Designing multi-level resistance states for multi-bit storage using half doped manganites

TL;DR

This paper demonstrates the design of multi-level resistance states in a half-doped manganite to enable multi-bit nonvolatile memory, utilizing electronic phase coexistence and metastable states stabilized against thermal cycling.

Contribution

It introduces a method to create and control multiple metastable resistance states in SCSMO manganite for multi-bit storage applications, supported by experimental and theoretical analysis.

Findings

Multiple metastable resistance states stabilized up to 62 K.

Monte Carlo simulations reveal phase coexistence due to chemical disorder.

A prototype multi-bit memory device pathway is outlined.

Abstract

Designing nonvolatile multi-level resistive devices is the necessity of time to go beyond traditional one-bit storage systems, thus enhancing the storage density. Here, we explore the electronic phase competition scenario to design multi-level resistance states using a half doped CE-type charge ordered insulating bulk manganite, $Sm_{0.5}Ca_{0.25}Sr_{0.25}MnO_3$ (SCSMO). By introducing electronic phase coexistence in a controllable manner in SCSMO, we show that the system can be stabilized into several metastable states, against thermal cycling, up to 62 K. As a result the magnetization (and the resistivity) remains unaltered during the thermal cycling. Monte Carlo calculations using two-band double exchange model, including super-exchange, electron-phonon coupling, and quenched disorder, show that the system freezes into a phase coexistence metastable state during the thermal cycling due to the chemical disorder in SCSMO. Using the obtained insights we outline a pathway by utilizing four reversible metastable resistance states to design a prototype multi-bit memory device.

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Full text

Fabrication of non-volatile memory (NVM) devices with high storage density, fast switching speed and low power consumption is of current research interest Scott ; Meijer ; Chen ; Pan ; Hwang . Present day NVM devices mostly use random access memories (RAM), based on resistive switching (RS) phenomenon Sawa ; Jeong ; Kim ; Ielmini ; Russo . A typical resistive memory device uses two resistive states to store binary digits 0 and 1. Such memory devices based on resistive switching between two states face scaling issues to deal with next generation computing systems Wang1 .

A promising and challenging direction to overcome the scaling issues is to design multi-bit memory devices where the intermediate resistivity states can also be used to store digital data. For example a four-level resistive system can store two-bit data (00 or 01 or 10 or 11) in each chips as compared to one-bit data (0 or 1) in prototype two-level resistive system. The feasibility of multi-level cell has been investigated for phase change memory (PCM) in chalogenides Wuttig ; Koelmans ; Wang ; Salinga ; Xie . In PCM cells the crystallinity is controlled to obtain different resistance states. In spite of having tremendous functionality, the elemental segregation upon repeated cycling remains a major drawback for PCM cells Raoux1 ; Raoux2 ; Beneventi ; Simpson ; Boniardi ; Chen1 . In this context, the obvious question arises: can one design multiple resistance states by controlling the electronic phases, commonly seen in phase coexisted transition metal oxides Asamitsu ; Uehara ; Ahn ; Sarma ; Odagawa ; Rubi ; Hoffman to overcome the problem of elemental segregation?

In the present communication, we report a multi-level resistive system by tuning the phase competition in a half doped manganites. The charge-ordered antiferromagnetic insulating (CO-AFM-I) state, in our ${Sm_{0.5}Ca_{0.25}Sr_{0.25}MnO_{3}}$ (SCSMO) sample, melts to a ferromagnetic (FM) metallic state at a moderate magnetic field 70 kOe (one can use any field greater than critical field value $\sim$45 kOe Sanjibnpg ) at 10 K and the system converts to a phase coexisted metallic state after the removal of the magnetic field. During the zero field warming, we stop at four representative temperatures (35 K, 45 K, 52 K, 58 K) and perform temperature cycling between each representative temperatures and 10 K. Distinctly different magnetization and resistivity data generated at above four representative temperatures remains more or less unchanged during the temperature cycling. Our Monte Carlo calculations using two-band double-exchange model verifies that the system freezes to a metastable phase during the thermal cycling and attributes it to the chemical disorder. In addition, we show that these metastable states are fully reproducible to use in memory devices. Then, using four such representative metastable states (in principle many more states can be generated) we outline a procedure to design a prototype multi-bit storage device.

Magnetic and magnetotransport measurements.

We prepared high quality polycrystalline $Sm_{0.5}Ca_{0.25}Sr_{0.25}MnO_{3}$ (SCSMO) sample using well-known sol-gel technique (please see the method section for details). Fig. 1(a) shows the magnetization ($M$) vs. temperature ($T$), measured in the presence of 100 Oe external magnetic field for SCSMO [and $Sm_{0.5}Ca_{0.5}MnO_{3}$ (SCMO)] using zero field cooled warming (ZFCW), field cooled cooling (FCC), and field cooled warming (FCW) protocols. FCW curve in both SCSMO and SCMO exactly overlay the FCC curve. The bifurcation between ZFCW and FCW curves in SCSMO as well as peak in ZFCW indicates that small but finite ferromagnetic fractions are induced in SCSMO which is absent in SCMO. This is due to the substitution of larger Sr ions in place of Ca in the parent compound ${Sm_{0.5}Ca_{0.5}MnO_{3}}$ Sanjibnpg . The dip in the $dM/dT$ vs. $T$ curve for SCSMO [see the inset of Fig. 1(a)] also substantiate the presence of ferromagnetic fractions below 62 K. Along with the ferromagnetic transition the inset also depicts an antiferromagnetic transition $(T_{N})$ at 110 K and a charge ordered transition $(T_{CO})$ around 195 K. All these results signifies the presence of phase coexistence at low temperatures.

To further study the phase coexistence in SCSMO, we apply 35 kOe magnetic field and measure $M$ vs. $T$ using three (ZFCW, FCW and FCC) protocols, as shown in Fig. 1(b). Here ZFCW curves also shows a maxima around 60 K similar to ZFCW curve in 100 Oe magnetic field. For SCSMO, 35 kOe magnetic field melts the CO-AFM-I state to FM metallic state although 70 kOe magnetic field had no effect on the parent compound SCMO (see the inset for resistivity comparison). The moderate hysteresis between the FCC and the FCW measurements in 35 kOe indicates the phase coexistence between the FM and The AFM phases over the temperature range 50–100 K, but the phase coexistence diminishes for 50 kOe magnetic field [see Fig. 1(b)].

In order to explore the evolution of phase coexistence with the temperature, we measure $M$ vs. $T$ and $\rho$ vs. $T$ using different protocols. Initially we cooled the system from 300 K to 10 K. For magnetization measurements a test field (100 Oe) is always applied unless otherwise specified. Magnetization at 10 K remains very small ($<10^{-2}$ $\mu_{B}$/f.u) and resistivity is found to be insulting in nature [see Fig. 2(a)and (b))]. At this point, we apply and then remove the 70 kOe magnetic field, and record the magnetization (the resistivity) data while increasing the temperature (denoted as ZFW-I) as shown in Fig. 2(a) and (b). We find that the remnant magnetization (0.33 $\mu_{B}$/f.u at 10 K) decreases with increasing temperature. Correspondingly the resistivity increases with increasing the temperature up to 65 K and decreases thereafter. This temperature is very close to the $T_{FM}$ as shown in inset of Fig. 1(a). These result suggest that the phase coexistence developed in the system at 10 K, due to the application and removal of 70 kOe field, persists up to $\sim$65 K.

Observation of multi-level resistance states

In the 2nd protocol (ZFW-II) rather than warming the sample continuously from 10 K to 200 K we heat the sample up to 35 K and perform the temperature cycling between 35 and 10 K as shown in Fig. 2(c) (indicated by step-1). After the temperature cycle we further increase the temperature from 35 K up to 45 K and repeat the temperature cycling (indicated by step-2). Similarly we have performed temperature cycling at 52 K and 58 K indicated by step-3 and step-4, respectively. During the temperature cycling, from 35 K, 45 K, 52 K, and 58 K to 10 K, the magnetization remains unchanged and mimics the memory effect. We also performed the resistivity measurements using the same protocol [see Fig.  2(d)] and there is a one-to-one correspondence between the magnetization and the resistivity data. Experimental data for sweep rate dependence, effect of repeated cycling, time dependence, reproducibility of multilevel states (see supplementary Figs.6–10) shows that the generated four resistance states are robust by its design. Not only four but large number of resistance states can be designed using the same protocol.

Physical origin of memory states

During the temperature cycling, say at 35 K [see Fig.  2(c)], it appears that the size of the ferromagnetic regions freezes in a metastable state and as a result the magnetization remains the same. In order to verify the presence of the metastable states we study a standard two-band model Hamiltonian for the manganites in 2D. Due to the octahedral crystal field splitting the Mn $t_{\rm 2g}$ levels have lower energy than the $e_{\rm g}$ levels and the itinerant $e_{\rm g}$ electrons are coupled with the $t_{\rm 2g}$ electrons [$t_{\rm 2g}$ form the core Mn spins S (= 3/2)] via large Hund’s coupling. The $e_{\rm g}$ electrons are also coupled to the Jahn-Teller phonons with a coupling strength $\lambda$. In addition, antiferromagnetic superexchange interaction $J$ between neighboring core Mn spins is taken in to account. This well investigated Hamiltonian in the double exchange limit dagotto reproduces the phase diagram of manganites yunoki ; pradhanepl ; pradhanprb . In SCSMO, ${Sr^{2+}}$ ions (larger in size as compared to $Sm^{3+}$ and $Ca^{2+}$ ions) occupy the A-sites randomly and creates chemical disorder. In order to incorporate this disorder $\sum_{i}\epsilon_{i}n_{i}$ is added at each Mn site picked from the distribution $P(\epsilon_{i})={1\over 4}\delta(\epsilon_{i}-\Delta)+{3\over 4}\delta(\epsilon_{i}+\Delta)$, where $\Delta$ is the disorder potential. In an external magnetic field $h$, a Zeeman coupling term $-\sum_{i}{\bf h}\cdot{\bf S}_{i}$ is added to the Hamiltonian, where ${\bf{S_{i}}}$ denote classical Mn t2g spin. We use spin-fermion Monte Carlo (MC) technique based on the travelling cluster approximation tca-ref ; pradhanprl (TCA) for 24$\times$24 lattice (see Ref.[30] for details). We ensured that the system is well annealed (using $10^{4}$ Monte Carlo system sweeps in general) at each temperature.

We measure $\lambda$, $J$, $\Delta$, $h$ and $T$ (temperature) in units of kinetic hopping parameter $t$. The estimated value of $t$ in manganites is 0.2 eV dagotto . We use $J$ = 0.1, $\lambda$ = 1.65 and $\Delta$=0.3 for SCSMO Sanjibnpg . Magnetization [= $(S(\textbf{q}))^{0.5}$ at wave vector ${\bf q}=(0,0)$, where $S(\textbf{q})$ is magnetic structure factor = ${1\over 24^{2}}$ $\sum_{ij}$ $\bf{\bf S}_{i}\cdot{\bf S}_{j}$ e${}^{i\bf{q}\cdot({\bf r}_{i}-{\bf r}_{j})}$] is averaged over ten different disorder configurations in addition to the thermal averages obtained during the Monte Carlo simulations.

Initially we cooled the system (from $T$ = 0.1 to $T$ = 0.005) and the corresponding temperature dependence of the magnetization (M) for electron density $n$ = 1-$x$ = 0.5 is shown in Fig. 3(a) using circle symbols. At $T$ = 0.005, we apply and remove the external magnetic field ($h$ = 0.2). The magnetization of the system drops to 0.6 from 1 upon removal of the field. The temperature dependence of magnetization after removing the magnetic field at T = 0.005 (defined as ZFW-I) is shown by the square symbol in Fig. 3(a). In the second protocol (ZFW-II), similar to our experiment, after removing the field at T = 0.005, we increase the temperature only up to 0.01 and perform a temperature cycling below it [i.e. system is cooled to T = 0.005 and then heated up to T = 0.01] as represented by step-1 in Fig. 3(b)]. The magnetization remains unchanged during the temperature cycle. Then from T = 0.01 we further increase the temperature to 0.0125 and perform a temperature cycling below it. Similarly system is recycled to lower temperature from T = 0.015 and T = 0.0175. In all cases the magnetization remains unchanged during the temperature cycling. So, our Monte Carlo calculations systematically reproduce the experimental results.

We move now to analyze the phase coexistence of ferromagnetic-metallic and charge-ordered insulating phases using Monte Carlo snap-shots. Fig. 4(a) shows magnetization data using ZFW-II protocol (shown in Fig. 3(b)) indicating four representative points. Figs. 4(c)–(f) and Figs. 4(g)–(j) show the z components of $t_{2g}$ spins and electron density for each sites for a disorder configuration, respectively. Fig. 4(b) shows $\epsilon_{i}$ distribution for that disorder configuration. At T = 0.005 (after applying and removing $h$ = 0.2) the system consists of ferromagnetic metallic and charge-ordered insulating [see Fig. 4(c) and (g)] phases. The electron density is more or less homogeneous ($\sim$0.65) within the ferromagnetic clusters and charge-ordered (short-range) elsewhere. Comparing with the impurity locations [Fig. 4(b)] it is apparently clear that the ferromagnetic-metallic clusters are within the homogeneously distributed $\epsilon_{i}$ regions and are pinned to the disorder configuration. This is the reason for which the magnetization remains finite even after removing the magnetic field. The size of the ferromagnetic-metallic clusters decreases in size with temperature as shown in Figs. 4(d) and (h). Interestingly going from T = 0.005 to T = 0.01 [i.e. from Fig. 4(c) to Fig. 4(d)] the magnetic regions get depleted but remnant ferromagnetic regions at T = 0.01 are always part of the bigger ferromagnetic regions seen in T = 0.005. During the temperature cycling from T = 0.01 to T = 0.005 (i.e. step-1) the ferromagnetic regions [compare Figs. 4(d) and (e)] get pinned in a metastable state due to the disorder configuration [shown in Fig. 4(b)] and as a result magnetization remains the same. For T = 0.0125 the ferromagnetic regions (see Fig. 4(f) and (j)) further shrink in size and the magnetization decreases further.

Design of two-bit memory device

We have purposefully designed four-level states to store a two-bit (00 or 01 or 10 or 11) digital data in each states. Say, we assign 00 to step-1, 01 to step-2, 10 to step-3 and 11 to step-4. Then the question we ask ourselves: can we write and erase the two-bit data repeatedly in any of the four states? For this we go to 10 K [as discussed in Fig. 2(a)] in the original sample. Then we apply and remove 70 kOe external field, and increase the temperature to 52 K directly (i.e. going to step-3 directly) as shown in Fig. 5(a). Magnetization data from the thermal cycling at 52 K follows the same path as shown in Fig. 2(c). This is to write two-bit information (10) which can be read from resistivity measurement even after removing the temperature probe. We have shown the one-to-one correspondence between magnetization resistivity in Fig. 2. To erase the data we again apply and remove 70 kOe magnetic field at 10 K of step-3. Now in order to write another two-bit data, say 01, we increase the temperature up to 45 K (i.e. step-2) and perform a thermal cycling. This step-by-step procedure establishes a concrete way to write, read, and erase the two-bit digital data in our four-level resistive system.

Similar to experiment we also increase the temperature to T = 0.015 (step-3) directly from T = 0.005 (temperature at which magnetic field is applied and removed) by passing two intermediate temperature cycles in our Monte Carlo calculations and perform a temperature cycling below T = 0.015 [see Fig. 5(b)]. The magnetization data during temperature cycling at T = 0.015 perfectly matches with the step-3 of ZFW-II (dashed line). During the temperature cycling from T = 0.015 we apply and removed the magnetic field at T = 0.005 (i.e. going from filled circle symbol to filled square symbol) to erase the data. Then to write a new data by using the step-2 we increase the temperature directly to 0.0125 and perform a temperature cycling below it. Magnetization data from new step-2 also matches well with the step-2 data of ZFW-II. So, our calculations reproduce the qualitative nature of the experimental results.

We have used a direct temperature probe in our experiments. Temperature probe based on the Joule heating Lee , by using voltage pulse, can be used to design the device. The electronic phase separation (and in turn resistive states) can also be controlled by numerous ways like, applying substrate strain, using mode-selective vibrational excitations, using photo-induction and applying pressure Gillaspie ; elovaara ; Chai ; Rini ; Baldini etc.

Conclusion

In summary, our combined experimental and theoretical study outline a simple yet effective path to achieve multi-level resistance states that can give new direction to architect multi-bit storage devices for future spintronic applications. Here we devised the phase coexistence in a controllable manner in a half doped manganite below 60 K and showed that a temperature probe can be used to access four distinct metastable phases for designing a two-bit memory device. In principle it can be extended to generate many more distinctly resistive/magnetic states to devise more than two-bit devices. At the end we demonstrate the writing, reading and erasing mechanism in our prototype two-bit device. It is expected that our results will motivate experimenters to explore electronic phase separated materials to engineer future multi-bit memory devices.

Methods

Sample preparation

High quality polycrystalline ${Sm_{0.5}(Ca_{0.5}Sr_{0.5})_{0.5}MnO_{3}}$ compound was prepared by the well-known sol-gel technique by taking appropriate amount of $Sm_{2}O_{3}$, $CaCO_{3}$, $Sr(NO_{3})_{2}$ and $MnO_{2}$ as the starting materials of purity 99.9%. To prepare the bulk polycrystalline sample the decomposed gel was palletized and subsequently heated for 36 h at 13000C. For more details (also for crystalline structure study) please see Ref. 30.

Magnetic property measurements

Magnetic properties was measured by utilizing Superconducting Quantum Interference Device Magnetometer (SQUID-VSM) of Quantum Design with maximum magnetic field value of 70 kOe in the temperature range 10 K - 300 K.

Electrical and magneto-transport measurement

The electrical transport and magnetotransport measurements were performed by four probe method using the longitudinal geometry of the bar-shaped samples. Zero field and in field resistance measurements in the temperature range 20 K to 300 K was carried out using Keithley source and measure unit 2651A with the measurement limit of $10^{11}$ ohm. Below 20 K, the zero field resistance measurement was extended by using Keithley Electrometer 6517A in the capacitor arrangement method and at 10 K it exceeds our measurements limit ($10^{13}$ ohm).