Pressure–Temperature Phase Diagram Reveals Spin–Lattice

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Pressure−Temperature Phase Diagram Reveals Spin−Lattice Interactions in Co[N(CN)2]2 J. L. Musfeldt,* K. R. O’Neal, T. V. Brinzari, and P. Chen Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States

J. A. Schlueter Division of Materials Research, National Science Foundation, Arlington, Virginia 22230, United States

J. L. Manson Department of Chemistry and Biochemistry, Eastern Washington University, Cheney, Washington 99004, United States

A. P. Litvinchuk Texas Center for Superconductivity and Department of Physics, University of Houston, Houston, Texas 77204, United States

Z. Liu Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, United States ABSTRACT: Diamond anvil cell techniques, synchrotron-based infrared and Raman spectroscopies, and lattice dynamics calculations are combined with prior magnetic property work to reveal the pressure− temperature phase diagram of Co[N(CN)2]2. The second-order structural boundaries converge on key areas of activity involving the spin state exposing how the pressure-induced local lattice distortions trigger the ferromagnetic → antiferromagnetic transition in this quantum material.

both magnetic field- and pressure-driven phase transitions.21−29 Co[N(CN)2]2 in particular attracted our attention as a system with a soft, flexible lattice, modest exchange interactions (J ≈ 4 K), well-established magnetoelastic and electron−phonon coupling, and the propensity to display strongly interacting and competing phases.21,23,25,26,30−34 The pressure-induced ferromagnetic → antiferomagnetic transition23 is an excellent example of this competition. The absence of hydrogen bonding in the transition metal dicyanamides also differentiates this effort from high pressure spectroscopy on other magnetic crossover systems.7,35,36 In this work, we reached beyond the use of high magnetic field spectroscopy25 to uncover the mechanism of the ferromagnetic → antiferromagnetic transition in Co[N(CN)2]2 under pressure. Our infrared and Raman scattering measurements reveal a series of compression-induced local lattice distortions involving CoN6 rotations, distortion and elongation of the octahedra, shortening of the C ≡ N distances, and

I. INTRODUCTION There is broad interest in the use of external stimuli to manipulate the properties of complex materials. In magnetic solids, for instance, field is the control parameter, and the energy scale is given by the exchange interactions.1,2 Pressure is different from the magnetic field, temperature, and light3 in that it acts directly on bond lengths and angles to modify crystal structure on a microscopic scale.4 As a result, compression gives rise to large free energy changes. In materials with spincontaining centers, pressure-induced distortions can modify the magnetic properties.5−14 The effect can be as classic as a change in magnetic ordering temperature9,15,16 or as complex as magnetostructural interactions in Prussian blues, MnO, multiferroics like HoMnO 3 , and multiplateau systems like SrCu2(BO3)2.10,17−20 When the size of the control parameter is large compared to the energy scales in the target material, intrinsic interactions between the charge, lattice, and spin channels can be suppressed. This allows access to completely new states of matter that often display dramatically different properties. The M[N(CN)2]2 isostructural series (where M = Mn, Fe, Co, and Ni) provides a superb platform for exploring © 2017 American Chemical Society

Received: December 23, 2016 Published: April 17, 2017 4950

DOI: 10.1021/acs.inorgchem.6b03097 Inorg. Chem. 2017, 56, 4950−4955

Article

Inorganic Chemistry

Figure 1. (a,b) Close-up views of the Raman response of Co[N(CN)2]2 as a function of pressure at 300 K. The spectra are offset for clarity. (c) Frequency vs pressure data extracted from the Raman spectra in panels a and b. Error bars are on the order of the symbol size.

Figure 2. Close-up views of the Raman response of Co[N(CN)2]2 as a function of pressure in the vicinity of (a,b) the 685 cm−1 symmetric, in-phase, in-plane C−Nax-C bend and (c,d) the 2214 cm−1 C ≡ N stretch at 300 K. The spectra are offset for clarity. Error bars are on the order of the symbol size.

behavior allows us to define the α, γ, and δ phases as well as the 1 and 3 GPa critical pressures.26 For instance, the 67 cm−1 CoN6 octahedral rotation around c diminishes noticeably at the α → γ transition, whereas the equatorial out-of-phase N−Co− N bending mode (originating near 76 cm−1) hardens significantly (∂ω/∂P = 15.4 cm−1/GPa) on approach to the γ phase and splits in the δ phase. Coalescence of the doublet near 150 cm−1 is another good indicator of the α → γ phase boundary at 1 GPa. At the same time, the 685 cm−1 symmetric, in-phase, in-plane C−Nax-C bend softens systematically and broadens over the full pressure range of our investigation (Figure 2),42 and the Raman active C ≡ N stretch softens significantly through the 1 GPa transition.43 Together, the variable pressure Raman and infrared spectra uncover two different structural transitions through which compression modifies the successive CoN6 counter-rotations, distorts and elongates the octahedra, shortens the C ≡ N distances, and flattens the C−Nax-C linkages.26 The spectra reveal amorphous character above 8 GPa but are reversible upon release of pressure (not shown). This is more than simple line broadening because the entire character of the spectrum becomes illdefined and without fidelity.

flattening of the C−Nax-C linkages26,28 that we track over a wide pressure and temperature range. Bringing this data together with prior magnetic properties work,23 we create a pressure−temperature (P−T) phase diagram in which the second-order structural transitions converge on key areas of phase space where spin and lattice compete. Drawing together an analysis of mode behavior, we reveal how the pressuredriven α → γ structural distortion triggers the ferromagnetic → antiferromagnetic transition and why pressure destabilizes the resulting antiferromagnetic state. The rich spin−lattice interactions uncovered in Co[N(CN)2]2 illustrate the interdependence between magnetism and structure. Similar triggering events take place in oxides and chalcogenides.37−41 The primary advantages to exploring these mechanisms in molecule-based materials are, of course, their simple flexible chemical structures and overall low energy scales.

II. RESULTS AND DISCUSSION A. Developing the Pressure−Temperature Phase Diagram. Figure 1 displays the low frequency Raman response of Co[N(CN)2]2 as a function of pressure at 300 K. Mode 4951

DOI: 10.1021/acs.inorgchem.6b03097 Inorg. Chem. 2017, 56, 4950−4955

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Inorganic Chemistry

Figure 3. Close-up views of the infrared response of Co[N(CN)2]2 as a function of pressure at 150, 200, 250, and 300 K. The spectra are offset for clarity.

We followed the local lattice distortions in Co[N(CN)2]2 as a function of both pressure and temperature, using peak splitting and shifting, the appearance or disappearance of peaks, and inflection points in the frequency vs pressure curves to develop a P−T phase diagram. As an example of this procedure, Figure 3a displays a close-up view of two representative infrared features as a function of pressure at 150 K. Based upon our dynamics calculations,25 we assign the cluster of modes between 190 and 260 cm−1 as combined N−Co−N bending and Co−N stretching. The fingerprint for the α → γ transition is the appearance of a new feature at 180 cm−1. Diminishment of the 200 cm−1 structure and a change in peak shape near 235 cm−1 signals the δ phase. The features at 500 and 525 cm−1 are assigned as ligand modes. Subtle frequency shifts signal the α → γ transition. The collapse of the out-of-plane symmetric N ≡ C−N bend into the in-plane asymmetric NC−N bend and the development of a low frequency shoulder near 495 cm−1 are good indications of the γ → δ transition. By performing these measurements at different temperatures (Figure 3), we reveal not only crossover points at 150 K but boundaries that separate the α, γ, and δ phases. We bring our findings together with prior variable pressure susceptibility work of Nuttall et al.23 to create a comprehensive P−T phase diagram (Figure 4). This representation illustrates the delicate interplay between structure and magnetism in Co[N(CN)2]2. Small perturbations allow access to a number of different states, making the phase diagram surprisingly complex. As a reminder, the α phase of Co[N(CN)2]2 is orthorhombic (space group Pnnm),21,23,30,32 whereas the γ phase is monoclinic (P21/n).28 B. Thermodynamics of the Phase Diagram. We begin by discussing the thermodynamics revealed in the P−T phase diagram. The α → γ transition takes place with ∂P∂T ≈ 0, indicating that there is similar order above and below the 1 GPa transition. The γ → δ transition is more interesting. Since ∂P∂T)V = −∂S∂V)T, the fact that ∂P∂T ≥ 0 implies that (i) entropy is increasing and that (ii) the δ phase is more disordered.44 The absence of a significant density change at either boundary, evidenced by the lack of large volume changes when the diamond anvil cell is compressed, suggests that both transitions are second order. This is in agreement with recent structural work.28 Extrapolating the α → γ and γ → δ lines to

Figure 4. P−T phase diagram of Co[N(CN)2]2. Blue symbols indicate the locations of the pressure-induced local lattice distortions measured in this work. Gray points denote magnetic transitions as reported by Nuttall et al.,23 and the textured areas indicate long-range ordered states. The solid green lines guide the eye, whereas the dashed green lines are extrapolations of the data (for instance, below our measurement temperature and into the magnetically ordered regime). Error bars are on the order of the symbol size.

lower temperature, we see that the boundaries representing local lattice distortions converge on key areas of activity involving the magnetic state. Compression initially stabilizes the low temperature ferromagnetic state (from TC = 9 K at 0 GPa to 9.38 K at 0.8 GPa, ∂TC/∂P ≈ 0.5 K/GPa),23 in line with the Ehrenfest criteria for a second order transition. This trend is consistent with what is observed in Prussian blues: the ferromagnetic state is stabilized when the octahedra antirotate.10 Ordering temperatures change at a similar pace in TDEA-C60 and 4952

DOI: 10.1021/acs.inorgchem.6b03097 Inorg. Chem. 2017, 56, 4950−4955

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Inorganic Chemistry CoO.9,15 This makes sense because TC ∼ J ∼ 2t(Δ2 − δ2)0.5,10 so small changes in bond lengths and angles impact t which changes TC. Here, t is the overlap integral, Δ is the energy gap between mixed orbitals, and δ is the energy gap between unmixed orbitals. Above ≈1 GPa, pressure drives the system into the antiferromagnetic state.23 The horizontal green dashed line in Figure 4 illustrates the strong likelihood that the ferromagnetic → antiferromagnetic transition persists to lower temperatures. Additional compression destabilizes antiferromagnetism (∂TN/∂P ≈ −2.7 K/GPa).23 This boundary is also second order according to the Ehrenfest criteria. From the vibrational properties point of view, the low temperature antiferromagnetic state is diminished due to unfavorable local lattice distortions (like increased octahedral tilting and shorter C ≡ N linkages), which reduce magnetic orbital overlap and may, under additional compression, eventually favor a lower volume antiferromagnetic state.35 C. Local Lattice Distortions Trigger New Magnetic States. The P−T phase diagram shows that the α → γ transition at 1 GPa dovetails perfectly with the 1 GPa magnetic crossover, an indication that the α and γ structures support two different magnetic states.45 Energy scale arguments dictate that the structural distortions trigger the ferromagnetic → antiferromagnetic transition, but exactly how do the local lattice distortions drive the magnetic crossover? Local structure modifications are well-known to impact overlap integrals and superexchange interactions in a wide variety of materials.5 The effect of such local lattice distortions (u’s) on the hopping integrals (ti,j’s) might be expressed in a simple way as ti,j = t0i,j + (∂ti,j/∂u)(δu). When magnetic orbitals are involved, these changes affect JAFM as t2/U, where U is the on-site Coulomb integral.24,46−48 We can use these mechanistic ideas on the positional dependence of exchange interactions below TC to model how local structure modifications are connected with the magnetic crossover in Co[N(CN)2]2. Let us consider the behavior of the C−Nax-C linkage (Figure 2a,b) as an example of how spin−lattice coupling is wrapped up in the mechanism of the magnetic transition. At ambient conditions, the C−Nax−C angle is 117.13°.21,30 We also know that the angle must widen for the ligand bend to relax. Using the softening of the 685 cm−1 symmetric, in-phase, in-plane C− Nax−C bend (Δω/ω = 2% over 5 GPa)26 and a simple ratio calculation, we estimate that the C−Nax−C angle increases to ≈117.6° at 1 GPa (the critical pressure for the magnetostructural transition) and to ≈119.5° by 5 GPa. Our dynamics simulations also predict that this mode softens with increasing pressure, with a 4 cm−1 red shift and a 1.5° expansion of the C− Nax−C angle at 1.5 GPa. Thus, we find a flatter C−Nax−C linkage under compression. This change in magnetic orbital overlap modifies the superexchange pathway, consistent with the ferromagnetic → antiferromagnetic transition23 and the Goodenough−Kanamori−Anderson rules5 that indicate a tendency toward the antiferromagnetic state as the superexchange angle increases toward 180°. We can estimate the impact of the modified superexchange pathway on the exchange interaction as ΔJ ∼ e−αΔΘ where α is on the order of 1 degree−1 and Θ is an angular displacement.48,49 A 1.5° change in the C− Nax−C angle yields ΔJ ≈ 0.2, on the order of 5%. Comparison of the wider C−Nax−C angle in the high pressure state of Co[N(CN)2]2 with that in the antiferromagnetic Mn analogue under ambient conditions (C−Nax−C angle of 118.14°)21,30,50 reveals that the local structure of the diamagnetic superexchange ligands and the associated exchange interactions in

Co[N(CN)2]2 become more like Mn[N(CN)2]2 under compression.51 The lattice also plays a role in destabilizing the high pressure antiferromagnetic state. Extrapolation of the γ → δ transition coincides neatly with the diminution of the long-range ordered antiferromagnetic state (Figure 4). Overall, this transition seems to take place within the context of a rather similar space group.26 Analysis of the Raman and infrared response under pressure reveals the local structure distortions that accompany the γ → δ transition.26 The equatorial out-of-phase N−Co−N bending mode hardens on approach to the δ-phase and splits through the transition, the 685 cm−1 C−Nax−C ligand bend softens continuously and widens considerably, and the 2214 cm−1 C ≡ N stretch also softens slightly. This implies that the octahedral tilt increases and that CoN6 rotates uniquely about the a and b axis. Furthermore, the C−Nax−C portion of the superexchange pathway continues to flatten, the two different C−Nax−C environments become more dissimilar,42 and the C ≡ N linkages contract a little further under compression.43 All are effective volume reduction pathways. D. What about the Gibbs Phase Rule? Strikingly, when structural and magnetic aspects are brought together, the phase diagram seems to include possible triple and quadruple points. Of course, the phase boundaries are governed by the condition of equivalent chemical potentials, and we can write down Maxwell equations in each case.11 But, is there really a quadruple point separating the ferromagnetic α phase, the antiferromagnetic γ phase, and the paramagnetic α and γ phases? If we consider the well-known Gibbs phase rule, P + F = C + 2, where P is the number of phases, F is the number of degrees of freedom, and C is the number of components, we see that two degrees of freedom fully define a single component system. This means that while we can understand a triple point, a quadruple point cannot be justified. We therefore conclude that the apparent tetracritical regime in Co[N(CN)2]2 (Figure 4) contains several near-degenerate, coexisting phases that are not in true equilibrium. A similar situation with closely related but unique phases arises in multiferroics like HoMnO3 and intermetallics like CeRhIn5.20,52−54 When explored in additional depth, the apparent multicritical regimes are likely to separate into several different nearly degenerate phases in accord with the phase rule. The development of a two-phase region is also a possibility. This region of uncertainty is indicated in Figure 4.

III. CONCLUSION To summarize, we combined diamond anvil cell techniques, Raman and infrared spectroscopies, and complementary lattice dynamics calculations to investigate the magnetic crossover mechanism in Co[N(CN)2]2. We brought our findings together with prior high pressure magnetic property work to create a P−T phase diagram. The latter reveals complex interactions involving both structure and magnetism. The confluence of second-order phase boundary lines suggests that local lattice distortions trigger the ferromagnetic → antiferromagnetic transition. As a specific example, we discuss how changes in the C−Nax−C angle support the development of new magnetic states. This analysis reveals the importance of local structure in tuning magnetic functionality. Although spin− lattice mixing processes are most easily investigated in low energy scale materials like Co[N(CN)2]2, similar triggering events may also be present in higher Curie temperature systems. 4953

DOI: 10.1021/acs.inorgchem.6b03097 Inorg. Chem. 2017, 56, 4950−4955

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(7) O’Neal, K. R.; Brinzari, T. V.; Wright, J. B.; Ma, C.; Giri, S.; Schlueter, J. A.; Wang, Q.; Jena, P.; Liu, Z.; Musfeldt, J. L. Pressureinduced magnetic crossover driven by hydrogen bonding in CuF2(H2O)2(3-chloropyridine). Sci. Rep. 2014, 4, 6054. (8) O’Neal, K. R.; Liu, Z.; Miller, J. S.; Fishman, R. S.; Musfeldt, J. L. Pressure-driven high to low spin transition in the bimetallic quantum magnet [Ru2(O2CMe)4]3[Cr(CN)6]. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 104301. (9) Struzhkin, C. C.; Goncharov, A. F.; Syassen, K. Effect of pressure on magnetic excitations in CoO. Mater. Sci. Eng., A 1993, 168, 107− 110. (10) Verdaguer, M.; Girolami, G. S. Magnetism: Molecules to Materials V; Miller, J. S., Drillon, M., Eds.; Wiley-VCH: Weinheim, Germany, 2005. (11) Gignoux, D.; Schlenker, M. Magnetism: Fundamentals; du Trémolet de Lacheisserie, E., Schlenker, M., Eds.; Springer Science: Boston, MA, 2005. (12) Yuan, S.; Kim, M.; Seeley, J. T.; Lee, J. C. T.; Lal, S.; Abbamonte, P.; Cooper, S. L. Inelastic light scattering measurements of a pressure-induced quantum liquid in KCuF3. Phys. Rev. Lett. 2012, 109, 217402. (13) Tarafder, K.; Kanungo, S.; Oppeneer, P. M.; Saha-Dasgupta, T. Pressure and temperature control of spin-switchable metal-organic coordination polymers from ab initio calculations. Phys. Rev. Lett. 2012, 109, 077203. (14) Thirunavukkuarasu, K.; Winter, S. M.; Beedle, C. C.; Kovalev, A. E.; Oakley, R. T.; Hill, S. Pressure dependence of the exchange anisotropy in an organic ferromagnet. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 014412. (15) Allemand, P.-M.; Khemani, K. C.; Koch, A.; Wudl, F.; Holczer, K.; Donovan, S.; Grüner, G.; Thompson, J. D. Organic molecular soft ferromagnetism in a fullerene C60. Science 1991, 253, 301−302. (16) Fishman, R. S.; Shum, W. W.; Miller, J. S. Pressure-induced phase transition in a molecule-based magnet with interpenetrating sublattices. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 172407. (17) Kunes, J.; Lukoyanov, A. V.; Anisimov, V. I.; Scalettar, R. T.; Pickett, W. E. Collapse of magnetic moment drives the Mott transition in MnO. Nat. Mater. 2008, 7, 198−202. (18) Sun, Q. C.; Baker, S. N.; Christianson, A. D.; Musfeldt, J. L. Magneto-elastic coupling in bulk and nanoscale MnO. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 014301. (19) Jaime, M.; Daou, R.; Crooker, S. A.; Weickert, F.; Uchida, A.; Feiguin, A. E.; Batista, C. D.; Dabkowska, H. A.; Gaulin, B. D. Magnetostriction and magnetic texture to 100.75 T in frustrated SrCu2(BO3)2. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 12404. (20) Lorenz, B. Hexagonal manganites (RMnO3): class (I) multiferroics with strong coupling of magnetism and ferroelectricity, ISRN Condensed Matter Physics 2013; article ID 497073. DOI: 10.1155/2013/497073. (21) Kurmoo, M.; Kepert, C. J. Hard magnets based on transition metal complexes with the dicyanamide anion, N(CN)2. New J. Chem. 1998, 22, 1515−1524. (22) Manson, J. L.; Kmety, C. R.; Epstein, A. J.; Miller, J. S. Spontaneous magnetization in the M[N(CN)2]2 (M = Cr, Mn) weak ferromagnets. Inorg. Chem. 1999, 38, 2552−2553. (23) Nuttall, C. J.; Takenobu, T.; Iwasa, Y.; Kurmoo, M. Pressure dependence of themagnetization of MII(N(CN)2)2: mechanism for the long range magnetic ordering. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 2000, 343, 227−234. (24) Brinzari, T. V.; Chen, P.; Sun, Q.-C.; Liu, J.; Tung, L. C.; Wang, Y. J.; Singleton, J.; Schlueter, J. A.; Manson, J. L.; Litvinchuk, A. P.; Whangbo, M.-H.; Musfeldt, J. L. Quantum critical transition amplifiesmagnetoelastic coupling in Mn(dca)2. Phys. Rev. Lett. 2013, 110, 237202. (25) Brinzari, T. V.; Haraldsen, J. T.; Chen, P.; Sun, Q.-C.; Kim, Y.; Tung, L.-C.; Litvinchuk, A. P.; Schlueter, J. A.; Smirnov, D.; Manson, J. L.; Singleton, J.; Musfeldt, J. L. Electron-phonon and magnetoelastic

IV. METHODS 30

Polycrystalline Co[N(CN)2)]2 was prepared as reported previously and loaded into a symmetric diamond anvil cell with a pressure medium to maintain hydrostaticity and a ruby ball. We tested several different pressure mediums: vacuum grease, KBr, neat, Si oil, and a liquid argon load. There is no run-to-run variation that correlates with the pressure medium. In fact, most molecule-based materials are so soft and flexible that they can even act as their own pressure medium. Ruby fluorescence was used to determine pressure.55,56 The variable pressure infrared and Raman scattering (λexc = 514 nm, 1 mW) measurements employed the U2A beamline facilities at the National Synchrotron Light Source.26,57 Resolution is between 0.5 and 1 cm−1, depending on the scan. In order to apply pressure in situ at low temperature, the diamond anvil cell was placed inside an open-flow helium cryostat, the thermal contact of which limited our temperature range to 150 K. Fortunately, structural phase transitions tend to sharpen and strengthen at lower temperatures, making a linear extrapolation of what appears to be a fairly linear phase boundary reasonable and reliable. Compression was reversible within our sensitivity. Traditional peak fitting techniques were employed, as appropriate, to follow frequency vs pressure trends. Density functional theory combined with the linear response method was employed to calculate mode frequencies, symmetries, and displacement patterns on isostructural Mn[N(CN)2]2 as described previously.24 These calculations were carried out at both ambient pressure and with a small applied force (to simulate 1.5 GPa) in an effort to predict mode trends under compression.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

J. L. Musfeldt: 0000-0002-6241-823X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Science Foundation DMR 1707846 (to J.L.M., UT), DMR-1306158 (to J.L.M., EWU), COMPRESS EAR 1606856 (to Z.L.), ACSPRF 52053-ND10 (to J.L.M., UT), the U.S. Department Energy (NHMFL), the Independent Research/Development Program at the NSF (to J.A.S., NSF), DE-AC98-06CH10886 (to Z.L., NSLS, BNL), CDAC DE-NA-0002006 (to Z.L., U2A, CIW), and the State of Texas via the Texas Center for Superconductivity (to A.P.L., UH). We thank B. Maple, S. Tozer, and S. Saxena for useful conversations.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.6b03097 Inorg. Chem. 2017, 56, 4950−4955