Influence of pressure on the transport, magnetic, and structural properties of superconducting Cr0.0009NbSe2 single crystal

We investigate the superconducting critical current density (Jc), transition temperature (Tc), and flux pinning properties under hydrostatic pressure (P) for Cr0.0009NbSe2 single crystal. The application of P enhances Tc in both electrical resistivity (∼0.38 K GPa−1: 0 ≤ P ≤ 2.5 GPa) and magnetization (∼0.98 K GPa−1: 0 ≤ P ≤ 1 GPa) measurements, which leads to a monotonic increase in Jc and flux pinning properties. The field-dependent Jc at various temperatures under P is analyzed within the collecting pinning theory and it shows that δTc pinning is the crossover to δl pinning above the critical pressure (Pc ∼0.3 GPa). Our systematic analysis of the flux pinning mechanism indicates that both the density of pinning centers and pinning forces greatly increase with the application of P, which leads to an enhancement in the vortex state. Structural studies using synchrotron X-ray diffraction under pressure illustrate a stable hexagonal phase without any significant impurity phase and lattice parameter reduction with P shows highly anisotropic nature.


Introduction
The interaction of superconductivity and density wave orders is an essential part of various superconductors such as high-T c cuprates, Fe-based, BiS 2 -based, topological and twodimensional (2D) layered superconductors. 1-8 2D transition metal dichalcogenide (TMDC) materials have attracted remarkable attention because of their exclusive properties that exhibit many features similar to those seen in high-T c cuprates, 1,2 MgB 2 , 9 Fe-based 3,10 and BiS 2 -based 4,5,11 and 2D layered 7,8,[12][13][14][15] superconductors. The interplay of the static modulation of the electronic density of states close to the Fermi level and superconducting properties at lower temperatures in the layered TMDC has been of interest for a few decades. 7,8,12,13,16,17 Most of these TMDCs have been built by three atomically dense layers stacked on each other like a sandwich that are held together by weak van der Waals forces, which results in a small coupling parameter between the layers. The spontaneous formation of periodic lattice distortions and charge density waves (CDWs) can be thermodynamically favorable under certain conditions in low dimensional metals, where the wave vector is generally known to depend on the nesting properties of the Fermi surface. Niobium diselenide (NbSe 2 ) has one of the most studied van der Waals interactions, rendering it feasible to achieve a free-standing ultrathin structure that exhibits both CDW and superconductivity at low temperatures. 7,12 The coupling between two long-range orders is responsible for the observation of the elusive Higgs bosonic amplitude mode of the superconductor, as revealed by Raman scattering on NbSe 2 . 18,19 The crystal structure of TMDC materials is made up of hexagonal Se-Nb-Se sandwiches, which are united through weak forces, prominent hexagonal layers, and strong anisotropic properties. The changes in the electronic properties 20,21 are produced by altering the lattice parameters, 22 compositional tunings such as doping, 23,24 irradiation 25,26 and intercalation between the layers, 13,[27][28][29][30] and applying external hydrostatic pressures. 3,8,31,32 The superconducting nature of TMDC has been studied intensively due to scarce magnetic and electronic properties and potential in technological applications. The superconducting properties can be modied by the intercalation of magnetic and non-magnetic impurities in NbSe 2 , such as M x -NbSe 2 (M ¼ Cu, Fe, Co, Mn, Sn, Cr). 12,13,[27][28][29][30] The application of external pressure has been the most advantageous compared to other perturbations such as chemical doping, lattice disorder, impurity phases, and phase separation. The application of pressure uctuates the interstitial distance and changes the electronic band structure of the material without providing any chemical stability. The variation in superconducting properties under pressure leads to lattice instability, which leads to the understanding of the superconducting mechanism of various materials such as high T c -cuprates, pnictides, and TMDC; these materials are most suitable to examine with theoretical models. By the application of external pressures (hydrostatic, quasihydrostatic, and uniaxial) to explore variation in physical properties and create new ground states for various types of matter. The uniaxial pressure effects evidently indicate that the in-plane compression is mainly accountable for reduction in the tilt angle and, hence, for the suppression of the pinning potential strength of cuprates. 33 The enhancement in the superconducting nature with pressure has been reported with the highest T c (164 K) in Hg-based cuprates 34,35 and conventional superconducting T c (203 K at P $200 GPa) induced by the application pressure in sulfur hydride systems. 36 The application of external P is responsible for the increment in hole density in the superconducting layers of 11 and 122 families of pnictides. 10,37,38 The effects of pressure on the superconducting and structural properties of oxypnictide compounds have been extensively explored. 3,39,40 The external pressure induces the uctuations in the Fermi surface (FS) with a positive pressure coefficient in NbS 2 . 41 Hydrostatic pressure induces a transition from the spatial variation in the superconducting transition temperature pinning (dT c ) to the spatial variation in the mean free path pinning (dl) mechanism in NbSe 2 (ref. 8) and FeSe. 42 The application of external P induces both T c and CDW in TaS 2 and TaSe 2 . 43 The superconducting uctuations such as enhancement in the superconducting T c , CDW instability, narrow superconducting transition width (DT), critical current density, and ux pinning properties are observed with the application of external P on TMDC compounds. 8,31,32,41,44,45 Flux pinning is strongly related to vortex motion, which is an interesting physical phenomenon and plays a crucial role in practical applications. Cr x NbSe 2 is a type II superconductor and a versatile model system to study the interplay of magnetic interaction, superconducting, structural, and ux pinning properties at ambient and high pressures. In this present work, we investigated superconducting properties such as T c , upper critical eld (H c2 ), lower critical eld (H c1 ), irreversible eld (H irr ), superconducting critical current density (J c ), and ux pinning of the superconducting Cr x NbSe 2 single crystal at ambient and high pressures ($1 GPa). Further, structural properties under ambient and high pressures at low temperature (9 K) were also investigated using synchrotron radiation to have a better understanding of the crystal structure and to correlate it with the superconducting properties.

Experimental procedure
Single crystals of Cr intercalated NbSe 2 were grown using the chemical vapor transport method with iodine as the transport agent. The magnetic, superconducting, and ux pinning properties of Cr x NbSe 2 single crystals at ambient conditions have been recently reported. 27 Structural measurements at ambient pressure were performed at X-ray diffraction (XRD) beamline BL-11, INDUS-II synchrotron radiation source (Raja Ramanna Centre for Advanced Technology, Indore, India) with Angle Dispersive X-ray Diffraction (ADXRD) beamline (BL-11). The samples were powdered, drop cast on copper-coated carbon grids aer sonication in iso-propyl alcohol for 1 h, and air-dried for 5 h. Microstructural analyses of the sample were performed using a Tecnai G2 30ST (FEI) transmission electron microscope. Both temperature and eld dependence of DC magnetization measurements (M(T) & M(H)) under various hydrostatic P was carried out using Physical Property Measurement System-Vibrating Sample Magnetometer (PPMS-VSM, Quantum Design, USA). The external P of up to $1 GPa was generated in the clamp type miniature hydrostatic pressure cell, which was made of non-magnetic Copper-Beryllium alloy. Fluorinert FC #70 and FC #77 mixture (1 : 1) was used as a pressure transmitting medium and in situ pure Sn was loaded with the sample in a capsule; actual P was calculated from the M(T) measurements of Sn under various P at 10 Oe. Electrical transport measurements were carried out in PPMS using the standard four-probe technique both at ambient and high pressure up to $2.5 GPa. The pressure cell consists of a double-wall cylinder, which is made of hardened BeCu (outer) and NiCrAl (inner) alloy, and the obturator is made of hardened BeCu alloy. Daphne #7474 was used as the pressure medium and the pressure cell was calibrated with the Bi-phase transitions at room temperature.
To understand the valence band (VB) evidence of the Cr x -NbSe 2 single crystalline sample, ultraviolet photoelectron spectroscopy (PES) measurements were performed at the Angle-Resolved Photoelectron Spectroscopy beamline in BL-3, INDUS-II with synchrotron radiation source (RRCAT, Indore, India). Raman measurements at low temperature were carried out using LABRAM HR-800 spectrometer from Horiba JY, Japan equipped with a 488 nm excitation source, an 1800 g mm À1 grating, and a CCD detector; temperature stability of AE1 K was maintained during the measurements. Structural measurements under high pressure at room temperature were performed at the ADXRD beamline BL-11, INDUS-II synchrotron radiation source (RRCAT, Indore, India). Powder X-ray diffraction measurements under high pressure at room temperature were carried out using a Mao Bell-type diamond anvil cell (DAC). A pre-indented thickness of 0.2 mm Cu material served as the gasket, a mixture of methanol-ethanol (4 : 1) was used as the pressure medium, and the sample chamber was lled with both Cr x NbSe 2 powder sample and a ruby chip. The ADXRD patterns were measured using a beam wavelength of 0.4828 A with a sensitive detector (Mar3450). The actual P in DAC was measured using the ruby uorescence technique.
were estimated with pseudo-Voight function for peak prole tting using FullProf soware 46 and the obtained lattice parameter values (300 K) are a ¼ b ¼ 3.4432(5) A, c ¼ 12.5467(3) A, and V ¼ 128.825 A 3 with tting parameters c 2 ¼ 3.493, R wp ¼ 0.05, and R p ¼ 0.07. Further, the XRD patterns conrmed that there is no impurity peak and secondary phase due to Cr intercalation in NbSe 2 . Photoelectron spectroscopy (PES) was performed using a synchrotron radiation source (100 eV photons) at room temperature and 3d core levels of Se, 4p level of Nb, and 3p level of Cr were measured aer subtraction of background using the standard Shirley method, as shown in Fig. 1(b). 47 The binding energy of Se 3d 5/2 and 3d 3/2 peaks are located at $53.05 and $53.8 eV, respectively, and designate the occurrence of two most important Se species peaks separated by $0.75 eV, when deconvoluted using typical constrained parameters. The peak binding energies of $30.99 and $32.77 eV originate from Nb 4p 1/2 and 4p 3/2 , respectively, 48,49 and the Cr 3p level is observed at $42.16 eV. 50 These results conrm the presence of Nb, Se, and Cr elements in the as-grown single crystal. The stacking of (004) planes of the NbSe 2 crystal structure (ref: JCPDS card no. 01-070-5612, 72-0864, and 72-1618) can be easily identied in the HRTEM images ( Fig. 1(c)). The interplanar distance corresponds to the (004) plane, which was calculated to be approximately 0.31 nm, using the ImageJ soware. This was further established both by the corresponding Fast Fourier Transform (FFT) and Selected Area Electron Diffraction (SAED) patterns. The SAED pattern clearly shows the single-crystal diffraction characteristics with sharp and discrete Bragg reections. The characteristic Bragg reections corresponding to the NbSe 2 crystal structure could be identied in the SAED pattern, as shown in Fig. 1(d). The EDX results show the presence of Cr, Nb, Se, Cu, and C, where the signals of Cu and C are due to the copper-coated carbon grid and the signals of Cr, Nb, and Se are from the sample ( Fig. 1(e)). Quantitative analysis shows the atomic percentage of Cr, Se, and Nb in the sample to be 0.10%, 64.96%, and 34.93%, respectively; the elemental compositions are present in the stoichiometric ratios of the as-grown crystals and no impurity was found in this sample. Fig. 2(a), (c), and (d) show the temperature dependence of resistivity (r(T)), superconducting region in the temperature region 5 to 8 K at various hydrostatic P up to $2.5 GPa, and dc magnetization (M(T)) in zero-eld cooling and eld cooling at H ¼ 20 Oe under ambient and high pressures up to $1 GPa in the vicinity of T c on the Cr 0.0009 NbSe 2 single crystal. We found that the in-plane resistivity decreases from 0.56 mU cm to 0.061 mU cm as temperature decreases from 300 to 6 K and then drops suddenly to zero due to the manifestation of superconductivity, and the residual resistance ratio (RRR ¼ r 300 K /r T c ) is 9.2, which indicates that the quality of the single-crystal sample is good. The superconducting T c from r(T) measurements is dened using different criteria such as T on c , T mid c , and T off c . The onset of superconducting transition temperature (T on c ) is determined from the intersection of two extrapolated lines; one is drawn through the resistivity curve in the normal state just above the appearance of superconductivity and the other line is drawn through the sheer part of the resistivity curve in the superconducting state. The midpoint of superconducting transition (T mid c ) is estimated from the peak position of dr/dT vs. T, i.e., the temperature at which r displays the maximum value and the offset of superconducting transition (T off c ) is estimated from the temperature at which resistance becomes zero. The Fig. 1 (a) Powder X-ray diffraction was measured at room temperature using synchrotron radiation source, (b) photoelectron spectrum at 300 K recorded at 100 eV photon energy with a synchrotron source, (c) HRTEM image shows the stacking of (004) planes corresponding to the NbSe 2 crystal structure, (d) SAED pattern with (004) reflection marked, and (e) EDX analysis shows the presence of Se, Nb, Cu, C, and Cr signals coming from the copper-coated carbon grid of the Cr 0.0009 NbSe 2 single crystal. superconducting transition width (DT ¼ T on c À T off c ) was found to be 0.54 K with narrow DT, reecting the virtuous quality of the as-grown single crystal. The observation of the narrow superconducting width of T c and zero resistance indicates that the hydrostatic nature is good in our resistivity experiments. Fig. 2(c) shows a very sharp transition at 5.8 K at ambient pressure, where diamagnetism starts appearing and it conrms the bulk superconducting nature, which is in good agreement with the r(T) measurements of the same sample. The superconducting nature of T on c , T mid c , and T off c are enhanced by external pressure, as shown in Fig. 2(e). The rate of change of T on c with P(dT c /dP) up to $1 GPa is 0.27 K GPa À1 at less than 1 GPa pressure and is 0.46 K GPa À1 in the pressure range of 1 # P # 2.5 GPa, which is observed from the r(T) measurements. Normal state resistivity was found to gradually decrease with external hydrostatic P, as shown in Fig. 2(b), and it exhibits metallic nature in the entire pressure region up to $2.5 GPa. The similar nature of r(T) under high P $2.5 GPa has been reported in various superconducting materials. 31,32,35,[38][39][40][43][44][45] This is related to the fact that the application of P brings the layers close together and simplies the overlap of wave functions of the conduction electrons in the neighboring layers. The T c observed from the magnetization measurements is less than the r(T) measurements and such a difference in T c has been reported in various superconducting samples. The sample exhibits a sturdy diamagnetic signal and the high superconducting shielding fraction ($82%) represents that bulk superconductivity is exhibited by Cr intercalated NbSe 2 . The T c of Cr x NbSe 2 is found to be less than that of pure NbSe 2 (ref.  Fig. 2(d). The external pressure increases the superconducting nature and it reveals the strong enhancement in the pinning potential. The onset of SC transition temperature (T c ) is found from the ZFC curve shis towards higher temperature by the application of hydrostatic pressure. The external pressure inuences the Fermi surface topological uctuations that seem to be responsible for the enhancement in T c and it is consistent with the previous report. 20 On increasing the P up to 0.98 GPa, it was found that both T c and the superconducting shielding fraction increase gradually up to 0.98 GPa, as shown in Fig. 2(e). We dened the onset of diamagnetic shielding fractions at 5.8 K (0 GPa) and 6.76 K (0.98 GPa) and the pressure dependence of T c are shown in Fig. 2(e). It is found that dT c /dP ¼ 0.98 K GPa À1 and it is higher than the r(T) measurements. T c enhancement under P in Cr x NbSe 2 is found to be larger than the P dependence of T c reported for other 2D layered metallic superconductors, 8,31,32,41 such as BiS 2 -based 4 and Fe-based superconductors. 3 The application of P leads to a reduction in the interlayer distance, which is responsible for the enhancement in the superconducting nature of TMDC compounds. Further, the reduction in the interlayer distance under pressure paves the way for an increase in the electronphonon coupling constant, which leads to broadening of the energy bands, thus providing a dominant contribution to the enhancement in T c . These results imply that an increase in the density of states (DOS) at the Fermi level is due to the application of P. The electronic structures have been dominated by the hybridization between the transition metal 4d and the Se 4p orbital, which is accountable for the covalent Se-Nb-Se bonds.
The hybridization is very weak in Se 4p and d electrons in transition metal ions, which conrms the formation of the Cr-Se bond. 20,21 The Fermi level is primarily contributed by d electrons of Nb and intercalated transition metal ions, which are responsible for the metallic character and give a better understanding of intercalated NbSe 2 compounds. The external P effect on the superconducting properties of the 2D layered NbSe 2 compounds was characterized by the fact that the compressibility is seven times larger perpendicular to the layers than parallel to the layers 44 and hence, it is causes the layers to move close together. The application of P suppresses the lattice instability with simultaneous increase in T c by 1.4 K GPa À1 , as shown in the phase diagram P(T c ) ( Fig. 2(e)). The lattice instabilities increase under P, which eventually increases the electron-phonon interactions and leads to an increase in T c from both r(T) and M(T) in Cr x NbSe 2 systems. We analyzed the r(T) measurements under various P by analyzing the Fermi-liquid model, r(T) ¼ r 0 (T) + AT 2 , where r 0 and A are the residual resistivity and electron-phonon scattering factor, respectively, in the temperature range of 10 < T < 50 K. The pressure dependent values of r 0 and A are shown in Fig. 4(a) and it is clearly indicated that both are reduced by the application of P. As seen from the r(T) curve in the low temperature region under various pressures, the Fermi-liquid nature is followed. r(T) in the 10 to 50 K range is invariably linear for all P, arising entirely from the electron-acoustic phonon interaction. This is the general behavior of r(T) due to the presence of phonons in all types of superconducting materials. In the framework of Fermi-liquid theory, factor A is proportional to the charge carrier effective mass. The suppression of the scattering factor with external pressure suggests that the reduction in effective mass leads to a gradual loss of electron correlation with the enhancement in superconductivity. The temperature dependent upper critical eld H c2 (T) is determined from the onset of Meissner signal observed from M(T) with various H yields in the H c2 -T phase diagram tted with the Ginzburg-Landau function, H c2 (t) ¼ H c2 (0)((1 À t 2 )/(1 + t 2 )), where t ¼ T/T c , as shown in Fig. 4(b). The orbital limit upper critical eld of type II superconductors was estimated using Werthamer-Helfand-Hohenberg (WHH) theory in dirty limit, which is H orb c2 (0) ¼ À0.693T c (dH c2 /dT) T c . 56 Beneath the orbital limiting case, pair breaking takes place due to an increase in the kinetic energy of the Cooper pair, which are comparable to the condensate state in the presence of both external magnetic eld and hydrostatic pressure. In Pauli paramagnetic limit, the spin alignment with the application of magnetic eld that favors energy conditions leads to the breaking of Cooper pairs. According to the weak coupling case, the Pauli limited upper critical eld is given by H p (0) ¼ 1.84T c , which indicates the inuence on both the pair breaking mechanism and Pauli spin paramagnetic effect. The upper critical elds (H orb c2 (0), H c2 (0), & H P (0)) are found to increase with the application of P and it is given in Table 1. The enhancement in the upper critical elds under various P indicates that strong ux pinning is exhibited in Cr intercalated NbSe 2 single crystal. The Maki parameter measures the relative strengths of the orbital and Pauli limiting elds are calculated using the relation a ¼ ffiffiffi 2 p H orb c2 ð0Þ=H p ð0Þ. The Maki parameter was found to be 1 for both ambient and high P, which indicates that bulk superconductivity is Pauli limited (H c2 (0) < H orb c2 (0) < H p (0)); the Flude-Ferrell-Larkin-Ovchinnoikov (FFLO) state, which is insightful of the spatially moderated order parameter, is not favorable. 57 The coherence length is calculated from the Ginzburg-Landau expression as H c2 (0) ¼ f 0 /2px(0) 2 , where f 0 ¼ 2.07 Â 10 À7 G cm 2 and the estimated values are listed in Table 1. The value of a increases with P, which indicates that the Pauli spin paramagnetic effect drastically increases as external P is increased.
We measured the magnetic eld dependent magnetization (M(H)) below the superconducting state under various P and it reveals the linear variation of magnetization, which is a signature of the Meissner state and it is clearly seen in the low eld region, as shown in Fig. 3. At ambient pressure, there are no additional peaks in the isothermal magnetization curves for Cr 0.0009 NbSe 2 . 27 The application of pressure isothermal magnetization exhibits a small magnetization peak close to 0.1 T below the superconducting transitions and it is known as the second magnetization peak (SMP). The isothermal magnetization curves (Fig. 3) show a kink in the eld close to 0.1 T on the application of pressure, which is called as the second magnetization peak. This is the rst time that we observed SMP behaviour in 2D layer superconductors and we recently reported a similar behaviour in Fe intercalated NbSe 2 . 8 The SMP behaviour exists in few selective superconductors (cuprates and Fe based superconductors) in a limited temperature range below T c . 58,59 The doping effect also induces the SMP behaviour and it has been observed in cuprates and Fe based superconductors. 58,59 The lower critical eld (H c1 (T)) is estimated by a deviation from linearity in the diamagnetic state of the M(H) curve, as shown in Fig. 3. Above this eld, Abrikosov vortices become energetically favorable and start entering the sample edges. 60 H c1 (T) can be described in terms of the monotonic curve with a quadratic dependence, which is dictated by the empirical relation, H c1 (T) ¼ H c1 (0)(1 À (T/T c ) 2 ) and shown in Fig. 4(c). Further, the experimental data with G-L tting suggests that the vortex that penetrates into this sample could be well described by BCS theory. The deection of eld lines around the sample leads to a more pronounced Meissner slope given by M ¼ ÀH a / (1 À N), where N is the demagnetization factor. Although the demagnetization effect is very small, the corrected value of the lower critical eld H 0 c1 ð0Þ aer demagnetization correction is incorporated in H c1 (0) by using Brandt's formula, 61 Table 1. H c1 (0) is related to two fundamental length scales such as the London penetration depth (l(0)) and the coherence length (x(0)). According to the Ginzburg-Landau relation, H H 0.25 ) indicated that the depinning of magnetic ux pinning occurs within the H irr of the superconducting sample. Fig. 4(d) shows the extrapolation of the H-T phase diagram tted with the parabolic function H irr (T) ¼ H irr (0)(1 À (T/T c ) 2 ) 3/2 in the P range of 0 to 1 GPa. It shows the enhancement in H irr with the application of P and it is inuenced by ux pinning. The extrapolated values of H irr (0) at ambient and high pressures are tabulated in Table 1. All these may robustly propose the existence of the quantum vortex state due to quantum instability of the vortices.
The magnetic eld dependence of critical current density (J c (H)) at various temperatures is estimated from the magnetic hysteresis loop (M(H)) using Bean's model under various pressures up to $1 GPa, as shown in Fig. 5. The M(H) curve exhibits both bulk superconductive and vortex pinning nature in the Cr x NbSe 2 single crystal. Unquestionably, the observed demagnetization is not due to the superconducting surface   shielding fraction effect and it could be understood using the Bean critical state model. 63 For the rectangle sample, J c (T, H) ¼ 20Dm(T, H)/(u 2 (3l À u)), where Dm(T, H) is the separation between the two branches of M(H), and l and u are the length and width of the sample (l > u), respectively. At lower magnetic elds, the width of the magnetic moment (Dm(T, H)) is essentially caused by the inter-granular current. The estimated J c exponentially decreases with the application of external H and it seems to be correlated with weak H dependence of the pinning potential. The weak dependence of J c on H and T suggests that the Cr 0.0009 NbSe 2 single crystal has a greater J c behaviour, which is benecial for potential application in low and high H. P enhances J c in the sample and consequently increases the vortex dynamics properties, which leads to the enhancement in point pinning centers. The values of J c (0) at 2 K under various P were found to be are 304 732 (0 GPa), 1 180 204 (0.09 GPa), 1 209 901 (0.30 GPa), 1 214 477 (0.70 GPa), and 1 247 649 (0.98 GPa) A cm À2 , which are larger than the parent NbSe 2 . 13 Further, J c increases four-fold with the increase in P ($1 GPa) compared with the ambient P. However, J c (H) was found to decrease moderately at a low eld and it shows a sharp decrease in higher elds. From collective theory, 64 the exponential law by the relation follows as J c (H) ¼ J 0 exp(À(H/H 0 ) 3/2 ) under various P, where J 0 and H 0 are the zero eld J c and normalization parameter, respectively, and it is shown in Fig. 5(d). The divergence at low magnetic elds is associated with the crossover from single-vortex pinning regime to the small bundle pinning regime. The high eld departure that is very close to the irreversibility eld (H irr ) line could be associated with large thermal uctuations, a view that is supported by the three-dimensional (3D) ux creep reliance observed for the dissimilarity of H irr , as shown in Fig. 4(d). The temperature dependent H irr at various P is linearly extrapolated using Kramer's plot (H vs. J c 0.5 H 0.25 ). 65 The high eld peculiarity that is very close to the irreversibility line could be associated with huge thermal instabilities, a view that is supported by the 3D ux creep dependence detected for the variation in eld dependence of J c at various temperatures and pressures. J c is connected with thermally activated ux ow, which is explained by the empirical formula, J c (T) f (1 À (T/T c )) b , where b is a critical exponent. The value of the b parameter denotes the distinct vortex pinning mechanism in superconducting materials and it is consistent with the G-L theory. From the G-L theory, the critical exponent is used to classify the vortex pinning mechanisms at precise magnetic elds. The value b ¼ 1 indicates non-interacting vortices and b $ 1.5 signies the core pinning mechanism. 66 The various values of b have been found for transition metal intercalated NbSe 2 , which illustrate different core pinning mechanisms under ambient and high pressures. 8,13,27,31 These empirical relations estimate the temperature dependence of various critical parameters and reveal the freezing out of quasiparticle excitations by the BCS energy gap. The critical exponent is estimated from tting the scaling relation, as shown in Fig. 6, under various magnetic elds and external P. It reveals that the values of b are found to be 1.  This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 13112-13125 | 13119 P is larger than that under ambient P, which demonstrates the vigorous enhancement in current density with pressure. Fig. 6(d) shows J c dependence of P at 2 K under various H and the solid lines show the linear ts to the experimental data, which gives the slopes (d(log J c (T, H))/dP) of 0.06, 0.39, 0.68, and 1.34 GPa À1 at 0, 0.1, 0.2, and 0.3 T, respectively. The striking interface between the vortices and the pinning centres prevent the movement of vortices in type II superconductors. These results indicate that the application of P leads to enhancement in J c and it helps to understand the pinning mechanism in this sample.
The ux pinning is reected in J c (H) and J c (T) with the application of P, as shown in Fig. 7, and the pinning mechanism varies with the application of P at the critical pressure (P c ) of 0.3 GPa. J c (T) is well explained in the framework of the model of the collective ux pinning and creep. 64 For type II superconductors, the vortices interact with the pinning centers through spatial uctuations in T c (dT c pinning) with h max $0.67, 0.6, and 0.5 for point, surface, and body pinning, respectively. The vortices interact by the scattering of charge carriers with l (dl pinning) with h max $0.33 and 0.2 corresponding to the point and surface pinning, respectively. The external pressure increases both the dislocation and deformation stress in Cr x -NbSe 2 . These dislocations might interact with one vortex line when the dislocation is parallel to the local eld with several vortex lines when there is an angle that exists between the dislocation and the local eld. Consequently, we believe that the extensively occurring dislocations also contribute to the vortex pinning. The normalized J c as a function of reduced temperature (t ¼ T/T c ) is described by dT c -pinning (J c (t) f (1 À t 2 ) 7/6 (1 + t 2 ) 5/6 ) for less than P c , when T c uctuates due to both Cr intercalation and point defects (Fig. 7(a)), which are the foremost sources for trapping the vortices. Further, J c (t) shows completely different behavior for P $ P c , which leads to an increase in J c , followed by a crossover from dT c -pinning to dl-pinning (J c (t) f (1 À t 2 ) 5/2 (1 + t 2 ) À1/2 ) at 0.98 GPa with various magnetic elds up to 0.2 T are shown in Fig. 7(c) and a similar nature has been observed by us in the parent NbSe 2 . 8 A similar crossover occurs from dT c to dl pinning and it has been reported in NbSe 2 and FeSe, and this phenomenon occurs due to both chemical doping 13 and application of external hydrostatic pressure. 8,42 This suggests that spatial uctuation in the mean free path (l) of the charge carrier becomes crucial for ux pinning above P c . From the above results that indicate the intercalated nonmagnetic (Cr), it was found that the impurity is not uniformly distributed in the layered structure of NbSe 2 , which leads to the random distribution of dislocations. By the application of external P, the decrease in the interlayer distance prompts the formation of dislocations in the Se-Nb-Se layers. The enlarged uctuation in l is due to the variation in coherence length (x) with external P. This implies that the disorder parameter characterizes the collective vortex pinning, which is proportional to x and to 1/x 3 for dT c and dl-pinning, respectively. H c2 (0) is enhanced by the application of P, indicating that the variation in x is possibly signicant for the crossover.
To understand the nature of pinning mechanism in more detail, it is useful to study the variation of vortex pinning force density (F p (H) ¼ J c (H) Â m 0 H) as a function of magnetic eld. The normalized magnetic eld (h ¼ H/H irr ) dependence of normalized pinning force density (f p ¼ F p /F max p ) at 0.98 GPa for various temperatures is shown in Fig. 8(a) and Fig. 8(b), which shows f p vs. h 1 under various P up to 0.98 GPa at 2 K. We analyzed the pinning mechanism using Dew-Hughes model 67 f p (h) ¼ Ah m (1 À h) n + Bh p (1 À h) q to t our experimental data in order to describe the nature of pinning mechanism for unconventional superconductors. The exponents are characteristic for the dominant pinning mechanism, where m ¼ 1, n ¼ 2 and p ¼ 0.5, q ¼ 2 correspond to the normal point and surface pinning mechanism, respectively. By the application of external P, the pinning mechanism may be changed easily and it can be veried using the Dew-Hughes model; these results suggest that the occurrence of both point and surface pinning is observed. The dl pinning is more dominant because of the increase in core point pinning with the application of P. The normal core point pining is more prominent than the surface pinning mechanism on the application of P. These outcomes imply that Cr x NbSe 2 have a number of decient pinning centers in the high eld region. It is outstanding that the external P inuences the pinning centers, which in turn prompts the enhancement in J c . The best t of the experimental data is achieved in the exponent range of 0.98 # m # 1.52 and 2.82 # n # 3.52: 0.48 # p # 0.31 and 1.69 # q # 2.03 in the pressure range of 0.09 GPa to 0.98 GPa. It reveals that the best t exponents are close to the value predicted for the surface and point pinning and prove the coexistence of both pinning at high P. Further, for understanding the actual pinning mechanism of Cr x NbSe 2 under P, we analyzed the peak positions at which the maximum pinning force is exhibited from the relation dened as h max (h max ¼ p/(p + q)). The values of h max are 0.26 (0.09 GPa) and 0.30 (0.98 GPa) for point pinning, and 0.22 (0.09 GPa) and 0.13 (0.98 GPa) for surface pinning respectively. This conrms that core point pinning is actually the dominant pinning mechanism prevailing in the sample, which is caused by external P. We also have analyzed the pinning mechanism by using the method adopted by Higuchi et al. 68 using the relations f p (h 2 ) ¼ (9/4)h 2 (1 À (h 2 /3)) 2 and f p (h 2 ) ¼ (25/16)h 0.5 2 (1 À (h 2 /5)) 2 for point and surface pinning, respectively. Fig. 8(c) and (d) illustrates that both point and surface pinning coexist in ambient and high pressures, and it shows good agreement with the point pinning mechanism for various temperatures in the low eld region with ambient and high pressures. The normalized magnetic eld is higher than H peak ; point pinning occurs in lower magnetic eld and surface pinning is observed in Fig. 8  higher magnetic eld for all applied P. However, the samples do not exhibit strong pinning centres with the application of high eld. These results suggest that both Dew-Hughes and Higuchi methods give similar nature of the ux pinning mechanism.
The Raman spectra of Cr x NbSe 2 single crystals are shown in Fig. 9(a) in the temperature range between 3.2 to 300 K. The prominent features observed below 300 cm À1 include two high energy in-plane (E 2g ) and out-of-plane (A 1g ) phonon modes at $256 cm À1 and $233 cm À1 , respectively. 29,69 The wide feature occurs at $190 cm À1 , which is assigned as the so mode and it is marked by a down arrow, which involves a second-order scattering process on two phonons of frequency u 0 at wavevector $(2/3)GM. These phonons consist of both intralayer and interlayer vibrations in the bulk NbSe 2 . 15,29,70 The broad feature of the low energy mode is observed only in the parallelpolarization scattering geometry. The localized longitudinaloptical (LO) mode of Cr-Se appears in the Cr intercalated samples and it is marked as a star symbol at the Raman shi of 277 cm À1 . 71 The low temperature powder X-ray diffraction pattern for Cr x NbSe 2 under various temperatures from 9 to 300 K is shown in Fig. 9(b) using the synchrotron source with wavelength 0.7962 A and there are no impurity peaks found in Cr x NbSe 2 . These results conrm that there is no structural transition observed at room temperature and further decreasing the temperature down to 9 K does not show any changes in the XRD pattern. Hence, it conrms that there is no structural transition that occurs in this sample, as shown in Fig. 9(b). Fig. 10(a)-(f) shows the synchrotron powder ADXRD patterns for the Cr 0.0009 NbSe 2 sample under various P up to $7.5 GPa; the two-dimensional (2D) image plate patterns are converted into one-dimensional patterns and plotted as a function of intensity using the Fit2D soware package. As the pressure gradually increases, the XRD peaks shi steadily towards a higher angle. Apart from the peak shi, the diffraction peaks do not undergo any signicant variations in the intensity up to the pressure of 7.4 GPa. All the XRD peaks of Cr x NbSe 2 under various pressures at 300 K have been tted by the Rietveld renement method using FullProf soware. 46 The spectra are well tted using a hexagonal crystalline structure with space group P6 3 /mmc with very good values of goodness of t parameters. The lattice parameters are kept free during the tting and it has been observed that the difference between the values of a and c parameters decreases with the application of pressure. The patterns obtained from both ambient and highpressure regions reveal the absence of peak splitting, indicates the hexagonal phase, and it is found to be stable up to $7.4 GPa. All the XRD peaks and crystalline phases are wellmatched with that shown by NbSe 2 except for the 17.5 peak. In particular, the peak at 17.5 does not match with the NbSe 2 pattern and it is due to the tungsten gasket used in the DAC. The variation in the normalized cell parameters and unit cell volume are plotted as a function of pressure, as shown in Fig. 10(e), and the estimated values are listed in Table 2. The aand b-axis are less compressed under external P than the c-axis, which are made of the Nb-Se layer that is connected with a covalent bond. However, the Nb-Se layers are held together by van der Waals force parallel to the c axis and it leads to large and less compression along the c and a-axis, respectively. Transition metals have low electronegativity, which indicates that Fig. 9 (a) Raman spectra (3.2 to 300 K) and (b) synchrotron powder X-ray diffraction pattern (9 to 300 K) at ambient pressure for Cr x NbSe 2 single crystals.
electrons can be transferred to the non-metallic constituent more easily, hence increasing the coulombic repulsion and causing difference in the compression among the stacking layers. Hence, a high anisotropy ratio is observed in the compressibility of Cr x NbSe 2 layered superconducting materials.

Conclusions
We extensively studied the superconducting parameters such as T c , H c2 , H irr , J c , and F p under various hydrostatic pressures for the Cr 0.0009 NbSe 2 single crystal. However, the relative contributions of the pinning mechanisms are strongly P dependent and it increases the J c due to enhancement in both pinning centers and pinning strength. We found that the mechanism for both dT c and dl pinning is associated with spatial uctuations of mean free path and spatial uctuations of the transition temperature from J c (H) at ambient and high P using collective pinning theory. The analysis was done using Dew-Hughes and Higuchi model, and it was proposed that the point and surface pinning coexist at ambient and high P. Further, point pinning is more dominant than surface pinning with the application of P. Hence, these results are important for practical application because they demonstrate that P can tune the formation of pinning centers. The investigation of structural analysis under high pressure up to 7.5 GPa demonstrated that the superconducting sample remains in the hexagonal crystal structure without any secondary phase and it shows high anisotropy along the c-axis than along the ab-plane.

Conflicts of interest
There are no conicts to declare.