Static magnetic order in A-site ordered perovskite

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150 K. However, due to the presence of an impurity CuCr2O4 phase with Tferri = 150 K, the magnetic ground state of CaCu3Cr4O12 is still not clarified.
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Static magnetic order in A-site ordered perovskite, LaCu3Cr4O12, probed with muon spin spectroscopy Jun Sugiyama1,2∗, Hiroshi Nozaki1 , Izumi Umegaki1 , Eduardo J. Ansaldo3 , Jess H. Brewer4,5 , Hiroya Sakurai6 , Masahiko Isobe7 , and Hidenori Takagi7 1 2

Toyota Central Research and Development Laboratories, Inc., Nagakute, Aichi, Japan Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, Japan 3 University of Saskatchewan, Saskatoon, SK, Canada 4 University of British Columbia, Vancouver, BC, Canada 5 TRIUMF, Vancouver, BC, Canada 6 National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan 7 Max Planck Institute for Solid State Research, Stuttgart, Germany

Abstract The microscopic magnetic nature of a novel A-site ordered chromium perovskite, LaCu3 Cr4 O12 , has been studied with muon spin rotation and relaxation (µ+ SR) measurements down to 2 K using a powder sample. Magnetization and resistivity measurements indicated the presence of a magnetic transition at Tm = 225 K together with a metal-to-metal transition. Moreover, since the magnetization versus temperature curve showed a step-like decrease at Tm with decreasing temperature, LaCu3 Cr4 O12 was thought to enter into a spin-singlet like state below Tm . However, µ+ SR together with magnetization measurements demonstrate the appearance of static antiferromagnetic (AF) order below Tm , i.e. Tm = TN . Furthermore, the AF order was assigned to be incommensurate (IC) to the lattice and such IC-AF phase was most likely to change to a commensurate-AF phase below 25 K. Keywords: muon spin rotation and relaxation, chromium perovskite, antiferromagnetic order

1

Introduction

The tilting of BO6 octahedra in the perovskite ABO3 lattice sometimes reduces the coordination number of 3/4 of the A cations from 12 to 4, leading to a square-planar coordination. As a result, we have a AA03 B4 O12 structure (see Fig. 1), in which the coordination number of A is 12, B is 6, and A0 is 4, respectively [1, 2]. Such perovskite is usually called as an A-site ordered perovskite. Particularly, due to a Jahn-Teller effect, Cu2+ and Mn3+ ions occupy the square planer A0 site. In fact, the first AA03 B4 O12 compound was found in 2002 for ACu3 Ti4 O12 and ACu3 Ru4 O12 [1, 3, 4]. ∗ email:

[email protected]

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Static magnetic order in A-site ordered perovskite . . .

Sugiyama et al.,

Figure 1: (a) the crystal structure of LaCu3 Cr4 O12 of cubic symmetry with space group Im¯3, (b) the CuO4 square plane, and (c) the CrO6 octahedra. In order to introduce the orbital degree of freedom, the A-site ordered chromium perovskite with Cr4+ (d2 , S = 1) and Cr3+ (d3 , S = 3/2), i.e. ACu3 Cr4 O12 has attracted a special attention. In fact, since many ACu3 Cr4 O12 compounds exhibit a metallic conductivity at ambient temperature, they are expected to become a parent of new superconducting materials by adjusting the competition between Kondo-effect and RKKY [5]. A first ACu3 Cr4 O12 compound, CaCu3 Cr4 O12 was synthesized by a high-pressure technique at 1100◦ C under 60 kbar (= 6 GPa) in 2003 [6]. Although CaCu3 Cr4 O12 is believed to be a Pauli-paramagnetic metal, the magnetic ground state of CaCu3 Cr4 O12 has been predicted as a ferrimagnet with the order of Cr and Cu moments by first principles calculations [7, 8]. In addition, magnetization measurements revealed the presence of magnetic transition at around 150 K. However, due to the presence of an impurity CuCr2 O4 phase with Tferri = 150 K, the magnetic ground state of CaCu3 Cr4 O12 is still not clarified. The compounds with trivalent ions at the A site have been also synthesized by a highpressure technique. The first compound, LaCu3 Cr4 O12 , was found in 2012 by M. Isobe and H. Sakurai [9], and independently in 2014 by S. Zhang and coworkers [10]. Magnetization measurements revealed the presence of a sharp magnetic transition at 225 K (Fig. 2), implying the appearance of a spin-singlet-like state. Nevertheless, there is still no microscopic magnetic information on LaCu3 Cr4 O12 . We have, therefore, measured muon spin rotation and relaxation (µ+ SR) spectra for LaCu3 Cr4 O12 using a powder sample down to 2 K, because µ+ SR provides microscopic magnetic information of a sample due to its unique spatial and time resolution [11, 12], even for chromium oxide compounds [13, 14, 15, 16, 17, 18, 19, 20, 21].

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Experimental

A polycrystalline sample of LaCu3 Cr4 O12 was synthesized from a stoichiometric mixture of La2 O3 , CuO, Cr2 O3 , and CrO3 at 1200◦ C under a pressure of 7.7 GPa for 2 hours. The details of the synthesis have been described elsewhere [9]. Powder x-ray diffraction (XRD) analyses showed that the sample was a almost single phase with a small amount of CrO2 (less than 2 wt%). The µ+ SR spectra were measured at a surface muon beam line using the LAMPF spectrometer on M20 of TRIUMF in Canada. An approximately 200 mg powder sample was placed in an envelope with 1 × 1 cm2 area, made with Al-coated Mylar tape with 0.05 mm thickness in 2

Static magnetic order in A-site ordered perovskite . . .

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2

(a) H=10 kOe

(b)

2.5

H=10 kOe 2

-3

1.5

M/H (10 emu/mol-Cr)

2.5

-3

M/H (10 emu/mol-Cr)

3

1 0.5 0 0

on cooling on heating

100 200 300 TEMPERATURE (K)

1.5 1 210

on cooling on heating

215 220 225 230 TEMPERATURE (K)

Figure 2: (a) The temperature dependence of magnetic susceptibility (χ = M/H) for LaCu3 Cr4 O12 measured with H = 10 kOe. (b) the magnification at the vicinity of the magnetic transition. order to minimize the signal from the envelope. Then, the envelope was attached to a low-back ground sample holder in a liquid-He flow-type cryostat for measurements in the T range between 2 and 250 K. The experimental techniques are described in more detail elsewhere [11, 12].

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Results and Discussion

Figure 3(a) shows the zero field (ZF-) µ+ SR spectrum measured at T = 2 K and 225 K. The ZF-spectrum exhibits a clear muon spin oscillation at 2 K, while such oscillatory signal disappears at 225 K. This clearly indicates the formation of static magnetic order in LaCu3 Cr4 O12 between 2 and 225 K. In other words, considering the χ(T ) curve, it is found that LaCu3 Cr4 O12 undergoes an antiferromagnetic (AF) transition below 225 K. In addition, the ZF-spectrum at 72 K indicates the presence of multiple oscillatory signals with different oscillation frequencies, while the ZF-spectrum at 2 K looks to include one oscillatory signal. In order to understand the variation of the internal magnetic field (Hint ) with temperature below 225 K, Fig. 3(b) shows the Fourier transform frequency spectrum of the ZF-µ+ SR time spectrum as a function of temperature. At 2 K, the Fourier spectrum poses one peak at around 75 MHz, and the peak position shifts towards a lower frequency side with temperature, and finally disappears around 225 K. This suggests that the AF transition temperature is about 225 K (= TN ), which is consistent with the temperature at which the χ(T ) curve exhibits a step-like change. In addition, the Fourier spectrum includes one more broad peak around 50 MHz, particularly at temperatures between 25 and 200 K, suggesting a wide distribution of Hint in LaCu3 Cr4 O12 . We therefore fitted the ZF-µ+ SR spectrum with a combination of three signals; namely, an exponentially relaxing zeroth-order Bessel function of the first kind [J0 (ω1 t)], an exponentially relaxing cosine function [cos(ω2 t+φ2 )], and an exponentially relaxing non-oscillatory component 3

0.6

A0PZF(t)

225 K LaCu3Cr4O12 ZF-µSR 72K

0.2 2K 0 0

0.05 0.1 TIME (µs)

0.15

(b)

LaCu3Cr4O12 ZF-µSR

-100 0

TEMPERTAURE (K)

(a) 0.4

Sugiyama et al.,

FOURIER POWER (arb. units)

Static magnetic order in A-site ordered perovskite . . .

100 200 0

20 40 60 80 100 FREQUENCY (MHz)

Figure 3: (a) The ZF-µ+ SR time spectrum for LaCu3 Cr4 O12 measured at 2 K, 72 K, and 225 K. Solid lines represent the best fit using Eq. (1). The fit was performed in the whole measured time range between 0 and 10 µs. Each spectrum is shifted upward by 0.15 for clarity of display. (b) Temperature variation of Fourier power of the ZF-µ+ SR time-spectrum. for the tail signal of a powder sample. Here, the exponential relaxation is caused by microscopic inhomogeneity of Hint at the muon site. A0 PZF (t) = A1 J0 (ω1 t) exp(−λ1 t) + A2 cos(ω2 t + φ2 ) exp(−λ2 t) + Atail exp(−λtail t),

(1)

where A0 is the initial asymmetry, and for the present experiment, A0 = 0.23 from the measurements of a silver reference. PZF (t) is the muon spin polarization function under ZF. A1 , A2 and Atail are the asymmetries associated with the three signals, J0 (ωt) is a zeroth-order Bessel function of the first kind that is commonly used for describing an incommensurate (IC) magnetic field in a sample [11, 12, 22, 23]. Here, the generic IC magnetic field distribution is given by [24]; PIC =

2 H √ . 2 2 2 π (H − Hmin )(Hmax − H 2)

(2)

PIC has a non-zero value only when Hmin ≤ H ≤ Hmax . And, Hmin and Hmax are upper and lower limits of the distribution. Since J0 (ω1 t) provides a good approximation for PIC besides the vicinity of Hmin , the cos(ω2 t + φ2 ) signal is added in Eq. (1). Therefore, ω1 > ω2 , and ω1 /γµ = Hmax and ω2 /γµ = Hmin , where γµ is the muon gyromagnetic ratio and γµ /2π=13.55342 kHz/Oe. Figure 4 shows the temperature dependences of the µ+ SR parameters for LaCu3 Cr4 O12 . In the two frequencies, the main component, i.e. the f1 (T ) curve exhibits an order parameter like temperature dependence, as expected. A very abrupt change of f1 at TN implies that 4

Static magnetic order in A-site ordered perovskite . . .

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100 1

A i / A0

f i (MHz)

LaCu3Cr4O12 ZF-µSR

50 f1 f2 0 0

(b) 0 0

100 200 300 TEMPERATURE (K)

100 200 300 TEMPERATURE (K)

2 λ1 λ2

1.5

40

-1

λ tail (µs )

-1

λ i (µs )

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(a)

60 50

A1 A2 Atail ATF

30 20

1 0.5

10 0 0

(c) 100 200 300 TEMPERATURE (K)

(d) 0 0

100 200 300 TEMPERATURE (K)

Figure 4: The temperature dependences of (a) the muon Larmor frequencies (f1 and f2 ), (b) the normalized asymmetries (Ai /A0 ), (c) the relaxation rates (λ1 and λ2 ), and (d) the relaxation rate of the tail signal (λtail ) for LaCu3 Cr4 O12 . The data were obtained by fitting the ZF-spectrum with Eq. (1). In (a), the red solid line on the f1 (T ) curve is a guide to the eye. In (b), ATF is the weak transverse field (TF) asymmetry, which is roughly proportional to the volume fraction of non-magnetic phases in a sample. Here, TF means the field perpendicular to the initial muon spin polarization and “weak” means that TF (= 25 Oe) is very small compared with the internal AF field.

the AF transition is not continuous but discontinuous. This is consistent with the presence of the thermal hysteresis in the χ(T ) curves measured on cooling and on heating [see Fig. 2(b)]. We attempted to fit the f1 (T ) curve with the following two functions; one is the temperature dependence of the BCS gap energy, as expected for the order parameter of the IC-AF state 5

Static magnetic order in A-site ordered perovskite . . .

Sugiyama et al.,

[25], and the other is a power law, f /f0 = ((TN − T )/TN )β . However, the two functions DO NOT reproduce the f1 (T ) curve, particularly a very rapid change of f1 at TN . This is probably because the AF transition is accompanied with the discontinuous structural phase transition. The f2 (T ) curve does not show a systematic temperature dependence, meaning that the IC field distribution (δf = f1 − f2 ) varies with temperature. The fact that f1 ∼ f2 (δf ∼ 0) at 2 K indicates that the IC field distribution becomes very small and probably suggests the occurrence of a transition from a high-T IC phase to a low-T commensurate (C) phase at temperatures between 25 and 2 K. This would be good agreement with a rapid increase in χ with decreasing temperature below around 50 K [Fig. 2(a)]. In fact, if we fitted the ZFµ+ SR spectrum not with Eq. (1) but with a combination of two exponentially relaxing cosine functions and an exponentially relaxing non-oscillatory component, the initial phase of the main oscillatory signal ranged around -45 degree in the temperature range between 50 and TN . Such phase delay is well known as an indicator of IC magnetic order [11, 26, 27]. However, at 2 K, the initial phase of the main signal was almost 0, suggesting that the magnetic order is C to the lattice. In order to determine the magnetic structure, it is highly preferable to perform neutron diffraction measurements on LaCu3 Cr4 O12 . Besides below the vicinity of TN , we used the relationship, Atail = (A1 + A2 )/2, because Atail /A0 should be 1/3 for the tail signal of a powder sample. The two normalized asymmetries (A1 /A0 and A2 /A0 ) are roughly temperature independent below 200 K; that is, A1 /A0 ∼ 0.52 ± 0.1 and A2 /A0 ∼ 0.15 ± 0.1. Above 200 K, the three asymmetries exhibit complex temperature dependences. But, it is very difficult to clearly separate the three signals due to the fact that the amplitudes of the oscillatory signals become weaker and weaker with increasing temperature [see Fig. 3(b)]. On the contrary, as temperature decreases from 230 K, the normalized weak transverse field asymmetry (ATF /A0 ) suddenly drops from 1 to 0 at TN . This indicates that the whole volume of the sample enters into an AF ordered phase below TN . Also, this suggests the absence of a background signal coming from muons stopped outside of the sample. This is because we used a low background sample holder. The relaxation rates, λ1 and λ2 , are likely to show a broad maximum around 100 K at temperatures below 200 K, but they increase with temperature above 200 K. On the contrary, λtail is relatively large below the vicinity of TN , and decreases with decreasing temperature, and finally approaches 0, when the temperature becomes 0. This is a typical behavior for the tail signal.

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Summary

In order to understand the magnetic ground state of a novel A-site ordered chromium perovskite, LaCu3 Cr4 O12 , we have measured µ+ SR spectra mainly under zero magnetic field. It was found that LaCu3 Cr4 O12 undergoes an antiferromagnetic (AF) transition at TN = 225 K. The AF order is incommensurate to the lattice. Then, the incommensurate phase is most likely to change to a commensurate AF ordered phase at temperatures between 25 and 2 K. The abrupt change of the order parameter, i.e. muon Larmor frequency, at TN suggests that the AF transition is not continuous but discontinuous.

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Acknowledgments

We thank the staff of TRIUMF for help with the µ+ SR experiment. All images involving crystal structure were made with VESTA [28]. IM was supported by Japan Society for the Promotion 6

Static magnetic order in A-site ordered perovskite . . .

Sugiyama et al.,

Science (JSPS) KAKENHI Grant No. 24540362. This work was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan, KAKENHI Grant No. 23108003 and JSPS KAKENHI Grant No. 26286084.

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