Effect of A-site ionic radius on metamagnetic transition in charge ordered $Sm_{0.5}(Ca_{0.5-y}Sr_{y})MnO_3$ compounds

TL;DR

This study explores how increasing the A-site ionic radius via Sr doping affects the metamagnetic transition in charge-ordered Sm-based manganites, revealing a decrease in critical magnetic field and phase separation enhancement.

Contribution

It provides new insights into the role of A-site ionic radius and Sr doping in controlling metamagnetic transitions and phase separation in Sm-based manganites, supported by experimental and theoretical analysis.

Findings

Critical field decreases with Sr doping.

Phase separation increases with A-site ionic radius.

Metamagnetic transition is martensitic in nature.

Abstract

We investigate the ultra-sharp jump in the isothermal magnetization and the resistivity in the polycrystalline $Sm_{0.5}(Ca_{0.5-y}Sr_{y})MnO_3$ $(y = 0, 0.1, 0.2, 0.25, 0.3, 0.5)$ compounds. The critical field $(H_{cr})$, required for the ultra-sharp jump, decreases with increase of `Sr' concentration, i.e. with increase of average A-site ionic radius $\langle r_A\rangle$. The magnetotransport data indicate that the phase separation increases with the increase of $\langle r_A\rangle$, i.e. with $y$. The dependency of $H_{cr}$ with magnetic field sweep rate reveals that the ultra-sharp jump from antiferromagnetic (AFM) state to the ferromagnetic (FM) state is of martensitic in nature. Our two-band double exchange model Hamiltonian calculations show that the `Sr' doping induces the ferromagnetic clusters in the antiferromagnetic insulating phase and in turn reduces the critical field. In the end we present a phenomenological picture obtained from our combined experimental and theoretical study.

Tables

Table 1. Table 1: The lattice parameters and average A-site ionic radii for the samples S ​ m 0.5 ​ ( C ​ a 0.5 − y ​ S ​ r y ) ​ M ​ n ​ O 3 𝑆 subscript 𝑚 0.5 𝐶 subscript 𝑎 0.5 𝑦 𝑆 subscript 𝑟 𝑦 𝑀 𝑛 subscript 𝑂 3 Sm_{0.5}(Ca_{0.5-y}Sr_{y})MnO_{3} ( y = 0 , 0.1 , 0.2 , 0.25 , 0.3 , 0.5 𝑦 0 0.1 0.2 0.25 0.3 0.5 {y=0,0.1,0.2,0.25,0.3,0.5} )

y	a ($\AA$)	b ($\AA$)	c ($\AA$)	$⟨r_A⟩$ ($\AA$)
0	5.423	5.370	7.582	1.156
0.1	5.415	5.381	7.593	1.169
0.2	5.410	5.401	7.626	1.182
0.25	5.404	5.413	7.629	1.188
0.3	5.410	5.416	7.634	1.195
0.5	5.441	5.425	7.660	1.221

Equations

$$H$$

Full text

I Introduction

Recently, materials exhibiting field induced metamagnetic phase transition between two energetically competing phases have attracted a lot of attention due to its complex nature Mahendiran ; Autret ; Fisher ; Hardy1 ; KrishnaM . The occurrence of metamagnetic transition is perceptible by the sharp jump in isothermal magnetization. It is well established that this transition is independent to the microstructure and actually related to the intrinsic nature of the materialsc̃iteOuyang. Many extensive studies on this magnetic field induced metamagnetic transition have been carried out over the last decades Roy ; Velez ; Choi ; Danjoh . Examples of such materials studied include certain phase separated manganites, inter-metallic alloys such as $Nd_{5}Ge_{3}$, $Gd_{5}Ge_{4}$, $CeF_{2}$, etc. and some phase separated well known multiferroic $Eu_{1-x}Y_{x}MnO_{3}$ systems. The appearance of the magnetization steps is found to be sensitive to the cooling magnetic field as well as on the magnetic field sweep rate Mahendiran ; Hardy1 . Hardy et al Hardy2 have shown that, in $Pr_{0.5}Ca_{0.5}Mn_{1-x}Ga_{x}O_{3}$, the spontaneous magnetization jump occurs in the time evolution of magnetization for a fixed temperature and magnetic field. Wu et al. Wu have also observed the same phenomenon in manganite thin films. The observation of magnetization (and resistivity) steps in $(La_{0.5}Nd_{0.5})_{1.2}Sr_{1.8}Mn_{2}O_{7}$ is also reported by Liao et al Liao . But, the origin of these metamagnetic transition is still a matter of investigation. Very different kind of mechanisms have been proposed, such as field dependent orbital ordering in $Pr_{0.5}Ca_{0.5}Mn_{0.95}Co_{0.05}O_{3}$ Mahendiran , spin quantum transition in $Pr_{5/8}Ca_{3/8}MnO_{3}$ Cao , spin reorientation in $FeRh$ thin films Bordel , geometrical frustration in garnets Tsui , spin flop transition in $Ca_{3}CoMnO_{6}$ Flint and burst like growth of the ferromagnetic fraction in the phase separation picture. According to the most of the authors the origin of the magnetization steps is of martensitic in nature Hardy1 ; Hardy2 ; Hardy3 . In spite of having lot of study to analyze metamagnetism in various systems the origin through detailed analysis has been rarely addressed.

In manganites the metamagnetic transition is usually observed in low bandwidth charge ordered systems. Therefore, in our investigation, to understand the origin of metamagnetic transition we have chosen $Sm_{0.5}Ca_{0.5}MnO_{3}$ (SCMO) as parent compound, which is one of the lowest bandwidth and robust charge ordered system. It needs 470 kOe magnetic field at 4 K for the metamagnetic transition Tokura . As the electronic bandwidth depends on the average A-site ionic radius $\langle r_{A}\rangle$ Moritomo ; Mathieu , our study by changing the average A-site ionic radius will give us the lead to figure out the origin of the metamagnetic transition. To obtain materials with different electronic bandwidth, we replace ‘Ca’ ions in $Sm_{0.5}Ca_{0.5}MnO_{3}$ compound by ‘Sr’ ions. This ‘Sr’ doping undoubtedly increases the $e_{g}$ electronic bandwidth as ‘Sr’ has higher ionic radius as compared with ‘Ca’. By varying the concentration of ’Sr’ doping we prepared a set of samples with different $\langle r_{A}\rangle$ and analyzed their structural, magnetic and electrical transport properties. We observe that the critical field decreases with the increase of $\langle r_{A}\rangle$. We explain this by taking the induced ferromagnetic clusters with ’Sr’ doping in to account, which act as the nucleation centers for the metamagnetism. In addition, we performed spin-fermion Monte Carlo calculations using double exchange model Hamiltonian to support our experimental results.

II Sample preparation and characterization

All the bulk polycrystalline compounds $Sm_{0.5}(Ca_{0.5-y}Sr_{y})MnO_{3}$ (${y=0-0.5}$) have been prepared by the well known sol-gel method with $Sm_{2}O_{3}$, $CaCO_{3}$, $Sr(NO_{3})_{2}$ and $MnO_{2}$ as the starting chemicals of purity $99.9\%$. In order to prepare the bulk samples decomposed gel has been pelletized and heated at $1300^{0}C$ for 36 hours.

The single phase nature of the samples have been characterized from room temperature x-ray diffraction (XRD) measurements by using Rigaku-TTRAX-III with 9 kW rotating anode copper source of wavelength $\lambda=1.54\AA$. Magnetic measurements have been performed using quantum design SQUID-VSM. The transport and magnetotransport measurements have been carried out on bar shaped samples in longitudinal geometry by four probe method using Cryogenic setup.

III Results and discussion

III.1 Structural characterization

The room temperature XRD study (Fig. 1) display the single phase nature of all the bulk polycrystalline compounds. The crystal structure information has been obtained from Rietveld refinement of the XRD data using FULLPROF software which shows that all the samples crystallize in orthorhombic structure with ‘Pnma’ space group. The extracted lattice parameter and the average A-site ionic radius $\langle r_{A}\rangle$ are calculated from shanon effective ionic radii for different $y$ (see Table. 1). $\langle r_{A}\rangle$ increases gradually with ‘Sr’ concentrations because of its larger ionic radius as compared with ‘Ca’.

We estimate the orthorhombic distortion [defined as ${\delta=\frac{a+b-c/\sqrt{2}}{a+b+c/\sqrt{2}}}$] from the lattice parameters. The variation of $\delta$ and the unit cell volume with $\langle r_{A}\rangle$ are plotted in Fig. 2. Initially distortion decreases rapidly up to $y=0.2$ with increase of $\langle r_{A}\rangle$ and then increases very slowly with $\langle r_{A}\rangle$. On the other hand, unit cell volume increases steadily with increase of $\langle r_{A}\rangle$.

III.2 Magnetotransport and magnetization study

The increase of average A-site ionic radius and reduction of orthorhombic distortion greatly influences the transport and magnetotransport properties as the bandwidth of $e_{g}$ electrons in manganites is directly proportional to the $\langle r_{A}\rangle$. The temperature dependence of resistivity ${[\rho(T)]}$ in absence of any external magnetic field has been performed for all the samples. The measurements were done during warming cycle after cooling the samples in zero magnetic field. The evolution of ${\rho(T)}$ with different ‘Sr’ concentrations ($y$) (Fig. 3) shows that the samples are insulating down to the measurable resistance limit.

There is a relative suppression of resistivity value with increase of ‘Sr’ concentrations at low temperatures. Moreover, the ‘Sr’ substitution also decreases the charge ordering temperature ($T_{CO}$) from 260 K for ${y=0}$ to 210 K for ${y=0.5}$ [see inset (A) of Fig. 3] and increases the fragility of the CO state. The reduction of resistivity with ‘y’ as well as softening of CO state is due to the increase of bandwidth by increasing A-site ionic radius. For further investigation, we analyze the high temperature (${T>T_{CO}}$) resistivity data with the help of small polaron hopping model (SPH). It is known that in manganites the electrical resistivity in paramagnetic region is mainly governed by the polaronic activation. According to the SPH model Banik the expression of resistivity is $\rho=\rho_{0}Texp(E_{A}/k_{B}T)$ where $E_{A}$ is the polaronic activation energy. From the fitting of the high temperature (${T>260K}$) resistivity data, the activation energy $E_{A}$ for ‘Sr’ doped samples has been calculated and its evolution with ‘y’ is shown in the inset (B) of Fig. 3. The activation energy reduces with ‘y’ as expected (bandwidth decreases the activation energy). Previously, it was shown that the increase of $\langle r_{A}\rangle$ converts the charge ordered state to electronically phase-separated state Gutierrez ; Rao ; Kumar1 ; Shankar and results a spontaneous metal insulator transition. Though in our case, there is no spontaneous metal insulator transition, but the reduction of resistivity and softening of CO state with ‘y’ points towards a phase coexistence scenario at larger $y$.

To have a clear vision about this phase coexistence scenario we perform the temperature variation of resistivity in presence of 90 kOe magnetic field (see Fig. 4). There is almost no effect of 90 kOe field on the resistivity of ${y=0}$ sample as expected (critical field for robust charge ordered material $Sm_{0.5}Ca_{0.5}MnO_{3}$ is 470 kOe at 4K). With substitution of ‘Sr’ in place of ‘Ca’ a huge suppression of resistivity is observed on application of 90 kOe magnetic field and shows an insulator to metal transition. Moreover, with increasing ‘Sr’ concentration the curve around the $T_{MI}$ gets broaden, which signifies the enhancement of phase coexistence. Thus, it can be firmly said that the ‘Sr’ doping weaken the robustness of CO state and introduces the phase separation.

Manganite systems being strongly correlated in nature, the phenomena of phase separation should also be reflected in magnetization data. In this regard, magnetization as a function of temperature [M(T)] has been measured in the field cooled warming (FCW) protocol in presence of 100 Oe magnetic field for (${y=0,0.1,0.2,0.25,0.5}$). The evolution of M(T) for these samples are shown in Fig. 5. At low temperature (${T<50K}$) with ‘Sr’ doping the magnetization increases. The value of magnetization increases from ${0.004\mu_{B}}$ to ${0.303\mu_{B}}$ at ${25K}$ with increasing ‘Sr’ concentration from ${y=0.25}$ to ${y=0.5}$. This result verifies the enhancement of ferromagnetic phase fraction with ‘Sr’ doping. At the same time ‘Sr’ substitution decreases the charge ordering temperature ($T_{CO}$) as well as the anti-ferromagnetic ordering temperature (${T_{N}}$) (see the inset of Fig. 5). For ${y=0.5}$ composition there is no signature of $T_{N}$. This is due to the existence of tri-critical point around ${100K}$ Hiraka .

For further investigation, we analyze the high temperature (${T>260K}$) inverse dc susceptibility (H/M) versus temperature data at 100 Oe magnetic field with the Curie-Weiss law $\chi=C/(T-\theta_{CW})$ where $C=\mu_{eff}^{2}/3k_{B}$ [$\mu_{eff}$ and $\theta_{CW}$ are the effective paramagnetic moment in Bohr magneton and paramagnetic curie temperature, respectively]. The variation of dc susceptibility (H/M) with temperature for ${y=0.1,0.25,0.5}$ samples and their corresponding Curie-Weiss fitted data are presented in Fig. 6. From the fitting, paramagnetic curie temperature comes out to be 110 K, 122 K and 145 K for the samples with ‘Sr’ concentrations ${y=0.1,0.25}$ and ${0.5}$, respectively. Furthermore, the enhancement of the effective paramagnetic moment ($\mu_{eff}=6.16\mu_{B}$ for ${y=0.1}$ to $\mu_{eff}=6.76\mu_{B}$ for ${y=0.5}$) has also been observed. This increase of $\theta_{CW}$ and $\mu_{eff}$ clearly indicates the enhancement of ferromagnetic interactions with ‘Sr’ doping. Here another point needs to mention is that the values of the effective moments are larger than the theoretical calculated value of ${4.42\mu_{B}}$. It indicates the presence of ferromagnetic clusters in the high temperature region (${T>260K}$). These clusters behaves as an individual paramagnetic entity which contains more than one Mn ions Banikrsc . This is why $\mu_{eff}$ value [= ${4.32\mu_{B}}$] for ${y=0}$ sample (without any ferromagnetic clusters) is close to the theoretical expected value. These systematic result further implies that ‘Sr’ doping induces the ferromagnetic clusters in the host antiferromagnetic phase.

III.3 Metamagnetic transition

To see the effect of magnetic field in these phase separated state, we measure the field dependence of magnetization at ${2K}$ for these samples as presented in Fig. 7. For the samples without any ‘Sr’ concentrations (i.e. ${y=0}$) and with small ‘Sr’ concentrations (i.e. ${y=0.1}$) we find a linear increase of magnetization with magnetic field up to the 70 kOe field due to the strong CO-AFM phase in parent compound SCMO. With further increase of ‘Sr’ concentration i.e. to ${y=0.2}$, a sharp metamagnetic transition is observed at 55 kOe (the magnetization increases from ${0.75\mu_{B}}$ to ${3\mu_{B}}$). So at this point the system converts completely from a CO antiferromagnetic (CO-AFM) phase to a ferromagnetic (FM) phase. The descending branch of the M-H curve remains almost flat down to 10 kOe field which indicates the irreversible nature of the field induced CO-AFM to FM transformation. With further decreasing of the field from 10 kOe we find that the magnetization rapidly decreases. On the other hand, with further increase of ‘Sr’ concentrations requirement of critical field for the metamagnetic transition decreases to 47 kOe for ${y=0.25}$ and to 20 kOe for ${y=0.5}$. Although in ${y=0.5}$, the initial increase of magnetization is like a soft ferromagnet, which indicates the dominance of ferromagnetic phases as compared to the antiferromagnetic phases in the sample. Previously, the same kind of sharp metamagnetic transition has been observed in Mn site doped CO manganites, for instance in $Pr_{0.5}Ca_{0.5}Mn_{1-x}M_{x}O_{3}$. According to Raveau et al. Mahendiran the occurrence of this step like behavior in Mn site doped manganites is because of the presence of the short range ordered ferromagnetic regions in the CO-AFM region. Here, the existence of ferromagnetic clusters and their growth with ‘Sr’ doping is also observed from the analysis of dc susceptibility data. These ferromagnetic clusters play the role of nucleation centers in the metamagnetic transitions (from CO-AFM to FM phase) and sharpness of steps indicates the jerky growth of these FM clusters. The downward shifting of the critical fields with increasing ‘Sr’ concentrations is possibly because of the increasing number of ferromagnetic clusters.

Next, we measure the resistance with variation of magnetic fields at 2 K for our samples to correlate the shifting of the critical field as seen in magnetization data. Here in the sample ${y=0.1}$, metamagnetic transition is observed at 89.7 kOe which was not visible in magnetization because of the instrumental limitation. In ${y=0}$ sample there is almost no effect of magnetic field (not shown in the figure). In the subsequent ‘Sr’ doped samples i.e. for ${y=0.2}$ metamagnetic transition occurs at 58.8 kOe [and 48.5 kOe for ${y=0.25}$]. The slight higher values of the critical field determined from R-H compared with M-H is possibly due to different average sweep rate of the field. For example for ${y=0.25}$ sample, in M-H sweep rate was 100 Oe/sec and in R-H it was 24 Oe/Sec. The dependence of critical field on sweep rate is a signature of martensitic like transition as smaller sweep rate assist the progressive accommodation of the martensitic strain which push the instability towards higher magnetic field as discussed in our earlier work Sanjibnpg .

III.4 Theoretical study

In order to further explain the experimental results we perform spin-fermion Monte Carlo calculations. Our prime motive is to analyze the role of ‘Sr’ disorder on the metamagnetic transition. In SCMO, ’Sr’ doping is simulated by adding quenched disorder to a well studied model Hamiltonian for manganites in the large Hund’s coupling limit $(J_{H}\rightarrow\propto)$ Dagotto1 ; Pradhanprl . Our model Hamiltonian:

[TABLE]

where $t_{\alpha\beta}$ is the hopping amplitude between nearest neighbor $e_{g}$ electrons with orbitals ($\alpha$, $\beta$) and $\sigma\,(=\uparrow,\downarrow)$. $\alpha$ (and $\beta$) denotes $d_{x^{2}-y^{2}}$ and $d_{3z^{2}-r^{2}}$ Mn-orbitals. $J_{H}$ (Hund’s coupling) is between Mn $t_{2g}$ spin ${\bf S_{i}}$ and $e_{g}$ electron spin $\sigma_{i}$ at site $i$, whereas J is the superexchange interaction between neighboring Mn $t_{2g}$ spins. $\lambda$ is the electron-phonon interaction between $e_{g}$ electrons and the Jahn-Teller phonon modes $(\textbf{Q}_{i})$ in the adiabatic limit. We treat $(\textbf{S}_{i})$ and $(\textbf{Q}_{i})$ as classical Dagotto2 variables. $K$ (stiffness of Jahn-Teller modes) and $|{\bf S}_{i}|$ are set to be 1. For more details please see Ref.30

We incorporated the effect of ’Sr’ disorder by adding $\sum{\epsilon_{i}n_{i}}$ term to the Hamiltonian. One generally add $\sum_{i}\epsilon_{i}n_{i}$ to the Hamiltonian such that average $\overline{\epsilon}_{i}=0$ to model A-site disorder in manganites with two A-type elements Tokura ; Anamitra [example: for $Sm_{0.5}Ca_{0.5}MnO_{3}$ (SCMO) or $Sm_{0.5}Sr_{0.5}MnO_{3}$ (SSMO) like samples]. This is done by choosing $\epsilon_{i}$ at each site from $P(\epsilon_{i})={1\over 2}\delta(\epsilon_{i}-\Delta_{H})+{1\over 2}\delta(\epsilon_{i}+\Delta_{H})$ distribution. In $Sm_{0.5}Ca_{0.25}Sr_{0.25}MnO_{3}$ (SCSMO), with three A-type elements, ${Sr^{2+}}$ ions (with larger ionic radius than $Sm^{3+}$ and $Ca^{2+}$ ions) occupy one fourth of the A-sites randomly. So by neglecting the ionic mismatch between Sm and Ca elements we model Sr and Sm-Ca disorder by adding $\sum_{i}\epsilon_{i}n_{i}$ at each Mn site picked from the distribution $P(\epsilon_{i})={1\over 4}\delta(\epsilon_{i}-\Delta_{Q})+{3\over 4}\delta(\epsilon_{i}+\Delta_{Q})$ Sanjibnpg ; Sanjibarxiv . Both $\Delta_{H}$ and $\Delta_{Q}$ are quenched disorder potentials. $\Delta_{H}$ (H stand for half) and $\Delta_{Q}$ (Q stand for quartern) are binary disorder with ratio 50-50 and 25-75, respectively. In an external magnetic field we add a Zeeman coupling term $-\sum_{i}{\bf h}\cdot{\bf S}_{i}$ in our model Hamiltonian. We measure all the parameters in terms of the hopping energy $t$. The estimated value of $t$ in manganites is 0.2 eV Dagotto1 .

We use an exact diagonalisation scheme for the $e_{g}$ electrons using different background $t_{2g}$ spins and phonon mode $(\textbf{Q})$ configurations. Background configurations were chosen using travelling cluster approximation (TCA) based spin-fermion Monte Carlo technique to access the large system size $(24\times 24$ lattice) Kumar ; Pradhanprl . In different magnetic field our measured magnetization is thermally averaged over ten different disorder samples in addition to the thermal averages during the Monte Carlo sweeps. Over 10,000 Monte Carlo sweeps were performed to thermalize the system.

First we start our calculations using $\lambda$ = 1.65 and $J$ = 0.1 that reproduces the correct magnetic phase (CE-CO-OO-I phase) at low temperatures for electron density $n$ = $1-x$ = 0.5 Pradhanprb . At T = 0.005 the magnetization (M) remains very small even for $\Delta_{Q}$ = 0.3 Sanjibnpg . In Figs. 9(a)–(d) we show the magnetization vs. field ($h$) curve for the clean system (without any disorder) using dotted lines. The metamagnetic transition is at $h$ = 0.11. For $\Delta_{Q}$ = 0.1 the metamagnetic transition remains sharp, but the critical field $h_{cr}$ decreases to 0.09 as shown in Fig. 9(a). For $\Delta_{H}$ = 0.1, the critical field for the magnetic transition remains the same to that of $\Delta_{Q}$ = 0.1. So, for $\Delta_{Q}$ = $\Delta_{H}$ = 0.1 the system behaves more or less like clean system. Also the inset of Fig. 9(d) shows that the magnetic transition for $\Delta_{Q}$ = 0.1 remains sharp even for higher temperature (T = 0.01) unlike SCSMO experiments Sanjibnpg . Therefore we believe that the disorder strength is larger that $\Delta_{Q}$ = 0.1 in SCSMO. For $\Delta_{H}$ = 0.2 and 0.3 the magnetic transition is continuous with the field and qualitatively agrees with previous work Anamitra . But the correct way to model ’Sr’ disorder in SCSMO is to add disorder that is $\Delta_{Q}$ type. It is apparently clear that the critical field for metamagnetic transition decreases to $h$ = 0.08 for $\Delta_{H}$ = 0.2 and 0.3. For $\Delta_{Q}$ = 0.2, the sharpness of magnetic transition vanishes at T = 0.01, which qualitatively matches with the trend of SCSMO experimental data Sanjibnpg .

Next, we move to analyze the M-h curve for the series (SCMO-like, SCSMO-like and SSMO-like) of materials as prepared in the experiments. We know that SSMO (SCMO) has larger (smaller) bandwidth than SCSMO. We incorporate the bandwidth variation by changing $\lambda$ (and $J$) values in our model Hamiltonian. Smaller $\lambda$ (and $J$) implies larger bandwidth or vice versa. For clarity we treat SCMO as a clean system (due to the small mismatch between Sm and Ca ionic radii) and use $\lambda$= 1.73, $J$ = 0.105 for SCMO-like materials. For SSMO-like materials we set $\Delta_{H}$ = 0.2, $\lambda$= 1.57, $J$ = 0.095. For SCSMO we choose $\Delta_{Q}$ = 0.2, $\lambda$= 1.65, $J$ = 0.1 as discussed above. Fig. 10(a) shows that our results qualitatively agree with the experiments. We denote $\Delta$ = 0.2 (0.3) [i.e. $\Delta_{Q}$ = 0.2 (0.3) for SCSMO-like material and $\Delta_{H}$ = 0.2 (0.3) for SSMO like material] for brevity. Magnetization of SCMO-like material remains small even for $h=0.12$. For SCSMO-like material the metamagnetic transition is at critical field $h_{cr}=0.08$. For SSMO we find sizeable magnetization even at $h=0.0$ and the metamagnetic transition is at $h=0.06$ (smaller than that of SCSMO). For clarity and completeness we also plot the two curves using $\Delta_{Q}$= 0.3 and $\Delta_{H}$= 0.3 (along with the clean SCMO) in Fig. 10(b). The trend of M-H curves from SCMO-like to SSMO-like materials remains qualitatively same for both set of parameters.

So the experimental scenario can be explained by a simple phenomenological picture obtained from our experimental and theoretical study (see Fig. 11). According to this picture ‘Sr’ doping (in place of ‘Ca’) in SCMO induces ferromagnetic clusters. The area and number of ferromagnetic cluster increases gradually with ‘Sr’ doping and at ${y=0.5}$ area of each ferromagnetic cluster phase is maximum. These clusters act as the nucleation center that give rise to martensitic like transformation and convert the CO-AFM phase to a FM phase. With increasing the bandwidth (by increasing $y$) the phase separation increases, i.e. the strength as well as number of these nucleation center increases and as a result the critical field decreases with $y$.

IV Conclusions

In summary, we have investigated the metamagnetic properties of the $Sm_{0.5}(Ca_{0.5-y}Sr_{y})MnO_{3}$ compounds through isothermal magnetization and resistivity measurements. The presence of ultra-sharp jump at low temperature ($T<5K$) in both isothermal resistivity and magnetization is due to the strong spin and charge coupling in the systems. The sweep rate dependence of the critical field ($H_{cr}$) indicates the martensitic scenario. ‘Sr’ doping (in place of ‘Ca’) in SCMO induces ferromagnetic clusters and the volume of these ferromagnetic clusters increases in the CO-AFM materials with average A-site ionic radius $\langle r_{A}\rangle$ as perceived from the magnetotransport and magnetization data. Our model Hamiltonian calculations also confirm this scenario. These ferromagnetic clusters act as the nucleation center in the CO-AFM background for the burst like growth from CO-AFM to FM phase at critical field. The FM fraction increases with $\langle r_{A}\rangle$ and as result the $H_{cr}$ decreases with ’Sr’ doping.

V Acknowledgements

The work was supported by Department of Atomic Energy (DAE), Govt. of India.