Second magnetization peak effect and the vortex phase diagram of V0.0015NbSe2 single crystal

Journal of Magnetism and Magnetic Materials 507 (2020) 166817

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Second magnetization peak effect and the vortex phase diagram of V0.0015NbSe2 single crystal Rukshana Pervina, Manikandan Krishnanb, Sonachalam Arumugamb, Parasharam M. Shiragea, a b

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Discipline of Metallurgy Engineering and Materials Science & Physics, Indian Institute of Technology Indore, Simrol, Indore 453552, India Centre for High Pressure Research, School of Physics, Bharathidasan University, Tiruchirappalli 620024, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Single crystal Fishtail effect Second magnetization peak Collective creep Lattice softening

Effect of the weak point disorder on vortex matter phase diagram is studied by incorporation of V atoms through magnetic and magnetoresistance measurement in layered NbSe2 single crystal. We observe that the point disorder introduces fishtail effect and the second magnetization peak (SMP) in the M-H curve of V0.0015NbSe2 at magnetic field far below upper critical field (Hc2). 3D Collective creep of elastic flux line lattice (FLL) support the vortex motion below the onset of SMP. However, the crossover from collective to plastic deformation of FLL support the occurrence of SMP effect. Presence of the peak effect in pinning force density near irreversible magnetic field (Hirr) indicates the 2D to 3D distortion of FLL due to lattice softening associated with the rapid reduction of elastic modulus. Magneto transport measurement shows the glassy transition near the zero resistance region. In the glassy region, the flux line shows 2D characteristics. Above zero resistive region, thermally activated flux flow region is well described by Arrhenius relation. It is seen that the activation energy is decreased significantly by the incorporation of V atoms in NbSe2. The magnetic field dependence of activation energy follows a power law of U0(H) ~ H-α where the exponent α changed from 0.5 to a 0.9 at a crossover field of Hcr = ~ 0.7 T, indicating the transition from weak plastic deformation of FLL to the strong entangled state in vortex liquid phase. Finally a vortex phase diagram is constructed demonstrating all the different phases of vortex lattice of V0.0015NbSe2 at different magnetic fields and temperatures.

1. Introduction The vortex lattice (VL) in a type II superconductor can be considered as an ideal system to study several notions associated with disordering and pinning [1,2]. In a clean superconductor, the VL structure is characterised by several factors. The foremost characteristic is the interaction between vortices which orders them into a hexagonal Abrikosov vortex lattice. The other significant characteristic is thermal fluctuation which favours disordering and melts the lattice into vortex liquid phase at a characteristics temperature [3,4]. Structural imperfection (i.e., quenched disorder, twinned boundaries) also play important role to destroy the long range Abrikosov lattice by creating a disordered background potential in type-II superconductors [5]. The external pinning centres add more novel pinned vortex phases to the phase diagram of clean superconductor [6,7]. The nature of these phases and the transition amongst themselves remain always controversial matter. Two remarkable consequences of the transition between various vortex states are the fishtail effect (FE) and the peak effect (PE) phenomena. It is well known that the critical current density

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(Jc) obtained from the magnetization hysteresis loops (MHLs) decreases with increase of magnetic field due to the dissipative motion of flux line lattice (FLL). Some superconductors show enhancement of Jc after the first peak of penetration field with increasing magnetic field. This is known as the fishtail effect or prominent second peak effect (SMP). SMP has been detected in high quality and clean crystals of cuprate superconductors [8,9]. This has been also studied in single crystals as well as polycrystalline samples of FeAs-1111 and also in FeAs-122 superconductors [10–12]. While in the low Tc superconductors, e.g., Nb3Sn, MgB2, etc., peak effect has been generally perceived [13,14]. The PE, i.e. the anomalous enhancement of the Jc and the pinning force per flux line occurs at the Hc2 line near the normal-state phase boundary in lowTc systems and almost overlap with the melting line in the HTSC’s [15]. It is considered as the outcome of rapid softening of the lattice and the phenomenon of plastic deformations [16]. This creates topological defects in FLL. As a consequence the lattice shows amorphous nature at and above the peak position in Jc. In cuprates, the PE phenomenon can only be seen in ultra-clean crystals with a low level of pinning centres which is discussed by Nishizaki et al. in YBCO systems [17].

Corresponding author. E-mail address: [email protected] (P.M. Shirage).

https://doi.org/10.1016/j.jmmm.2020.166817 Received 5 September 2019; Received in revised form 7 February 2020; Accepted 25 March 2020 Available online 27 March 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.

Journal of Magnetism and Magnetic Materials 507 (2020) 166817

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Surprisingly, with increasing weak point disorders by electron irradiation [17], the Jc(H) peak broadens in clean YBCO and the peak position shifts towards the intermediate fields. This is the clear signature of SMP that differentiates the peak effect. However, the anomalous SMP appears due to different mechanism in different superconducting systems. It appears at different fields for REBa2Cu3O7-δ (REBCO) bulks (RE = rare earth element) at different temperatures [18]. Contrarily, the peak position is temperature independent for Bi-based and Tl-based cuprate [19,20]. To explore such anomalous behaviour of critical parameter (like Jc) and the associated different vortex states of superconducting material, doping or addition of foreign atoms appear as a potential method. It is also a major concern for technological applications because it is an effective method for improving the structural, superconducting, transport and flux pinning properties that allow superconductors to be suitable for application at higher temperatures and magnetic fields. These additives lead to structural stability and aid to understand the structure and diversity of different FLL. In this paper, we investigated the SMP effect, PE and the different vortex phases associated with the vortex phase diagram of NbSe2 single crystal at an optimal concentration of Vanadium atom (V) (i.e. V0.0015NbSe2) through magnetic and magneto-transport measurement. For this, we first analyse the magnetic field dependence of Jc obtained at different (H, T) space in V0.0015NbSe2. The peak of the SMP effect appears as the regime where a three dimensional collectively pinned ordered vortex phase terminate and precisely exposes to the plastic creep region. The presence of peak in Fp near Hirr (i.e., PE) demonstrates the lattice softening and the two dimensional to three dimensional FLL distortion. The thermally activated vortex motion is studied through Arrhenius relation in thermally activated flux flow (TAFF) region. The estimated apparent thermal activation energy (U0) shows power law dependence on magnetic fields and a crossover field (Hcr) that differentiates the plastically deformed vortex liquid state from more entangled state. Finally, we constructed the vortex phase diagram of V0.0015NbSe2 demonstrating the collective creep region, plastic creep region, vortex glassy state and vortex liquid phase in H-T plane.

Fig. 1. Powder xrd pattern of V0.0015NbSe2 single crystal.

3 K, 3.5 K, and 5 K temperatures parallel to ab-plane of V0.0015NbSe2. 3. Results and discussion First, the crystal structure of V0.0015NbSe2 single crystal is characterized by XRD using Rigaku SmartLab X-ray diffractometer with Cu Kα source (λ = 1.54 Å) for structural information regarding the phase purity. The X-ray diffraction (XRD) pattern of V0.0015NbS2 single crystal is represented in Fig. 1 which demonstrates the hexagonal phase with P63/mmc space group (JCDPS card no. 01–070-5612). The pattern shows the presence of only (00 l) plane without any impurity phase confirming the single crystalline nature of V0.0015NbSe2. The estimated c axis lattice parameter is 12.49 (2 ± 4 Å) which is less than the reported c axis parameter (~12.55 Å) of NbSe2 [23]. In contrast, Luo et al. [24] reported the linear increase of c axis parameter with increasing Cu contents as a signature of the 3d metal intercalation in NbSe2. V is the same group elements of Nb. The ionic radius of V4+ atom (58 pm) is less than that of Nb4+ atom (68 pm) instead of having same coordination number of V4+ to that of Nb4+. So, following the Vegard’s law, the reduction of c-axis parameter can be predicted as the substitution of Nb by V atom in V0.0015NbSe2. Chen et al. [25] reported that substitution of Nb atom (by V atom) is more energetically favourable than that intercalation of V atom into the interlayer of the 2H-NbSe2 supercell. The detail analysis of the crystallographic cell regarding the position of V atoms in V0.0015NbSe2 are not the subject of this study and are not presented here. To study the evolution of superconducting properties with V doping in V0.0015NbSe2, we investigated the temperature dependence of magnetization measurement in both ZFC and FC processes. Fig. 2(a) represents the diamagnetic transition of V0.0015NbSe2, which is estimated from the deviation of ZFC curves from zero magnetization value at dc magnetic fields of 0.005 T, 0.01 T, 0.05 T, 0.3 T and 0.7 T. The ZFC curve shows perfect diamagnetism with sharp transition at the onset transition temperature (Tcon ) 3.65 K and transition width 1.6 K. Tcon is designated by red arrow in Fig. 2(a). This confirms the bulk superconductivity of V0.0015NbSe2. The magnetic susceptibility (χ(T)) as a function of temperature is shown in Fig. 2(b) from 2 K to 10 K temperature under an external magnetic field of 0.7 T. The χ (T) rises rapidly at low temperature and reaches a maximum at TFM = 2.5 K for 0.7 T. At even lower temperature, a rapid drop is observed similar to that observed in Fe0.05TaSe2 [26]. It is difficult to decide the exact origin of the maxima from the dc susceptibility measurement. However, the presence of the susceptibility maxima indicates the onset of magnetically ordered state which might be either to a two-or-three

2. Experimental technique 2.1. Preparation of single crystal V0.0015NbSe2 single crystals were grown through the method of chemical vapour transport reactions using Iodine as a transporting agent. The precursors Niobium (Nb), 99.95%, Selenium (Se) 99.99%, and Vanadium (V) 99.99% purity were obtained from Alfa Aeser and grinded in an agate motor to form circular pellet without any further refinement. The pellet (~4 gm) was sealed with 2–3 mg of iodine in a quartz tube at a pressure of 9 × 10-6 mbar at the liquid nitrogen atmosphere. Then the sealed quartz tube was heated inside a two zone furnace keeping charge zone and growth zone temperatures fixed at 800 °C and 720 °C respectively for one week. Similar procedure is used to form large single crystals in our previous studies [21,22]. 2.2. Characterization techniques The temperature dependence of resistance of V0.0015NbSe2 was measured via standard four-probe technique with homemade resistivity set up performing superconducting magnet system (Oxford Instrument Inc.), UK in the temperature range 3–300 K. The resistance measurement at different magnetic fields was carried out running 10 mA DC current through the sample. Magnetization measurements were achieved by using the Vibrating Sample Magnetometer option in the Physical Property Measurement system (PPMS-VSM) (Quantum Design, USA). The temperature dependence of magnetization (M (T)) measurement was recorded following both zero-field cooling (ZFC) and field cooling (FC) methods at different magnetic fields. Furthermore, the isothermal magnetization curve (M-H) was measured at 2 K, 2.5 K, 2

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Fig. 2. (a) The superconducting transition in the ZFC and FC processes at 0.005 T, 0.01 T, 0.05 T, 0.3 T, 0.7 T magnetic fields. The arrow indicates the onset of the diamagnetic transition at 0.005 T. (b) DC susceptibility measurement (χ(T)) for the V0.0015NbSe2 from 2 K to 11 K with an external field of 0.7 T. The arrows indicate the susceptibility maxima (~TFM) and the superconducting transition (Tc) at 0.7 T. (c) The Hc2-T plot and the corresponding fit of V0.0015NbSe2 using Ginzburg-Landau phenomenological equation. (d) MHLs at the temperatures of 2 K, 2.5 K, 3 K, 3.5 K with the fishtail effect in the high field region.

channel is more effective. Then the paramagnetic effects might be visible at low-temperature and high field, only. The orbital limited upper critical value of V0.0015NbSe2 at zero temperature (Hcorb 2 (0)) is obtained as 0.4 T using the WHH formula, Hc 2 (0) = −0.69 |dHc 2 (T )/ dT|Tc Tc [33], excluding the contribution of Pauli pair breaking effect and the spin-orbit effect. Contrarily, the Pauli limiting upper critical field (Hp (0)) of V0.0015NbSe2 is estimated from the relation Hp(0) = 1.84Tc) that shows much larger value (~6.7 T) than the obtained Hc2(0). This suggests the major contribution of orbital effect in the pair breaking mechanism of V0.0015NbSe2 in presence of external magnetic field. Further, the orbital effect is related to both Tc and the slope of Hc2 (T) at Tc (i.e., |dHc 2 (T )/ dT|Tc ), which strongly depend on the impurity induced scattering. So, the significantly reduced Hc2(0) value of V0.0015NbSe2 indicates the disorder occurred due to the V doping decreasing both Tc and |dHc 2 (T )/ dT|Tc values compared to pure NbSe2. However, at higher magnetic field region (H ≥ 0.3 T), the internal field induced by the antiferromagnetic ordering also participate in the destruction of the diamagnetic signal. In addition, one couldn’t also exclude the possibility of the variation of the Fermi surface due to V doping behind the degradation of the Hc2(0) value. The MHLs, which are measured at different temperatures from 2 K to 3.5 K are demonstrated in Fig. 2(d). The asymmetric curves indicate that the surface barrier pinning instead of the volume pinning dominates in the sample. Paltiel et al. [34] has demonstrated the significance of the surface barrier pinning at low fields in the NbSe2 crystal. At the high field region, there is increment of the width of irreversible magnetization (ΔM) with increasing magnetic field indicating the fishtail effect (FE) phenomenon. However, the SM effect which is associated with the FE can be easily detected in Fig. 2(d) at all temperatures especially for T > 2 K. With increasing the temperature, the peak moves to the lower magnetic field and finally disappears near transition temperature region as shown in Fig. 2(d). The detail analysis of this monotonous reduction of the second peak position with increasing temperature is discussed in the phase diagram plot later. The analogous mechanism is observed in REBa2Cu3O7-δ (REBCO) superconductors (RE = rare earth element) [35]. To investigate further, the field dependence of Jc is extracted from the MHL using Bean critical

dimensional spin-glass transition (SG), a spin-density-wave (SDW) of the electron gas system, or a local-antiferromagnetic ordering (LAO) in the atomic clusters of V impurities. Neutron diffraction measurement will be required to reveal the real magnetic ordering structure of V0.0015NbSe2. Although the magnetic field dependence of the susceptibility maxima and the negative Weiss constant (θ) (suggesting the short range antiferromagnetic interaction) is consistent with the LAO hypothesis in V0.0015NbSe2. The FC and ZFC magnetic susceptibilities also bifurcate at roughly the same temperature (~TFM), suggesting a weak ferromagnetic component associated with a canted antiferromagnetic order similar to (Li0.8Fe0.2) OHFeSe [27]. So, we can conclude that, V impurities induce a weak magnetic moment which displays antiferromagnetic ordering and competes with superconductivity in presence of external magnetic field in V0.0015NbSe2. The magnetization measurement permits a further detail analysis in the upper critical field (Hc2). Hc2 (T) values are estimated from the M−T curve considering the onset point of the superconducting transidH tion at each magnetic field. It gives a slope of dTc2 |Tc = −0.14T / K . The Hc2 (T) vs. T plot is shown in Fig. 2(c), which is fitted with the anisotropic G-L single band formula, Hc 2 = Hc 2 (0)[1 − (T / Tc )a]b with a = 1.39 and b = 1 [28]. The Hc2 (0) (~1.18 T) of V0.0015NbSe2 is calculated from the G-L fitting showing lower value than NbSe2. This indicates V doping enhances the pair-breaking phenomena in the presence of magnetic field. However, many recent experiments performed on NbSe2 [29,30], suggest that more than one energy scale is required for describing the superconducting properties. The evidence of the multiband superconductivity of V0.0015NbSe2 is also prominent in the temperature dependence of Hc2 plot. The Hc2 (T) curve exhibits a positive curvature close to Tc and then increases linearly with lowering temperature similar to the multi-gap superconductor MgB2 [31]. In order to have more quantitative understanding, additional two-band Werthamer-Helfand-Hohenberg (WHH) model, which takes into account the orbital and Pauli pair breaking effect, is needed [32]. In a spin-singlet type-II superconductor, a magnetic field destroys the superconductivity through two pair-breaking mechanisms which are known as orbital diamagnetic effect and the Pauli paramagnetic effect. Usually, at high temperature below Tc, the suppression in the orbital 3

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Fig. 3. (a) The Jc plot at 2 K, 2.5 K, 3 K and 3.5 K in V0.0015NbSe2. The solid lines correspond to the power-law decay Jc α H-n for H||ab plane with n = 1.38, 1.35, 1.23, 1.20. The marks I, II, III, IV represent the individual pinning regime, large bundle pinning regime, SMP regime and the PE regime. The arrows indicate the peaks associated with FE (or SMP) and PE phenomena. (b) The normalised pinning force density (fp = Fp/Fp, max) versus the reduce field (h = H/Hirr) for V0.0015NbSe2 at the temperatures of T = 2 K, 2.5 K, 3 K and 3.5 K.

(

w

)

has been also reported in YBa2Cu3O7-δ [41,42]. In contrarily, the Jc characteristic of V0.0015NbSe2 shows SMP anomaly along with the indication of PE effect near the irreversibility line similar to that described in weakly pinned NbSe2 by Thakur et al. [43]. So, the Jc characteristics at the extremely lower magnetic field (I region), intermediate magnetic field (II region) and the higher magnetic field (III and IV region) of Fig. 3(a) has been identified as the individual pinning regime, collectively pinned elastic vortex solid, SMP regime and the PE regime, respectively. In order to find out the type of pinning mechanism operating in the SMP or PE region, the Fp value is evaluated using Fp = Jc × H. DewHughes proposed a model in terms of elementary pinning forces to explain pinning mechanism ignoring the flux line elasticity and flux creep effect [44]. In this model the Fp follows a scaling relation fp = Ah p (1 − h)q with p = 1 and q = 1 for volume pinning, p = 1 and q = 2 normal core point pinning with hmax ~ 0.33, p = 0.5 and q = 2 normal surface pinning mechanism with hmax ~ 0.2. Here h is defined as h = H/Hirr where Hirr is obtained from the zero value of Jc in Jc-H curves. Fig. 3(b) represents the normalized pinning force density (fp = Fp/Fp, max) as a function of reduced field (h = H/Hirr) of V0.0015NbSe2 at 2 K, 2.5 K, 3 K, and 3.5 K temperatures. The peak in fp don’t follow the normal point pinning and surface pinning mechanism So, it can be predicted that another mechanism is responsible for this fp peak. There are lots of literature survey about the PE in Fp of NbSe2 system [45]. According to these analysis, the PE mechanism in NbSe2 appears only when a dimensional crossover occurs. Koorevaar et al. [46] reported high field’s peak in Fp in thin single crystals of NbSe2 which sets at about bco ≈ 0.8Hc2 in fields directed perpendicular to the layers. The onset of the peak is demonstrated as the transition to threedimensional (3D) FLL disorder following to the considerable reduction of tilt modulus (C44) of FLL. This means V0.0015NbSe2 acts as a 3D anisotropic vortex lattice with flexible FLL structures allowing a rapid relaxation of diamagnetic magnetization. The variation of Fp with H and most significantly the peak in Fp near Hc2 i.e. the “peak effect”, has also been studied extensively by Pippard et al. [47] He ascribed it to the softening of the FLL and the easy compliance of the same to the pinning configuration. In case of V0.0015NbSe2, at the onset of the PE, screw dislocations enter in the FLL and destroy the positional correlation along the field direction (i.e., the longitudinal correlation length), thereby changing the FLL from 3D to 2D. However, this 3D to 2D transition of the FLL results enhancement of the anisotropy parameter (Γ), which softens the nonlocal C44 parameter drastically. So, the softened 2D FLL of V0.0015NbSe2 easily accommodate to the defect centres for a better adaptation to the underlying random inhomogeneities that triggers the sudden enhancement of Fp and hence, the PE phenomenon near Hirr. However it is seen (Fig. 3(b)) that the peak of fp shifts to h = 0.33 for T = 3 K which indicates the point pinning mechanism as a dominating one. Even at higher temperature (T = 3.5 K) there is an overlap of peaks associated with different pinning mechanism due to thermal fluctuation. So, it can be concluded that due to the rapid

state model Jc = 20ΔM / ⎡w 1 − 3l ⎤, where ΔM is measured in emu/ ⎣ ⎦ cm3, and the width w and the length l of the sample (w < l) are measured in cm. [36]. The estimated Jc(0) value at 2 K reaches to 9 × 105 A/cm2, and drops down to 7 × 103 A/cm2 at 3.5 K. So, V0.0015NbSe2 superconductor displays good current carrying capability. Fig. 3(a) shows the resulting Jc (H) plot in V0.0015NbSe2 single crystal at 2 K, 2.5 K, 3 K, 3.5 K temperatures. At extremely low magnetic fields, a field independent Jc characteristics is observed for all temperatures which is the signature of nearly zero interacting region (i.e. the single vortex pinning region) [23]. Below H = 0.23 T, the Jc (H) curves follow a power-law relationship Jc α H-n with n = 1.38 for 2 K. For a 3D elastic flux-line lattice (FLL), it is demonstrated by Blatter et al. [2] that Jc is leaded by a power law Jc (H) α H-3 in the large bundle-pinning regime. This is a qausi long range Bragg glass phase where vortices creep in the form of large bundle [37]. The 2D elastic FLL shows single pancake pinning at low magnetic fields with field independent Jc, then a 2D collective-pinning region at higher fields with Jc α 1/H. In case of thermal fluctuations, the n value is found to be as large as 20 which results from the giant flux creep [2]. The relatively lower value of n (i.e. 1 < n < 3) indicates the weak disorders in 3D elastic FLL of V0.0015NbSe2. It indicates the dissipation of FLL associated with large bundle flux creep. So, the power law response of Jc supports the presence of collective creep at low magnetic fields which destructs the long-range order of Abrikosov vortex lattice. The exponent n tends to decrease with increasing temperature (i.e. n changes from 1.38 to 1.2) within the temperature span of 2 K to 3.5 K, which is associated with the rate of change of flux creep. Again above 0.23 T, the Jc curve of V0.0015NbSe2 deviates from the power-law scaling and the SMP starts with a maximum at HSMP = 0.27 T. At 2.5 K, the departure from the power-law response occurs at H = 0.13 T. A fast drop in Jc in Fig. 3(a) is observed after SMP because of the fast creeping of vortices associated with large magnetic field. The power-law behaviour of Jc (H) also implies the existence of a fairly dense distribution of weak pins in V0.0015NbSe2 [38]. Besides diminishing the density of cooper pair electrons and reducing Tc, the presence of the V atoms may also be responsible for this novel anomalous vortex state in V0.0015NbSe2. Ahmed et al. [39] reported that the Co doping results the prominent secondary peak at the optimally doped and overdoped NaFe1-xCoxAs system. However, another intense peak of Jc (H) characteristic is observed at the edge of the irreversibility line (where Jc → 0) indicating the presence of PE phenomenon. HSMP and the Hp mark (as indicated by the red arrows in Fig. 3(a)) the maxima accompanying the SMP and the PE phenomena, respectively. The evolution of Jc (H) curves in V0.0015NbSe2 is comparable to the quenched disorder dominated NbSe2 as reported by Banerjee et al. [40]. They demonstrated the collective pinning of ordered lattice regime at intermediate fields and the PE phenomenon in the vicinity of highly disorder (i.e. at the amorphous limit) of Jc characteristics of NbSe2 at t (=T/Tc(0)) = 0.973, 0.983, 0.990. These PE evolves to FE with increasing temperature towards the transition region. The evolution of Jc (H) curves from the PE to the FE 4

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Fig. 4. (a) Normalised temperature dependent resistance of V0.0015NbSe2 indicating metallic characteristics (indicated by red solid line) in the temperature interval 50 K < T < 300 K. The inset shows excellent fitting of the data from 4 K to 50 K considering electron–electron scattering (~T2) and interband scattering (~T3). (b) Resistance measurement of V0.0015NbSe2 at 0.2 T, 0.4 T, 0.6 T, 0.8 T, 1 T and 1.5 T magnetic fields along the ab-plane of the crystal surface. (c) Inverse logarithmic derivative of resistance of V0.0015NbSe2 at H = 1 T. The red solid line represents the fitting to vortex glass critical region using the relation [d (lnR)/ dT ]−1 = (1/ s )(T − Tg ) . The red arrows indicate the vortex glass transition temperature (Tg) and the vortex glass critical temperature (T*). (d) The magnetic field dependence of critical exponent s (H). (e) Arrhenius plot of resistance at H = 0.2 T, 0.4 T, 0.6 T, 0.8 T, 1 T and 1.5 T where the solid lines are linearly fitted to the TAFF region. (f) Apparent activation energy (U0 (K)) is plotted against H on log–log scale. The solid lines represent power-law fitting with U0 (H) ~ H-α. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

softening of the tilt modulus and hence the FLL, the high field peak appears in V0.0015NbSe2. The onset of the PE supports crossover from the 2D to 3D disorder with the presence of random screw dislocations in FLL. Fig. 4(a) shows the temperature dependence of the normalized resistance (R/R300 K) of V0.0015NbSe2 demonstrating a metallic characteristic (dR/dT > 0) between T ≈ 50 K temperature and 300 K temperature. This characteristic is similar to Fe0.0015NbSe2 single crystals [48]. The residual resistivity (ρ0), room temperature resistivity (ρ300) and the residual resistivity ratio (RRR = (ρ (300 K)/ ρ (Tc)) of V0.0015NbSe2, which are calculated from Fig. 4 (a), have values 6.5 × 10-5 Ω-cm, 7.58 × 10-4 Ω-cm, 6.95, respectively. In V0.0015NbSe2, ρ0 was estimated by assuming a power law dependence for the ideal resistance (Ri = R-R0). The estimated in-plane ρ0, ρ300 and RRR values of V0.0015NbSe2 crystal deviate appreciably from the bulk NbSe2 reported by Naik et al. [49] and the NbSe2 flakes (12 layer)

reported by El-Bana et al. [50]. Low temperature region (5 K ≤ T ≤ 50 K) of R (T) of V0.0015NbSe2 (inset of Fig. 4(a)) shows good fitting considering the contribution from electron-electron scattering (~T2) and phonon mediated inter-band s-d scattering (~T3) which can be attributed to the disorder induced by V impurities. Furthermore, by taking the criteria of 90% Rn (where Rn indicates the resistance at T = 5 K), the onset transition temperature of superconductivity at zero field (Tcon (H = 0)) is estimated at 4.07 K, while the zero resistance temperature (Tc(R = 0) ) is as 3.7 K. The Tcon (H = 0) value of V0.0015NbSe2 shifts to lower temperature as compare to NbSe2 (~7.2 K) [24] indicating V as an electronically disruptive element for the superconductivity of NbSe2. The reduced superconducting transition temperature might be arise from the change in the density of states at the Fermi level due to charge transfer between the constituents and/or the disorder induced scattering from V impurities. Chen et al. [25] reported variation in the intensity as well as position of the narrow sharp 5

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in TAFF region. The U0 values are extracted from the slopes of the fitted lines to the linear regions of Arrhenius plot (as presented by the solid lines in Fig. 4(e)). All the fitted lines intersect at Tcross at 4.06 K which is in good agreement with Tconset of V0.0015NbSe2. The inset of Fig. 4(e) shows the linear relationship between lnR0 and U0 with the Tc value (i.e. inverse of the slope of linear fitting) at 4.06 K which is also comparable to Tconset . This proves the Arrhenius plot gives the correct value of U0. Further, Fig. 4(f) represents the magnetic field dependence of U0 that has value 266 K at 1 T for V0.0015NbSe2. It can be seen that the U0 value is decreased significantly in V0.0015NbSe2 as compare to NbSe2 [52]. These results suggest that FLL become more entangled due to the point defects and emerges 2D nature in TAFF region of V0.0015NbSe2. This makes the easy movement of flux lines through FLL resulting reduction of U0 [53]. However, another reason behind the reduction of U0 (H) can also be the weakening of the Fp(H). Liu et al. [54] reported the reduction in U0 (H) in optimally doped and overdoped (Ba1-xKx)Fe2As2 single crystals due to the weak δTc pinning. In contrast, the underdoped (Ba1-xKx)Fe2As2 single crystal shows large U0(H) value which is associated with strong vortex pinning. Ağil et al. [55] also reported that the addition of Gd to BSCCO superconductor weakens the link of the grains (i.e. reduces the surface pinning) and thus there is a reduction of U0 compare to pure sample. However, the higher Jc(0) value and the high field Fp peak excludes the possibility of reduction of pinning energy of V0.0015NbSe2 compare to pure NbSe2 [23]. So it can be concluded that the FLL is in more entangle state in V0.0015NbSe2 due to the presence of point defects resulting lower U0(H). In order to examine the field dependence nature of U0, a log–log graph of U0 is plotted against the applied magnetic field in Fig. 4(f). The U0 values of V0.0015NbSe2 follows the power law dependence on magnetic field in the form of,

peak of density of states (N (εF)) near Fermi level of NbSe2 with the variation of the magnitude of the transferred charge of the different NbSe2 complexes. Luo et al. [24] estimated the N (εF) values range from 4.08 states eV−1 (formula unit)-1 for NbSe2 to 2.60 states eV−1 (formula unit)-1 for Cu0.07NbSe2, which results Tc as low as 2.9 K in Cu0.07NbSe2 compared to 7.1 K of NbSe2. So, the rapid destruction of Tc can be assigned here due to the reduction in density of states associated with the charge transfer by V impurities in the V0.0015NbSe2 system. Again, the scattering of the charge carriers from the disorder induced (to the conduction plane) by the V doping may also have an influence on Tc. The temperature dependent R (T) analysis confirms that V atoms act as strong scattering centres by enhancing the interband s-d scattering as well as electron–electron scattering, which might diminish the Tc of V0.0015NbSe2. However, the presence of V impurities as magnetic cluster has also been explored using the dc susceptibility measurement that suggests the local antiferromagnetic ordering of V0.0015NbSe2 at low temperature but only in presence of external field (H ≥ 0.3 T). So, the near halving of the Tc of NbSe2 by V doping indicates the combined effect of the charge transfer of the V0.0015NbSe2 complex and the disordering introduced scattering by the V doping. Furthermore, Fig. 4(b) shows the temperature dependence of resistance at 0.2 T, 0.4 T, 0.6 T, 0.8 T, 1 T and 1.5 T magnetic fields. To investigate the presence of the glassy state of FLL in V0.0015NbSe2, we have analysed the magnetoresistance data of different external fields. The electrical resistance is studied below the TAFF region following to the vortex glass theory. The temperature dependence of resistance in the vortex - glass critical region (i.e. the region between vortex glass transition temperature (Tg) and vortex glass critical temperature (T*)) follows the linear relation R (T ) ∝ (T − Tg ) s , where s is the critical exponent [51]. As shown in Fig. 4(c), the linear resistance below vortex glass critical temperature T* is well described by this equation and a straight line is shown in the critical region of the glass transition of

U0 (H )~H−α

∂lnR −1 ⎡ ⎣ ∂T ⎤ ⎦

The exponent α has a smaller value 0.5 up to H = ~ 0.7 T and a large value 0.9 over ~ 0.7 T, for H||ab plane. This is the similar mechanism as shown in many iron-based superconductors [56]. As mentioned by Choi et al. [53], the U0(H) value of Co doped NaFe1-xCoxAs (with × = 0.01, 0.03 and 0.07) follows power law relation with lower α value (~0.29) below H ~ 2 T and large α value (~0.7) at high magnetic field for H || ab plane indicating two different pinning mechanism. Under the E-P crossover model, U0 should increase with magnetic fields in the elastic creep regime following the relation U0 ∝ HνJ-μ with a positive ν value. However, according to the plasticflux-creep-theory, the magnetic field dependence of U0 should follow the relation U0 ~ H-0.5[57]. In this region, the vortices are plastically deformed and entangled due to the point defects in potential background of weak pinning. In the high magnetic fields, the entangled vortices are cut and disconnected due to the faster motion of vortices so that the U0(H) follows the relation U0 ~ H-0.7[58]. The even faster reduction in U0 with magnetic fields is obtained due to the entangled vortex liquid behaviour in a state of stronger pinning associated with point defects. From this point of view, it is reasonable to assume that the field dependence of U0 in V0.0015NbSe2 is governed by weak plastic pinning upto H = 0.7 T and after that it follows stronger entangled state in the vortex liquid phase. In Fig. 5, we represent the vortex phase diagram of V0.0015NbSe2 based on the magnetization and magneto-transport studies. The characteristic fields like Hc2, Hirr, H*, Hg are confirmed from the magnetotransport measurement and the other two fields - HSMP and Hp are confirmed from the magnetization measurement. The Hc2(T) and Hirr(T) are formulated from the 90% and 10% Rn of R-T curve at a constant magnetic field (as shown by the open and solid circles in Fig. 5), respectively. The locations of H* and Hg are obtained from the deviation of the temperature dependence of resistance from vortex glass critical region (as shown by open and solid squares in Fig. 5), respectively. However, HSMP and Hp indicate the peaks associated with SMP effect and PE effect which are determined from the anomalous variations of Jc

versus T plot. The Tg value at each magnetic field is determined from the extrapolation as shown in Fig. 4(c). Here T* is described as the temperature which departs from the linear electrical resistance of the vortex glass state and is approximately equal to the temperature at the lower side deviating from the TAFF fitting. In Fig. 4(d), the estimated critical exponent s is plotted as a function of magnetic field which is smaller than 2.7 for all magnetic fields. This is the lower limit of s predicted by 3D vortex glass theory [2]. So, it can be concluded here that the vortices are frozen to 2D vortex glassy state below TAFF region and coincide with the region of SMP effect. Now to investigate the effect of V substitution on the motion of thermally activated vortices in TAFF region of NbSe2, we evaluated the temperature and magnetic field dependence of thermal activation energy (TAE) from the magnetoresistance measurement. The broadening of the superconducting transition width in external magnetic field is strongly related to the thermally activated flux flow mechanism. Considering the lower value of Jc and JBVL≪1, (where V and L are the bundle volume and hopping distance) the temperature dependence of resistance in TAFF region can be described as

R=

2R c U U U exp ⎛− ⎞ = R 0f exp ⎛− ⎞ T ⎝ T⎠ ⎝ T⎠

(1)

where U(=JC0 bVL) symbolises TAE of FLL in TAFF region and R c =v0 LB / Jc 0 is a temperature independent constant. Assuming 2R U R 0f = Tc = constant and linear dependence of TAE on temperature

(

)

(

(i.e., U (T, H) = U0 (H ) 1 −

T Tc

(2)

) ), the relation between lnR vs. 1/T

provides the Arrhenius plot letting lnR (T , H ) = lnR 0 (H ) − U0 (H )/ T where lnR 0 (H ) = lnRof + U0 (H )/ Tc . The slope of lnR vs. 1/T curve gives U0(H) value which is known as apparent activation energy with the y intercept as lnR0(H). Fig. 4(e) demonstrates the Arrhenius plot of V0.0015NbSe2 single crystal at magnetic fields of H = 0.2 T, 0.4 T, 0.6 T, 0.8 T, 1 T and 1.5 T 6

Journal of Magnetism and Magnetic Materials 507 (2020) 166817

R. Pervin, et al.

the regions above H*(T) has been named as vortex liquid state. Finally, the state above Hc2 is referred as normal state suggesting the complete destruction of superconducting state of V0.0015NbSe2. 4. Conclusions We investigated here the nature of the vortex motion and the corresponding vortex phase diagram in different position of mixed state of V0.0015NbSe2 using the magnetic and magnetoresistance measurement for H//ab plane. The presence of the V atoms act as weak point defect centres which result the SMP effect in the M-H curves. At the low fields, the Jc follows 3D collective creep following the single vortex, and large bundle pinning regime. At higher temperatures, the SMP moves away from Hc2 to the lower magnetic field and finally disappear near transition region. The fp vs. h curve shows prominent PE near Hirr indicating 2D to 3D lattice distortion associated with lattice softening. Magnetotransport measurements show glassy transition below TAFF region with 2D characteristics. The temperature dependence of resistance at TAFF region is analysed with Arrhenius relation by considering the linear temperature dependence of U0(H). The magnetic field dependence of U0(H) shows a power law relationship of U0(H) ~ H-α. The exponent increases from 0.5 to 0.9 at a crossover field of ~ 0.7 T indicating two different pinning mechanism. It suggests that there is a crossover from weak plastic pinning to strong entangled state in the vortex liquid state due to the presence of weak disorder. Finally the vortex phase diagram of V0.0015NbSe2 shows collective creep region (i.e., the Bragg Glass state), plastic creep region, vortex glass state, vortex glass critical state and the vortex liquid state at different regions of magnetic fields and temperatures.

Fig. 5. Vortex phase diagram plot of V0.0015NbSe2 shows different phases, i.e., the collective creep region, plastic creep region, vortex glass state, vortex glass critical state, and the vortex liquid state. The solid lines correspond to the fits 90% − T , Hirr – T, HSMP - T and Hp - T curves. performed to the Hc2

with magnetic field. The Hc2-T curve is fitted with the anisotropic

(

)

a b

T Ginzburg-Landau model, Hc 2 (T ) = Hc 2 (0) ⎡ 1 − T ⎤ (as indicated by c ⎣ ⎦ black solid line) associated with the Nb bands at Fermi energy level as we stated earlier [28]. The Hirr-T curve is fitted with the relation, Hirr (T ) = Hirr (0)[1 − ((T / Tc )2]3/2 as represented by red solid line in the vortex phase diagram. This confirms the presence of giant flux creep in V0.0015NbSe2 [59]. As HSMP -T curve don’t follow linear behaviour, so it can be predicted to have different origin from those superconductors having linear dependence of HSMP on T. The curve is well fitted with functional relationship having the expressions T HSMP (T ) = HSMP (0) × (1 − Tc )1.5 with HSMP(0) = 0.85 T. Sugui et al. [60] reported similar positive curvature with decreasing temperature for T ≥ 6 K in deoxygenated YBa2Cu3O6.65 single crystal with the relation (1 − T / Tc )m with m = 1.5. They refer it to the crossover from collective pinning below Hp to the plastic pinning that controls creep above Hp. The author latter shows the difference in the relaxation rate with temperature for these two pinning mechanisms resulting the positive curvature of SMP with decreasing temperature. Similar case is observed by Ahmed et al. [39] in the optimally doped and overdoped NaFe1-xCoxAs single crystals (with x = 0.03, 0.05 and 0.07) for H//c axis. However, Abulafia et al. [61] showed the temperature dependence of SMP position with the relation Hp = [1- (T/Tc)4]1.4 which supports the origin of the fishtail effect as a crossover from elastic to plastic creep in YBCO crystals. So, the temperature dependence of SMP studies indicates the HSMP-T line as a transition from collective pinning region to the plastic pinning region. Based on the above analysis, the H-T space of V0.0015NbSe2 (especially the region between HSMP (T) and the Hc2 (T) curves) has been divided into several vortex phase regions. The regime below HSMP represents the collective creep phase which is also marked as the quasi ordered Bragg glass state. It is avoided here to make the domains of the low field single vortex pinning region of V0.0015NbSe2 as distinct from the collectively pinned state. The region between HSMP and Hp is designated as the plastic creep regime which merges with the disorder dominated vortex glass state at Hp. The transition at Hp might be an indication of the disorder similar to melting, i.e., from the plastically deformed solid to a pinned amorphous state. The region after Hp specifies the dislocation mediated vortex glass phase where FLL shows 2D characteristics. The narrow regime between the Hg(T) and H*(T) has been noticeable as the vortex glass critical state indicating the initialization of the resistive region of vortex phase diagram. However,

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the Department of Science and Technology (SERB-DST), India by granting prestigious‘Ramanujan Fellowship’award (SR/S2/RJN-121/2012) and a CSIR support project (grant no. 03(1349)/16/EMR-II) to PMS. PMS is thankful to Prof. Pradeep Mathur, Director and SIC (Sophisticated Instrument Centre) of IIT Indore, India for making availability of essential facilities for research. The author RP acknowledges DST, India for the esteemed SRF Inspire fellowship (DST/INSPIRE/03/2014/004196). The author MK thanks UGC-RGNF-SRF for granting its esteemed fellowship. The author SA thanks DST (SERB, FIST, and PURSE), India for supporting financially. The authors also express gratitude to Dr. R. Rawat, Scientist, UGC-DAE, India Consortium for Scientific Research, Indore for permitting low temperature 4-probe resistivity measurement facility. References [1] M.J. Higgins, S. Bhattacharya, Varieties of dynamics in a disordered flux-line lattice, Phys. C 257 (1996) 232–254. [2] G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Vortices in high-temperature superconductors, Rev. Mod. Phys. 66 (1994) 1125–1388. [3] E. Zeldov, D. Majer, M. Konczykowski, V.M. Vinokur, H. Shtrikman, Thermodynamic observation of first-order vortex-lattice melting transition in Bi2Sr2CaCu2O8, Nature 375 (1995) 373–376. [4] A. Schilling, R.A. Fisher, N.E. Phillips, U. Welp, D. Dasgupta, W.K. Kwok, G.W. Crabtree, Calorimetric measurement of the latent heat of vortex-lattice melting in untwinned YBa2Cu3O7-δ, Nature 382 (1996) 791–793. [5] D.S. Fisher, M.P.A. Fisher, D.A. Huse, Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors, Phys. Rev. B 43 (1991) 130–159. [6] M. Daeumling, J.M. Seuntjens, D.C. Larbalestier, Oxygen-defect flux pinning, anomalous magnetization and intra-grain granularity in YBa2Cu3O7-δ, Nature 346

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