Structural and magnetic properties of a new cubic spinel LiRhMn
We report the structural and magnetic properties of a new polycrystalline sample LiRhMnO (LRMO) through x-ray diffraction, bulk magnetization, heat capacity and Li nuclear magnetic resonance (NMR) measurements. The LRMO crystallizes in the cubic space group . From the DC susceptibility data, we obtained the Curie-Weiss temperature = -26 K and Curie constant = 1.79 suggesting antiferromagnetic correlations among the magnetic Mn ions with an effective spin = . At = 50 Oe, the field cooled and zero-field cooled magnetizations bifurcate at the freezing temperature, = 4.45 K, which yields the frustration parameter . AC susceptibility, shows a cusp-like peak at around , with the peak position shifting as a function of driving frequency, confirms a spin-glass-like transition in LRMO. The LRMO also shows the typical spin-glass behaviors such as memory effect, aging effect and relaxation. In the heat capacity, there is no sharp anomaly down to 2 K indicative of long-range ordering. The field sweep Li NMR spectra show broadening with decreasing temperature without any spectral line shift. The spin-lattice and spin-spin relaxation rates also show anomalies due to spin freezing near about .
pacs:75.50.Lk, 75.40.Cx, 76.60.-k
In the last few decades, most of the scientific work in condensed matter physics has chiefly been devoted to study the strongly correlated electron systems (SCES) Dagotto (2005); Dagotto and Tokura (2008). Materials with strong electronic correlations are the materials, in which the movement of one electron depends on the positions and movements of all other electrons due to the long-range Coulomb interaction (U). In this regard, the transition metal oxide (TMO) compounds Tokura and Nagaosa (2000) have become the center stage of attraction to the physicists since the TMO have outermost electrons in d-orbitals which are strongly localized. Hence, the electron density is no longer homogeneous and the striking properties of the system are in fact dependent on the presence of strong electron-electron interactions. Also the frustration in TMO, either imposed by the geometry of the spin system or by the competing interactions, leads to many exotic behavior Ramirez (1994); Greedan (2001); Moessner and Ramirez (2006); Balents (2010). The rich physics of magnetically frustrated systems, continue to attract interest in condensed matter research community. The resurgence of interest began with the discovery of high- superconductivity (observed in layered cuprates Bednorz and Müller (1986) and pnictides Kamihara et al. (2008)), and novel phenomenon such as metal-insulator transition (MIT) MOTT (1968), colossal magneto-resistance (CMR) Tokura (2000), charge ordering and quantum magnetism. It is soon realized that the strong interplay of spin, charge, lattice and orbital degrees of freedom in these correlated systems resulted in such diverse properties. In recent years, the interest on solids with conducting lithium ions has increased considerably because of the potential applications of such solids in rechargeable lithium batteries. In this context, the spinel oxide LiMnO has attracted wide attention as an intercalation cathode material for rocking chair batteries due to its low cost and non-toxicity Eftekhari (2003); Arillo et al. (2005). At room temperature LiMnO Thackeray et al. (1983) is cubic (space group ), with the following cation distribution (Li)[MnMn]O, where the subscripts A and B stands for tetrahedral and octahedral sites, respectively. Likewise, Takagi et al. found the metal-insulator transition (MIT) property in Okamoto et al. (2008); Arita et al. (2008); Knox et al. (2013), which behaves like a paramagnetic metal at high temperature; whereas below about 170 K it becomes a valence bond insulator and the ground state of mixed-valent is basically a charge frustrated. How will the ground state of this system vary if one replaces it with higher spin, say = ? With this motivation, we decided to explore (LRMO) which is structurally identical to but magnetically different. None has reported the magnetic property of LRMO so far. Only the structure of LRMO was first reported long back in 1963 by G. Blasse Blasse (1963). It is a mixed metal oxide with spinel structure Onoda et al. (1997) where 50% of the B-sites are occupied by non-magnetic ( = 0) and the other 50% by magnetic ( = ) ions. Usually, the B-site spinel has the corner-shared tetrahedral network like pyrochlore lattice which is geometrically frustrated. But due to the B-site disorder, the frustration may relieve and ultimately result in spin-glasses Mydosh (1993) where spin directions are frozen in at random direction at a low .
We have synthesized the polycrystalline LRMO and studied its bulk and local magnetic properties through various characterization techniques such as x-ray diffraction, DC and AC magnetization, heat capacity and field sweep Li nuclear magnetic resonance (NMR). We found that LRMO has antiferromagnetic (AFM) correlations among Mn ions and conventional spin-glass ground state with the spin-freezing temperature = 4.45 K.
Ii experimental details
Polycrystalline was prepared by solid-state reaction. Pre-heated starting materials (LiCO, Rh metal powder and MnO were mixed in stoichiometry and ground thoroughly for hours. Finally a hard pellet was made and calcined at , , and for 24 hours each time. As there is a chance of lithium evaporation above 900C, 15% excess LiCO was mixed to get the pure LRMO. The processes of grinding and firing were done until we obtained the single phase sample. Single phase of LRMO is confirmed from the powder x-ray diffraction (XRD) measurements at room temperature with Cu radiation () on a PANalytical X’Pert PRO diffractometer. DC and AC magnetization data were measured as a function of temperature K) with the applied field kOe) and the frequency (11000 Hz) using a commercial superconducting quantum interference device (SQUID) magnetometer. Low-field magnetization measurements were performed utilizing the reset magnet mode option of the SQUID. Heat capacity measurements were performed in the temperature K) and in the field kOe) using the heat capacity option of a Quantum Design PPMS. As the Li NMR spectra are very broad especially at low- and it is difficult to obtain the full line-shape only by the Fourier transform of the time echo signal in our fixed field NMR setup, we have performed field sweep Li NMR measurements at 60 MHz and 95 MHz. The spin-lattice relaxation rate () is measured by the saturation recovery method and the spin-spin relaxation rate () is obtained by measuring the decay of the echo integral with variable delay time.
Iii Results and Discussion
A. Crystal structure
The powder XRD data has been recorded with Cu- radiation over the angular range in step size and treated by profile analysis using the Rietveld refinement Rietveld (1969) by Fullprof suite Rodriguez-Carvajal (1993) program. From the XRD pattern analysis, we found that the prepared is crystallized in single phase and there is no sign of any unreacted ingredients or impurity phases. The Rietveld refinement of XRD pattern is shown in Fig. 1. From refinement, we obtained the cell parameters of , = = = 8.319 Å (which is close to the earlier reported value 8.30 Å Blasse (1963)), == and the atomic coordinates of LRMO is given in Table 1. The reliability of the x-ray refinement of LRMO is given by the following parameters : 4.63; : 2.98%; : 5.68%; : 2.63%.
The structure of LRMO has been drawn and analyzed by using Vesta software Momma and Izumi (2011). We have obtained the atomic coordinates from Rietveld refinement done on XRD pattern of LRMO which crystallizes in the non-centrosymmetric cubic spinel structure (space group 227). The Rh or Mn atoms are connected to each other via a tetrahedral network as shown in Fig. 2(a). These tetrahedral are corner-shared and form a geometrically frustrated magnetic system. In the structure, form perfect octahedra with (Rh/Mn)-O bond distance 2.055 Å (shown in Fig. 2(b)). The presence of non-magnetic ( = 0) at the B-site of the spinel, in a tetrahedral unit, distorts the corner-shared arrangement of ( = ) ions. This makes the B-sites diluted.
B. Bulk magnetization
1. DC susceptibility
The temperature dependence of the bulk dc magnetic susceptibility is measured on LRMO under different applied magnetic fields in the temperature range of (2-400) K. The main features of our observations from the dc susceptibility measurement are discussed here. With increasing fields, the reduces in the low temperature region (see inset of Fig. 3). Below 5 K, there is splitting between the zero-field cooled (ZFC) and field cooled (FC) data at = 50 Oe and 500 Oe as shown in the inset of Fig. 3. Also, the below 500 Oe shows some anomaly around 5 K. This may be due to regular antiferromagnetic (AFM) ordering which is very sensitive to the applied field as splitting between ZFC-FC is suppressed with fields higher than 5 kOe. The existence of ZFC-FC splitting below 500 Oe suggests the presence of a glassy state below 5 K. This is a signature of conventional spin-glass Binder and Young (1986). Fig. 3 shows the paramagnetic behavior of the dc susceptibility at 20 kOe. The Curie-Weiss fitting in the high temperature region (200-400 K) gives a Curie constant = 1.79 and a Curie-Weiss temperature . The negative value of the Curie-Weiss temperature suggests AFM interaction among the magnetic ions. The effective moment of ions [using = 1.79 ] is which is close to the expected value 3.87 for the ion.
2. AC susceptibility
The ac susceptibility is measured by keeping the dc applied field to be zero and with an ac field of 3.5 Oe amplitude. The frequency dependence of the in-phase component is shown in Fig. 4. The freezing temperature () shifts towards higher temperatures as the frequency increases which are typical features in glassy systems Mulder et al. (1981). Also, the out of phase component of the ac susceptibility has a frequency dependence with an anomaly around . The is non-zero positive below and is negative above . All these above features point to the formation of a spin-glass ground state. The frequency dependence of is often quantified in terms of the relative shift of the spin-freezing temperature, defined as = [ / log()] Mahendiran et al. (2003), which is calculated to be 0.022 for the LRMO compound. This value of indicates that the sensitivity to the frequency is, in fact, intermediate between the value of canonical spin-glass systems and superparamagnets. It is of interest to note that the present value is close to 0.037 seen in metallic glasses Luo et al. (2008).
The Vogel-Fulcher fit by equation of the variations of the freezing temperature () with frequency suggests short-range Ising spin-glass behavior Fisher and Huse (1986) (shown in Fig. 5). From the fit, we obtained the activation energy / 3.46 K, the characteristic frequency rad/s and the Vogel –Fulcher temperature . The characteristic frequency obtained from the fitting is less than that of conventional spin-glass systems, which is about rad/s. This large deviation may not be the true scenario as the error involved in determining the freezing temperature is large and the measured frequency range is limited to only two decades.
The freezing temperature is found to obey the critical slowing down dynamics (see Fig. 5) governed by the relation: = ( / - 1) , where is relaxation time and is known as dynamic exponent Dho et al. (2002). We found the best fit with = 4.38 K, 2.85 10 s and 4.88. For a conventional spin glass, is 10 to 10 s and lies in the range of 4 - 13 Luo et al. (2008). The present value of and is close to that of conventional spin glasses. This implies that the ground state of LRMO is a conventional spin-glass.
3. Memory effect
Fig. 6 shows a memory effect in LRMO. We have measured the field cooled (FC) magnetization using the following protocol. The magnetization was recorded during cooling of the sample at 300 Oe from 100 K down to 1.85 K at a constant cooling rate of 1 K/min. The cooling process was interrupted at 2.8 K and 2.3 K for a waiting time = 2 hours in each case. During , the field was switched off and the system was allowed to relax. After each stop and wait period, the FC process was resumed. The stops at 2.8 K and 2.3 K are evident in the obtained FC stop curve in Fig. 6, as step-like features. Once the cooling process was completed by reaching 1.85 K, the sample was heated continuously in the same magnetic field while recording the magnetization data. The magnetization obtained this way, referred to as FC warming , exhibits a change of slope at 2.8 K and a prominent minimum at 2.3 K although there was no heating at these temperatures. This indicates that the system has its previous behavior during the cooling operation imprinted as a memory. This sort of behavior has been observed in inter-metallic compounds such as GdCu Bhattacharyya et al. (2011), NdGeMaji et al. (2011)) and in super spin glass nanoparticle systems Sasaki et al. (2005); Sun et al. (2003). This is considered to be a typical characteristic of spin-glasses. The dip at 2.8 K in the FC warming curve is weak because at 2.8 K the system is not much below the blocking temperature ( = 3.8 K at = 500 Oe) which is the peak of the ZFC curve. This indicates that at 2.8 K, the system is not deep enough into the SG state. A reference curve (FC cooling) was also measured by simply cooling the sample continuously at = 300 Oe.
To further test the signature of the memory effect we have investigated the ZFC and FC relaxation behavior with negative temperature cycling as shown in Fig. 7. In the ZFC method, the sample was first zero field cooled down from the paramagnetic phase to the measuring temperature = 3 K, which is below the spin freezing temperature . Subsequently, a magnetic field of 500 Oe was applied and the magnetization was recorded as a function of time for a time period = hr. After that, the sample was quenched to a lower temperature = 2.5 K without changing the field and the magnetization was recorded for a time = hr. Finally, the temperature was restored to = 3 K and the magnetization was recorded for a time = hr. The relaxation curve obtained this way is depicted in Fig. 7(a). When the system was returned to temperature = 3 K after the temporary quenching, the magnetization resumes from the previous value it reached before the temporary quenching. This indicates that the temporary quenching does not erase the memory in ZFC relaxation. In the FC process, the sample was first field cooled to = 3 K in 500 Oe. Once the measuring temperature was reached, the field was switched off and subsequently the magnetization was measured as a function of time (see Fig. 7(b)). Similar to the ZFC method, the FC method also preserves the state of the system even after a temperature quench. In both ZFC and FC methods, the relaxation curve during is just a continuation of the curve during if we neglect the curve during , which represents a memory effect.
The hierarchical model predicts that a positive temperature cycle can destroy the previous memory and initialize the relaxation again, which means that response is expected to be asymmetric. In order to compare the response with respect to intermittent heating and cooling cycles, the relaxation experiment with a temporary heating cycle was also performed. The results are shown in Fig. 8(a) and (b). As can be seen from these figures, a positive temperature cycling erases the memory and re-initializes the relaxation in both ZFC and FC processes. This clearly suggests that the response of the system is asymmetric, therefore it supports the hierarchical picture proposed for spin-glasses.
4. Aging effect and relaxation
The Fig. 9 shows the growth of the magnetization data as a function of time, in the meta-stable state. The sample was cooled to 2.5 K in the ZFC mode and a field of 200 Oe was applied after a variable waiting time (t). The magnetization was then measured as a function of time. It is clear that the magnetization growth is slower for larger waiting time. This points towards the formation of meta-stable state associated with the low temperature magnetic state.
We also measured the isothermal remanent magnetization () of LRMO to explore the meta-stable behavior of the glassy state below the spin-glass transition temperature. For this, first we cooled the sample in the zero field mode from 300 K to the desired temperature, then a field of 300 Oe was applied for 300 s and then the applied field was switched off. The magnetization was then recorded as a function of time up to 2 hours. Fig. 9 shows the decay curves normalized to the magnetization before making the field zero, These isothermal remanent magnetization were well fitted with stretched exponential and from the fitting, we got the characteristic relaxation time at different temperatures (shown in Fig. 9). Here is the characteristic relaxation time and is the stretching exponent, which ranges between 0 and 1. Here and are magnetization at 0 and . The best fit is obtained for each isotherm is listed in Table 2. It is natural that the decay of is faster as one gets closer to . This indicates that the application of a field below causes the system to go to a meta-stable and irreversible state. As expected, above here at 6 K, is independent of time.
|(K)||Stretching exponent||Relaxation time|
C. Heat capacity
The heat capacity of magnetic LRMO was measured at different fields (0 - 90 kOe) in the temperature range 1.8- 300 K. There is no sharp anomaly in the vs. data as might usually be expected at an LRO transition. In the inset of Fig. 10, vs. , there is no significant influence of the applied magnetic field on the heat capacity. Also, no Schottky type anomaly was found in this system at low temperature.
The total heat capacity of LRMO has the contribution from lattice () and magnetic () both. As there was no suitable non-magnetic analog available we have fitted the data with Debye term and several Einstein terms in the -range (55-130) K and then extrapolated to low- to determine the . Among them, one Debye function plus two Einstein functions (1D+2E) fit was the best where the coefficient stands for the relative weight of the acoustic modes of vibration and coefficients and are the relative weights of the optical modes of vibrations. After fitting we obtained :: = 1:1:5. The sum of these coefficients is equal to the total number of atoms (n = 7) per formula unit of LRMO. The deviation of the from the Debye-Einstein fit below 50 K indicates the presence of a significant magnetic contribution to the heat capacity. The magnetic heat capacity is obtained by subtracting the lattice contribution from total heat capacity and shown in Fig. 11 on the left -axis. The magnetic heat capacity is almost independent of the strength of the applied field. It shows a hump around 18 K which indicates onsets of short-range interactions among the magnetic atoms. Also the magnetic entropy change is calculated using relation and shown in the right -axis of Fig. 11. Its value is 8.55 (J/mol K) which is 75% of the expected 11.52 (J/mol K) for = spin. Considering the uncertainty involved in determining the lattice specific heat, the value of obtained is not far from the expected value.
D. NMR Result
nuclei has a high natural abundance (92.6%) and it has nuclear spin = with the value of gyromagnetic ratio = 16.54607 (MHz/T). We have measured the field sweep NMR at 60 MHz and 95 MHz. We also measured spin-lattice relaxation rate (1/) and the spin-spin relaxation rate (1/) at 60 MHz (36 kOe). These measurements throw light on the nature of the intrinsic interactions of magnetic atoms.
1. NMR Spectra
For the spectra, we use the optimal pulse sequence () = 5 -100 -10 at 60 MHz. The 100 refers to the time duration between the starting of the two pulses. The spectra at different temperatures (from 92.7 K to 2.6 K) are shown in Fig. 12. There is no significant shift in the spectra. The lithium surroundings in one unit cell are shown in the inset of Fig. 12. From the spectra, we have obtained the full width at half maxima (FWHM) at different temperatures which track the dc susceptibility well as shown in Fig. 13.
The spectra at different temperatures are plotted without normalization of the spin-echo intensity as a function of sweep field (see Fig. 14). On lowering the temperature the total spectral intensity is constant down to about 20 K and then begins to decrease below 20 K. In the inset of Fig. 14, the echo integral (which is obtained by integrating the line-shape as a function of field the area under the spectrum at a particular temperature) times the temperature is plotted as a function of temperature. It shows a drop below 20 K. This suggests a loss of signal most probably due to development of frozen magnetic regions in the sample below 20 K.
2. Spin-lattice relaxation rate, 1/
The spin-lattice relaxation rate ) of was measured by using a saturation recovery of the longitudinal magnetization using saturation pulse () of 10 at various temperatures from 93 K to 2.65 K. The saturation recovery curves are shown in the inset of Fig. 15. The curve above 7 K are best fitted with the single exponential function and below about 7 K are best fitted with a stretched exponential function . Here stands for the amount of saturation and is the stretching exponent. The spin-glass-like systems possess a distribution of spin-lattice relaxation times due to different relaxation channels. That’s why here, is a measure for the width of the distribution window. This stretched exponential behavior of the saturation recovery of the spin-lattice relaxation data gives an indication of the presence of the local moments. The Fig. 15 shows the spin-lattice relaxation rate as a function of temperature. Below 20 K it starts to increase and at around 7 K it shows a peak. It appears that the onset of freezing of the magnetic regions starts around 20 K and at 7 K they lock into a spin-glass state. This supports the dc magnetic susceptibility as well as the magnetic heat capacity data which shows a hump just below 20 K.
3. Spin-spin relaxation rate, 1/
The inset of Fig. 16 shows the decay of the transverse nuclear magnetization data at 60 MHz with different temperatures. The data above 7 K are well fitted to a Gaussian modified exponential function  and the data below 7 K are fitted with a stretched exponential function . From fitting, we obtained the values and plotted the spin-spin relaxation rate (1/) as a function of temperature in Fig. 16. It shows that the spin-spin correlation begins to increase around 15 K with a peak at 3.2 K.
With respect to the crystallography of polycrystalline LRMO we confirmed a single-phase nature from our XRD investigation. In (), ZFC-FC bifurcation was found below 4.45 K which is very much field sensitive. This ZFC-FC splitting suggests the presence of a glassy state. The frequency dependent , where the freezing temperature () shifts towards higher values as the frequency increases is a signature of glassy systems and thus it confirms the presence of the spin-glass ground state. Also, the out of phase component of the ac susceptibility has a frequency dependence with an anomaly around . The is non-zero positive below and is negative above . This observation ruled out any bond disordered antiferromagnetic state. The characteristic frequency rad/s obtained from the Vogel –Fulcher fit is less than that of conventional spin-glass systems ) rad/s, but the characteristic time 2.85 10 s and critical exponent 4.88 values are close to a conventional spin-glass range is 10 to 10 s and lies in the range of 4 - 13) Luo et al. (2008). This implies that the ground state of LRMO is more likely to be a conventional spin-glass. From heat capacity measurement, there occurs significant contribution of magnetic heat capacity and no sharp anomaly presents down to 2 K. The calculated magnetic entropy change is 75% of the theoretical value ln(4) for this system. These numbers are not far from the usual LRO transition. However the change of entropy starts to decrease below 30 K, which is close to the CW temperature also. From NMR, there is no significant shift of the spectrum and the FWHM of spectra at high temperatures follows the Curie-Weiss behavior like dc susceptibility. The echo integral intensity times the vs. shows a drop below 20 K. This suggests a loss of signal probably due to development of frozen magnetic domains within the sample. In order to shed more light on the spin dynamics of ions, we have measured spin-lattice relaxation rate () and spin-spin relaxation rate (1/) for nuclei. Both show anomalies below 7 K like in the dc susceptibility indicating the spin-glass ground state of .
SK acknowledges the discussion with Dr. Aga Shahee and R. K. Sharma and the financial support from IRCC, IIT Bombay. AVM would like to thank the Alexander von Humboldt foundation for financial support during his stay at Augsburg Germany. We kindly acknowledge support from the German Research Society (DFG) via TRR80 (Augsburg, Munich).
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