Multiferroic materials with both magnetic ordering and ferroelectricity are promising candidates for applications in mutual control of magnetism and ferroelectricity.^[1,2] This research is heated by the discovery of materials with magnetoelectric couplings.^[3–7] Unfortunately, applications in these materials are still limited either because of weak magnetoelectric coupling, or their low transition temperatures. In case of type-II multiferroics, where strong magnetoelectric coupling is manifest by the magnetic driven ferroelectricity,^[8] their transition temperatures T_N (=T_C) usually set in at fairly low temperatures. Understanding of magnetoelectric coupling and searching for tuning method to enhance the T_N in type-II material are still on the way. In this aspect, broader investigation of material properties are strongly urged in this field.^[9]

In addition to most oxide type-II multiferroics, CuCl₂ was only discovered in 2009 as a non-oxide material, which has large electrical polarization below the antiferromagnetic (AFM) transition temperature .^[10,11] Though its transition temperature is fairly low, it has promoted exploration of new multiferroics on its sister compounds. A recent discovery is the multiferroicity in CuBr₂, which has the same distorted CdI₂ structure as CuCl₂ (see Fig. 1(a)), with a high transition temperature T_N (T_C) of 73.5 K and a low loss charge character.^[12] Magnetic frustration with quasi-one-dimensional (quasi-1D) interactions and the inverse Dzyaloshinskii–Moriya (DM) interaction seem to play an important role for the emergent spiral magnetic ordering and the magnetic-driven ferroelectricity.^[13–15]

NMR studies have been reported on several oxide multiferroics, but mostly limited to the magnetic properties.^[16,17] CuBr₂ provides a superior system to study the magnetoelectric and/or magenetoelestic couplings, because ⁷⁹Br and ⁸¹Br are S = 3/2 nuclei with large natural abundances and quadrupole moments, which is suitable for both NQR and NMR measurements. Indeed, several NMR and NQR studies have been reported on CuBr₂,^[18–21] although mostly focusing on properties above T_N.

Here we report the combined zero-field NQR (above T_N) and NMR (below T_N) studies to reveal the interplay of magnetism and charge properties. We first resolved the ⁷⁹Br and ⁸¹Br NMR spectra. A large anomalous enhancement of the spin-lattice relaxation rates and is seen when cooled far below T_N. Surprisingly, our detailed analysis on both nuclear sites resolves that the enhanced 1/T₁ is primarily caused by charge fluctuations, rather than magnetic fluctuations. Meanwhile, we found that the enhanced charge fluctuations are accompanied with the abnormal increases of the NMR linewidth, the reduction of the dielectric constant, and the increase of the magnetic susceptibility. These phenomena reveal an anti-correlation between charge fluctuations and the magnetic ordering, and suggest a competing ground state for this quasi-1D magnetic system.

The paper is organized as following. In Section 2, we show the crystal structure and measurement techniques. In Section 3, the high quality of the single crystals is demonstrated by the sharp magnetic and ferroelectric transition at about 74 K, with evidences of magnetoelectric coupling. The high-temperature NQR data are briefly shown in Section 4. In Section 5, we present the zero-field NMR spectra, with the assignment of the ⁷⁹Br and the ⁸¹Br resonance peaks. Details data and analysis on the spin-lattice relaxation rates are given in Section 6. Discussions with charge fluctuations are presented in Section 7, with a short summary given in Section 8.

As shown in Fig. 1, Cu²⁺ spins are strongly coupled along the b-axis to form a 1D CuBr₂ ribbon. The couplings along the a and c axis are much weaker, because of much large lattice parameters of a and c. Along the ribbon, ferromagnetic exchange coupling J₁ is induced among nearest Cu²⁺ neighbors from the Kramers theorem, because the adjacent Cu–Br–Cu bond has a nearly 90° angle. On the other hand, antiferromagnetic exchange coupling J₂ is formed between next nearest neighbors. Such competing interactions lead to the spiral magnetic ordering, which also causes magnetic-driven ferroelectricity due to DM interactions.^[12]

Fig. 1.

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	Fig. 1. (color online) Crystal structure of CuBr2. a, b, and c are axis of the monoclinic structure of the crystal. CuBr2 ribbons are directed along the crystalline b-direction to form the quasi-1D structure. Br− ions in three adjacent ribbons forms elongated octahedron, proximately along the a direction.

The single crystals of anhydrous CuBr₂ were grown by slow evaporation of aqueous solutions.^[22] The crystals are plate like with a dimension of 10 × 10 × 1 mm³, with cleavage surfaces along the ab plane of the crystal. The magnetic susceptibility is measured by a VSM in a 14 T PPMS (Quantum Design). The ferroelectric measurement is performed by a capacitive method. A pair of conducting plates are attached to two cleavage surfaces of a single crystal, and the capacitance between two plates is measured by a LCR meter (Agilent 4263B).

For the NQR and NMR studies, the sample is cut into a size of 3 × 5 × 1 mm³. All NQR and NMR measurements are performed under zero field, taking advantage of the electric field gradient (EFG) above T_N and the static internal hyperfine field in the magnetically ordered state. The spectra are accumulated by the standard spin-echo sequence , with π pulses and . The spin-lattice relaxation times, and , are measured by the inversion-recovery method, where the magnetization data are fit to the standard recovery functions for S=3/2 spins. We found only a single component of T₁ with no stretching behaviors in the magnetization recovery, in the presented T₁ data, which rules out extrinsic contributions.

Both the magnetic and dielectric measurements are performed on CuBr₂ single crystals. The low-field magnetic susceptibility χ is measured with field along the ab plane, with data shown in Fig. 2(a). The magnetic transition into the spiral magnetic ordering is seen at T_N, by a small kinked feature in χ. The T_N is precisely determined to be 74 K by a sharp peaked feature in the temperature derivative of , as shown in the inset of Fig. 2(a). The T_N is slightly higher than earlier reports.^[12]

Fig. 2.

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Fig. 2. (color online) (a) Magnetic susceptibility of CuBr2 as a function of temperature, with a 1000 Oe magnetic field applied in the ab-plane, under zero-field-cooling (ZFC) condition. Inset: the temperature derivative, . The blue arrow points at a sharp peak characterizing the magnetic transition at TN. (b) The ac dielectric constant ε of the sample measured under different magnetic fields, with capacitance measurement frequency of 20 kHz. The magnetic field are applied along the ab-plane of the crystal. Inset: The enlarged view of the data close to transition temperature TN.

The dielectric constant along the c-direction is obtained by calculating , where c is the capacitance between two copper plates attached the sample, d is the thickness of the sample, and S is the surface area of the copper plates. As shown in Fig. 2(b), ε demonstrates a sharp increase just at T_N (∼74 K), evidencing the magnetic-driven ferroelectric transition.^[12] Compared with powder samples, our ferroelectric transition exhibits a very rapid increase just below T_N. In fact, from the inset of Fig. 2(b), the transition width is only about 0.5 K, indicating very high quality of our single crystals.

The magnetoelectric coupling is further demonstrated by the change of ε under magnetic field applied in the ab-plane, as shown in the inset of Fig. 2(b). With field increased from 0 to 5 T, a large decrease of ε is clearly seen below T_N. With further increase of field up to 11.5 T, the change of ε becomes weak. This is consistent with a spin–flop transition at about 5 T.^[12] With this field orientations, the spin–flop transition rotates the magnetic moment with a c-axis component, and thus reduces the charge polarization along the same direction. This observation should be a strong support for the mechanism of magnetic-driven ferroelectricity.^[6,7]

Below 50 K, a small uprise in χ and a reduction in ε are clearly seen with decreasing temperature. Since the onset temperature is very high, these anomalous behaviors should be attributed to an intrinsic cause of our high quality samples. This will be further discussed in Section 7.

In CuBr₂, four types of isotopes, ⁶³Cu, ⁶⁵Cu, ⁷⁹Br, and ⁸¹Br are available for NQR/NMR studies. Their nature abundance, gyromagnetic ratio γ, quadrupole moments Q, and ν_Q in CuBr₂ at the ambient conditions are shown in Table 1.

Table 1.

Table 1.

Table 1. NQR characteristics for CuBr2. The νQ listed here are measured at 293 K.[19] . Spin Abundance/% γn/ Q/10−28 m2 νQ/MHz 63Cu 3/2 69.09 11.285 −0.21 30.37 65Cu 3/2 30.91 12.099 −0.195 28.18 79Br 3/2 50.54 10.667 0.33 83.98 81Br 3/2 49.46 11.499 0.28 70.10

Table 1. NQR characteristics for CuBr2. The νQ listed here are measured at 293 K.[19] .

We measured the NQR spectra of ⁷⁹Br and ⁸¹Br above T_N, whose resonance frequency are determined by local EFG. In Fig. 3(a), the NQR spectra of ⁷⁹Br and ⁸¹Br are shown at typical temperatures. The spectrum of each type of nucleus has a single line at all temperatures above T_N. Their resonance frequencies are shown as functions of temperature in Fig. 3(b), consistent with earlier reports.^[18,19,21] Both and follow a linear increase with decreasing temperature, indicating a progressive lattice contraction.

Fig. 3.

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	Fig. 3. (color online) (a) The NQR spectra of 79Br and 81Br, at typical temperatures above TN. Data are offset for clarity. (b) The and as functions of temperature determined by the NQR measurement above TN.

When the temperature drops below T_N, zero-field NMR can be performed, since static hyperfine field is produced by the ordered moments of Cu²⁺. Both the local hyperfine field and the local EFG act on the nucleus^[23] as follows:

In all, twelve zero-field NMR lines are expected in the ordered state, considering that ⁶³Cu, ⁶⁵Cu, ⁷⁹Br, and ⁸¹Br are spin-3/2 isotopes. Figure 4 shows a scan of zero-field NMR spectra in the measured frequency range from 70 MHz to 220 MHz, at a fixed temperature of 1.56 K. Here, four sets of NMR lines are clearly seen, labeled as (1)–(4). In order to assign all these spectra, we consider the following facts. i) ⁶³Cu and ⁶⁵Cu have close values of gyromagnetic ratios and the quadrupole moments, which would lead to their NMR spectra with close frequencies. ii) ⁷⁹Br and ⁸¹Br also have close values of gyromagnetic ratios and quadrupole moments. Therefore, their NMR spectra should also have close frequencies. iii) ⁶³Cu and ⁶⁵Cu has much larger gyromagnetic ratios than that of ⁷⁹Br and ⁸¹Br. ⁶³Cu and ⁶⁵Cu should have much larger internal fields in the ordered state than that of ⁷⁹Br and ⁸¹Br, because the ordered moments are on the Cu ions. iv) ⁶³Cu and ⁶⁵Cu has much smaller quadrupolar frequencies than that of ⁷⁹Br and ⁸¹Br, as already shown in the high-temperature data in Table 1.

Fig. 4.

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	Fig. 4. (color online) The zero-field NMR spectrum of CuBr2 measured at 1.5 K, in the frequency window from 70 MHz to 220 MHz.

With points i) and ii), six groups of lines are expected for zero-field NMR in the ordered state, including , , and transitions for Cu and Br, respectively. Point iii) leads to a much higher zero-field NMR resonance frequency for ⁶³Cu and ⁶⁵Cu, and point iv) causes a narrower NMR linewidth for ⁶³Cu and ⁶⁵Cu, than that of ⁷⁹Br and ⁸¹Br. Therefore, we attribute lines (1) and (2) to the Br signals, and lines (3) and (4) to Cu signals. Another two lines are missing, which likely fall out of our resolution window and/or frequency window respectively, with one Br spectra below 60 MHz and one Cu spectra above 235 MHz.

Line (4) is reasonably described as the center transition ( ) of ⁶³Cu and ⁶⁵Cu. Here we cannot separate ⁶³Cu and ⁶⁵Cu lines. ⁶³Cu has a larger quadrupole moment Q, but a smaller γ than ⁶⁵Cu, and the combination of both effects may lead to the mixing of two lines. Line (3) is about 30 MHz lower and has a similar line shape to line (4), which is consistent with ⁶³Cu/⁶⁵Cu satellite lines ( ), with and close to 30 MHz as shown in Table 1. From this, the ( ) is estimated to be at 237 MHz, out of our measurement range.

We assigned low-frequency (80–160 MHz) peaks as ⁷⁹Br and ⁸¹Br lines with different transitions, as denoted in Fig. 4. Lines (1) and (2) are broad, simply because of the incommensurate magnetic structure and the large EFG of the ⁷⁹Br and ⁸¹Br sites, where the second-order EFG contribution broadens the spectra largely. The ( ) is estimated to be below 60 MHz. We did not find an apparent peak at such low frequencies, possibly because of weak signal to noise ratio.

The relative assignment of the ⁷⁹Br and ⁸¹Br peaks in the line (1) is also supported by their nearly equal peak height, given that the natural abundance of both isotopes are about 50%. We further assign the two peaks in line (1) as ⁷⁹Br and ⁸¹Br lines as shown in Fig. 5. The temperature dependence of ⁷⁹Br and ⁸¹Br resonance frequencies follows a combined effect of hyperfine field and EFG contributions as shown below. The spectra of both isotopes with escalating temperatures are shown in Fig. 5. The two peaks are well resolved at low temperature, and then mixed into a single peak at 67 K. Above 67 K, the two-peak feature reemerges. This is understood by the fact that ⁸¹Br has a γ 8% higher than that of ⁷⁹Br, but a 15.2% lower Q. With temperature increasing toward T_N, the hyperfine field decreases because of the reduction of the ordered moment of Cu²⁺, and the EFG contribution becomes relatively larger. This is exactly demonstrated in the spectra: at low temperatures, a larger resonance frequency is seen on the ⁸¹Br nuclei because of dominant hyperfine contributions, but a higher resonance frequency is seen on the ⁷⁹Br nuclei close to T_N when the EFG has a larger contribution. Close to T_N, all NMR signals are wiped out due to slow magnetic fluctuations.

Fig. 5.

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	Fig. 5. (color online) Zero-field 79Br and 81Br NMR spectra at typical temperatures below TN. Data are offset for clarity. Inset: the resonance frequencies 79f and 81f deduced by the peaked positions, shown as functions of temperature, with scales on the left axis. Their differences 79f –81f are shown with scales on the right axis.

In principle, a double peak feature should also be seen in the line (2). However, the line (2) has a broad linewidth of 10 MHz, and it is not surprising if the ⁷⁹Br and ⁸¹Br lines are mixed in this set of spectra for real materials, even though a double line feature is seen in the line (1). Our relative assignment of two peaks of line (1) to ⁷⁹Br and ⁸¹Br is further supported by 1/T₁ data later, because this assignment gives dominant spin fluctuations close to T_N as theoretically expected. Any other assignment will not lead to this effect. Nevertheless, the main conclusion of this article is based on the relative assignment of ⁷⁹Br and ⁸¹Br of the line (1), and we will not further discuss line (2), (3), and (4).

In the inset of Fig. 5, the respective resonance frequencies ⁷⁹f and ⁸¹f, and the difference between them, are plotted as functions of temperatures. When temperature goes up close to T_N, a rapid drop in ⁷⁹f and ⁸¹f are seen, which follows the decrease of the ordered magnetic moments. ⁷⁹f –⁸¹f increases rapidly and crosses zero, due to increased EFG contributions as described above. At 71 K, the two resonance frequencies are about 80.2 MHz and 82.37 MHz, slightly higher than the and at 80 K, but much higher than and (see Table 1), again supporting our assignment of the ⁷⁹Br and the ⁸¹Br NMR lines.

Another prominent observation is that both NMR peaks broaden significantly upon cooling. In Fig. 6, the full-width-at-half-maximum (FWHM) of both peaks are plotted as functions of temperature. A large increase of the FWHM emerges when cooled below ∼50 K, which does not saturate even at 10 K. By contrast, the peak frequencies ⁷⁹f and ⁸¹f, presented in Fig. 5, increase sharply when cooled below 70 K, and level off with temperature below 50 K. The contrasting behaviors between the center frequency and the NMR linewidth indicates the formation of local magnetic inhomogeneity, which will be discussed in Section 7.

Fig. 6.

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	Fig. 6. (color online) The FWHM of the 79Br and the 81Br NMR spectra, as a function of temperature.

With the assignment of two NMR lines to ⁷⁹Br and ⁸¹Br, we are now ready to study the low-energy fluctuations by the spin-lattice relaxation rates. As shown in Fig. 7, the spin-lattice relaxation rates divided by temperature, 1/T₁T, are shown for both ⁷⁹Br and ⁸¹Br under zero-field conditions. Figure 7 shows a peaked feature in 1/T₁T at T_N for isotopes, consistent with a critical slowing down behavior at the magnetic transition.

Fig. 7.

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	Fig. 7. (color online) Spin-lattice relaxation rates divided by temperature, 1/T1T, measured by ZF NMR (below TN) and by NQR (above TN) respectively. Inset: the ratio of the 1/T1 of two types of isotopes.

When the sample is cooled below ∼40 K, an upturn arises in 1/T₁T, which suggests the onset of low-energy spin fluctuations, even though the temperature is far below T_N. The ratio between and , as shown in the inset of Fig. 7, also varies with temperature. is a constant from 200 K down to 60 K, and then increases upon further cooling. The change of the ratio results from varying contributions from spin and charge fluctuations as described below.

For nuclei with quadrupole moments, both a magnetic channel (electronic spin fluctuations) and a charge channel (local EFG fluctuations) contributes to the spin-lattice relaxation. for purely magnetic fluctuations, and for purely charge fluctuations.^[24,25] From Table 1, (⁷⁹γ/⁸¹γ)²=0.861 and (⁷⁹Q/⁸¹Q)²=1.389. In the inset of Fig. 7, two horizontal lines, with values of (⁷⁹Q/⁸¹Q)² and (⁷⁹γ/⁸¹γ)², are plotted as reference. In the temperature range from 200 K down to 60 K, our measured data are very close to (⁷⁹γ/⁸¹γ)², but far from (⁷⁹Q/⁸¹Q)². This is consistent with dominant magnetic fluctuations when the systems is close to the magnetic ordering ( ). Below 60 K, the value of increases and moves toward (⁷⁹Q/⁸¹Q)², which suggests enhanced contribution from charge fluctuations.

In the following, we decompose 1/T₁ into both a charge and a magnetic contribution,

With Eqs. (5) and (6), the 1/T₁ data shown in Fig. 7 are decomposed into charge and spin contributions. In Fig. 8, the and are shown as functions of temperature. The charge contributions are nearly absent at temperatures above 60 K, and then arises rapidly upon further cooling. By contrast, the keeps decreasing with temperature below T_N. In particular, the exceeds below 40 K, indicating dominant charge fluctuations, rather than spin fluctuations.

Fig. 8.

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	Fig. 8. (color online) Charge (left axis) and spin (right axis) contribution to the , deduced from Fig. 7 (see text).

For all above measurements on high-quality CuBr₂ single crystals, our studies have revealed four prominent observations when cooled below ∼60 K, which include (i) an enhancement of the in the charge channel, (ii) an increase of the FWHM of the NMR lines, (iii) a progressive decrease of ε, and (iv) a small increase of the magnetic susceptibility. Since all these behaviors onset at similar temperatures, the same physical origin is suggested. NMR as a low-energy probe, the increase of upon cooling is an clear evidence for enhanced low-energy EFG, or charge fluctuations.

These behaviors make large difference from charge and magnetic properties at high temperatures. For example, the low-energy spin fluctuations are dominated by magnetic fluctuations even with temperature up to 200 K. The , on the other hand, becomes large far below the ferroelectric transition temperature, which suggests that the charge fluctuations are unlikely related to the spiral magnetic ordering and the ferroelectricity.

In fact, the increase of the magnetic susceptibility also indicates a suppression of spiral antiferromgnetic ordering with the onset of charge fluctuations. The decrease of the ε below 60 K suggests that charge fluctuations compete with ferroelectricity. Furthermore, a small reduction of the zero-field NMR resonance frequencies were also observable below 10 K, as shown by ⁷⁹f and ⁸¹f in the inset of Fig. 5, which suggests a reduction of the ordered magnetic moments. By contrast, the continuous increase of down to 10 K also supports a competition relation between charge fluctuations and the spiral magnetic ordering.

In the following, we describe possible origin for the charge fluctuations. In a crystal, lattice and electronic charge are combined to give the local EFG environment of nucleus. For quasi-1D and quasi-2D systems, charge fluctuations were reported with valence transition, orbital ordering, charge ordering, or charge density wave (CDW) transitions. In the current compound, since Cu²⁺ has a stable 3d⁹ electronic configuration, any orbital ordering or valence fluctuations is unlikely to happen.

For quasi-1D magnetic compound, instabilities other than magnetic ordering, such as the spin-Peierls state and the charge ordering, can also arise. In particular, the spin-Peierls state is a popular ground state for antiferromagnet, where local spin singlets are formed among nearest neighbors. In this case, the unite cell is doubled with reduced atomic distance on the singlet bond, due to magnetoelastic coupling. When the system moves toward the spin-Peierls state, structural fluctuations can induce the large charge fluctuations. However, since the nearest exchange coupling J₁ is ferromagnetic in CuBr₂, the local singlet is unlikely to be formed among nearest neighbors. On the other hand, an incommensurate spin-Peierls state may be formed from the J₁–J₂ interactions. Recently, incommensurate spin-Peierls has been suggested in some quasi-1D material, such as CuGeO₃^[26] and TiOCl.^[27]

Charge ordering or CDW states are also frequently reported in quasi-1D and quasi-2D materials, arising from strong Fermi surface nesting in low-dimensional systems. For example, charge ordering was reported in quasi-1D cuprates^[28] or organic conductors (TMTTF)₂X.^[29] Recently, charge ordering has gained renewed interests in the cuprate superconductors^[30] and the iron-based superconductors.^[31]

Both the spin-Peierls and the CDW state are in strong competition with the magnetic ordering. Our observation of reduced low-temperature dielectric constant seems to be consistent with such a competing picture. Furthermore, the large broadening of the NMR spectra is also consistent with the formation of an incommensurate state. Unfortunately, our NMR measurement is unable to differentiate these two candidate states, and other measurement techniques are strongly demanded. Recently, phonon modes below T_N has been reported by a Raman study,^[22] although it was unclear whether it is caused by the magnetorelastic coupling or a competing mechanism with the spiral ordering. Our data suggests a competing charge fluctuations with the spiral ordering. Further investigation between the relations of these active phone modes and our observed charge fluctuations are strongly urged.

To summarize, we reported combined dielectric, susceptibility, NQR and zero-field NMR measurements on single crystals of a multiferroic compound CuBr₂. Below 60 K, we have resolved the zero-field NMR ⁷⁹Br and ⁸¹Br spectra, and found enhanced charge fluctuations from the spin-lattice relaxation rates. The charge fluctuations are accompanied with the NMR linewidth broadening, the increase in the magnetic susceptibility, and the reduced dielectric constant. Since the high quality of the samples has been demonstrated by the sharp magnetic transition at , our data suggest emergent charge fluctuations with an intrinsic origin, which affects both the charge and the magnetic properties of the system, but in competition with the spiral magnetic ordering and the ferroelectricity. Other measurement techniques are requested to reveal the nature of such an competing instability.