microscopic magnetic study on the nominal composition li[li 1/3 mn 5/3 ]o 4 by muon-spin...

Microscopic Magnetic Study on the Nominal Composition Li[Li1/3Mn5/3]O4 by Muon-SpinRotation/Relaxation Measurements

Kazuhiko Mukai,*,† Jun Sugiyama,† Yutaka Ikedo,†,O Hiroshi Nozaki,† Kazuya Kamazawa,†

Daniel Andreica,‡,§ Alex Amato,‡ Martin Månsson,| Jess H. Brewer,⊥ Eduardo J. Ansaldo,# andKim H. Chow∇

Toyota Central Research and DeVelopment Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan,Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, PSI Villigen CH-5232, Switzerland, Faculty ofPhysics, Babes-Bolyai UniVersity, 400084 Cluj-Napoca, Romania, Laboratory for Neutron Scattering, ETHZurich and Paul Scherrer Institut, PSI Villigen CH-5232, Switzerland, TRIUMF, CIfAR, and Department ofPhysics and Astronomy, UniVersity of British Columbia, VancouVer, British Columbia V6T 1Z1, Canada,TRIUMF, 4004 Wesbrook Mall, VancouVer, British Canada V6T 2A3, Canada, and Department of Physics,UniVersity of Alberta, Edmonton, Alberta T6G 2G7, Canada

ReceiVed: March 18, 2010; ReVised Manuscript ReceiVed: May 24, 2010

In order to elucidate the structural and physical properties of the nominal composition Li[Li1/3Mn5/3]O4

compound, we have investigated the nature of polycrystalline Li[LixMn2-x]O4 (LMO) with 0 e x e 1/3 andLi2MnO3 samples by electrochemical charge and discharge analysis, X-ray diffraction (XRD), magneticsusceptibility (�), and muon-spin rotation/relaxation (µSR) measurements. Here, µSR signal roughly correspondsto the volume fraction of the local magnetic phases in the sample. The Rietveld analysis suggested that thex ) 1/3 sample contains ∼11 weight% Li2MnO3 phase. This was also supported by electrochemical chargeand discharge analysis and zero-field (ZF-) µSR measurements. If we follow the past reported relation for thex ) 1/3 compound, i.e. Li[Li1/3Mn5/3]O4 consists of a (1 - z)Li[Li1/3-ωMn5/3+ω]O4 phase and a zLi2MnO3

phase, the average chemical formula of the former spinel phase is represented as Li[Li0.21Mn1.79]O4. However,weak-transverse-field µSR measurements demonstrated that the spinel phase undergoes a spin-glass-liketransition at 21 K with a large transition width (∆T ) 28 K). Since both x ) 0.2 and Li2MnO3 samplesexhibit a very sharp magnetic transition at 24 and 36 K, respectively, the spinel phase in the x ) 1/3 sampleis found to be magnetically inhomogeneous in a microscopic scale. This indicates that the distribution of Liions is microscopically inhomogeneous in the spinel lattice, although Li[Li1/3-ωMn5/3+ω]O4 has been assignedas a single-phase by macroscopic analyses such as XRD.

Introduction

In the (Li)8a[LixMn2-x]16dO4 (LMO) spinel lattice with spacegroup of Fd3jm, the tetrahedral 8a site is occupied by Li ions,while the octahedral 16d site is occupied by both Li and Mnions. Since the Li ions at the 8a site are extracted/insertedreversibly by an electrochemical oxidation/reduction reactionin a nonaqueous electrolyte, LMO has been heavily studied asa positive electrode material for Li-ion batteries.1 In spite ofthe extensive studies on LMO, structural and physical propertiesfor the LMO compound with x ) 1/3 are not fully understood.For instance, if we assume that the theoretical charge/dischargecapacity [Qtheo(x)] of LMO is determined by the amount of Mn3+

ions, more correctly, the electrochemical reaction of LMO isformulated as

Qtheo(x) in mAh ·g-1 should be given by

where Qtheo(LiMn2O4) and M(LiMn2O4) is the theoretical charge/discharge capacity () 148 mAh ·g-1) and the molecular weight() 180.81) for the LiMn2O4 phase, respectively, and M(x) isthe molecular weight of LMO with x > 0. This means that therechargeable capacity below 4.5 V vs Li+/Li (Qrecha

e4.5 V), which isequivalent to Qtheo(x) for the reversible extraction/insertion ofthe Li ions at the 8a site, decreases monotonically withincreasing x, and finally reaches 0 mAh ·g-1 at x ) 1/3.However, it is widely reported that Qrecha

e4.5 V ∼ 60 mAh ·g-1 forthe x ) 1/3 compounds regardless of the synthesis temperature(T) between 400 and 750 °C.2-4 The discrepancy between Qtheo

and Qrechae4.5 V was initially thought to be caused by the oxygen

deficiency (δ) in the x ) 1/3 samples (δ e 0.2).5 However, inorder to explain the fact that Qrecha

e4.5 V ∼ 60 mAh ·g-1, the

* To whom correspondence should be addressed. E-mail: [email protected]. Tel: +81-561-71-7698. Fax: +81-561-63-6137.

† Toyota Central Research and Development Laboratories, Inc.‡ Paul Scherrer Institut.§ Babes-Bolyai University.| ETH Zurich and Paul Scherrer Institut.⊥ University of British Columbia.# TRIUMF.∇ University of Alberta.O Present address: Muon Science Laboratory, Institute of Materials

Structure Science, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

Li[LixMn1-3x3+Mn1+2x

4+]O4 f yLi+ + ye- +

Li1-y[LixMn1-3x-y3+Mn1+2x+y

4+]O4 (0 e y e 1 - 3x)(1)

Qtheo(x) ) Qtheo(LiMn2O4) × (1 - 3x) ×M(LiMn2O4)/M(x) (2)

J. Phys. Chem. C 2010, 114, 11320–1132711320

10.1021/jp102453r 2010 American Chemical SocietyPublished on Web 06/07/2010

composition of the samples should be Li[Li1/3Mn5/3]O4-δ withδ ) 0.3. Furthermore, since Qrecha

e4.5 V is independent of thesynthesis T, we require an other mechanism to explain the valueof Qrecha

e4.5 V for the x ) 1/3 samples. In fact, Paulsen and Dahnclarified that δ is negligibly small (less than 0.025) forLi[LixMn2-x]O4 by solid electrolyte coulometry analyses.6 Onthe contrary, a complex phase relation among theLi[LixMn2-x]O4 and Li2MnO3 phases was reported below 1000°C.6-9 Thus, the x ) 1/3 compounds have been assigned as amixture of a Li[LixMn2-x]O4 phase and a Li2MnO3 phase.10-12

Since the Mn ions are in the 4+ state in Li2MnO3, the formationof the Li2MnO3 phase naturally reduces the average valence ofthe Mn ions in the spinel phase. Here, the weight fraction ofthe Li2MnO3 phase is reported as ∼10% for the x ) 1/3 sampleprepared at 750 °C.11,12 The chemical formula for the spinelphase in this sample is, thus, represented by Li[Li0.23Mn1.77]O4,based on the following relation:13

where

However, the observed Qrechae4.5 V for the x ) 1/3 samples (∼60

mAh ·g-1)2-4 is slightly larger than Qtheo for the x ) 0.23 phase(∼46 mAh ·g-1). Moreover, the x ) 1/3 sample synthesized at400 °C still exhibits Qrecha

e4.5 V ∼ 54 mAh ·g-1,4 although the weightfraction of the Li2MnO3 phase is almost 0% by XRD analyses.12

This implies that there is another factor to govern Qrechae4.5 V for

the x ) 1/3 sample.Recently, we examined the microscopic magnetism for a

zigzag chain compound Li0.92Mn2O4 and clarified the volumefraction of the coexisting Li2MnO3 phase in the sample bymuon-spin rotation/relaxation (µSR) measurements.14 Here, µSRis a powerful technique to detect local magnetic fields causedby both nuclear and electronic origin.15 Moreover, µSR signalroughly corresponds to the volume fraction of the magneticphases in the sample.15 We have, therefore, performed µSRmeasurements for the LMO with 0 e x e 1/3 and Li2MnO3

samples, in order to elucidate the homogeneity/inhomogeneityof the samples through their microscopic magnetism. In thispaper, we report the structural and microscopic magnetic naturefor the nominal composition Li[Li1/3Mn5/3]O4 sample.

Experimental Section

It is known that the decomposition reaction in eq 3 is acceleratedabove 850 °C.6,7 However, if we decrease the reaction T below850 °C, both the solid state diffusion of each element and the graingrowth of LMO are suppressed, resulting in an inhomogeneouscompositional distribution in the obtained sample. Fortunately,highly crystallized LMO compounds with xe 0.1516,17 are recentlyavailable by a “two-step solid-state reaction” technique, which wasoriginally used in Li[Ni1/2Mn3/2]O4 (P4332).18,19 That is, in the firststep, a crystallization process is completed at high T (∼1000°C), then in the second step, a chemical composition iscontrolled precisely below ∼700 °C. This technique is, inprinciple, applicable for the preparation of the x ) 1/3 sample.Therefore, powder samples of LMO with x ) 0, 0.1, 0.2, and1/3 were prepared by the two-step solid-state reaction techniqueas reported previously.16,17 The reaction mixture of LiOH ·H2Oand MnOOH (Manganite) was well mixed with a mortar and

pestle, and pressed into a pellet of 23 mm diameter and ∼5mm thickness. The pellet was heated at 1000 °C under air for12 h in order to develop crystallites. Indeed, the morphologyof the primary particle for all the samples showed an octahedralshape with smooth (111) facets. The obtained powder wascrushed, repressed into a pellet, then oxidized at 700 °C for x) 0, 600 °C for x ) 0.1, and 550 °C for x ) 0.2 under air for24 h. For the x ) 1/3 sample, the pellet was oxidized at 650,600, 550, and 500 °C under air for 24 h successively withoutcooling down to room T.

For comparison, a powder sample of Li2MnO3 was alsosynthesized by heating the reaction mixture of LiOH ·H2O andMnOOH (Li/Mn ) 2.00/1.00) at 900 °C under air for 12 h.The lattice parameters of the samples was determined by apowder X-ray diffraction (XRD, type XD-3A, Shimadzu Co.Ltd., Japan) analysis with an Fe KR radiation equipped with agraphite monochromator. For the x ) 1/3 sample, XRDmeasurement was performed with a synchrotron radiation usingthe large Debye-Scherrer camera installed at BL19B2 inSPring-8. The wavelength of the X-ray was estimated to be0.99772(1) Å by the XRD measurement on NIST CeO2 standard(674a). Note that the actual chemical formula for the x ) 1/3sample is no longer Li[Li1/3Mn5/3]O4, since the x ) 1/3 samplesegregates into the Li[Li1/3-ωMn5/3+ω]O4 phase with ω ) 0.124and Li2MnO3 phase. According to an inductively coupledplasma-atomic emission spectral (ICP-AES, CIROS 120, RigakuCo. Ltd., Japan) analysis, the Li/Mn ratios for the x ) 0, 0.1,0.2, and 1/3 samples were determined to be 1.00/2.00, 1.09/1.90, 1.20/1.80, and 1.33/1.67, respectively.

The electrochemical properties were examined by a chargeand discharge test in nonaqueous lithium cells. The LMOelectrodes for the electrochemical measurements were preparedas follows. Polyvinylidene fluoride (PVdF) dissolved in N-meth-yl-2-pyrrolidone (NMP) solution was used as a binder forpreparing the electrodes. The black viscous slurry, whichconsists of 88 wt % LMO, 6 wt % acetylene black, and 6 wt %PVdF, was cast onto an aluminum foil (thickness 20 µm) usinga conventional doctor-blade method with a blade gap 0.35 mm.Then, NMP was evaporated at 120 °C for 30 min, and finallythe electrodes (1.5 cm × 2.0 cm) were dried under vacuum at150 °C for 12 h. For the electrochemical tests, the counterelectrode was prepared by pressing a Li metal sheet onto astainless steel substrate. Two sheets of porous polypropylenemembrane (Celgard 2500) were used for a separator, and 1 MLiPF6 dissolved in ethylene carbonate (EC)/dimethyl carbonate(DMC) (3/7 v/v) solution was used for an electrolyte.

Magnetic susceptibility (�) was measured using a supercon-ducting quantum interference device magnetometer (MPMS,Quantum Design) in the T range between 5 and 400 K undermagnetic field H e 10 kOe. µSR experiments were performedat PSI in Switzerland and TRIUMF in Canada. µSR techniqueis particularly sensitive to the local magnetism, because themuon detects the magnetism due to nearest neighbors. It is,therefore, sensitive to short-range magnetic order, whichsometimes appears in frustrated systems, while both neutronscattering and � measurements mainly detect long-range mag-netic order. Here, zero-field (ZF-) µSR is useful to detect a weaklocal magnetic [dis]order produced by quasi-static paramagneticmoments. On the contrary, weak (relative to the spontaneousinternal fields in the ordered state) transverse field (wTF-) µSRis effective to study the volume fraction of paramagnetic phasesin the sample. The powder samples were pressed into a disk ofabout 15 mm diameter and 1 mm thickness, and subsequently

Li[LixMn2-x]O4 T (1 - z)Li[Lix-ωMn2-x+ω]O4 +zLi2MnO3 + z/2O2 (3)

ω ) (x - z)/(1 - z) (4)

Magnetic Study on Li[Li1/3Mn5/3]O4 J. Phys. Chem. C, Vol. 114, No. 25, 2010 11321

placed in a muon-veto sample holder. The experimental setupand technique are described more detail in elsewhere.15

Results and Discussion

3.1. Magnetism of Li2MnO3. Since Li2MnO3 coexists in thex ) 1/3 sample as a second phase,3,10-12 we have, at first,investigated its macro- and microscopic magnetism by � andµSR measurements. The past neutron scattering measurementson a single crystal sample indicated that the crystal structurebelongs to a monoclinic symmetry with space group of C2/m.20 Li2MnO3, more specifically, Li[Li1/3Mn2/3]O2 has a layeredstructure with stacking alternatively by the Li1/3Mn2/3 and Lilayers. The Mn4+ ions in the Li1/3Mn2/3 layer are surrounded bythree Li+ ions, and consequently, form a honeycomb sublattice.However, the other structural model with space group C2/c wasreported by the XRD study using a polycrystalline sample.21

The difference between C2/m and C2/c is caused by a differentstacking sequence along the cm axis.22,23 The crystal structureof the present Li2MnO3 sample can be indexed by a monoclinicsetting, although the details of the crystal structure is currentlyunknown. The lattice parameters, which are calculated by a least-squared method using 13 diffraction lines, are am ) 4.928 Å,bm ) 8.527 Å, cm ) 5.021 Å, and �m ) 109.27°.

Figure 1 shows the T dependence of (a) � and (b) �-1 for theLi2MnO3 sample measured in field-cooling (FC) mode with H) 10 kOe. The �(T) curves in zero-field-cooling (ZFC) and FCmodes with H ) 100 Oe are also shown in Figure 1a. As Tincreases from ∼100 K, �-1 increases monotonically withincreasing T. The Curie-Weiss parameters are, hence, estimatedby the following relation:

where N is the number density of Mn ions, µeff is the effectivemagnetic moment of Mn ions, kB is the Boltzmann’s constant,T is the absolute temperature, Θp is the Weiss temperature, and�0 is the T-independent susceptibility. Using eq 5 in the T rangebetween 200 and 400 K, we obtained µeff ) 3.787(2) µB andΘp )-25.3(2) K. These values are comparable to the past resultby Jansen and Hoppe (µeff ) 3.83 µB and Θp ) -33 K),although they assigned the crystal structure of Li2MnO3 as C2/cspace group.21 Here, the spin-only effective magnetic momentµeff

pre is calculated as 3.873 µB, by assuming that Mn4+ ions arein the S ) 3/2 state with t2g

3 and gyromagnetic factor g is 2.Therefore, the observed µeff is almost consistent with µeff

pre. As Tdecreases from 100 K, � increases with decreasing T. The �(T)curve with H ) 10 kOe exhibits a broad maximum around 47K as reported previously for a polycrystalline sample () 50K),21 whereas the d�/dT(T) curve shows a sharp peak at 35 K() T N

� ) (see the inset in Figure 1a). This indicates the presenceof an antiferromagnetic (AF) transition in the sample. Note thatthe �(T) curves in both ZFC and FC modes show a broadmaximum around 47 K (Figure 1a).

In order to confirm the existence of static AF order inLi2MnO3 below T N

� , µSR measurements were performed. Figure2 shows the T dependence of ZF-µSR spectra for the Li2MnO3

sample in the time domain below 0.3 µs. The ZF-µSR spectrumabove 38 K shows a typical Kubo-Toyabe24 behavior, indicatingthat muon-spins are depolarized by randomly oriented nuclearmagnetic moments of 6Li, 7Li, and 55Mn. However, as Tdecreases from 38 K, the ZF-µSR spectrum clearly exhibits anoscillation. This unambiguously shows the formation of staticAF order in the sample. Indeed, the ZF-µSR spectra were wellfitted by a combination of the oscillatory signal and a nonoscil-latory relaxing signal, which corresponds to a “tail” caused bythe AF component parallel to the initial muon-spin polarization

where A0 is the initial asymmetry, AAF and Atail are theasymmetries for the two signals, λAF and λtail are their relaxationrate, ωµAF is the Larmor frequency due to the AF internal fieldat the muon site, and �AF is the initial phase of the oscillatorysignal. Although the wTF-µSR measurements (described later)showed that the whole Li2MnO3 sample enters into the magneticphase below TN, the AAF/A0 ratio is limited to be ∼0.42(2) evenat 1.8 K. Here, the value of A0 is determined to be ∼0.23 fromthe ZF-µSR spectra far above TN. Thus, the large internalmagnetic field which exceeds the muon time scale partiallyexists in the sample. It should be noted that the value of �AF

ranges -15 ( 3° below 35 K. This indicates that the period ofAF order is commensurate with the lattice.

Figure 3a shows the T dependence of the muon precessionfrequency fAF () ωµAF/2π) for the Li2MnO3 sample. As Tdecreases from 38 K, fAF increases with decreasing the slope(dfAF/dT) and then reaches 42.2(1) MHz at 1.8 K. Here, thefAF(T) curve is well fitted by the following expression

Figure 1. Temperature dependence of (a) magnetic susceptibility (�)and (b) inverse susceptibility (�-1) for the Li2MnO3 sample measuredin field-cooling (FC) mode with H ) 10 kOe. The inset in (a) showsthe temperature (T) dependence of the d�/dT slope. The �(T) curves inzero-field-cooling (ZFC) and FC modes with H ) 100 Oe are alsoshown in (a). The effective magnetic moment (µeff) and Weisstemperature (Θp) are estimated by fitting the �(T) curve in thetemperature range between 200 and 400 K [red line in (a)] with theCurie-Weiss relation described in eq 5.

� )Nµeff

2

3kB(T - Θp)+ �0 (5)

A0PZF(t) ) AAF exp(-λAFt) cos(ωµAFt + �AF) +Atail exp(-λtailt) (6)

fAF(T) ) fAF(0 K)(TNµ - T

TNµ )�

(7)

11322 J. Phys. Chem. C, Vol. 114, No. 25, 2010 Mukai et al.

where fAF(0 K) is the fAF at 0 K, TNµ is the transition T, and � is

the critical exponent of the transition. The fitting with eq 5provides fAF(0 K) ) 43.9(3) MHz, TN

µ ) 35.4(5) K, and � )0.24(1), although we need accurate data in the vicinity of TN

µ todetermine � more precisely. But, the obtained � ranges betweenthe predictions for the 2-dimentional and 3-dimensional Isingmodel (� ) 0.125 and 0.3125, respectively).25

Figure 3(b) shows the T dependence of the normalized weakTF asymmetry (NATF) for the Li2MnO3 sample. The appliedmagnetic field (HwTF) was 30 Oe. Here, NATF is defined by NATF

) ATF/ATF,max ∼ ATF/0.23, and is roughly proportional to thevolume fraction of paramagnetic (PM) phases in the sample.In other words, when NATF ) 1, the whole sample is in the PMphase, while, when NATF ) 0, the whole sample is in themagnetic phase, such as, ferromagnetic (FM), AF, ferrimagnetic,or spin-glass-like phase. As T decreases from 70 K, the NATF(T)curve exhibits a step-like decrease from 1 to 0 at ∼36 K,demonstrating the presence of a sharp magnetic transition. Thus,the AF transition with TN ) 36 K is found to be intrinsicbehavior of Li2MnO3. The magnetic transition TN

mid at whichNATF ) 0.5 is almost equivalent to TN

� , TNµ , and TN () 36.5 K)

determined by neutron scattering measurements using a singlecrystal sample,20 but is ∼10 K lower than the broad maximumin the �(T) curves (see Figure 1a). Such discrepancy is alsoreported on the AF transition for the Co3O4 compound;26 the�(T) curve exhibits a broad maximum around 40 K, whereasthe d�/dT(T) curve, T dependence of heat capacity, and µSRmeasurements show a sharp transition at 30 K.

3.2. Structural and Electrochemical Properties for the x) 1/3 Sample. According to XRD measurements, the presentLMO samples with x ) 0, 0.1, and 0.2 are identified as a singlephase of the spinel structure with space group of Fd3jm. Thecubic lattice parameter (ac), which was calculated by a least-squares method using 7 diffraction lines, is determined to be8.240(1) Å for the x ) 0 sample, 8.203(1) Å for the x ) 0.1sample, and 8.177(1) Å for the x ) 0.2 sample. On the otherhand, weak diffraction peaks from the Li2MnO3 phase areobserved for the x ) 1/3 sample, because the rate of the reversereaction of eq 3 is very slow.6 In order to estimate the amountof the Li2MnO3 phase (z) and ω in eq 3, a Rietveld analysiswas carried out for the XRD data of the x ) 1/3 sample byRIETAN2000.27 Figure 4 and Table 1 show the result of the

Figure 3. Temperature dependence of (a) oscillation frequency (fAF)of the antiferromagnetic (AF) phase and (b) normalized wTF-asymmetry(NATF) determined by the wTF-µSR measurements for the Li2MnO3

sample. fAF was obtained by fitting the ZF-µSR spectra with eq 6. Notethat NATF roughly corresponds to the volume fraction of paramagneticphases in the sample. The magnetic transition TN

mid was determined asthe temperature, at which NATF ) 0.5. fAF for the Li[LixMn2-x]O4 samplewith x ) 1/3 is also shown in (a) for comparison. Here, due to a smallvolume fraction of the Li2MnO3 phase in the x ) 1/3 sample (∼10%),fAF was clearly determined only below 15 K.

Figure 2. Temperature dependence of ZF-µSR spectra for the Li2MnO3

sample in the time domain below 0.3 µs. The top of four ZF-µSRspectra are shifted by +0.2 for clarity of display. The solid line is thefitting result with eq 6.

Figure 4. Rietveld analysis for the Li[LixMn2-x]O4 sample with x )1/3. The observed (Iobs) and calculated (Icalc) intensity data are plottedas points and solid line. The bar-code type indications show all thepossible Bragg reflections from both Li[Li1/3-ωMn5/3+ω]O4 (upper) andLi2MnO3 (lower) phases. The difference between Iobs and Icalc (∆I) isalso shown.


Rietveld analysis. Here, we assume that the crystal structure ofLi2MnO3 is a monoclinic system with space group of C2/m, asproposed by the work using a single crystal.20 The weightfraction of the Li2MnO3 phase [W(Li2MnO3)] is calculated by

where Wp is the relative weight fraction of the phase p in amixture of the n phase, Sp the its Rietveld scale factor, Z thenumber of formula units per unit cell, M the mass of the formulaunit, and V the unit cell volume, respectively. Here, it is difficultto determine both values of W(Li2MnO3), i.e., S(Li2MnO3) andω in Li[Li1/3-ωMn5/3+ω]O4 simultaneously, because the con-strains between the scale factor and cite occupancy among thedifferent phases are currently not available in a conventionalRietveld analysis.27 This means that the value of ω is initiallyrequired to satisfy the Li/Mn ratio () 1.33/1.67). Therefore,we first assume that W(Li2MnO3) ) 0.1 (ω ) 0.125) by thepeak intensities at 2θ ∼ 12°, and repeat the refinements stepby step. The W(Li2MnO3) and ω were finally determined to be0.11 and 0.124, respectively, by minimizing the “goodness-of-fit” parameters such as R-weighted pattern factor (Rwp), R-Braggfactor (RB), and goodness-of-fit indicator (S) (Table 1). Thechemical formula for the present spinel phase in the x ) 1/3sample is, thus, estimated as Li[Li0.21Mn1.79]O4.

Figure 5a shows the charge and discharge curves of thelithium cell with the x ) 1/3 sample for the first five cycles.The cell was operated with a constant current mode at a rate of0.17 mA · cm-2 in the voltage range between 3 and 5 V at 25°C. Assuming a simple electrochemical reaction described ineq 1, Qtheo for the ideal x ) 1/3 phase is calculated to be 0mAh ·g-1. However, since Qrecha ∼ 46 mAh ·g-1 for the x )1/3 sample, x is estimated as 0.23, being almost consistent withthe result of the Rietveld analysis (x ) 0.21).

3.3. Microscopic Magnetism for the x ) 1/3 Sample byµSR Measurements. The structural and electrochemical analy-ses indicated that the chemical formula of the spinel phase inthe x ) 1/3 sample is Li[Li0.21Mn1.79]O4. According to ourprevious µSR study on the xe 0.15 samples, only a fast relaxingsignal was observed in the ZF-µSR spectrum in the time domainbelow 0.1 µs even at lowest T measured (1.8 K).16 If the x )1/3 sample is a mixture of the Li[Li0.21Mn1.79]O4 and Li2MnO3

phases, the µSR spectrum should be the sum of the signals fromthe Li[Li0.21Mn1.79]O4 and Li2MnO3 phases. Furthermore, im-

planted muons are expected to sit in both phases with the sameprobability. Therefore, the asymmetries of the two signals areroughly proportional to their volumes in the sample. Here, Arizaet al.28,29 already reported the microscopic magnetism for theLi[Li1.33Mn1.67]O4 compound, which prepared by heating areaction mixture at 400 °C. However, since they performed µSRmeasurements at the pulsed muon beam facility in RutherfordAppleton Laboratory (RAL),28,29 the muon-spin relaxation forLMO with x > 0.15 in the time domain below ∼0.5 µs was notstill clarified. This is because the muon beams are distinguish-able by their time structure:15 the pulsed muon beam facilitiessuch as RAL and J-PARC are ideal for studying relatively slowrelaxation, whereas the continuous muon beam facilities suchas TRIUMF and PSI are suitable for the detection of largermagnetic fields and fast relaxing signals.

Figure 6 shows the ZF-µSR spectra for the LMO sampleswith (a) x ) 0, (b) x ) 0.1, (c) x ) 0.2, and (d) x ) 1/3 at 1.8K in the time domain below 0.1 µs. The ZF-µSR spectrum forthe Li2MnO3 sample is also shown for comparison (e). The ZF-µSR spectra for the samples with x e 0.2 lack an oscillatorysignal even at 1.8 K but pose a first minimum at t ) 0.015 µs,indicating a spin-glass like freezing of the Mn moments at lowT.16 On the contrary, a clear oscillation due to the Li2MnO3

phase is observed for the x ) 1/3 sample. The ZF-µSR spectrumwas, hence, fitted by a combination of a dynamic Gaussian

TABLE 1: Structural Parameters Determined by the Rietveld Analysis for the Li[LixMn2-x]O4 Sample with x ) 1/3

phasea space group atomWyckoffposition g x y z Biso

b/Å2

Li[Li1/3-ωMn5/3+ω]O4 (ω ) 0.124) Fd3jm Li11 8a 1.0 1/8 1/8 1/8 0.5(1)Li12 16d 0.105 1/2 1/2 1/2 0.1(2)Mn11 16d 0.895 1/2 1/2 1/2 0.1(2)O11 32e 1.0 0 0 0.259(2) 1.1(1)

ac ) 8.1679(1) ÅLi2MnO3 C2/m Li21 2b 1.0 0 1/2 0 0.1(2)

Li22 2c 1.0 0 0 1/2 0.1(2)Li23 4h 1.0 0 0.694(5) 1/2 0.1(2)Mn21 4g 1.0 0 0.168(1) 0 0.1(2)O21 4i 1.0 0.252(6) 0 0.178(4) 1.1(1)O22 8j 1.0 0.247(6) 0.329(1) 0.235(2) 1.1(1)

am ) 4.9251(8) Å, bm ) 8.5215(7) Å, cm ) 4.9997(9) Å, and �m ) 109.13(2)°

Rwp ) 4.17%, RB ) 2.54%, and S ) 1.56. a The weight fraction of the Li2MnO3 phase in the x ) 1/3 sample was estimated to be 0.110. Thevalue of ω in Li[Li1/3-ωMn5/3+ω]O4 is, thus, calculated to be 0.124 using the relation described in eq 3. b Constrains: B(Li12) ) B(Mn11) )B(Li21) ) B(Li22) ) B(Li23) ) B(Mn21) and B(O11) ) B(O21) ) B(O22).

Wp ) Sp(ZMV)p/ ∑i)1

n

Si(ZMV)i (8)

Figure 5. Charge and discharge curves of the lithium cell with theLi[LixMn2-x]O4 sample with x ) 1/3 for the first five cycles. The cellwas operated at a current density of 0.17 mA · cm-2 in the voltage rangebetween 3.0 and 5.0 V at 25 °C. The charge and discharge curves atthe initial cycle (shown in red) significantly differs from those at thesubsequent cycles, probably due to the decomposition reaction betweenthe electrolyte and lithium metal.


Kubo-Toyabe24 (DGKT) signal (from the freezing phase), a fast-relaxing nonoscillatory signal (from the “tail”), and an oscillatorysignal (from Li2MnO3)

where AKT, Afast, and AAF are the asymmetries associated withthe three signals, λKT, λfast, and λAF are their relaxation rates, ∆is the static width of the local frequencies at the disordered sites,and ν is the field fluctuation rate. When ν ) 0, GDGKT(t, ∆, ν)is the static Gaussian Kubo-Toyabe function Gzz

KT (t, ∆) givenby24

The magnitude of fAF for the x ) 1/3 sample is estimated as42.3(3) MHz at 1.8 K, and is almost the same to that for thepure Li2MnO3 sample at 1.8 K, as expected. Moreover, the fAF(T)curve for the x ) 1/3 sample below ∼15 K traces that for theLi2MnO3 sample (see Figure 3a). Therefore, the oscillatorysignal in the ZF-µSR spectrum for the x ) 1/3 sample isassigned to be caused by the AF order of the Li2MnO3 phase.Note that the volume fraction of the Li2MnO3 phase (AAF/A0) is∼0.1 and is very consistent with the result of Rietveld analysis.

Figure 7 shows the T dependence of the normalized wTFasymmetry (NATF) for the samples with x ) 0, 0.1, 0.2, and1/3. Here, the NATF corresponds to the volume fraction of PMphases in the sample. A step-like decrease in NATF from 1 to 0

for the samples with x e 0.2 shows the existence of a sharpmagnetic transition for these samples at TN

mid; that is, TNmid ) 61

K for the x ) 0 sample, TNmid ) 29 K for x ) 0.1, and TN

mid )24 K for x ) 0.2. Furthermore, since NATF reaches almost 0below the vicinity of TN

mid, the whole sample enters into themagnetic phase below TN

mid for LMO with x e 0.2. On thecontrary, as T decreases from 40 K, the NATF for the x ) 1/3sample slightly drops around 36 K, then gradually decreaseswith further decreasing T, and finally approaches 0 at ∼10 K.Here, the NATF(T) curve for Li2MnO3 exhibits a step-likedecrease around 36 K (see Figures 3b and 7). The small decreasein NATF for the x ) 1/3 sample around 36 K is, hence, attributedto the AF transition of the Li2MnO3 phase.

Next, if the x ) 1/3 sample is a mixture of Li[Li0.21Mn1.79]O4

and Li2MnO3, the NATF(T) curve should show two step-likedecreases at 36 and 24 K, as in the case for a zigzag chaincompound Li0.92Mn2O4,14 since TN

mid ) 36 K for Li2MnO3 andTN

mid ) 24 K for the x ) 0.2 sample. However, as T decreasesfrom 40 K, the magnitude of NATF for the x ) 1/3 sample slightlydrops around 36 K and then decreases monotonically down to0 at ∼10 K. For the spinel phase in the x ) 1/3 sample, TN

mid )21 K with a large transition width (∆T ) 28 K). This could beexplained by the presence of multiple magnetic phases withdifferent TN

mid in the x ) 1/3 sample. In other words, the x )1/3 sample is most likely to be magnetically inhomogeneouson a microscopic scale.

Recently, Komaba et al. indicated that the crystallizationprocess for the LMO compounds with x ) 0, 0.05, 0.1, and 0.2by in situ high-T XRD measurements.9 That is, both x ) 0 and0.05 compounds are thermodynamically stable up to 700 °C,whereas the x ) 0.1 and 0.2 compounds separate into theLi[Lix-ωMn2-x+ω]O4 phase with ω ≈ x and Li2MnO3 phaseaccompanying the release of O2 around 700 °C.9 They alsoreported that ac (∼8.28 Å) for the x ) 0.1 and 0.2 compoundsare almost similar to that for the x ) 0 compound above 700°C.9 This means that the LMO compound with x > 0 is formedby the LiMn2O4 and Li2MnO3 phases from the high-T above700 °C

As seen in Figure 7, the spinel phase in the x ) 1/3 samplehas a large transition width compared to those for the x ) 0,

Figure 6. ZF-µSR spectra in the time domain below 0.1 µs for theLi[LixMn2-x]O4 samples with (a) x ) 0, (b) x ) 0.1, (c) x ) 0.2, and(d) x ) 1/3 at 1.8 K. The top of three ZF-µSR spectra are offset by+0.2 for clarity of display. The solid line represents the fitting resultwith eq 9. ZF-µSR spectrum for the Li2MnO3 sample is also shownfor comparison.

A0PZF(t) ) AKTGDGKT(t,∆,ν) exp(-λKTt) + Afast exp(-λfastt) +AAF exp(-λAFt) cos(ωµAFt + �AF) (9)

GzzKT(t, ∆) ) 1/3 + 2/3(1 - ∆2t2) exp(-∆2t2

2 )(10)

Figure 7. Temperature dependence of the normalized wTF-asymmetry(NATF) for the Li[LixMn2-x]O4 samples with x ) 0, 0.1, 0.2, and 1/3.The result for the Li2MnO3 sample is also shown. Note that NATF

roughly corresponds to the volume fraction of a paramagnetic phasein the samples.

(1 - x)LiMn2O4 + xLi2MnO3 + x/O2 f

Li[Li1+xMn2-x]O4 (11)


0.1, and 0.2 samples. This implies that the value of ω inLi[Lix-ωMn2-x+ω]O4 is microscopically different in the spinellattice, although it has been widely believed that theLi[Lix-ωMn2-x+ω]O4 phase is a single-phase by X-ray diffractionand neutron scattering measurements.10-12 In other words, theLi ions at the 16d site distribute inhomogenously even in amuon-scale. As pointed out by Paulsen and Dahn,6 the numberof phases that can coexist in the Li-Mn-O compound isestimated to be two, if we assume the Gibbs phase rule.However, such multiple phases in the x ) 1/3 sample indicatethat the rate of the eq 11 reaction is too slow to reach thethermodynamically equilibrium state. It should be emphasizedthat the present x ) 1/3 sample was oxidized at 650, 600, 550,and 500 °C under air for 24 h, respectively, after heating at1000 °C. Although the coexistence of multiple phases isinconsistent with the prediction by the Gibbs phase rule,6

nonequilibrium (or metastable) phases are also observed for thefully delithiated LixNiO2 compounds with x e 0.1;30-32 that is,there are at least four different phases in the both electrochemi-cally30,31 and chemically31,32 delithiated LixNiO2 compounds.

Finally, we wish to comment an application of µSR measure-ments on other lithium insertion materials. The compositecompounds of yLi2MnO3 · (1 - y)LiMn2O4

4 and/or yLi2MnO3 ·(1 - y)LiMO2 with M ) Co, Ni, and Mn33,34 have been recentlypromising as a positive electrode material for high-energy densityL-ion batteries (LIB). The cation ordering between Li ions andMn ions like the Li2MnO3 (Li[Li1/3Mn2/3]O2) phase coexists intheses compounds. On the other hand, the Li[Ni1/2Mn3/2]O4 com-pound18,19 with a space group of P4332 is attractive for high powerdensity LIB. However, a “non-stoichiometric” Li[Ni1/2Mn3/2]O4

compound is easily formed depending on the reaction conditions,and its macroscopic magnetic properties are very different formthose for the Li[Ni1/2Mn3/2]O4 (P4332).35 Since the µSR signalroughly corresponds to the volume fraction of each magneticphase in the sample, µSR measurements can also be apowerful tool for investigating the local structural environ-ment in these compounds.

4. Conclusion

The microscopic magnetism for the Li[LixMn2-x]O4 samplewith x ) 1/3 was investigated by muon-spin rotation/relaxation (µSR) measurements. Since the Rietveld analysisindicated that the weight fraction of the Li2MnO3 impurityis estimated as 11%, the average chemical formula of thespinel phase is represented as Li[Li0.21Mn1.79]O4, if we assumethat the relation between the (1 - z)Li[Lix-ωMn2-x+ω]O4 andzLi2MnO3 phases. However, the spinel phase in the x ) 1/3sample is found to be magnetically inhomogeneous on amicroscopic scale, indicating the inhomogeneous distributionof Li ions at 16d site in the spinel lattice. We arrive at thesesconclusions because the temperature dependence of thenormalized weak-transverse-field asymmetry for the spinelphase exhibits a large transition width (∆T ) 28 K), whereasboth x ) 0.2 and Li2MnO3 samples show a sharp magnetic.Therefore, it is most likely that the distribution of Li ions atthe 16d site correlates with the abnormal charge/dischargecapacity below 4.5 V (Qrecha

e4.5 V) for the x ) 1/3 compound.Although we restrict present µSR measurements on the highlycrystallized Li[LixMn2-x]O4 and Li2MnO3 samples, furtherµSR studies on the Li[LixMn2-x]O4 sample synthesized atlow temperatures would provide crucial information forunderstanding the microscopic structural nature for lithiuminsertion materials.

Acknowledgment. We appreciate T. Ohzuku, K. Ariyoshi,and H. Wakabayashi of Osaka City University for preparationand electrochemical characterization of Li[LixMn2-x]O4 andY. Kondo of TCRDL for ICP-AES analysis. µSR measure-ments were made both at the Swiss Muon Source, PaulScherrer Institut, Switzerland, and TRIUMF, Canada. Wethank the staff of PSI and TRIUMF for help with the µSRmeasurements. The XRD measurements were performed atthe SPring-8 with the approval of the Japan SynchrotronRadiation Research Institute (Proposal No. 2007A1917). Wealso thank the staff of SPring-8 for help with the XRDmeasurement. JHB is supported at UBC by CIfAR, NSERCof Canada, and at TRIUMF by NRC of Canada. KHC issupported by NSERC of Canada. DA acknowledges financialsupport from the Romanian CNCSIS-UEFISCU Project PNII-IDEI 2597/2009 (Contract No. 444). This work is partiallysupported by Grant-in-Aid for Scientific Research (B),1934107, MEXT, Japan.

Supporting Information Available: Temperature depen-dence of (a) initial phase of the oscillatory signal (�AF), (b)normalized asymmetries of ATF, AAF, and Atail, and (c) theirrelaxation rate for the Li2MnO3 sample. This material is availablefree of charge via the Internet at http://pubs.acs.org.

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microscopic magnetic study on the nominal composition li[li 1/3 mn 5/3 ]o 4 by muon-spin...

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