# Charge Order Breaks Magnetic Symmetry in Molecular Quantum Spin Chains

Authors: M. Dressel; M. Dumm; T. Knoblauch; B. Köhler; B. Salameh; S. Yasin
Journal: Advances in Condensed Matter Physics
 (2012)

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## Abstract

Charge order affects most of the electronic properties but is believed not to alter the spin arrangement since the magnetic susceptibility remains unchanged. We present electron-spin-resonance experiments on quasi-one-dimensional(TMTTF)2X salts (X= PF6, AsF6, and SbF6), which reveal that the magnetic properties are modified below TCO when electronic ferroelectricity sets in. The coupling of anions and organic molecules rotates the g-tensor out of the molecular plane creating magnetically nonequivalent sites on neighboring chains at domain walls. Due to anisotropic Zeeman interaction a novel magnetic interaction mechanism in the charge-ordered state is observed as a doubling of the rotational periodicity of ΔH.


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## Body

## 1. Introduction

Charge disproportionation is a common ordering mechanism in correlated electron systems that is intensively investigated in transition-metal oxides as well as organic compounds [1, 2] because it is recognized to influence charge, lattice, and magnetic degrees of freedom. For static charge order (CO) the electrons are (partially) localized resulting in an insulating state, most evident in manganites or at the 1/8 anomaly observed in cuprates [3]. Fluctuating stripes, however, may be relevant for high-temperature superconductivity [4], but also in organic systems evidence accumulates that charge fluctuations mediate superconductivity [5–7].As far as the magnetic properties are concerned, the situation is even more puzzling. CO can induce ferroelectricity when the inversion symmetry is broken, as suggested (and also disputed) for some mixed-valence oxides [9, 10], magnetite [11–15], manganites [16, 17], or nickelates [18, 19]. For perovskites, however, there seems to be a mutual exclusion of magnetism and ferroelectricity [20–22], albeit the field of multiferroics drew enormous attention over the last years [23–25]. About ten years ago, electronic ferroelectricity was discovered in quasi-one-dimensional organic compounds (TMTTF)2X (where TMTTF stands for tetramethyltetrathiafulvalene and X denotes a monovalent anion such as PF6, AsF6, SbF6, Br) around 50–160 K [26]. X-ray investigations could not identify any superstructure, on this account it is known as a “structureless” transition [27].In these strongly correlated electron systems, nearest-neighbor Coulomb repulsion causes CO upon cooling belowTCO characterized by a charge gap in the transport properties [28]. From the magnetic point of view, these are S=1/2 antiferromagnetic chains with some ordering at low temperatures [29, 30]. Surprisingly, by now no indications of the CO transition could be observed in the magnetic properties, such as spin susceptibility (cf. Figure 1). Here we, report comprehensive electron spin resonance (ESR) investigations that reveal a novel magnetic interaction mechanism caused by charge disproportionation; we observe first evidence that charge order breaks the symmetry of the magnetic degree of freedom in these quantum spin chains.Figure 1
Electronic, magnetic, and optical characterization of the three compounds(TMTTF)2PF6, (TMTTF)2AsF6, and (TMTTF)2SbF6. (a)–(c) The open symbols correspond to the spin susceptibility (χs)V(T) along the a direction evaluated at constant volume (left axis). The dashed blue lines correspond to fits using the model [8] of a Heisenberg chain with J as indicated. For (TMTTF)2PF6 and (TMTTF)2AsF6, (χs)V(T)drops exponentially at TSP=19 and 13 K, respectively, indicating a transition to a nonmagnetic spin-Peierls ground state. In contrast, (TMTTF)2SbF6 orders antiferromagnetically at TN=8K. The solid red dots show the temperature-dependent dc resistivity ρ(T) measured along the a-axis (right scale). The solid arrows indicate the charge localization at Tρ and the charge-order transition TCO (d)–(f) Temperature development of the asymmetric vibration of the TMTTF molecule involving the C=C bonds obtained with light polarized perpendicular to the ab plane. For T<TCO the mode splits due to charge imbalance.


## 2. Results and Analysis

Single crystals of(TMTTF)2X with octahedral anions X=PF6, AsF6, and SbF6, are grown electrochemically. The planar TMTTF molecules stack in a slight zig-zag fashion normal to the molecular plane; this a-axis is the best-conducting direction. The stacks are arranged next to each other with some minor interaction in b direction and separated in the c direction by the anions. Since one electron is transferred to each anion, the organic molecules are left with half a hole, on average. Triggered by the A2B stoichiometry, the TMTTF molecules form dimers along the a-axis; a fact that enhances the charge localization observed as a broad minimum in resistivity at Tρ≈250K [31–35]. In Figures 1(a)–1(c), ρ(T) is plotted for the three compounds under consideration [28].In addition, basically all TMTTF salts develop charge imbalance forT<TCO, resulting in charge-rich (0.5e+δ) and charge-poor molecules (0.5e-δ) as first proven by nuclear magnetic resonance [36, 37]. The charge disproportionation can be best visualized by the splitting of the intramolecular vibration ν28(B1u) plotted in Figures 1(d)–1(f) [38–40]. The results are summarized in Table 1; for further details, see [41].Table 1
Transition temperatures for charge localizationTρ, charge-order  TCO, spin-Peierls transition TSP and Néel order TN of different (TMTTF)2X salts. J denotes the antiferromagnetic exchange constant obtained from susceptibility measurements fitted according to [8],  2δ is the charge imbalance between two TMTTF molecules (for T→0) measured by vibrational spectroscopy and ΔCO indicate the zero-temperature charge gap derived from dc transport along the a-direction.  ϕ is the angle the g-tensor rotates around the molecular axis in the CO state determined at  T≈TCO/2.
Compound
T
ρ
T
CO
T
SP
T
N
J
2
δ
Δ
CO
ϕ
(K)
(K)
(K)
(K)
(K)
(e)
(K)
(∘)
(
TMTTF
)
2
P
F
6
250
67
19
—
420
0.15
small
22
(
TMTTF
)
2
AsF
6
250
102
13
—
410
0.21
310
22
(
TMTTF
)
2
Sb
F
6
240
157
—
8
400
0.29
745
32Charge order causes an additional gap to open in the density of states atTCO, leading to a kink in the electrical resistivity ρ(T) indicated by arrows in Figures 1(a)–1(c); as the temperature decreases it evolves in a mean-field fashion to ΔCO(T→0)≈745K, for the example of (TMTTF)2SbF6 [28].Although the effect of charge ordering on the spin degree of freedom has attracted considerable attention from the theoretical side [42], it is not completely clear how the spin and orbital magnetic moments behave in the charge-order state and in the metallic state under the influence of charge fluctuations. Naively, one would expect that a phase transition, which has such a severe effect on the electric transport, evidences also in the spin susceptibility, albeit spin-charge separation is an issue for one-dimensional conductors [34, 35]. Despite numerous charge-ordered systems investigated over the years, no sign of the charge-order was revealed in the magnetic behavior. This is demonstrated in Figures 1(a)–1(c) which show χs(T) for various TMTTF salts [29, 30]. The obtained coupling constants J are listed in Table 1.We have performed comprehensive multifrequency ESR investigations (X-, Q- and W-band) in the temperature range from 4 to 300 K at different orientations of the magnetic field and by rotating around the molecular axes (cf. Figure6). In Figure 2 the linewidth ΔH(T) and the g-shift (from the free-electron value ge=2.002319) are plotted as a function of temperature of (TMTTF)2SbF6. The g-factor is determined by the π electronic wavefunction on the TMTTF molecule, the anisotropy arises from spin-orbit coupling of the conduction electrons [43, 44]; in other words the arrangement of the g-tensor can be solely deduced from the molecular symmetry. At room temperature the g-factor and linewidth are maximum when the external magnetic field is oriented along the molecular axis c~, while g and ΔH are smallest when measured normal to the TMTTF molecules (a~-axis which is along the stacks). No indications of the charge-order transition are observed in the g-shift; Δg(T) is basically temperature independent except a small reduction of the in-plane anisotropy upon cooling. The intriguing observation is the clear anomaly in the linewidth at TCO which can also be seen in [45]: the linear decrease in ΔH(T) becomes weaker indicating an additional interaction channel to develop for T<TCO. Basically, the same behavior at TCO is observed for (TMTTF)2AsF6, while for (TMTTF)2PF6 the effect is smaller due to stronger coupling J and less charge imbalance 2ρ, which coincide with the much lower transition temperature TCO and almost vanishing charge gap ΔCO, summarized in Table 1.Figure 2
Temperature dependence of the linewidthΔH, and the change in the g-value for (TMTTF)2SbF6 measured by X- (left panels) and W-band (right panels) ESR along three orientations. The green solid dots correspond to the a~-axis, the open red squares indicate the b~ direction, and the blue triangles are measured along the c~ direction. The inset exhibits the TMTTF molecule with its molecular axes.In order to gain more insight how charge order affects the spins, we performed detailed angular-dependent measurements ofΔH and Δg at selected temperatures. While the rotational symmetry of the Δg remains unchanged with temperature, ΔH exhibits a very unusual behavior as demonstrated in Figure 3. For T>TCO the g-factor and the linewidth are dominated by spin-phonon scattering with an angular dependence [29]
(1)ΔHsp(θ)=[ΔHsp2(a~)cos2θ+ΔHsp2(b~)sin2θ]1/2
in the a~b~ plane, for instance. Most remarkably, the periodicity doubles as the charge-ordered state is entered. In the CO state the orientational dependence of the linewidth can be fitted by the sum of (1) and (2):
(2)ΔHmod(θ)=ΔHmod(45∘)|sin{2θ}|,
where ΔHmod is the excess linewidth. The enhancement of the linewidth observed in the diagonal direction ΔHen=ΔH(45∘)-(1/2)[ΔH(a~)+ΔH(b~)] becomes more pronounced as the frequency ν increases, as depicted in Figure 4. The quadratic behavior
(3)ΔHen(ν)=A+Bν2
strongly indicates anisotropic Zeeman interaction [46]. The same period doubling in ΔH(θ) can be observed in our X-band experiments on (TMTTF)2PF6, although the effect is much weaker.Angular dependence of the ESR linewidth within thea~b~ plane of (TMTTF)2AsF6 and (TMTTF)2SbF6 measured at different temperatures above and below the charge-order transition (TCO=102 and 157 K, resp.) using X-band (blue crosses), Q-band (red stars), and W-band (green dots) spectrometers. The lines represent fits of the linewidth using (1) and (2).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)Figure 4
Frequency dependence of the enhanced ESR linewidthΔHen of (TMTTF)2SbF6 measured in the a~b~ plane along the diagonal direction (θ=45∘). The data are shown at T=10K (blue dots), 60 K (green triangles), and 130 K (red squares). The lines are fits using (3).In the case of staggered fields, antisymmetric Dzyaloshinskii-Moriya interaction also causes aν2 frequency dependence of the linewidth; however, leading to a T-2 temperature dependence [47–49] in contrast to our findings. Note also that in those references Heisenberg spin chains with significant intrachain Dzyaloshinskii-Moriya interaction were considered. In the present case, the alternating contributions result from interaction between the chains, for which the iostropic exchange J′ is already small. Thus the antisymmetric Dzyaloshinskii-Moriya exchange can be neglected.From similar observations on inorganic linear-chain compounds, Pilawa derived a contribution of the anisotropic Zeeman interaction to the linewidth [50]
(4)ΔHAZ≈μBH02gekB|J′|π8|Δg|2,
where J′ is the exchange interaction between two inequivalent magnetic sites on the neighboring chains; Δg is the difference between their g-tensors. In our case the interchain exchange constant is J′=1.1K [51].  Note, their Hamiltonian differs by a factor of 2 compared to the one used in  [50].  With B0=33.6 kOe for the W-band, we obtain Δg=7.82×10-3 and 16.78×10-3 for (TMTTF)2AsF6 and (TMTTF)2SbF6, respectively. In the case of (TMTTF)2PF6 we performed only X-band measurements which in general yield results similar to the Q-band; we estimate Δg=7.45×10-3. The fact that we do not observe two distinct  features but only a single Lorentzian line implies that the hopping rate between the nonequivalent sites is much larger than the splitting (strong-coupling limit). The difference in Larmor frequencies in the W-band Δν=(Δg/g)×95GHz corresponds to only 27 mK, which is much smaller than J′.The magnetically inequivalent sites have to be located on adjacent stacks; intrachain interaction is so strong that it would suppress the anisotropic Zeeman effect at these frequencies. From the fact that the maximum ofΔH occurs at θ=45∘ and that Δg is not zero, we conclude that the g-tensors of the two sites do not coincide with the principle magnetic axes any more but are rotated around the c~-axis by an angle ϕ in opposite directions as depicted in Figure 5; at temperature well below TCO we obtain ϕ=±22∘ for X=PF6, AsF6 and ±32∘ for (TMTTF)2SbF6, respectively Note that this effect is distinct from the gradual rotation of the g-tensor around the a~-axis due to thermal contraction, reported by Furukawa et al. [44]. That rotation causes a reduction of the g-value anisotropy in the b~c~ plane as the temperature is reduced   (Figure 2).Angular dependence of theg-value of (TMTTF)2PF6, (TMTTF)2AsF6, and (TMTTF)2SbF6 evaluated at T=30, 50, and 60 K, respectively, when a static magnetic field B0 is rotated in the a~b~ plane. The dashed lines indicate the calculated variation  (equation C1 in the appendix) of the g-values of the two magnetically inequivalent sites. A view along the molecular axis c~ is sketched in the lower panel. Below TCO the charge distribution on the dimer becomes imbalanced (indicated by the different grey shades). The distinct coupling to the anions (green circles) modifies the electronic wavefunction causing the g-tensor to rotate in opposite directions, as depicted by the brown arrows. The transfer integrals t1 and t2 differ by about 40% at room temperature.
(a)
(b)Crystal structure of(TMTTF)2SbF6, as an example, viewed (a) along the stacking direction a, (b) along the b-axis and (c) along the c direction. The strongest coupling between the octahedral anions and the sulfur atoms is indicated by the red dashed lines I and II which are related by inversion symmetry for T>TCO. In the charge-ordered state, not only the TMTTF molecules develop a charge disproportionation with alternating charge-rich and charge-poor molecules along the stacks, but also the octahedral anions are slightly distorted. The inversion symmetry is lifted and contact I becomes stronger than II, for instance. Two kinds of domains are formed separated by domain walls preferentially in the ab or ac planes. Also shown is the configuration between the TMTTF molecular structure and the principal axes of the g-tensor. Note there exists only one electron per dimer. At elevated temperatures the g-tensor (blue arrows indicate the principal magnetic directions a~, b~, and c~) is determined by the molecular structure. The a~-axis of the g-tensor is normal to the molecular plane and along the stacking direction, while the c~-axis points along to the longest molecule extension. For T<TCO the principal axes of the g-tensor rotate around the c~-axis by an angle ϕ in opposite directions, resulting in the brown arrows.
(a)
(b)
(c)


## 3. Discussion

The crucial question now is why CO triggers a rotation of the g-tensors. ESR experiments by Furukawa et al. [44] revealed that the Coulomb potential of the anions influences the electronic wavefunctions on the TMTTF molecules. Depending on whether the adjacent molecules are charge rich or charge poor, this constitutes nonequivalent charge and spin distributions as sketched in Figure 5. The imbalance of the spin density causes a rotation of the g-tensor by an angle of ϕ. Our findings are in accord with the suggestion by Riera and Poilblanc [52] that charge order in TMTTF salts is a cooperative effect between the Coulomb interaction and the electronic coupling of the TMTTF stacks to the anions The charge disproportionation also causes an imbalance in the Coulomb attraction on the anions, which become slightly distorted in bc plane in accord with thermal expansion results by de Souza et al. [53].The occurrence of spontaneous dipole moments [26] and second harmonic generation [55] evidences the loss of inversion symmetry (with one center located at the anions, for instance) for T<TCO. Our vibrational spectra (Figure 1) show the presence of charge-rich and charge-poor molecules, which, however, can be arranged on the dimerized stacks in two possible ways: +− +− +− or −+ −+ −+. This immediately implies that the rotation of the g-tensor can occur in both directions ±ϕ. Thus at T<TCO domains are formed with inequivalent magnetic sites on neighboring stacks at the boundaries, as depicted in Figure 5. Without interaction two distinct ESR signals are expected below TCO, but the strong coupling leads to a significant broadening, that might get resolved by going to even higher frequencies.Structural investigations could not identify any superstructure or change in symmetry, however, a strong increase in mosaicity atTCO, as shown in Figure 7 [54]. We conclude that the ordering occurs on a local scale with nanometer-sized CO domains. Similar, but larger ferroelectric domains of electronic origin have been directly observed in the two-dimensional organic compound α-(BEDT-TTF)2I3 below the CO transition [56].Figure 7
Temperature dependence of the normalized mosaicity of(TMTTF)2SbF6 and (TMTTF)2PF6 determined from the width of the X-ray spots (after [54]). When the temperature drops below 200 K, the mosaicity of (TMTTF)2SbF6 increases dramatically approaching a maximum at the charge-order temperature TCO=157K. For comparison the behavior of (TMTTF)2PF6 is also presented where only a small increase is observed. Note, in the case of (TMTTF)2PF6 the phase transition happens only at TCO=67K.As the averaged g-tensor does not abruptly change atTCO, the charge ordering can be pictured as follows: For T>TCO random charge disproportionation exists on the TMTTF stacks giving rise to an averaged g-factor as observed, but without any anisotropic Zeeman effect, which is suppressed due to narrowing by large intrachain exchange. Below TCO, the charge imbalance becomes cooperative within each stack; there is some weak interaction of adjacent chains. At the boundary of two domains defined by the direction of charge and spin distortion, translational symmetry is lost. This gives rise to two inequivalent chains that yield the same averaged g-tensor along the a~-Bindestrich and b~-Bindestrich axes as above TCO. In the diagonal directions, however, the anisotropic Zeeman effect now becomes visible in our ESR data because the signal is narrowed by the much weaker interchain exchange.


## 4. Conclusions

In summary, the charge order observed in the linear-chain compounds(TMTTF)2X by the splitting of the molecular vibrations opens a gap in the charge excitations. It also affects the magnetic behavior via mutual interaction with the anions. For T<TCO the inversion symmetry is broken; charge disproportionation leads to a different electronic distortion on the organic molecules that eventually rotates the g-tensors, with two possible directions ±ϕ. From our multifrequency ESR measurements we conclude that in the charge-ordered regime two inequivalent magnetic TMTTF chains coexist, which produce a doubling in the angular periodicity of the linewidth as well as the characteristic quadratic frequency dependence. Thus, our experiments show that charge order not only causes ferroelectricity, but can also break the symmetry of the magnetic degree of freedom in quantum spin chains.



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*Source: 398721-2012-12-13.xml*