The experimental site was implemented on agricultural soil at Dan Phuong district (21˚06'21.0''N, 105˚39'45.0''E)—a suburban area of Hanoi city, Vietnam for 2 years (2016 and 2017). This area has been growing crop sequence of maize - maize-rice for approximately 10 years.

The experiment site has a tropical monsoon climate with an average annual precipitation of 1721 mm, an average annual temperature of 25.14˚C, atmosphere humidity of 75.58% and a mean annual sunshine hour of 1207 h (according to the Report of Center for Agricultural Meteorological Research, Institute of Hydrometeorology and Climate Change). The soil profile of the experimental site was classified as alluvial soil of the Red river or Eutric Fluvisol (FAO, 1990). Rice-rice-maize or maize-rice-maize cropping system was the most important cropping system in the region.

Briefly, rice (Khang Dan 18 variety) and maize (HN88 variety) rotation were planted in plots of 120 m² each with 3 replicates. The experiment included 3 treatments in 2017: 1) initial soil condition: maize-rice-maize cropping system no plant return; 2) rice-rice-maize cropping (RRM-NR) no plant return; and 3) rice-rice-maize (RRM-R) with plant return during a 1-year cultivation.

Each cropping season took around 3.5 months. Leaves, stems and roots of maize and rice from the previous crops were ploughed into the soil after harvest. Maize (HN88 variety) was grown with a plant spacing of 25 cm and a row spacing of 75 cm. The chemical fertilizer 16-16-8 (16%N; 16%P₂O₅; 8%K₂O content) was applied for maize at the rate of 500 kg/ha (divided in three times), the 166 kg/ha single fertilizer P₂O₅ was used 3 days after planting and the single fertilizer K₂O was applied 45 days after planting at the rate of 166 kg/ha. Rice seedlings (Khang Dan 18 variety) were transplanted by hand with three plants/hill and a spacing of 20 cm × 25 cm. Fertilizer was applied 3 times with total 416 kg/ha chemical fertilizer 16-16-8; broadcast application at the rate of 139 kg/ha 1 - 3 days after transplanting (DAT), 165 kg/ha at 12 - 15 DAT and 122 kg/ha at 40 - 45 DAT. Weed eradication was made at 20 and 50 DAT. Pesticide management of both rice and maize seasons was in accordance with the conventional.

Soil samples were collected at the beginning and before harvesting crops. Soil samples were taken using a core sampler (6 cm i.d.) to a depth of 30 cm and then it was divided into two layers: 0 - 15 cm and 15 - 30 cm depth. This depth was chosen because it contains most of the root apparatus of rice and maize species. For each crop, three replicates were taken according to a completely randomized experimental design. Each replicate was composed of three subsamples, which were combined. Then, the soil samples were sieved (<4 mm), visible plant debris was removed, and the soils were then air-dried. On the same date, separate samples (50 mm diameter) of undisturbed soil were taken for a bulk density analysis. The samples are spread on stainless steel trays with the use of a stainless-steel spatula, air-dried at room temperature or dried at 40˚C - 50˚C in a ventilated oven for two days. Dried soils were homogenized in ceramic mortar and sieved through 1 mm mesh sieve to remove bricks, stones, gravel and roots. Samples were then ground and sieved through 100 μm mesh sieve, dried the specimen at 50˚C for 24 hours. Finally, samples were subdivided into subsamples for determination pH, soil organic carbon, total N, total P, total K, and carbon stable isotope components in SOC (¹³C/¹²C ratio - δ¹³C_SOC).

The plant samples were collected at harvesting time for each crop. Random choosing of 10 maize plants or 10 rice clusters of each treatment, rinse and subdivide into 4 parts: root, stem, leave and seeds. Each plant part was cut into 0.5 - 1.0 cm, dried at 40˚C - 50˚C in a ventilated oven until unchanged weight. Dry mass of each part was determined by weight. The dried plant samples were then grounded and sieved through 100 μm mesh sieve for carbon stable isotope ratio and percent of C.

The soil samples were characterized using common methods. The content of clay, silt and sand in the fine soil samples (grains < 2 mm in diameter) was quantified by sedimentation after removing the organic matter in a 30% H₂O₂ solution (the H₂O₂ treatment was conducted at 80˚C in a water bath until no further reaction). Soil pH was examined using 1 M KCl (1:2.5, w/v); The soil bulk density (g·cm⁻³) of the 0 - 15 cm and 15 - 30 cm soil layers was measured by collecting undisturbed soil samples using steeless metal cores of known volume (5-cm internal diameter and 5-cm length). Three core samples were taken at random from each plot. The total nitrogen (TN) and organic carbon (OC) content of the bulk soil were measured by Elemental Analyzer (EA, EuroVector, Italy); we removed inorganic carbon in soil samples by HCl 1N before determination of soil organic carbon. The humic acid and fulvic acid content were determined based on Walkley-Black method—These organic acids were oxidized with excess K₂Cr₂O₇ solution in sulfuric acid then the excess potasium bicromate content were titrated by FeSO₄(NH₄)₂SO₄·6H₂O solution, thereby deducing humic and fulvic acid content. Based on the acid insoluble nature of humic acid to separate humic acid and identify humic acid content, and then fulvic acid content was calculated. For determining total phosphorus (TP), we used sulfuric acid and perchloric acid to break down and dissolve phosphorus compounds in the soil samples. After that, we measured of phosphorus content in solution by colorimetric method. The total potasium content in soil was digested by a mixture of hydrofluoric acid and pecloric acid. Determination of potassium content in solution by Atomic Absorption Spectrometric (AAS) method, all analytical measurements were performed in triplicate.

Stable carbon isotopic composition—δ¹³C values (the proportion of ¹³C with respect to ¹²C), measured for soil and plant samples were used to determine the contribution of plant carbon source to soil organic carbon. The rice and maize plant samples and those of the soil samples were dried at 60˚C, ball-milled, passed through a 100-μm sieve, and fumigated with 12 N HCl overnight to remove carbonates [13] [14] . The δ¹³C of plant and soil samples were analyzed using isotope ratio mass-spectrometer (IRMS, Micromass GV Instrument, UK) equipped with an elemental analyzer (EA, EuroVector, Italy) at the Isotopes Hydrology Laboratory, Institute for Nuclear Sciences and Technology, Vietnam.

The ¹³C/¹²C isotope ratio is expressed in the delta notation (δ¹³C) that was expressed as:

δ 13 C ( ‰ ) = ( R sample R standard − 1 ) ∗ 100 (1)

where:

R_sample is the mole ratio of the [¹³C]/[¹²C] in the sample;

R_standard is the mole ratio of the [¹³C]/[¹²C] in the standard.

The standard was Vienna Pee Dee Belemnite (VPDB this is biogenic calcite found in PeeDee fromation in South Carolina (USA) and it was prepared and supplied by IAEA in Vienna, Austria.

With respect to the different cropping treatments, the δ¹³C values of the SOM were used to calculate the proportion of new C (f_new, i.e., the C derived from current maize/rice residues) and old C(f_old = 1 − f_new, soil C present prior to tillage, i.e., C in the initial soil) using a mass balance equation [11] :

f new = δ new − δ old δ veg − δ o l d ∗ 100 % (2)

where:

δ_new represents the δ¹³C values of organic C in soil fractions after 1years of tillage,

δ_old represents the δ¹³C values of organic C in the initial soil, i.e., the soil samples prior to tillage,

δ_veg represents the δ¹³C values of the mixed samples, including plant materials (maize and/or rice leaves, stems and roots) in both cropping treatment.

Pearson’s test was used to evaluate the correlation coefficient and differences in means of the soil characteristics: soil humidity, bulk density, pH, humic, fulvic, SOC, TN, TP, TK and δ¹³C from two depths (0 - 15 and 15 - 30 cm) among three treatments. The statistical analyses were done with SPSS 20.0 software.

Results of seasonal analysis of maize and rice samples (stump + roots, stem and leaf parts) in the study area for 2 years from 2016 to 2017 were showed in Table 1. The average of total dry biomass (stem, stump + roots and leaf parts) per 1 rice crop of 3 models was 10.64 Mg/ ha for 2 years. The average of total dry biomass (stem, root and leaf parts) per 1 maize crop of 3 models was 9.09 Mg/ha for 2 years. The average of δ¹³C values of rice and maize parts were −29.78‰ and −12.61‰, respectively. These results are completely suitable with the world research on the δ¹³C value of C₃ plants—rice and C₄ plants—maize. The different in δ¹³C value of these plants is the signature for carbon sequestration study.

We conducted sampling and analyzing some soil properties according to the depth before and after harvest of some maize-maize-rice and rice-rice-maize cultivation models. The average analysis results of soils in 2016 and 2017 at 2 depths (0 - 15 cm and 15 - 30 cm) of the MRM, RRM-NR and RRM-R models were presented in Table 2 and Table 3. Results showed that there were minor changes in the parameters of pH, SOC, TN, TK and δ¹³C between 2016 and 2017 of MRM model. In 2017, for the 0 - 15 cm soil layer, the soil organic carbon content increases gradually when shifting from maize-rice-maize and rice-rice-maize cultivation in both forms of no plant return and plant return on the fields (increase from 0.702% to 0.748% and 0.855%, respectively). For the 15 - 30 cm soil layer, the SOC content increased insignificantly from 0.36% to 0.40%. The results also showed that, when shifting to 2 rice crops in a year, the soil pH decreased (5.12 - 5.07 - 4.75) and the isotopic component δ¹³C of SOC decreased relative to the amount of straw left in the field (−24.43‰, −24.70‰, −26.00‰). In other words, the value of δ¹³C in the SOC is correlated with the isotopic value δ¹³C of the plant grown on that soil (the average value of δ¹³C of maize and rice grown in Dan Phuong were −12.61‰ and −29.78‰, respectively).

Using SPSS 20.0 software for statistical analysis of the correlation between soil moisture content, density, pH, humic, fulvic, SOM, TN, TP, TK and δ¹³C. Results of soil analysis at a depth of 0 - 15 cm (Table 4) showed that the OC content was positively correlated with the parameters of TN, TP, and fulvic and inversely correlated with δ¹³C and pH parameters. The results in Table 5 also showed the positive correlation between OC and TN, TP parameters, and inversely correlated with the δ¹³C parameter. This correlation was consistent with the trend of shifting crops from cultivating of 2 corn crops + 1 rice crop/1 year to cultivating of 2 rice crops + 1 corn crop/1 year.

The variation of SOC content of 3 models (MMR, RRM-NR, RRM-R) in 2 soil layers in 2017 was presented in Figure 1 and Figure 2. The results showed that the SOC content tends to decrease during the time of winter-spring season in both depths 0 - 15 cm and 15 - 30 cm and gradually increase during summer-autumn season and reach the highest value in September. Figure 1 and Figure 2 also showed that the content of SOC changes significantly mainly in the soil layer 0 - 15 cm. This was the topsoil that contains most of the plant residues after harvest.

The SOM content and its relation with δ¹³C in SOM was shown in Figure 3 in. The results showed that SOM content in the 0 - 15 cm soil layer was higher from 2 to 2.5 times than SOM content of the 15 - 30 cm layer and the δ¹³C value of upper layer was depleted than the δ¹³C value from 2‰ to 3‰. The depleted δ¹³C value and the increasing SOC content of the topsoil were due to SOC being decomposed from rice straw and rice roots after harvest (the average δ¹³C value of rice was −29.78‰). At a depth of 15 - 30 cm, the concentration of SOC was lower than that of the surface layer and the δ¹³C value of SOC was enriched because this layer was not replenished regularly with plant matter except deep plant roots. In addition, many published works on SOC kinetics show that δ¹³C values tend to be enriched at deeper layer due to the natural isotope fractionation of the microbial decomposition process of microorganisms and the evaporation process of ¹²C light isotope of gases such as CO₂ and CH₄.

**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

Applying the formula (2) to calculate the amount of C accumulated in the soil layers when shifting the 2 maize - 1 rice crop model to 2 rice - 1 maize crop model with no plant return and plant return in Dan Phuong alluvial soil, the results are obtained in Table 6.

The δ¹³C_SOMnew value decreased from 1‰ to 1.5‰ when we changed from 2 maize - 1 rice cultivation to 2 rice - 1 maize cultivation in 2017. For the RRM-NR model, the results showed that the average contribution rate of new plants (rice) was about 11.31% at 0 - 15 cm depth, and 6.55% at 15 - 30 cm depth and the total amount of SOM accumulated after 1 year of cultivation on both layers was 2.259 MgC/ha. When leaving rice straw in the field (RRM-R), the average contribution rates of new plants to the total amount of SOM of 0 - 15 cm and 15 - 30 cm layers were accounted for 44.14% and 16.46%, respectively. The average cumulative amount of SOM in the 0 - 30 cm layer was 9.505 MgC/ha at the RRM-R model. This value was 4 times higher than that of the RRM-NR model (2.259 MgC/ha). Thus, if farmers leave plant residues (straw) after each harvest on the field, the amount of C from new plants accumulated in the soil in the form of SOM will increase significantly. This is a way to get more CO₂ from the air into plant tissues and store CO₂ as SOC in farmland.