Improper multiferroicity and colossal dielectric constants in Bi$_{2}$CuO$_{4}$

TL;DR

This study reveals that Bi$_{2}$CuO$_{4}$ is an improper multiferroic with colossal dielectric constants, showing complex magnetic and dielectric behaviors including short-range order and non-Debye relaxation.

Contribution

It demonstrates the coexistence of multiferroicity and colossal dielectric constants in Bi$_{2}$CuO$_{4}$, highlighting its potential for multifunctional applications.

Findings

Bi$_{2}$CuO$_{4}$ is an improper multiferroic with a ferroelectric state near magnetic transition.

Presence of polar and magnetic short-range order above Neel temperature.

Colossal dielectric constants with grain and grain boundary contributions exhibiting non-Debye relaxation.

Abstract

The layered cuprate Bi$_{2}$CuO$_{4}$ is investigated using magnetic, dielectric and pyroelectric measurements. This system is observed to be an improper multiferroic, with a robust ferroelectric state being established near the magnetic transition. Magnetic and dielectric measurements indicate the presence of a region above the antiferromagnetic Neel temperature with concomitant polar and magnetic short range order. Bi$_{2}$CuO$_{4}$ is also seen to exhibit colossal dielectric constants at higher temperatures with clearly distinguishable grain and grain boundary contributions, both of which exhibit non-Debye relaxation.

Figures

a depicts the temperature dependence of the broadening parameter $\alpha$ as determined by our fitting procedure for both the grain and grain boundary contributions. The increase in the value of $\alpha$ with increasing temperature can be ascribed to the recovery of a Debye like behavior of non-interacting dipoles when the effective co-operativity is reduced due to thermal fluctuations. On the other hand, the temperature dependence of the dielectric strength ($\Delta\epsilon$) determined from our fitting is seen to be very different for the grain and grain boundary contributions, as is seen in

Equations

$$\begin{split}\epsilon^{*}(\omega)=-i\ \Bigg{(}\frac{\sigma_{0}}{\epsilon_{o}\omega}\Bigg{)}^{N}+\sum_{k=1}^{2}\Bigg{[}\frac{\Delta\epsilon_{k}}{\bigg{(}1+(i\omega\tau_{k})^{\alpha_{k}}\bigg{)}^{\beta_{k}}}+\ \epsilon_{\infty k}\Bigg{]}\end{split}$$

Full text

I Introduction

The discovery of high temperature superconductivity in electron and hole doped cuprates Bednorz and Müller (1986); Tokura et al. (1989) have ensured that they have remained at the forefront of experimental and theoretical investigations in condensed matter physics. However, unconventional superconductivity is not the only exotic phenomena discovered in this class of materials. For instance, the under-doped cuprate La2CuO4+x was reported to exhibit a low temperature ferroelectric state arising as a consequence of a distortion in the CuO6 octahedra, with an associated magnetoelectric coupling being tuned through the antisymmetric Dzyaloshinskii-Moriya interaction Viskadourakis et al. (2012, 2015). As is well known, the magnetoelectric multiferroics refer to a class of materials where magnetic and polar orders co-exist, and such materials are in vogue for the rich physics associated with these novel states as well as potential device applications Eerenstein et al. (2006); Cheong and Mostovoy (1990); Wang et al. (2009). Of special interest are systems known as improper (or Type-II) multiferroics, where ferroelectricity arises as a direct consequence of magnetic order Kimura et al. (2003); Lawes et al. (2005); Kimura et al. (2006, 2005); Yamasaki et al. (2006); Taniguchi et al. (2006).

Layered cuprates of the form $R_{2}$CuO4 are known to crystallize in three different structural motifs, typically dictated by the ionic radius of the $R$ site ion. When $R=$ La, a highly distorted network of corner sharing CuO6 octahedra is observed (called the $T$-phase), whereas systems with smaller $R$ site ions (Nd, Sm or Pr) prefer a corner shared network of square planar CuO4 units (called the $T^{\prime}$-phase)Tokura et al. (1989). Some systems which constitute of both large and small $R$ site ions are seen to crystallize in a phase which is made up of half a unit cell each of the $T$ and $T^{\prime}$ phases, and are typically referred to as the $T^{*}$ phase in cuprate literature Tokura et al. (1989); Sawa et al. (1989); Cheong et al. (1989); Akimitsu et al. (1988). Interestingly, the closely related Bi2CuO4 system exhibits a very different structure, though the ionic radii of Bi3+ (1.31Å) is very similar to that of La3+ (1.30Å). This is presumably due to the strongly covalent nature of the Bi-O bond, which reduces the effective co-ordination of the $R$ site from 9 to 6 Garcia-Munoz et al. (1990); Pisarev et al. (2010). Bi2CuO4 is reported to crystallize in a tetragonal symmetry (space group $P4/ncc$) and is now established to be a 3D antiferromagnet, with a transition temperature ($T{{}_{N}}$) $\approx$ 50 K Garcia-Munoz et al. (1990); Yamada et al. (1991). As is shown in Fig.1, the structure of Bi2CuO4 is characterized by the presence of seemingly isolated CuO${{}_{4}}{{}^{6-}}$ square plaquettes which are staggered in a chain-like fashion along the crystallographic $z$ axis. Unlike other members of the $R{{}_{2}}$CuO4 family, where the magnetism is driven by conventional Cu-O-Cu superexchange and Cu-O-O-Cu extended superexchange pathwaysSzymczak et al. (1994), it has been suggested that in Bi2CuO4, the magnetism is driven by four dissimilar Cu-O-Bi-O-Cu paths Garcia-Munoz et al. (1990); Ong et al. (1990); Aïn et al. (1993). The magnetic structure has also been determined using neutron diffraction, and is thought to be made up of ferromagnetically ordered spins along the $c$ axis, with these chains being antiferromagnetically coupled to the neighbouring onesGarcia-Munoz et al. (1990); Attfield (1989). Though a preliminary report exists on the dielectric properties of this system Yoshii et al. (2011), the behavior of the dielectric properties in the vicinity of the magnetic transition remains to be investigated. The discovery of multiferroicity in the layered cuprates clearly warrants a more serious investigation of Bi2CuO4, especially since the presence of the 6$s{{}^{2}}$ lone pair on the Bi3+ ion could offer an additional means of inducing ferroelectric polarization in this system akin to that known in the perovskite BiFeO3 Khomskii (2009).

Here, we investigate the magnetic, dielectric and pyroelectric properties of Bi2CuO4, and observe that this system is a hitherto undiscovered multiferroic, with a ferroelectric polarization being set up in close vicinity to the magnetic phase transition. At temperatures well above the magnetic ordering temperature ($T{{}_{N}}$), this system exhibits a colossal dielectric behavior, and two distinct relaxation peaks in the dielectric loss arising from the grain and the grain boundary response can be clearly identified.

II Experimental

Polycrystalline specimens of Bi2CuO4 were prepared by the conventional solid state reaction method by using Bi2O3 and CuO as the ingredients. Stoichiometric amounts of these oxides were mixed and heated at 700oC in air for 24 hours, following which they were pelletised and reheated at 780o for another 24 hours. Powder X-ray diffraction data was recorded using a Bruker D8 Advance diffractometer with CuKα source under the continuous scanning mode. Magnetization measurements were performed using a Quantum Design (MPMS-XL) SQUID magnetometer. Temperature dependent dielectric measurements were performed by using Alpha-A High Performance Frequency Analyzer from Novocontrol Technologies. The dielectric measurements under magnetic field were performed by using the Manual Insertion Utility Probe of the MPMS-XL magnetometer. During the dielectric measurements, 1 Volt excitation signal was used to probe the dielectric response. The pyroelectric measurements were performed using a Keithley Sourcemeter (Model 2612B) and a Picoammeter (Model 6482) and the ferroelectric polarization was derived from the pyroelectric current by integrating over time.

III Results and Discussions

The dc magnetisation of Bi2CuO4 as measured in the Zero Field Cooled (ZFC) protocol is depicted in Fig. 2. A clear antiferromagnetic-like transition is observed at $\approx$ 50 K, in good agreement with previous reports Yoshii et al. (2011). The magnetic transition temperature of Bi2CuO4 is smaller than that of its La and Nd based counterparts, presumably as a consequence of the larger exchange path which drives magnetic long range order. The inset of Fig. 2 shows a $MH$ isotherm as measured at 2 K, which is typical of a robust antiferromagnet, with no sign of any saturation up to the highest applied field of 5 Tesla. At temperatures in excess of 150 K, the inverse of the susceptibility follows a Curie-Weiss fit, giving $\theta$ = -68.4 K and an effective magnetic moment of $\mu_{eff}$ = 1.76 $\pm$ 0.01 $\mu_{B}$, which matches very well with the spin-only value (1.73$\mu_{B}$) expected from a Cu*2+*system. Deviation from linearity extends to 2\times$$T_{N}, indicating that short range correlations persist well above the transition temperature as is shown in Fig. 3a.

Interestingly, the influence of these correlations is also evident in the dielectric measurements, and the loss tangent exhibits a clear relaxation peak in this regime (Fig. 3b). The temperature at which the peak is observed shifts to lower temperatures with decreasing measurement frequency, which is a typical signature of dielectric relaxation in polar glasses or relaxor ferroelectrics Cross (1987), with the relaxation time following a Vogel-Fulcher-Tamman (VFT) behavior given by $\tau={\tau_{0}}\exp\frac{E}{K_{B}(T-T_{f})}$. Here $\tau$ is the relaxation time, $\tau_{0}$ is the pre-exponential factor, $E$ is the activation energy of the process and $K_{B}$ is the Boltzmann constant. $T$ refers to the temperature at which the maxima is observed, and $T_{f}$ is the static freezing temperature where the dynamics of the relaxing entities become frozen. As is shown in the inset of Fig. 3a, this relaxation process conforms to the VFT model, with an activation energy of 5.52 $\pm$ 2.06 meV, and a $T_{f}$ of 41.2 $\pm$ 3.7 K. This feature can originate from polar nano regions (PNR) coupled to the short ranged magnetic correlations, and could be looked upon as a possible precursor to the onset of long range ferroelectric order. Interestingly, we do not observe any signature of this relaxation in the real permittivity, presumably due to a small change in the dielectric constant as a function of frequency. However, a prominent peak is observed in the real part of the the dielectric susceptibility $\epsilon^{\prime}$($T$) in the vicinity of the magnetic transition, indicating a coupling of the electric and magnetic order parameters in this system (Fig. 4). Moreover, within the magnetically ordered state, $\epsilon^{\prime}$($T$) also exhibits a clear magnetic field dependence, indicating that the polar state can be tuned as a function of the applied magnetic field. We note that the change observed in the dielectric constant on applying a magnetic field is not very large, and is of the order of $\approx$ 0.1 % at $T=$ 10 K and $H=$ 5 Tesla.

Confirmation of the multiferroic nature of Bi2CuO4 is provided by temperature dependent measurements of the pyroelectric current, as is shown in Fig. 5. These measurements were done in the standard parallel plate geometry with different poling fields, and the pyroelectric current was measured at a warming rate of 10 K/min (Fig. 5a). A peak in the pyroelectric current was detected in close proximity to the magnetic ordering temperature, with its sign being flipped on reversing the direction of the applied electric field, thus signifying a true ferroelectric state. The effective ferroelectric polarization values were deduced to be of the order of 120 $\mu C/m{{}^{2}}$ at a poling field of 1.73 kV/cm as is shown in Fig. 5b. These measurements were also validated by repeating the measurement with different warming rates (Fig. 5c), with the invariance of the ferroelectric transition temperature ruling out possible experimental artifacts Kohara et al. (2010).

Magnetically induced ferroelectric order can either arise from the antisymmetric exchange interaction as in the case of spiral magnets, or from the symmetric exchange striction as in the case of collinear magnets. The magnetic order in Bi2CuO4 is reported to be collinear, with spins being aligned along the crystallographic $c$ axis with ferromagnetic intra-chain and antiferromagnetic inter-chain interactions. Our dc susceptibility data also shows that the obtained effective magnetic moment per Cu site (1.76 $\pm$ 0.01$\mu_{B}$) is basically the spin-only moment (1.73$\mu_{B}$), thus indicating that the orbital contribution to the magnetic moment arising from the spin orbit coupling is negligible. Moreover, an early experimental report Attfield (1989) clearly shows that Bi2CuO4 exhibits a hysteretic exchange-striction driven discontinuity in both the $a$ and $c$ lattice parameters across the magnetic phase transition, though the symmetry of the crystallographic unit cell remains unchanged. All these factors point towards Bi2CuO4 being an exchange striction driven improper multiferroic. The values of ferroelectric polarization in this system are also comparable to that observed in polycrystalline specimens of other exchange striction multiferroics like CdV2O7 and HoMnO3 Giovannetti et al. (2011); Lorenz et al. (2007). We note that polarization measurements performed in polycrystalline specimens at moderate poling fields do tend to underestimate the true polarization value associated with the ferroelectric state. Though the strongly covalent Bi-O bond would be expected to be influenced by the exchange striction driven structural distortion, the data at our disposal does not indicate an appreciable contribution from the steriochemical activity of the Bi3+ lone pair to the effective polarization. For instance, polarization values measured in polycrystalline specimens of the lone-pair multiferroic BiFeO3 Shvartsman et al. (2007) are more than two orders of magnitude higher than that measured in Bi2CuO4. However, measurements on single crystalline specimens and additional theoretical inputs would be needed to conclusively elaborate on the role of the Bi3+ lone pair in this ferroelectric state.

With the multiferroic nature of Bi2CuO4 having been established, we now focus on the high temperature dielectric properties of this system. There have been reports of large dielectric constant values in related cuprate systems Park et al. (2005), though an earlier report on Bi2CuO4 reported rather modest values ($100-500$) of the dielectric constant at room temperatures. Fig. 6 shows the dielectric constant and loss tangent measured as a function of temperature at different frequencies. The room temperature value of dielectric constant in our Bi2CuO4 specimen is of the same order as that reported for other cuprates Peng and Liang (1994); Salame et al. (2014) and substantially higher than that reported for this system earlier Yoshii et al. (2011). $\epsilon^{{}^{\prime}}$($T$) exhibits two steps from low-temperature values ($\approx 400$) to intermediate higher values ($\approx$2000) succeeded by another step up-to colossal values of the order of 104. Correspondingly, the loss tangent shows two distinct relaxation peaks, both of which shift towards higher temperatures on increasing the measurement frequencies (Fig. 6b). These are features typical of materials exhibiting Colossal Dielectric Constants (CDC), with the cubic CaCu3Ti4O12 being a popular example Subramanian et al. (2000); Homes et al. (2001). Current wisdom is that this behavior can arise as a consequence of the interfaces between grain and grain boundaries which act as parallel plate capacitors with large dielectric constants. Originally proposed by Maxwell and Wagner in the context of heterogeneous specimens with varying dielectric constants, the dielectric behavior of such systems can be represented to arise from a combination of two lossy dielectrics in series. This internal barrier layer capacitance (ILBC) dominates the measured dielectric permittivity at higher temperatures and lower frequencies Sinclair et al. (2002); Lunkenheimer et al. (2004). At lower temperatures (and higher frequencies), the relative contribution from the layer capacitance reduces, allowing one to measure the contribution arising from the bulk Lunkenheimer et al. (2002). In our Bi2CuO4 specimen, we clearly observe two distinct features arising from these different contributions. The influence of the ILBC is observed in measurements with frequencies varying from 1 Hz to 400 Hz, above which this feature clearly moves to temperatures beyond 300K whereas at lower temperatures (and higher frequencies) the contribution arising from the grain can be easily discerned. We note that the value of the loss tangent is less than 1 for exciting frequencies in excess of 100 Hz, which makes Bi2CuO4 a more attractive candidate for applications in comparison with most other rare earth cuprates.

These separate contributions to the effective dielectric constant can also be observed when the dielectric data is plotted in the form of Cole-Cole plots, with the frequency dependent imaginary part of the dielectric constant $\epsilon^{\prime\prime}$($\omega$) being plotted as a function of the real part $\epsilon^{\prime}$($\omega$) at different temperatures. Fig. 7 depicts the Cole-Cole plots as measured in Bi2CuO4 in three different temperature regimes. At 150 K, a single semicircle is seen, indicating the presence of a single relaxation process which in this case arises from the contribution of the grains. At 200 K on the other hand, two distinct relaxation processes are observed, with the high frequency semicircle corresponding to the intrinsic (grain) contribution, and the low frequency contribution arising from grain boundaries. At even higher temperatures (225 K), an additional upturn is observed at lower frequencies, which is a signature of the electrode polarization effect which presumably arises as a consequence of the accumulation of charges (the so called space-charge region) at the metallic electrodes. The presence of two relaxation processes is also clearly reflected in the frequency-domain data as is shown in Fig. 8. In order to deduce quantities of interest, like the relaxation times, dielectric strengths and the peak parameters corresponding to the grain and grain boundary contributions, we have fitted the dielectric data with a generalized Hivriliak-Negami (H-N) function using the WinFit software from Novo-Control GmbH. Here, the frequency dependent complex dielectric permittivity is given by

[TABLE]

where $\omega=2\pi f$ is the probed frequency, $\epsilon_{o}$ is the permittivity of free space, $\tau$ is the associated relaxation time, $\sigma_{o}$ is the conductivity term resulting in the low frequency behavior of $\epsilon^{{}^{\prime\prime}}$, and N is the slope of $\epsilon^{{}^{\prime\prime}}(\omega)$ at lower frequencies ( $\approx$ 1 in most cases). The dielectric strength is denoted by $\Delta\epsilon=\epsilon{{}_{S}}-\epsilon{{}_{\infty}}$, where $\epsilon{{}_{S}}$ and $\epsilon{{}_{\infty}}$ refer to the low and high frequency dielectric permittivity. $\alpha$ and $\beta$ are broadening and asymmetry parameters linked to the relaxation peaks respectively, and can take values between 0 and 1. The H-N function modifies to a standard Debye function for $\alpha=\beta=$1. On the other hand, it modifies to a Cole-Cole function for $0<\alpha<1$ and $\beta=$1; and to a Cole-Davidson one for $\alpha=$1 and $0<\beta<1$. The fits to our frequency domain data are depicted in Fig. 8, and both the real permittivity and the loss tangent is seen to fit well to the Cole-Cole functional form. Fig. 9a depicts the temperature dependence of the broadening parameter $\alpha$ as determined by our fitting procedure for both the grain and grain boundary contributions. The increase in the value of $\alpha$ with increasing temperature can be ascribed to the recovery of a Debye like behavior of non-interacting dipoles when the effective co-operativity is reduced due to thermal fluctuations. On the other hand, the temperature dependence of the dielectric strength ($\Delta\epsilon$) determined from our fitting is seen to be very different for the grain and grain boundary contributions, as is seen in Fig. 9b. In the high temperature regime, a para-electric like decrease of the dielectric strength of the grain is observed as a function of increasing temperature. However, with increasing temperatures, the $\Delta\epsilon$ for the grain boundary contribution is seen to initially increase and then settle into a relatively $T$ independent value. The latter can be explained by invoking a scenario where increasing $T$ liberates more free charge carriers which are stuck at the grain boundaries, thus contributing to the extrinsic polarization. The relaxation times for both the grain and grain boundary processes have been calculated, and they are seen to confirm to an Arhenius type of activated behavior as is depicted in Fig. 9c. Data was fit using $\tau={\tau_{0}}\exp\frac{E}{k_{B}T}$, where $\tau$, $\tau{{}_{0}}$, $E$ and $k_{B}$ refer to the relaxation time, pre-exponential factor, the activation energy, and the Boltzmann constant respectively. The linear fit shown in the inset provides activation energies of 0.207$\pm$0.008 eV and 0.352$\pm$.003 eV for the grain and grain boundaries respectively. Our observation that the activation energy of the grain-boundary is larger than that of the grain is consistent with that reported for other ceramic systems Salame et al. (2014); Sinclair et al. (2002).

IV Conclusion

In summary, we have investigated the cuprate Bi2CuO4 using magnetic, dielectric and pyroelectric measurements. We observe that a robust ferroelectric state is established in the vicinity of the magnetic transition, making this system a hitherto unreported exchange striction driven improper multiferroic. Magnetic and dielectric measurements reveal a regime of short range magnetic and polar order at $T>T{{}_{N}}$. At higher temperatures we find typical signatures associated with colossal dielectric constant materials, along with two distinct grain and grain boundary non-Debye type relaxations.

V Acknowledgements

The authors thank A. M Awasthi for extending experimental facilities for dielectric measurements, and for a critical reading of the manuscript. J.K. acknowledges DST India for a SERB-NPDF. S.N. acknowledges DST India for support through grant no. SB/S2/CMP-048/2013. The authors acknowledge funding support by the Department of Science and Technology (DST, Govt. of India) under the DST Nanomission Thematic Unit Program