The tunable spin reorientation, temperature induced magnetization reversal, and spontaneous exchange bias effect of Sm_0.7Y_0.3Cr_1−xGa_xO₃

Abstract

In this work, we investigated the temperature dependent magnetic properties of SmCrO₃ by codoping nonmagnetic ions at Sm- and Cr-sites. The spin reorientation from Γ₄ to Γ₂ is tuned and the transition temperature T_SR is improved dramatically to near the liquid nitrogen temperature by Ga ion doping, which would be helpful to achieve its application in temperature sensitive spintronic devices and magnetic switching devices. An intrinsic temperature induced magnetization reversal effect from positive to negative under zero-field-cooling conditions is induced as well and its reversal evolution is strongly dependent upon doping. Moreover, the zero-field-cooling exchange bias effect still exists and shows a positive exchange bias field although it is suppressed with increase of doping concentration. Under the influence of doping nonmagnetic ions, lattice distortion is induced to some extent and the magnetic interactions of Cr–Cr and Sm–Cr are predominantly diluted, realizing control of the above phenomena. Those phenomena are discussed and successfully explained by considering the magnetic exchange interaction competitions including the isotropic, antisymmetric (or Dzyaloshinskii–Moriya interaction), and anisotropic superexchange interactions.

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Introduction

Orthochromites RCrO₃ (R = rare-earth) have received great attention recently due to their possessing abundant magnetic effects (such as temperature induced magnetization reversal (TIMR), magnetic exchange bias (EB) effect, and spin reorientation (SR) phase transition), and ferroelectricity, making them a potential candidate for technological applications.^1–7 Orthochromites RCrO₃ have a distorted orthorhombic perovskite structure (Pbnm space group) with a canted antiferromagnetic structure below the Neel temperature (T_N) caused by Dzyaloshinskii–Moriya (DM) exchange coupling between the Cr ions. Three types of antiferromagnetic configurations generally exist in orthochromites, noted in Bertaut notations⁸ as Γ₁(A_x, G_y, C_z, C^R_z), Γ₂(F_x, C_y, G_z, F^R_x, C^R_y), and Γ₄(G_x, A_y, F_z, F^R_x). The complex magnetic interactions of Cr–Cr, Cr–R, and R–R in RCrO₃, including the isotropic, symmetric, and antisymmetric anisotropic exchange interactions, result in an abundant magnetic phase diagram, such as, multiferroics,^4,9 multiple phase transitions,^10,11 a magnetic glassy phase,¹² TIMR,^13–15 conventional EB⁶ and zero-field-cooling EB (ZEB) effects,^14,16 and the SR transition.¹⁷

One of the most interesting examples of this family is the newly emerging SmCrO₃ which possesses two magnetic species, Sm and Cr ions. SmCrO₃ is reported to be ordered in Γ₄ configuration below T_N at 191 K and exhibits a SR transition to Γ₂ configuration at 34 K.^4,18 There is controversy about the SR transition so far. Gorodetsky et al.,¹⁹ reported that below the SR transition temperature (T_SR) the magnetic structure of SmCrO₃ changes from Γ₄ to Γ₂ continuously, making a second order transition. Most of the reports suggest that the second-order transition is attributed to a continuous rotation of Cr³⁺ moments.^17,20 There are a few factors that give rise to the second order SR transition, for examples, the antisymmetric exchange interaction between Cr³⁺ and Sm³⁺,⁶ and the exchange splitting and the t–e orbital hybridization between Cr³⁺ and Cr³⁺ ions.¹⁷ However, Tripathi et al.¹² suggested that the SR transition in SmCrO₃ would be a first order Morin type SR transition based on the analysis of the existence of phase coexistence and magnetic glass like freezing across T_SR, the reason of which is due to the discrete flipping of Cr³⁺ ions from the high temperature Γ₄ to low temperature Γ₁ configuration. Very recently, Tripathi et al.²¹ investigated the thermal evolution of magnetic configuration in SmCrO₃ by neutron diffraction and magnetometric study and confirmed that the uncompensated canted antiferromagnetic structure Γ₄ occurs below T_N, the collinear antiferromagnetic structure Γ₁ occurs below 10 K, and a non-equilibrium configuration with co-occurring Γ₁ and Γ₄ phases occurs at 10 K ≤ T ≤ 40 K. The competition between magnetocrystalline anisotropy and free energy derived from isotropic and antisymmetric exchange interactions among different pairs of magnetic ions is observed to govern the mechanism of SR effect.²¹ Therefore, the investigation of the SR transition, especially from the view of artificial control of the exchange interactions between chromium and samarium ions, is full of interest and finding its tunable factors and achieving its control will benefit for applications in thermomagnetic power generation, ultrafast spin switching.^22,23

Moreover, the complex magnetic exchange interactions of Sm–Cr or/and Cr–Cr and their competitions are mostly considered to be the origin of the TIMR and conventional EB and ZEB effects as well. There was no negative magnetization originally in SmCrO₃ itself and the TIMR effect can be induced by transitional metal ions doping, such as, Fe,^10,24 and Mn.^13,25 Nevertheless, negative magnetization in SmCrO₃ will be outstanding due to the intrinsic strong coupling between Sm³⁺ and Cr³⁺ spins sublattices,¹⁸ which would also be responsible for the existence of EB effect. Due to the coupling between Sm and Cr ions, a ZEB effect appears in SmCrO₃.^18,20 And nonmagnetic rare-earth ions doping at Sm-site confirm the influence of Sm³⁺ on the ZEB effect,^14,20 which would be of great interest to electric field control of EB devices as it eliminates the requirement of external magnetic field to create the unidirectional anisotropy.

In this work, we investigated the temperature dependent magnetic properties of SmCrO₃ by codoping nonmagnetic ions (Y³⁺ and Ga³⁺) at Sm- and Cr-sites, respectively. The SR transition from Γ₄ to Γ₂ is tuned and the transition temperature T_SR is improved dramatically to the liquid nitrogen temperature by Ga ions doping. The outstanding intrinsic TIMR effect from positive to negative with temperature decreasing under zero-field-cooling (ZFC) condition are induced as well at an appropriate doping content. Meanwhile, noting that a positive ZEB effect occurs at 5 K and is suppressed by doping and increasing of temperature. Those phenomena are mainly considered to be the competitions among the isotropic exchange interaction of Cr³⁺, the antisymmetric exchange interaction of Cr³⁺, the DM interaction, the single-ion magnetocrystalline anisotropy, and the isotropic and antisymmetric interaction of Sm and Cr. The dilution of Cr–Cr coupling by doping will highlight the Sm–Cr coupling, leading to the significant change in SR, TIMR and ZEB effect.

Experimental

Polycrystalline samples of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0, 0.1, 0.2, and 0.3) were prepared by conventional solid state reaction method.^14,15 High purity (99.9%) oxide of samarium (Sm₂O₃), yttrium (Y₂O₃), gallium (Ga₂O₃) and chromium (Cr₂O₃) were weighed and mixed at a stoichiometric ratio. The mixtures were first calcined at 1200 °C for 12 h with the heating rate of 2 °C min⁻¹ and cooled down with the furnace. Finally, after regrinding and tableting, the resulting products were sintered at 1400 °C for 12 h with the same heating rate. The samples were obtained after cooling with the furnace.

The X-ray diffraction (XRD) measurement was performed by Bruker D8 diffractometer with Cu Kα radiation at room temperature. The working current and voltage were 40 mA and 40 kV respectively and the diffraction angle ranges from 20–70 degree with step of 0.02 degree. And the XRD patterns were refined by Rietveld method using PC-GSAS and EXPGUI programs.²⁶ Measurement of Raman spectra of all samples with a range from 100 to 600 cm⁻¹ were conducted by EZRaman-M Portable Raman System with 532 nm excitation wavelength He–Ne laser. The field-cooling (FC) and ZFC temperature dependent magnetization curves of Sm_0.7Y_0.3Ga_xCr_1−xO₃ (x = 0.1, 0.2, 0.3) samples were measured at the temperature range of 5 K to 300 K under the magnetic field H = 100 Oe by a superconducting quantum interference device (MPMS-XL-7). The p-type magnetic hysteresis data (M–H loop) were recorded at constant 5 K in ZFC mode for Sm_0.7Y_0.3Ga_xCr_1−xO₃ (x = 0.1, 0.2, 0.3) and at various temperatures 5, 35 and 100 K for x = 0.1, at 5, 45 and 100 K for x = 0.2, and at 5, 50 and 100 K for x = 0.3, respectively.

Results and discussion

Fig. 1(a–c) shows the XRD patterns of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0, 0.1, 0.2 and 0.3) samples. The samples are regarded to be desired pure phase polycrystalline. Rietveld refinement results reveal that samples are the distorted orthorhombic perovskite structure with Pbnm (no. 62) space group, consistent with the parent sample SmCrO₃.^6,9,14 From Rietveld refinement results, we obtained data of lattice parameters a, b, c, cell volume of samples, the angle of out-of-plane Cr–O₁–Cr, and the bond length of out-of-plane Cr–O₁, listed in Table 1. It is noticeable that those parameters are not dramatically changed. Lattice parameters a and c both have the tendency to decrease with increasing doping concentration x, while parameter b almost monotonically increases. This results from the fact that the radius of Ga³⁺ (0.620 Å) ion is a bit larger than that of Cr³⁺ (0.615 Å). With an incorporation of Ga ions, the degree of crystal structure distortion to some extent increases as well, which leads to the increment of the Cr (Ga)–O bond length and Cr (Ga)–O–Cr bond angle. To quantify the CrO₆ distortion, we calculated the angles θ and φ of the CrO₆ octahedral based on the two equations θ = cos⁻¹(a/b) and φ = cos⁻¹(√2a/c) respectively,²⁷ listed in Table 1. Angle θ represents the rotation of CrO₆ octahedral about (001) axis and angel φ stands for the octahedral tilting about (110) axis. The values of both θ and φ have an upward trend with greater doping concentration x, shown in Fig. 1(e) and (f), which provides an evidence of the enhancement of lattice distortion.

Fig. 1 (a–c) The refined XRD patterns of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0.1, 0.2, and 0.3) samples. (d–f) The parameter b, the tilting angle φ and rotational angle θ of CrO₆ octahedral with doping concentration.

Table 1 The parameters a, b, and c, cell volume V, the bond angle (°) of out-of-plane Cr–O₁–Cr, the bond length of out-of-plane Cr–O₁ (Å), the rotational angle θ and the tilting angle φ of CrO₆, the compensation temperature T_comp (K), the Neel temperature T_N, the SR transition temperature T_SR, and the characteristic temperature (T′) of Sm moment ordering, and the Curie constant C (emu K mol⁻¹·Oe⁻¹), the Weiss temperature Θ, the fitted effective magnetic moment μ_eff by Curie–Weiss law and the theoretically calculated effective magnetic moment by eqn (2), and the coupling coefficient α from eqn (3)

Sample	x = 0	x = 0.1	x = 0.2	x = 0.3
a (Å)	5.34442 ± 0.00030	5.34109 ± 0.00029	5.34554 ± 0.00035	5.33979 ± 0.00029
b (Å)	5.51157 ± 0.00025	5.51421 ± 0.00022	5.51414 ± 0.00032	5.51600 ± 0.00028
c (Å)	7.62624 ± 0.00037	7.62276 ± 0.00032	7.62916 ± 0.00039	7.62133 ± 0.00045
V (Å^3)	224.63 ± 0.019	224.50 ± 0.018	224.88 ± 0.023	224.48 ± 0.021
Cr–O1–Cr	156.777(2)	153.090(1)	154.956(2)	149.456(1)
Cr/Ga–O1	1.97642(2)	1.97336(5)	2.00591(5)	1.98948(1)
χ^2	1.097	1.096	1.073	1.091
Θ	14.14676 ± 0.00028	14.39503 ± 0.00026	14.20497 ± 0.00035	14.52124 ± 0.00029
Φ	7.66203 ± 0.00078	7.73276 ± 0.00071	7.73547 ± 0.00086	7.75627 ± 0.00083
Tcomp	—	163	74	75
TN (K)	178	152	134	108
TSR (K)	28	43	58	73
T′ (K)	—	21	21	21
C	3.465 ± 0.014	2.674 ± 0.012	3.054 ± 0.011	2.965 ± 0.007
Θ (K)	−748.4 ± 3.1	−419.8 ± 2.1	−549.6 ± 2.1	−483.1 ± 1.4
μeff (μB)	5.27	4.63	4.94	4.87
(μB)	3.94	3.74	3.53	3.31

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Fig. 2 shows the room temperature Raman spectra of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0, 0.1, 0.2 and 0.3) samples. According to group theory, RCrO₃ with an orthorhombic (Pbnm) has 24 types of Raman-active modes (7A_g + 5B_1g + 7B_2g + 5B_3g).²⁸ For SmCrO₃, excluding some low-intensity modes, 11 modes (5A_g + 2B_1g + 2B_2g + 2B_3g) are detected, which are consistent with reported Raman spectra of SmCrO₃.^29–31 For only 30% Ga-doped SmCrO₃, the shape and position of Raman spectra show inconspicuous changes compared to SmCrO₃. Nonetheless, for Sm_0.7Y_0.3CrO₃ sample, the obvious peaks shift of Raman spectra relative to the parent SmCrO₃ occurs, which may be related to the prominent structural variations by Y doping, reflected and discussed in the previous work.¹⁴ For the Y- and Ga-codoped samples, the Raman spectra are almost the same to that of Sm_0.7Y_0.3CrO₃ sample. This indicates that due to the size effect and the heavier atom of Y than the transitional metal ions Raman modes are led to the obvious shift. Compared to the Raman modes and band position of YCrO₃ and SmCrO₃,²⁹ we assigned the phonon modes of Sm_0.7Y_0.3Cr_1−xGa_xO₃ samples, shown in Fig. 2. As is known that the phonon modes in RCrO₃ below 200 cm⁻¹ are related to lattice modes involving R atom vibrations and modes above 200 cm⁻¹ consist of various modes involving vibrations of the R atom and oxygen.^29–31 Specifically speaking: (1) A_g(3) and A_g(5) are CrO₆ octahedral rotations around the crystallographic y-axis and x-axis (Pbnm setting), respectively; (2) B_1g(2), B_2g(2) and B_3g(1) are related to R atomic motions; (3) A_g(6) and B_2g(3) arise from bending of the CrO₆ octahedral; (4) the B_3g(3) mode is related to the antisymmetric stretching vibrations of the O₁ and O₂ atoms.²⁹ For Sm_0.7Y_0.3Ga_xCr_1−xO₃ (x = 0.1, 0.2 and 0.3) samples, it indicated that Ga-doping does not affect the symmetric structure of the crystal. As doping concentration increases, A_g(5), B_3g(1) and B_2g(2) modes have a different degree of offset, in which A_g(5) shifts to lower wavenumber (red shift) while B_3g(1) and B_2g(2) are blue shift. Red shift of A_g(5) indicates the rotation of the CrO₆ octahedron increases, which is consistent with the calculated φ angle from XRD. The anomalous hardening of B_3g(1) and B_2g(2) modes reveals the possible displacement of R ions induced by spin-phonon coupling,³⁰ which may be related to the magnetic interactions between R³⁺ and Cr³⁺ ions.^4,30

Fig. 2 The room temperature Raman spectra of samples SmCrO₃, SmCr_0.7Ga_0.3O₃, Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0, 0.1, 0.2, and 0.3).

The FC and ZFC curves of temperature dependent magnetization of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0.1, 0.2, and 0.3) samples are shown in Fig. 3(a–c). From these graphs, it is evident that there indeed and still is antiferromagnetic transition, the SR transition, and the TIMR effect in the ZFC case. As the temperature decreases from high temperature, the magnetization curves undergo a paramagnetic to antiferromagnetic phase transition at T_N. And the Neel temperature occurs below the bifurcation temperature (T_bf) of ZFC and FC curves, the value of which is around 194 K and is independent of doping concentration. However, the value of T_N has strongly dependence on the doping concentration, which was obtained from the maximum position of the first derivative of ZFC curves and listed in Table 1. It almost decreases linearly with a tolerance of 24 K with 10% doping, which results from the dilution effect of Ga ions doping on destroying the Cr–O–Cr magnetic coupling. This leads to the fact that temperature difference between T_bf and T_N becomes bigger with increase of doping concentration. The bifurcation of ZFC and FC is the characteristic of the onset of the antiferromagnetic ordering, which is attributed to the coexistence of ferromagnetic and antiferromagnetic phases caused by magnetic anisotropy.^32–34 The destruction of Cr–O–Cr by the Ga³⁺ ions suppresses the formation of Cr³⁺ antiferromagnetic ordering and gives rise to the existence of ferromagnetic-like clusters, which can be demonstrated from the deviation of Curie–Weiss linear behaviour in the inverse susceptibility as a function of temperature (shown in Fig. 3(d)). Thus, an unchanged T_bf and reduced T_N are observed.

Fig. 3 (a–c) The ZFC and FC curves of Sm_0.7Y_0.3Cr_1−xGa_xO₃ (x = 0.1, 0.2, and 0.3). The insets show the enlarged parts of temperature near 190 K. (d) The inverse susceptibility as a function of temperature of x = 0.1, 0.2, and 0.3. The dot line stand for the fitting results by Curie–Weiss law.

For the paramagnetic region, it was best fitted by the Curie–Weiss law, χ = C/(T − Θ), where C is Curie constant and Θ is the Weiss temperature, as shown in Fig. 3(d). Based on the fitted Curie constant, the average effective magnetic moment was calculated by the following formula:

where k_B is Boltzmann constant, N_A is Avogadro constant. All the fitted and calculated values of the parameters are summarized in Table 1. Theoretically, the whole effective magnetic moment in paramagnetic region can be calculated using the free ionic moments of Sm³⁺ and Cr³⁺ as the following equationwhere μ_Sm = 0.84 μ_B, μ_Cr = 3.87 μ_B, μ_Y = 0, and μ_Ga = 0. Note from Table 1 that the fitted effective magnetic moments (μ_eff) is around 1.3 times larger than the theoretical ones , which demonstrates that the effective magnetic moments of samples are not only from the free ionic moments of Sm³⁺ and Cr³⁺. This large calculated effective paramagnetic moment in SmCrO₃ seems to be a common thing that most of the reported effective paramagnetic moment in SmCrO₃ is larger than the theoretical value calculated by free magnetic ions only.^{6,16,17,35,36} However, few of them discuss its origin. One of the work done by ab initio calculation suggested that the pressure produced by the tilting of the oxygen octahedral causes the difference between the experimental calculated effective paramagnetic moment and the theoretical one.³⁷ The experimental and theoretical investigations of this issue are appealed.

As temperature continues to decrease, a canted antiferromagnetic phase with weak ferromagnetic component is formed between chromium ions, showing a dramatic increment of the macroscopic magnetic moment. In the ZFC curve, an obvious negative magnetization occurs below T_N at x = 0 (shown in our previous work)¹⁴ and x = 0.1. Moreover, note that when x ≥ 0.2, the magnetization in ZFC mode is still positive when temperature is below T_bf and goes across the zero-magnetization-line to a negative value at the compensation temperature (T_comp), showing the magnetization reversal. And this TIMR effect becomes remarkable when x = 0.3, showing its evolution with doping concentration. Most reported TIMR effect from positive to negative occurs in FC mode while few in ZFC mode.^{2,10,25,38–42} Here, the TIMR effect observed in ZFC mode shows dependence on doping concentration and the compensation temperature for x = 0.2 and 0.3 is at near 74 K and almost the same, indicating its intrinsic feature.

In order to prove the intrinsic nature of TIMR effect in ZFC by ruled out the effect of a small negative trapped field in the superconducting magnet during cooling on the negative magnetization,⁴³ we measured the FC M(T) curves with very small cooling fields H_cooling = ± 10 Oe respectively and the applied field H still keeps 100 Oe. The results shown in Fig. 4 show that the TIMR effect still exists both in positive and negative cooling field. This signifies that even though there is a small trapped field when doing ZFC measurement, the negative magnetization and magnetization reversal observed in our measurement would not be affected. Moreover, the TIMR effect here is actually dependent on the applied field. The field-dependence of magnetization reversal is observed, as shown in Fig. 4(b). The ZFC and FC curves under applied small field H = 10 Oe were measured. It shows that magnetizations below T_N are negative in both ZFC and FC curves. And when the applied field increases upto 100 Oe the magnetization in the temperature interval T_comp < T < T_N becomes positive. These results prove the intrinsic nature of the TIMR effect.

Fig. 4 (a) The field-cooling M(T) curves of Sm_0.7Y_0.3Cr_0.7Ga_0.3O₃ sample with cooling fields H_cooling = ± 10 Oe respectively and the applied field is 100 Oe. (b) The ZFC and FC curves of Sm_0.7Y_0.3Cr_0.7Ga_0.3O₃ sample with applied field 10 Oe.

With temperature further cooling, magnetization drops abruptly in FC at T_SR for x = 0.1 and 0.2 while rises for x = 0.3, where the SR effect happens. In the meantime, there is a fluctuation of magnetization in ZFC at x = 0.1 and obvious drops at x = 0.2 and 0.3 while it never happened in SmCrO₃.

This SR effect is assigned to the transition from spin configuration Γ₄ to Γ₂.^4,6 In our previous work, Y³⁺ doping at Sm-site has a tiny effect on the value of T_SR with 6 K lower at 30% Y³⁺ doing sample than SmCrO₃.¹⁴ Interestingly, in the series of Ga-doped Sm_0.7Y_0.3CrO₃ samples here, the T_SR increases uniformly with an increment of 15 K and reaches to 73 K at x = 0.3, closely to the compensation temperature (75 K) and the liquid nitrogen temperature. Nonetheless, this inconsistency of T_SR and T_comp illustrates that the TIMR effect is independent of the SR effect and the TIMR occurs ahead of the SR effect with decreasing of temperature. Moreover, the magnetization of FC curve at Γ₂ increases while the one at Γ₄ decreases correspondingly with increasing of doping concentration. As x = 0.3, the magnetization at Γ₂ overcomes the one at Γ₄. It is reasonable because that the SR transition temperature is improved to 73 K where the contribution of Sm³⁺ moments is low. And the spontaneous moment parallel to a crystallographic axis (Γ₂) of SmCrO₃ is larger than the one parallel to c crystallographic axis (Γ₄).^4,19 Moreover, the occurrence of SR transition has been attributed to the strong antisymmetric exchange interaction between Sm³⁺ and Cr³⁺ and the dilution effect of Ga ions doping on Cr ions moment gives rise to the improvement of the whole net magnetization value. With further doping, the competitiveness of Cr³⁺ moment relative to Sm³⁺ moment decreases and it will reduce and even destroy the antisymmetric Sm–Cr interactions, leading to the parallel orientation of Sm and Cr spin moments, especially for the samples with high doping concentration. An enhancement of magnetization at low temperature thus will be reasonable caused for x = 0.3.

Now we turn to give the interpretation of the TIMR accompanied with SR effect in ZFC curve. In these oxides magnetization reversal was explained in terms of competition between single-ion magnetic anisotropy and antisymmetric DM interactions.^44–46 In antiferromagnetic materials with low symmetry, the appearance of weak ferromagnetism is predominantly determined by either single-ion magnetocrystalline anisotropy or DM interactions. It has been suggested that the net moment produced by these mechanisms can be oriented in opposite direction and have different temperature dependence in some cases.^47,48 The magnetic exchange interactions between magnetic ions generally include the isotropic, the antisymmetric (or DM interaction), and anisotropic symmetric superexchange interactions. Therefore, the Hamiltonian of the SmCrO₃ system in the absence of external magnetic field can be written as follows:

H = H^Cr–Cr + H^Cr–Sm (3)

H^Cr–Cr = H^M_iso + H^M_anti + H^M_sin (4)

H^Cr–Sm = H^RM_iso + H^RM_anti (5)

where H_iso, H_anti represent the isotropic, antisymmetric exchange interactions, respectively, and H_sin is the single-ion anisotropic term. Based on this model, we schematically plotted the spin evolution with temperature in the ZFC mode in Fig. 5 and discussed the mechanisms behind in detail in the following.

Fig. 5 The ZFC curves of samples x = 0.1, 0.2, and 0.3 and their schematic of spin evolution with temperature.

When x ≤ 0.1 and T < T_bf, the strong isotropic exchange interaction between Cr³⁺ spins leads to the antiferromagnetic ordering at T_N. The net moment of Cr is oppositely aligned to the measuring field, showing the negative magnetization and increases in the absolute value with further cooling. However, for x ≥ 0.2, the canted antiferromagnetic moments of Cr³⁺ spins are positive. The small canted antiferromagnetism of Cr³⁺ spins below T_N are attributed to two mechanisms, i.e., the single-ion anisotropy of Cr³⁺ ions and the antisymmetric Cr³⁺–Cr³⁺exchange interactions, which do not need to have the same sign.⁴⁸ Due to the dilution of Cr–Cr exchange interaction by Ga doping, the single ion anisotropy of Cr³⁺ ions dominates, leading to the net moment parallel to measuring field. With further cooling, for x = 0.1, the SR happens at 43 K, making the spin of Cr deflect. At this time, the DM interaction between Cr spins, which has an opposite sign with that of single-ion anisotropy of Cr³⁺, increases and competes with the interaction of single-ion anisotropy of Cr³⁺. When the DM interaction between Cr–Cr dominates over single-ion anisotropy of Cr³⁺, the net moment of Cr reverses and correspondingly the Sm³⁺ spin will also reverse due to isotropic and antisymmetric of Sm–Cr interaction. This process is accompanied by the SR effect making it happened step by step. At lower temperature, the antisymmetric Sm–Cr interaction that produces an effective field on Cr spins becomes increasingly predominant due to the increase of Sm moment. When the effective field with respect to this antisymmetric interaction is stronger than single-ion anisotropy of Cr ions and the antisymmetric interaction between Cr spins below T_SR, the Cr spins will rotate from the c axis to a axis.

With regard to samples for x ≥ 0.2, the magnetization reverses firstly due to the antisymmetric Sm–Cr interaction. When the moment of Sm equals to that of Cr, the net moment becomes zero at T_comp. Then the SR effect occurs, causing the dramatic drop of the magnetization in ZFC. If considering the isotropic and antisymmetric Sm–Cr interactions, the spin reversal of Cr will be accompanied with the reversal of Sm moment, leading to a fluctuation of the magnetization even positive one instead of a dramatic dropping. Here the drop of the magnetization means that the isotropic and antisymmetric Sm–Cr interactions are seriously reduced with Ga doping, making the magnetocrystalline anisotropy dominate. This is consistent with the reported result²¹ and results in the parallel arrangement of Sm³⁺ moment with Cr³⁺ net moment. Carefully seen from the ZFC curves that there is another transition at nearly 20 K, which is obvious at x = 0.1 and displays a broad peak at x = 0.2 and 0.3. This is attributed to the Sm³⁺ magnetic ordering with the stabilized Cr³⁺ spin of Γ₂ configuration.

Besides the TIMR and SR effect, the ZEB effect of these samples are also experimentally observed. For Sm_0.7Y_0.3CrO₃, it was reported to show the negative ZEB effect at low temperature and reversal to positive one at T_SR < T < T_N, similar to the behaviour of SmCrO₃¹⁴. The p-type M–H curves (0 → (+H_max) → (−H_max) → 0) measured under ZFC mode at various temperatures are shown in Fig. 6. All the curves show hysteresis loops with certain amount of coercivity (H_C) but are not saturated at high magnetic field, indicating the coexistence of weak ferromagnetism and antiferromagnetism. As is known that an EB effect is usually formed at the ferromagnetic/antiferromagnetic interface. The EB field H_EB was determined by H_EB = (H_C+ + H_C−)/2, where H_C+ and H_C− are the left and right coercive fields respectively. All the values of H_EB, H_C, and the remnant magnetization M_r are listed in Table 2. And the relationship of H_EB and H_C with doping concentration are plotted in Fig. 6(d). Note that at 5 K the ZEB effect does not only still appear but also show positive when doping Ga³⁺ ions and linearly decreases with increase of doping concentration. Then the ZEB effect disappears at temperature between T_N and T_SR, which may be due to the stronger performance of weak ferromagnetism than antiferromagnetism. The ZEB effect was reported to be observed in the parent SmCrO₃.^18,20 The EB field at 5 K can be reached to almost 5 kOe.¹⁸ The origin of ZEB effect in SmCrO₃ is considered to be the local interaction between the canted antiferromagnetic Cr sublattices and orientated Sm sublattices.¹⁸ The coupling between Sm³⁺ and Cr³⁺ via internal magnetic field H_I⁴⁹ results in large H_EB.²⁰ The positive ZEB effect may be related to the behaviour in layered magnetic systems,^50,51 where positive EB appears if the interactions at the interfaces are antiferromagnetic, whereas negative EB is present for ferro-magnetic interactions. As reported, by nonmagnetic rare-earth ions doping at Sm-site, such as La, the exchange bias field H_EB decreases monotonously with doping level increasing due to the weakness of the Sm–Cr coupling.²⁰ The H_EB of ZEB effect in our samples show the decrement as well with increase of nonmagnetic Ga³⁺ ions doping, similar to the reported results.²⁰ The nonmagnetic ions doping (Y³⁺, and Ga³⁺), nonmatter doping at Sm- or Cr-sites, would reduce the coupling between Sm³⁺ and Cr³⁺, leading to the decrease of ZEB effect.

Fig. 6 (a–c) The M–H curves at different temperature of samples x = 0.1, 0.2, and 0.3. (d) The relationship of H_EB and H_C with doping concentration.

Table 2 Exchange bias field H_EB, coercive field H_C, and residual magnetization M_r extracted from M–H loops of Sm_0.7Y_0.3Ga_xCr_1−xO₃ (x = 0.1, 0.2, 0.3) samples at different temperatures

Sample	Temperature	HEB (Oe)	HC (Oe)	Mr (emu g^−1)
x = 0.1	5K	412.6	8015.3	0.27455
	35K	5.3	2345.6	0.36946
	100K	2.5	7154.4	0.45936
x = 0.2	5K	202.6	7368.1	0.31416
	45K	−2.8	2388.6	0.41866
	100K	7.5	3945.3	0.29665
x = 0.3	5K	39.85	6796.3	0.31861
	50K	10.75	4361.3	0.35168
	100K	−2.1	1179.4	0.17103

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Conclusions

In conclusion, we investigated the temperature dependent magnetic properties of SmCrO₃ by codoping nonmagnetic ions at Sm- and Cr-sites. It is evident that there indeed and still exists antiferromagnetic transition, the TIMR effect, and the SR effect. The spin reorientation from Γ₄ to Γ₂ is tuned and the transition temperature T_SR is improved dramatically to the liquid nitrogen temperature by Ga ions doping, which would be helpful to achieve its application in temperature sensitive spintronic devices and magnetic switching devices. The intrinsic TIMR effect from positive to negative under ZFC condition are significantly induced as well and its reversal evolution is strongly dependent with doping. Moreover, the positive ZEB effect is formed in Ga doped Sm_0.7Y_0.3CrO₃ samples at 5 K although it is suppressed with increase of doping concentration and disappears in high temperature. Under the influence of doping nonmagnetic ions, lattice distortion is induced to some extend and the magnetic interactions of Cr–Cr and Sm–Cr are predominantly diluted, leading to tune the above phenomena. Those phenomena are discussed and successfully explained by considering the magnetic exchange interactions competitions including the isotropic, antisymmetric (or DM interaction), and anisotropic superexchange interactions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11605092 and 11704009) and Nanjing University of Posts and Telecommunications under research project (No. NY215091).

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