Phase coexistence and the magnetic glass-like phase associated with the Morin type spin reorientation phase transition in SmCrO₃

Abstract

The phenomenon of spontaneous spin reorientation phase transition (SRPT) in SmCrO₃ has been considered as a process comprising continuous rotation of magnetic moments of chromium ions. It is observed that in the vicinity of SRPT, the cooling and warming magnetic curves follow distinctly different paths and in the presence of low measuring fields this thermal irreversibility extends up to the Néel temperature marking a remarkable width of ∼163 K. Investigating the origin of thermal hysteresis and henceforth the nature of SRPT, we have qualitatively determined the phase fractions of phases involved in the transition. The thermal evolution of phase fraction closely resembles the theoretically predicted phase evolution in the well known Arvami model. The close resemblance suggests that the growth and nucleation mechanism across SRPT is similar to the crystallization process of solids from a supercooled liquid and further confirms the coexistence of two metastable phases in the neighborhood of SRPT. Moreover, the signatures of the magnetic glass like phase, which mainly arises due to the arrest of kinetics during a first order transition, are also noticed below T_SRPT. These observations suggest the discontinuous Morin type nature of the spin reorientation process due to discrete flipping of Cr³⁺ ions from the high temperature Γ₄ to low temperature Γ₁ configuration.

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Introduction

As a functional material family, RCrO₃ is of fundamental scientific interest due to a number of significant properties like spin reorientation,¹ magnetoelectric or multiferroic properties^2–4 and magnetic anisotropy,^5,6 making them a potential candidate for various technological applications such as optomagnetic ultrafast recording,^7–9 inertia driven spin switching,¹⁰ and humidity and gas sensors.^11,12 The Dzyaloshinskii–Moriya (D–M) exchange coupling between the Cr atoms causes RCrO₃ compounds to order in a canted antiferromagnetic structure below the Néel temperature (T_N). In orthochromites having a distorted orthorhombic perovskite structure (Pbnm space group), the following three types of antiferromagnetic configurations are generally observed: 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_z) in Bertaut notations.¹³ The magnetic configuration below T_N can be either Γ₂ or Γ₄ but if R ion is magnetic, then at a particular temperature value T_SRPT (<T_N), the complex magnetic exchange interactions between R³⁺ and Cr³⁺ ions may overcome the crystalline anisotropy forces and lead to the spontaneous change in the easy axis of magnetization from one crystallographic direction to another. This phenomenon is recognized as spin reorientation phase transition (SRPT).^14,15

The rare earth orthochromite SmCrO₃ is a newly emerging compound due to novel magnetic and dielectric anomalies, multiferroicity and abrupt spin reorientation phase transition (SRPT) occurring in a very narrow temperature regime.^4,16–18 The sudden SRPT within a short temperature interval has recently opened new avenues in thermomagnetic power generation, ultrafast spin switching to modify the speed in recording media and in magnetic refrigeration.^19–21 SmCrO₃ is reported to be ordered in Γ₄(G_x, A_y, F_z, F^R_z) configuration below T_N at 191 K and exhibits a spin reorientation transition at 34 K.^4,17 Based on acoustic velocity measurements, Gorodetsky et al.,²² reported that below SRPT the magnetic structure of SmCrO₃ changes from Γ₄ to Γ₂ continuously, marking a second order transition. Using dc magnetization measurement as a probe, we observed that in the vicinity of SRPT the warming and cooling M(T) curves do not coincide and this thermal hysteresis extends up to T_N with a very broad temperature width (ΔT ∼ 163 K at H = 0.01 T). To investigate the origin of this paradoxical behavior we assumed that the kinetics of SRPT follows the growth mechanism of a crystallization of solids from a supercooled liquid governed by Arvami Model.²³ The experimentally observed variation of phase fractions is closely similar to the theoretically predicted ‘S’ shaped transformation curve given by Kolmogorov–Jhonson–Mehl–Avrami (KJMA). The close similarity between theoretical prediction and experimental results confirms the validation of our assumption and coexistence of two metastable phases across SRPT. Below T_SRPT, we observed a number of signatures of magnetic glass like frozen state. In comparison to spin glass, the magnetic glass is comparatively a newly identified phenomena and attracting huge attention of researchers these days.^24–26 This kind of glassy state arises when the dynamics of a first order transition is slowed down beyond the experimental time scale and the thermal evolution of high temperature state (HT) to low temperature state (LT) completely ceases with further lowering of temperature. This situation is analogous to conventional ‘glass’ in which thermal atomic motions are frozen but this glassy phase is distinct from spin-glasses as magnetic field can serve as an external parameter to create and control this phase, hence also called as ‘magnetic glass’. We have comprehended the behavior of magnetic glass by field cooling and field annealing in unequal fields which show that HT clusters are glass like frozen in the matrix of LT phase. On the basis of these observations we suggest the possibility of SRPT in SmCrO₃ to be a first order Morin type transition in which spins spontaneously flip from high temperature Γ₄ to low temperature Γ₁ configuration discontinuously.

Experimental

The polycrystalline sample of samarium chromite was synthesized by solid state reaction of stoichiometric quantities of Sm₂O₃ and Cr₂O_3. The reactants were ground together and heated at 900 °C for 15 hours in air. This process was followed by intermediate grindings and heating steps at 1000 °C and 1200 °C for 24 hours each and prepared pallets were sintered at 1300 °C for 24 hours. X-ray powder diffraction data were collected at room temperature by Bruker D2 PHASER Desktop Diffractometer (Cu-Kα, λ = 1.54 Å) and the phase purity of prepared samples was confirmed by Rietveld refinement of XRD data using FULLPROOF software. X-ray photoemission spectroscopy (XPS) measurements were performed using Al-Kα (E = 1486.7 eV) lab-source. Magnetization measurements were carried out using SQUID-VSM (Quantum Design Inc., USA).

Results and discussions

X-ray diffraction pattern of SmCrO₃ is shown in Fig. 1(a) which is Rietveld refined with respect to the calculated pattern based on orthorhombic perovskite structures with Pbnm space group. The values of χ² and R parameters suggest a good agreement between calculated and experimentally observed patterns. The lattice parameters were found to be a = 5.36 Å, b = 5.50 Å and c = 7.64 Å. Inset of Fig. 1(a) demonstrates the structural unit cell of SmCrO₃ consisting of four formula units. The tilted CrO₆ octahedra causes the angle Cr–O(2)–Cr to be ∼166°. It is known that chromium can exist in various valence states ranging from 1 to 6 and thus it is very crucial to confirm the valence state of Cr in SmCrO_3. We performed XPS measurement of Cr-2p core shell as shown in Fig. 1(b). The Cr 2p core level is split in Cr 2p_1/2 and Cr 2p_3/2 states due to spin–orbit coupling. We fitted Cr 2p_3/2 peak with two peaks of combined Gaussian–Lorentzian function and the background is subtracted by the approximated combined Shirley (99.8%) – Linear (0.2%) function. Comparing our data with the observed binding energy positions of various valence states of Cr, we determine that Cr exists in +3 state.²⁷ The peak asymmetry or the minor feature in Cr 2p spectra is due to multiplet splitting of 2p energy levels. It should be recalled here that the minor peaks in the XPS spectra mainly arise due to three reasons – multiplet splitting, presence of satellites or existence of two or more valence states. Here, the origin of the asymmetry cannot be mixed valence states as the binding energy positions for these feeble features do not match with the binding energy positions of other possible valence state of chromium. Also, the two small peaks are not 3d satellites because as observed in earlier reports, satellite features are observed approximately 11 eV above the parent 2p lines.²⁸ Thus we can assign these small features as multiplet splitting of Cr-2p energy levels.

Fig. 1 (a) XRD pattern of SmCrO₃ along with Rietveld refined pattern based on Pbnm space group. Inset shows the structural unit cell of SmCrO₃ consisting four formula units. Blue (largest), green (medium), orange and pink (smallest) spheres represent Sm, Cr, apex and planer oxygen respectively. (b) X-ray photoemission spectrum of Cr core 2p level.

In Fig. 2(a) we show the dc magnetization versus temperature curves at various magnetic fields following zero field cool (ZFC), field cool cooling (FCC) and field cool warming (FCW) protocols with temperature sweep rate being half Kelvin per minute. At first glance we notice two distinct magnetic transitions at 191 K (T_N) and 34 K (T_SRPT) which are consistent with the previous reports.^16–18 The derivative of magnetic moment with respect to temperature dM/dT at various fields [inset of Fig. 2(a)] depicts that applied magnetic field has significant influence on T_SRPT since it decreases from 39 K when measured at 100 Oe to 27 K when measured at 7 Tesla. Inverse susceptibility curve follows Curie–Weiss law above 210 K at high magnetic fields and estimated μ_eff and θ_CW come out to be 0.98 μ_B/f.u. and −2050 K respectively. The frustration factor = |θ_CW|/T_N > 10 indicates the moderate geometrically frustrated magnetic structure. The observed lesser μ_eff than the theoretically calculated value could be due to distorted CrO₆ octahedra²⁹ or existence of short range correlations in paramagnetic regime. Fig. 2(b) shows the ZFC isothermal magnetization curves at various temperatures below T_N. Before every measurement SmCrO₃ sample was demagnetized above T_N. The loops do not saturate up to 7 T suggesting the predominant antiferromagnetic exchange interaction. In temperature regime 20 K < T < 175 K, the wide opening of M–H loops and huge coercivity favor the ferrolike magnetic ordering due to canted Cr³⁺ arrangement.

Fig. 2 (a) M(T) curves in ZFC, FCC and FCW modes at 0.05 T and 1 T. Inset shows the derivative of magnetic moment with respect to temperature at various fields. (b) The magnetic isotherms at different temperatures values ranging from 5–175 K. (c) The magnetic structure of SmCrO₃ in Γ₄(G_x, A_y, F_z, F^R_z) configuration below T_N. The blue and green spheres represent Cr and Sm ions respectively. The cubic lattice formed by eight nearest neighboring Cr³⁺ ions cause weak ferromagnetism along z axis.

The M–H at 5 K clearly shows a straight line behavior, akin to collinear antiferromagnetic phase. According to the group theoretical calculations and as suggested by ref. 16, the only possible low temperature configuration below T_SRPT should be Γ₁(A_x, G_y, C_z, C^R_z).

Now we discuss the nature of magnetic transitions in SCO. The first magnetic ordering at 192 K (T_N) is attributed to alignment of Cr³⁺ ions into the canted antiferromagnetic structure due to Dzyaloshinskii–Moriya antisymmetric superexchange interactions.^30,31 Below T_N, the Cr³⁺ magnetic moments order in the Γ₄(G_x, A_y, F_z, F^R_z) configuration which represents a canted antiferromagnetic structure in which the total uncompensated weak ferromagnetic vector F lies along z axis (z||c) and total antiferromagnetic vector G directs along x (x||c) axis. The magnetic unit cell of SmCrO₃ in Γ₄ configuration is illustrated in Fig. 2(c). According to the Pbnm symmetry, Cr³⁺ ions occupy (0, 0.5, 0) sites which include eight corner sharing and four face centered positions. The x-components of Cr moments follow the perfect G-type antiparallel alignment but the component along z axis could not be compensated and causes the weak ferromagnetism along c axis. An attentive look at the M–T plot also reveals that below T_comp ∼ 67 K, there is change in magnetization trend, either it decreases or sharply increases depending on whether the measuring field is lower than or higher than 0.2 T respectively. We do not find any reference to this observation in earlier reports but we believe that this second magnetic ordering is an indication of onset of Cr³⁺–Sm³⁺ exchange interaction. Below T_comp, the weak ferromagnetic component of Cr³⁺ matrix polarizes Sm³⁺ moments in opposite direction due to isotropic super-exchange interaction, which causes the gradual decrease in resultant moment. However, the contrary happens for M(T) curves with H ≥ 0.2 T, where below T_comp though moment continues to rise but a change in slope is clearly noticeable at T_comp. This increase can be attributed as magnetostatic energy of Sm³⁺ ions overcoming the competing isotropic exchange interaction and thus a contribution of Sm³⁺ moments towards the effective magnetization.

Below 39 K, the abrupt fall in the magnetization is observed which has been identified as spin reorientation transition. In the vicinity of T_SRPT, the antisymmetric and anisotropic exchange interactions produce a positive effective field for ↑Cr³⁺ moments and negative effective field for ↓Cr³⁺ moments in G_x configuration. These effective fields increase as temperature is decreased due to increase in Sm³⁺ moments and when this effective field energy overcomes the barrier of crystalline anisotropy, it rotates the whole magnetic configuration by 90°.¹⁴ The dynamics of magnetic configuration with respect to various transitions is illustrated in Fig. 3. For simplification we have chosen only one pair of nearest neighbors (Cr₁, Cr₂) and (Sm₁, Sm₂). There are only two possible paths for dynamics of magnetic configuration below T < T_SRPT permissible by group theoretical predictions in RCrO₃ family: (a) rotation to Γ₂(F_x, C_y, G_z, F^R_x, C^R_y) phase by continuously sweeping all infinitesimal intermediate angles and (b) discreet jump to Γ₁(A_x, G_y, C_z, C^R_z) phase.

Fig. 3 Dynamics of magnetic configuration in SmCrO₃ upon cooling below T_N is illustrated in simplified version. Pair of (Cr₁, Cr₂) and (Sm₁, Sm₂) represent two nearest neighbors in crystal unit cell. M_Cr is net uncompensated magnetic moment of Cr ions and M_Sm represents the total induced paramagnetic moment of Sm ions.

The rotation or jump of spin systems below T_SRPT is caused by the temperature dependency of anisotropic and antisymmetric magnetic exchange energies. To explain the mechanism of spin reorientation, the free energy of system can be written as

F(T, θ) = A₀ + A₁(T)sin² θ + A₂(T)sin⁴ θ

where θ is the angle of rotation for spin system, A₀ is temperature independent constant and A₁ and A₂ are continuous function of temperature. The stable solutions for θ can be found as,

θ₁ = 0, T ≥ T₁;

sin² θ₂ = −A₁/2A₂; [For T₁ < T < T₂; θ₂ is real]

θ₃ = π/2, T ≤ T₂; (1)

Horner et al.³² predicted the functional relationship of A₁(T) and A₂(T), according to which, when A₂ is positive, θ can take all the possible intermediate values of θ₂ which lie in between two extremum solutions θ₁ = 0 and θ₃ = π/2 continuously describing a second order phase transition. In case of negative A₂, θ₂ solution is imaginary and θ flips abruptly from 0 to π/2 as in Morin transition, making a first order phase transition. This type of transition leads to thermal hysteresis due to involvement of latent heat because it takes finite time to extract (release) heat from (to) environment and for the crystallization (melting) process to be completed. Thus both the phases coexist for a finite temperature interval.

Fig. 4(a) and (b) reveal the presence of distinct thermal hysteresis which extends to astonishing temperature width in low magnetic fields, for instance ΔT is ∼163 K at H = 0.01 T. This width can be tuned with magnetic field as it shrinks on higher values of applied magnetic fields. In the close vicinity of SRPT, the thermal irreversibility can be observed even at 7 T measuring field. The observed thermal irreversibility or coexistence of Γ₁ and Γ₄ phases cannot be explained on the basis of SRPT to be second order phase transition as predicted in earlier reports.²² Thermal hysteresis originates when two stable or meta stable states exist at same temperature. When we cool below T_SRPT, some clusters of Γ₄ may remain confined in super-cooled state as the high anisotropy of Cr³⁺ systems may hold the magnetic structure not to change. Below super-cooling temperature the high temperature Γ₄ becomes unstable, and then system can transform into Γ₁. Similar effect occurs on heating from low temperature except that in this case the anisotropy of Sm atoms causes retention of the low temperature Γ₁ phase in background of Γ₄ state as superheated clusters.

Fig. 4 (a) Thermal irreversibility in field cooled warming (FCW) and field cooled cooling (FCC) curves for 0.01 and 0.2 T. (b) Visibility of feeble thermal hysteresis at high field value 1 T and 7 T in the vicinity of T_SRPT. (c) FCW and FCC paths when sample was first cooled to 20, 28, 35, 40 and 45 K followed by warming till T_N. Inset shows the thermal evaluation of phase fractions matched with theoretically predicted Arvami law. (d) Non-monotonic behaviour of coercivity H_C and M_R.

The kinetics of first order transition assisted by supercooling/superwarming is theoretically described in Arvami model.²³ This model is developed with some experimental assumptions that the new phase is nucleated by a ‘germ nuclei’ which is already present in the parent phase matrix. The concentration of these germ nuclei decreases through activation of some of them into ‘growth nuclei’ and converting of these nuclei in grains of new phase. The variation of density of ‘growth nuclei’ or phase fraction of new phase with respect to time is given by well known Kolmogorov–Jhonson–Mehl–Avrami (KJMA) relation,

f = 1 − exp(−kt^η)

where k is related to activation energy and η is Avrami exponent which depends on structural parameters.

Similar growth kinetics of phase fractions across a first order transition can be observed with evolution of temperature (or magnetic field) instead of time as suggested by Manekar and Roy.³³

f = 1 − exp(−k(T − T₀)^η)

where T₀ is the onset temperature of transition. Now we try to study the evolution of phase fractions across SRPT to further confirm the origin of thermal irreversibility. As suggested in ref. 33, the differential susceptibility during cooling and warming cycles at a particular temperature cannot be directly assigned to phase fractions due to the random growth of nuclei in parent phase matrix. It is proposed that the area of the minor hysteresis loops (MHL) can be chosen as a convenient parameter to assign with volume of phase fractions. To generate MHL's we have cooled the sample down to various temperatures in the vicinity of vicinity of T_SRPT with applied field of 0.1 T followed by successive warming till T_N as shown in Fig. 4(c). It is clear that thermal irreversibility was negligible for path 4, when we cooled the system down to 40 K, whereas it reaches to a maximum value when cooled down till 20 K following path 1. A minor loop is resulted when we reverse the direction of temperature change before reaching into reversible temperature regime. Phase fractions at each temperature are evaluated as area of corresponding MHL normalized by the area of curve corresponding to maximum transformation, i.e. path 1. All the MHL's are initiated during cooling below T_SRPT which represents the growth of c-AFM Γ₁ phase in background of weak FM Γ₄ phase. To synchronize with conventional consideration of the variation of FM phase in AFM background,³³ we have plotted the unity minus phase fractions with respect to temperature as shown in the inset of Fig. 4(c). The shape of curve closely resembles to the stimulated KJMA equation where time is replaced by temperature, T₀ and η are 20 K and 2.903 respectively. This close similarity between theoretically predicted results and our experimental observations indeed confirms the coexistence of Γ₄ and Γ₁ phases in the vicinity of SRPT.

It should be noted that the thermal hysteresis far above from T_SRPT decreases rapidly with increasing magnetic field and almost disappears when applied field is greater than coercivity H_C. Fig. 4(d) shows the non-monotonic variation of coercivity (H_C) and remanent magnetic field (M_R). The huge coercivity of several kOe below T_N represents the highly anisotropic nature of SmCrO₃.

Although thermal irreversibility is intrinsically caused by SRPT in the closed vicinity of spin reorientation but the reason which extends the hysteresis up to T_N covering a wide temperature range, should be related to huge anisotropy or pining of domain walls in lattice defects. The bifurcation between ZFC and field cooled curves observable for whole temperature regime below T_N shows the irreversible nature of transitions. As expected when the anisotropy is driving the irreversibility, divergence of ZFC decreases for increase in measuring field which is the case observed for T_SRPT < T < T_N regime. But it is noteworthy that divergence behavior below SRPT is different as the divergence increases for increase of measuring field value (Fig. 5(a)). The similar behavior is observed in some Heusler alloys and doped manganite systems,^34–36 which is ascribed to magnetic glass behavior. The coexisting phase concentration is sensitive on cooling and measuring field as magnetic field can provide sufficient energy to HT clusters to overcome the energy barrier between LT–HT phases and favor crystallization into LT phase. Fig. 5(b) illustrates path A: the evolution of a first order transition ceasing to a reversible point below supercooling temperature (T*), and path B: evolution of an incomplete irreversible first order transition which leads to glass or frozen cluster like state. In Fig. 6(a), M(H) curves below 20 K clearly depict the irreversibility of transition as the virgin curve lies outside the envelope curve.

Fig. 5 (a) Evolution of thermal irreversibility ΔM = FCC–FCW with magnetic field at T = 15 K, 65 K. (b) Illustration of phase transformation with temperature when (A) system goes through a reversible phase transformation via supercooling (B) system goes through a glass like frozen state.

Fig. 6 (a) M(H) curves for 5–20 K, dotted line and solid line represents virgin curve and envelope curve respectively. (b) FC M(T) curves measured in H_MF = 0.5 T after cooling in presence of various fields H_CF ranging from 0–7 T.

To comprehend this glassy state further, we measured the warming M–T curves with measuring field H_MF = 0.5 T after cooling in various fields H_CF ranging from 0–7 T following the ‘cooling and heating in unequal field protocol (CHUF)’³⁷ shown in Fig. 6(b). Two distinct behaviors are observed for low cooling fields (H_CF < H_MF) and for high cooling fields (H_CF > H_MF). In first case, the curves follow the ZFC behavior i.e., magnetic moment initially decreases and beyond a particular temperature again starts to rise whereas in the second case the curves follow the behavior similar to FCW with moment increasing with temperature. This peculiar behavior can be explained as: on cooling with H_CF till 5 K, a magnetically inhomogeneous state with frozen clusters is obtained with coexisting HT Γ₄ phase and LT Γ₁ phase. When the field H_MF > H_CF is turned on, the magnetic field energy can overcome the barrier between two thermodynamic states and assist in further crystallization of weak FM Γ₄ phase into c-AFM Γ₁ phase as the temperature is increased, causing the magnetic moment to decrease. At a particular temperature, the glassy state completely devitrifies, and then the moments start to rise with further heating. In the second case, the curves follow the behavior similar to FCW with slightly higher moment. When H_CF > H_MF, there will be no further crystallization of HT Γ₄ into LT Γ₁ phase and hence no decrease in moment is observed in this case but the devetrification of glassy state can still be marked as the trend of curves slightly changes. This kind of behavior confirms the presence of magnetic glass like state in this compound.

Conclusions

Using bulk dc magnetization as a probe, we have observed a distinctly broad thermal hysteresis between cooling and warming cycles associated with spin reorientation phase transition (SRPT) in SmCrO₃ compound. In the vicinity of SRPT, we have qualitatively analyzed the fraction of phase involved in transition from area of minor hysteresis loops. The evolution of phase fractions across SRPT with respect to temperature follows the famous Avrami law of growth and nucleation during crystallization of solids from super-cooled liquid confirming the coexistence of two phases in the neighborhood of SRPT. In addition we have also studied the existence of magnetic glassy state below T_SRPT. With the help of field cooling and field annealing, we show that high temperature weak FM Γ₄ phase clusters are glass like frozen in the background of low temperature c-AFM Γ₁ state. Finally, the existence of phase coexistence and magnetic glass like freezing across SRPT lead to the conclusion that in differing to the earlier report, spin reorientation in SmCrO₃ should be a first order Morin type reorientation transition in which moments flip from high temperature Γ₄ to low temperature Γ₁ state discontinuously.

Acknowledgements

The authors are thankful to Mr A. Wadikar for help in XPS measurements.

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