperature in Fig. 2(b). By contrast, K  is relatively insensitive to tempera­ture for each pressure below about 25 K, as expected for the rescaled intersublattice exchange introduced in Eq. (1).As shown by the reduction in N Cr~ ^  with increasing pressure below 7 kbar in Fig. 2(e), pressure initially sup­presses the size £ of the fluctuating magnetic clusters. With increasing temperature, critical fluctuations produce the ex­ponential dependence N Cl-(T) ^ ( l - T / T ^ 1' seen in Fig. 2(f). Our results remain consistent with a mean-field-like critical exponent j>=1/2 for all pressures. In Cr(Ru2)3, the magnetic correlation length £ can be estimated directly from the mag­netization rather than from elastic neutron-scattering mea­surements.In the HP phase above 7 kbar, the sublattice spin M st drops dramatically. At low temperatures, M s, in Fig. 2(a) drops from about 2.2 at 5.46 kbar to 1 at 10.22 kbar. The intersublattice exchange K  plotted in Fig. 2(c) peaks at about 4 kbar but then rises by roughly 20% above 7 kbar. Some­what less dramatically. Fig. 2(e) indicates that N Cr also grows above 7 kbar, suggesting that thermal fluctuations are en­hanced in the HP phase.The lineai' susceptibility of each sublattice plotted in Fig. 3 also shows a dramatic change at 7 kbar. In the LP phase, the parallel susceptibility Xa is rather small and can be taken to be zero. Notice that the sublattice ground state becomes more rigid with increasing pressure below 7 kbar as the sus­ceptibilities Xn decrease in amplitude. Above 7 kbar, Xo be­comes non-negligible and the magnitudes of Xi alld Xi a1'13 significantly enhanced. For all pressures, ^ i < 0  and ,^2> 0 .We conclude that the atomic spins are more easily rotated by a magnetic field along the sublattice moment direction (0=0) in the HP phase above 7 kbar than in the LP phase below 7 kbar. Since the LP-HP transition is first order, it isvery likely that the material exhibits phase separation at 8.05 kbar with both LP and HP regions. Hence, the apparent re­duction in M s! at 8 K between 8.05 and 10.22 kbar probably reflects the disappearance of the LP phase rather than a change in the net sublattice spin within the HP phase. So the sublattice spin of the HP phase at low temperatures lies be­tween about 0.9 and 1.1. Despite the very small 0.45% te­tragonal expansion of the lattice observed at 12.2 kbar,6 any canting of the sublattice moments away from the cubic di­agonals in the HP phase is negligible: when the canting angle is allowed to be a variable in the fits to the magnetization, the net moment is always found along one of the cubic diago­nals.Based on these considerations, there are two possible ex­planations for the LP-HP phase transition. Pressure-induced valence changes have been previously observed among mixed-valent rare-earth compounds8 and intermetallic oxides.9 Applied pressure may also induce a valence change on one of the three inequivalent Ru2 complexes, reducing its spin from 3/2 to 1. The Cr ion would gain the electron re­moved from this Ru2 complex. Due to the surrounding six cyanide groups, the Cr(II) ion would likely support a low- spin state with S = l. But the sublattice moment would then still be too large compared to the result M st «= 1 expected for the HP phase.Many compounds, including those containing Fe, Co, or Mn ions, exhibit a high-to-low-spin transition with increas­ing pressure.10 If the Ru2 complex undergoes a high-to-low- spin transition, then the Ru2 spin would change from 3/2 to 1/2. In the absence of spin-orbit coupling, the spin-1/2 Ru2 ion would be decoupled from the crystal-field environment and the net sublattice moment would vanish. But due to the spin-orbit coupling X < 0 , the Ru2 moment would couple to the crystal field of the paddle wheel. The net sublattice mo­ment would then be substantially reduced from its value in the LP phase and, depending on the magnitude of the Ru2 moment, may lie either parallel or antiparallel to the Cr mo­ments. Considering that the different orbital configurations of the Ru2 core have nearly the same energy,11 it is not surpris­ing that both low-spin12 and spin-admixed13 diruthenium compounds are fairly common. Thus, Cr(Ru2)3 would pro­vide an example of a pressure-induced high-to-low-spin tran­sition for a diruthenium compound.To summarize, we have modeled the magnetization of Cr(Ru2)3 as a function of field and pressure. Up to 7 kbar, the magnetization grows with increasing pressure due to the en­hanced coupling between spins. Above 7 kbar, the sublattice moment drops by a factor of 2 and the lineai' susceptibility of each sublattice along the cubic diagonal rises dramatically. O f the two scenarios described above, it is most likely that the Ru2 ion undergoes a high-to-low-spin transition at 7 kbar. Further measurements are needed to verify this prediction. It would also be interesting to study the pressure dependence of the two-dimensional analog of Cr(Ru2)3.14We would like to acknowledge helpful discussions with Satoshi Okamoto. This research was sponsored by the Divi­sion of Materials Sciences and Engineering of the U.S. De­partment of Energy (R.S.F.) and by the U.S. National Sci­ence Foundation (Grant No. 0553573) (W.W.S. and J.S.M.).172407-3BRIEF REPORTS PHYSICAL REVIEW B 81. 172407 (2010)1 J. S. Miller and A. J. Epstein. Angew. Chem.. Int. Ed. Engl. 33. 385 (1994); J. S. Miller and A. J. Epstein. MRS Bull. 25. 21 (2000); J. S. Miller. Adv. Mater. 14. 1105 (2002).2Y. Liao. W. W. Shum. and J. S. Miller. J. Am. Chem. Soc. 124. 9336 (2002).3V. M. Miskowiski. M. D. Hopkins. J. R. Winkler, and H. B. Gray, in Inorganic Electronic Structure and Spectroscopy, edited by E. I. Solomon and A. B. P. Lever (Wiley. New York. 1999). Vol. 2. Chap. 6.4W. W. Shum. Y. Liao, and J. S. Miller. J. Phys. Chem. A 108. 7460 (2004).5R. S. Fishman. S. Okamoto. W. W. Shum. and J. S. Miller. Phys.Rev. B 80. 064401 (2009).6W. W. Shum. J.-H. Her. P. W. Stephens. Y. Lee. and J. S. Miller. Adv. Mater. 19. 2910 (2007).7 The virgin magnetization curves contain a constant magnetiza­tion at zero field. This constant is simply added to the theoretical result. Fits were performed using different cutoff fields. The re­sulting fitting parameters were averaged over all fits where the maximum increase x ^ H  in the sublattice moment with field was smaller than 1.2fj.RM si(H=0.T).8 A. Jayaraman. W. Lowe, and L. D. Longinotti. Phys. Rev. Lett. 36. 366 (1976); B. Perscheid. E. V. Sampathkumaran. and G. Kaindl. J. Magn. Magn. Mater. 47-48. 410 (1985); A. T. Holmes. D. Jaccard. and K. Miyake. Phys. Rev. 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Jimenez- Aparicio. J. L. Priego. E. C. Royer. M. R. Torres, and F. A. Urbanos. Polyhedron 23. 2637 (2004).13 M. C. Barral. S. Herrero. R. Jimenez-Aparicio. M. R. Torres, and F. A. Urbanos. Angew. Chem.. Int. Ed. 44. 305 (2005); M. C. Barral. T. Gallo. S. Herrero. R. Jimenez-Aparicio. M. R. Torres, and F. A. Urbanos. Chem.-Eur. J. 13. 10088 (2007).I4T. W. Vos and J. S. Miller. Angew. Chem.. Int. Ed. 44. 2416(2005); R. S. Fishman. S. Okamoto. and J. S. Miller. Phys. Rev. B 80. 140416(R) (2009).172407-4

Pressure-induced phase transition in a molecule-based magnet with interpenetrating sublattices

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Pressure-induced phase transition in a molecule-based magnet with interpenetrating sublattices

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