Electrodynamics of BaFeAs from infrared measurements under pressure
We report on an infrared study on the undoped compound BaFeAs as a function of both pressure (up to about 10 GPa) at three temperatures (300, 160, and 110 K). The evolution with pressure and temperature of the optical conductivity shows that, by increasing pressure, the mid-infrared absorptions associated with magnetic order are lowered while the Drude term increases, indicating the evolution towards a conventional metallic state. We evaluate the spectral weight dependence on pressure comparing it to that previously found upon doping. The whole optical results indicate that lattice modifications can not be recognized as the only parameter determining the low-energy electrodynamics in these compounds.
pacs:74.25.Gz, 62.50.-p, 78.30.-j
The discovery of superconductivity in pnictidesKami () has triggered tremendous interest in a large scientific community. Despite the large experimental and theoretical effortsreview1 (); review2 (), many questions are left unanswered, in particular concerning the subtle interplay among electronic, magnetic, and structural degrees of freedom.
The common characteristic of these systems is that the undoped parent compounds have a metallic behavior, and undergo a transition from a high temperature paramagnetic phase to an antiferromagnetic spin-density-wave (SDW) state at the temperature ( 150 K), accompanied by a tetragonal to orthorhombic (or monoclinic) structural transition. Upon entering the SDW state, the Fermi surface of these multi-band systems is only partially gapped, therefore the metallic state persists in spite of the reduction of the carrier density. Superconductivity is achieved, below , either by electron (or hole) doping or, in the undoped parent compounds, by applying external pressure Chu2009 (). Furthermore, in the case of superconducting systems, the applied pressure can remarkably enhance Ahilan2009 (). It is now known that structure and properties of chemically doped samples are strongly linkedrotter (); zhao (), for example a decrease of the Fe-Fe distance (that occurs upon chemical doping) has been found to strongly enhance . A similar lattice modification was found also in the case of applied pressureKim2009 () and the idea has been put forward that the structural changes play a major role in determining the electrodynamic properties. It is thus clear that a complex interplay among different degrees of freedom is at work in these systemsYin (), which makes challenging the understanding of their intriguing physical properties.
The complex phase diagram of pnictides has been carefully addressed in particular in systems of the so-called 122 family FeAs ( = Ba, Sr, Ca, Eu): superconductivity is here obtained either by chemical substitutions in the plane (hole doping) or in the Fe-As layer (electron doping), and large effects have been reported as a function of physical pressureKim2009 (); Ahilan2009 (); Duncan2010 (). For the undoped compounds, in particular, it has been shown that pressure progressively lowers , eventually suppressing the structural/magnetic transition, and can originate the insurgence of the superconducting phase at the cost of the SDW state. The same effect can be achieved by means of a chemical pressure by replacing smaller P- atoms for the larger As-atoms, with no effect of charge doping.cao () Most authors agree on the fact that chemical and physical pressure act similarly on these compounds, however it was recently pointed out that in Co-doped compounds the evolution of the Fe-As distance is differentzinth () with physical and chemical pressure (by replacing As with P). As this parameter is considered to be crucial in determining the properties of pnictides, a deeper insight in the equivalence doping-pressure is thus required.
Several infrared studies have been performed on Iron-based superconductors to probe both the normal and the superconducting stateSUST (); Dres_gap (); perucchi (); Wu2010 (). In 122 systems, in particular, studies have been performed in order to asses the effect of the magnetic transition at on the electronic structure. A general consensus has been achieved on the existence in the -plane optical response of at least two electronic subsystems, that can be described by two Drude contributions in the frequency dependent conductivity. In these two contributions, characterized by different scattering rates, the transition to the low-temperature SDW state can origin the opening of energy gaps with transfer of optical spectral weight from low to high frequencies Wu2010 (); Chen2010 ().
Recently particular attention has been devoted to the study of the degree of electronic correlationsBasov_manifesto (); quazilbash (); Schafgans (), that is the ratio between the experimental kinetic energy () and that obtained through band calculations () often performed in the Local Density Approximation. A value close to 1 indicates a conventional metallic state (i.e. with no tendency towards charge localization due to correlations) while the opposite limit / identifies a system with fully localized electrons. Although this interpretation of parameter has to be taken with some cautionarXiv_0910_4117 (); Schafgans (), especially in multi band systems, it has been shown that Basov_manifesto () there is a similar tendency towards localizationBasov_manifesto (); Schafgans () in different families of high- and that this parameter might be a key ingredient in high- superconductivityBasov_manifesto (); Schafgans (). In the above sketched scenario, infrared measurements are of basic interest since the integral of the Drude contribution to the frequency dependent conductivity (i.e. the Drude spectral weight) simply mimics the kinetic energy of the free carries. Moreover, an infrared study performed as a function of temperature and pressure on undoped pnictides, avoiding disorder or local distortions induced by doping, yields information on the pressure-driven changes in the frequency dependent conductivity, i.e. in the charge dynamics.
In the present work, we report on an infrared investigation on the undoped compound BaFeAs as a function of pressure at three temperatures, 110K, 160K and 300K, i.e. above and below T at ambient condition. By evaluating the evolution of the infrared spectral weight with pressure, and comparing it to that found upon doping, we find that lattice modifications can not be recognized as the only parameter determining the low-energy electrodynamics in these compounds.
Ii Experimental details
Infrared reflectance measurements were performed on high quality BaFeAs single crystal ( = 140 K at ambient pressure). The crystals were prepared by the self-flux methodJJ (). Ba pieces, Fe powder and As particles were mixed together according to the ratio of Ba:Fe:As=1:4:4. After mixing, the powder was wrapped with Nb foil and placed in a stainless steel ampoule. The ampoule was evacuated, welded shut, and compressed with a cold isostatic press at 275 MPa to press the powder into a pellet. The heat treatment was done in a hot isostatic press at 193 MPa. The samples were hold for 9 hours at 1120Â°C, and ramped down to 910 Â°C at 2 Â°C/h and then cooled to room temperature in a hour. The pressure was released at the end of the heat treatment. The single crystals were extracted by breaking the reacted pellet. Data were collected on increasing pressure up to a value of 10 GPa, at different temperatures between room- and 110 K.
Pressure-dependent reflectivity measurements were performed with a Diamond Anvil Cell (DAC). A 50 m thick CuBe gasket was placed in a screw-driven opposing-plate DAC, equipped with type IIa diamonds. A small piece of the sample has been cut and placed over a pre-sintered CsI pellet in the hole drilled in the gasket. The good quality of surface obtained by breaking the sample allowed to have a clean sample-diamond (s-d) interface. The DAC was mounted inside a N-flow microscope cryostat from Oxford, allowing us to cool the DAC down to 100 K. In order to determine both pressure and temperature of the sample, a ruby chip was placed inside the sample chamber while a second one was placed on the external face of the diamond. The pressure value was measured in situ by the standard ruby fluorescence Mao () technique. Since the shift of the two fluorescence lines depends strongly on both and , measurements were performed separately on the two ruby chips: on the external one to determine and on the internal for . We remark that, by measuring the -induced shift of the ruby line, we determine precisely the temperature of the sample which is in tight contact with the highly conducting diamond anvil.
The spacing, the linewidth, and the deep hole between the two ruby fluorescence lines are rather delicate markers of the hydrostaticity of the sample environment. Those have been mpnitored up to the highest measured pressure, ensuring us to be in reasonably good hydrostatic conditions.
The incident and reflected light were focused and collected with an optical microscope mounting Cassegrain objectives and equipped with a Mercury- Cadmium- Telluride (MCT) detector and a bolometer. The microscope was coupled to the IFs66/v Bruker Michelson interferometer. This measuring configuration allowed us to explore the 300-12000 cm spectral rangeeprhg (). Due to the small size of the sample, the high brilliance of Synchrotron Radiation at SISSI beamline at ELETTRA storage ring sissi () was exploited, with a great advantage especially for the measurements in the spectral region of the far-infrared. The measurement procedure was the same as described in Refs. v3o5, ; lavagnini, .
Iii Results and discussion
The reflectivity at the sample-diamond interface () is shown in Fig.1 in the 0-6000 cm frequency range for various pressures and temperatures. Data are not shown in the 1600-2700 cm due to the strong phonon absorption of the diamondsdore (). All curves merge at about 6000 cm, showing no pressure or temperature dependence above such frequency. At room temperature, all curves increase for decreasing frequency suggesting a metallic-like behavior and, by applying pressure, the reflectivity is enhanced in the whole energy range pointing to an increased metallic behavior. As (=1.6 GPa, =110K) increases its value in the mid-IR but shows only a small increase at low-frequency almost crossing the reflectivity curve recorded for =1.2 GPa and =300K.
To obtain the optical conductivity (real part of the complex conductivity) we have fitted the reflectivity with a Drude-Lorenz model, taking into account the sample-diamond interface.plaskett ()
This has been done by first modeling the refractive index as follows:Burns ()
where S, and are respectively the oscillator strength, its width and central frequency. The Drude contribution is obtained once . The reflectivity is thus modeled by using:
where is the refractive index of diamond from Ref.dore, .
We considered two Drude terms and three harmonic oscillators (h.o.), as proposed by S.J. Moon and coworkersmazin () and successfully used by other authorsLucarelli (); Hu2008 (). A high frequency h.o. has been used to mimic the absorptions that take place above the highest measured frequency and has been kept constant for all curves. Two Drude terms - one narrow and one broad - are necessary to fit our data: noteworthy this decomposition of the spectra holds for all the compounds of the 122 familyDressel (); Lucarelli (); mazin (). The lack of low-frequency data prevents in our case an unambiguous determination of the spectral weight (SW) of each Drude component, while the SW of their sum results to be well determined.
Two oscillators (that we call and , similarly to the notation in Ref.mazin, ) are needed to achieve satisfactory fittings in the mid-IR region below the SDW transition, while only one () is enough for . In Fig.2 we show the fitting curves together with the experimental data for 300 and 110 K and 1.2 and 1.6 GPa, i.e. in the normal and in the SDW state respectively. For both the states, the resulting optical conductivity and the corresponding components are shown in the lower panel of Fig.2: as the SDW state sets in, there is a depletion of the conductivity below 500 cm and the formation of strong mid-IR absorption bands above this frequency. At much lower frequencies the onset of the narrow Drude is visible. The SDW transition therefore results in a spectral weight transfer from the Drude terms to the and oscillators.
The optical conductivity is plotted in Fig.3 at selected temperatures and pressures. At room temperature the conductivity increases its absolute value with increasing pressure, especially towards low frequency, indicating that the system tends towards a more metallic state. This is clearly evident from the pressure evolution of the Drude SW, shown in the upper panel of Fig.4. On the other hand, as pressure is increased, the SW of the absorption band in the mid-IR at room temperature remains almost constant and then decreases above 9 GPa. The SW of the h.o. decreases with increasing also at 110 and 160 K as expected due to the progressive suppression of the magnetic state with pressure (), as reported by several authors Ahilan2009 (); Mani (); Ishi (). The SW of the oscillator in the mid-IR at 160 K and 110 K, for 6 GPa, is comparable with the SW attained at room temperature, suggesting that above this pressure the system is not undergoing any appreciable electronic phase transition. Once the SDW transition is suppressed, the external parameter that mainly drives the optical response is pressure, with only a small effect due to temperature. Note that, by applying pressure, the overall SW increases and it is not recovered in the measured spectral range.
An accurate determination of the optical conductivity allows to follow the evolution upon external parameters of both free carrier response (Drude terms) and inter-band excitations (harmonic oscillators centered at finite frequency). The outcome of the fitting procedure determines also the integral of the Drude contribution to , i.e. the Drude spectral weight. In order to evaluate the degree of correlation previously introduced, we considered the ratio between the experimental kinetic energy () directly provided by the Drude spectral weight (see Ref.quazilbash, for the complete formula), and the theoretical kinetic energy () givenquazilbash () by the square of the plasma frequency , obtained as a function of pressure in the paramagnetic phase by means of Density Functional Theory (DFT) computationsProfeta (). Despite the light increase of with pressures up to 10 GPa, the resulting / ratio increases smoothly on increasing pressure indicating that the system is shifting towards a conventional metallic state. It is worth noticing that the value that we find at the lowest measured pressure () is in good agreement with what is found (0.25-0.29) at ambient conditions by other authorsBasov_manifesto (); Schafgans (). A comparison between pressure and doping dependence of the degree of correlation is impossible, since its value was only reported for BaFeCoAs Schafgans () and its evolution with doping is not reported in literature.
A different, fully experimental approach to evaluate the degree of correlation has been proposed by L. Degiorgi and coworkersLucarelli (); Degiorgi (): instead of comparing the experimental kinetic energy with a theoretical value, they discuss the ratio between the experimental kinetic energy given by the Drude spectral weight and the SW of including both Drude and mid-IR contributions (). They find a degree of correlation lower than 0.65 for the superconducting samples (Ba(CoFe)As with ) and higher () as the system becomes overdoped. In order to compare the effect of pressure and Co-doping on the degree of correlation we have also calculated the ratio . For this comparison we used the scaling relation proposed by S. Drotzinger et al.Drotz (): by means of transport and magnetic measurements in the superconducting region, they suggested P/x 1.275 GPa/Co. In Fig.6 we plot the ratio for our data in the paramagnetic phase together with data (also in the paramagnetic phase) on Co-doped compounds (from Ref. Lucarelli, ).
We remark that we are not putting the accent on the differences of the absolute value of this parameter (that could depend also on details of the high-frequency extrapolation when performing KK analysis) but rather on its different evolution with doping and pressure. Supposing to start at the same value for undoped compound at ambient conditions, for low doping/pressure, chemical doping and pressure act differently: the former yields values lower than those given by pressure, at odd with the fact that upon inserting Co in the FeAs planes does not only modify the lattice parameters but also injects one carrier per dopant ion. It was shown that both pressure and doping suppress the magnetic/structural transitions but only certain dopants (i.e. certain doping levels) allow superconducting pairingcanfield_TM (). We know that upon doping BaFeAs with Co, for x0.12, the SW of the mid-IR absorption bands is strongly increased, at odd with the SW of the Drude termLucarelli (), suggesting that spin fluctuations are enhanced while long range magnetic order is suppressed. This probably is one of the key factors in originating superconductivity once the structure is modified enough due to the random insertion of Co ions. On the other hand, by applying pressure, the magnetic/structural transition is suppressed but the SW of the mid-IR contributions is reduced, suggesting that the magnetic fluctuations are lowered, probably due to reduced anisotropy and weaker nesting sacchetti (). The reduction of lattice parameters is enough for quenching the SDW state (and, at lower temperatures, to originate superconductivity), even though the system tends towards a fairly conventional metallic state. For x 0.12 the slope of values for Co-doped samples becomes similar to what we have measured under pressure, suggesting that once the system is in the overdoped regime, a common mechanism is driving the suppression of superconductivity.
In conclusion, we have studied the infrared response of BaFeAs under pressure down to 110 K. We remark that pressure dependent IR measurements can give the unique opportunity to go beyond the zero frequency conductivity, providing informations on the low energy charge dynamics. We observe no signature in the optical conductivity of SDW ordering in this temperature range when P 3 GPa, in agreement with the results of previous transport measurements. It has been possible to follow the evolution with pressure of the spectral weight of both Drude and mid-IR contributions, showing that the system tends towards a conventional metallic state and that the absorptions associated with fluctuative magnetic order are lowered by increasing pressure. On the basis of the obtained results we could compare the effect of pressure and Co-doping on the degree of correlation. The obtained results reported in Fig. 6 indicate that, in the underdoped regime, pressure and Co-doping favor the onset of superconductivity (destroy long-range magnetic order), by following different mechanisms displaying opposite effects on the degree of correlation parameter (see Fig.6). On the other hand, at high pressure/doping the correlation degree monotonically increases in both cases, thus suggesting that an increased itinerancy is the common mechanism for reduction in the overdoped regime. Our results indicate that the lattice distortions can not alone explain the evolution of the electrodynamics of underdoped compounds compared to that of the undoped sample under pressure since the routes taken to suppress the SDW and favour superconductivity are different in the two cases. A more realistic description of the interplay between different degrees of freedom is needed to understand the physics of pnictides.
Acknowledgements.We wish to thank M. Putti for providing the samples, G. Profeta and A. Continenza for useful discussions and for providing values computed at a number of pressures prior to publication. We acknowledge financial support from PRIN project No. 2008XWLWF9-002 and from CARIPLO Foundation (Project No. 2009-2540). The work at FSU was supported by NSF DMR-1006584 and 0084173, and by the State of Florida.
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