2. STRUCTURAL STUDIES OF RARE EARTH COMPOUNDS USING DIFFRACTION TECHNIQUES UNDER HIGH
2.2 Neutron diffraction under high pressure .1 Micro-pressure cell
In neutron-scattering experiments using piston-cylinder cells, neutrons penetrate not only the material studied but also the surrounding pres- sure-transmitting medium and materials used to construct the pressure cells. Therefore, it is important to know the neutron transmission proper- ties of these materials. Neutron transmission coefficients of various alloys use in manufacturing pressure cells are shown as a function of neutron energy inFigure 23. For example, only 9% of neutrons at a typical energy of 14.8 meV penetrate the MP35N alloy with thickness of 10 mm, while about 30% and 40% of neutrons will penetrate the NiCrAl and CuBe alloys with
120 100 80 60 40
20 RT
P (GPa)
r (mWcm)
0 5 10 15 20 25
CeAl2
FIGURE 22 Pressure dependence of the electrical resistivity of CeAl2up to 23 GPa at room temperature (Miyagawa, 2008).
the same thickness at this energy, respectively. Thus, it appears that NiCrAl and CuBe alloys are most suitable materials for making pressure cells.
The neutron transmission properties of various pressure-transmitting media were also studied as a function of neutron energy. In general, hydrogen-free Fruorinert and deuterated alcohol systems are both suit- able for neutron transmission. Therefore, one can use Fluorinert FC75, mixtures of FC84/87 and other, or deutrated methanol/ethanol mixtures suitable for the pressure range studied after taking into account the hydrostatic limit (Angel et al., 2007; Klotz et al., 2009; Osakabe and Kakurai, 2008; Sidorov and Sadykov, 2005).
High-pressure cells used in our experiments were designed for use with a cryostat with the sample space 65 mm in height and 30 mm in diameter.Figure 24A shows a schematic drawing of the CuBe cell that has 14 mm external diameter. Hardened CuBe alloy was used for most of the cell to obtain the maximum pressure of 2 GPa (Aso et al., 2006b). As an example of the pressurizing test for the cell, Figure 24B illustrates the pressure dependence of linewidths of Q ¼(2, 0, 0) Bragg reflections of single-crystalline NaCl, where a Fluorinert FC75 was used as a pressure- transmitting medium. The pressure was estimated by determining the change in the lattice parameter of NaCl (Skelton et al., 1984). The rocking curve linewidth is constant up to 0.3 GPa, and it increases at higher pressure. The radial scan linewidths, which roughly measures the pressure distribution in the cell, are unchanged within the accuracy of a few percent
Transmission coefficient (cm–1)
Energy (meV) 1
0.01 0.1 1 10
10
2 2 4 2 4 2 4
4 6 2 4 6 2 4 6
100 1000
JRR-3/PONTA MP35N NiCrAl CuTi CuBe A7075
FIGURE 23 Neutron transmission properties of various alloys that are used in manufacturing pressure cells represented as a function of neutron energy.
up to 1.3 GPa and then slowly increases. These findings indicate that the hydrostatic limit is near the critical pressure ofP¼1.3 GPa for FC75.
A smaller CuBe cell of 8.8 mm external diameter was also designed on the basis of the former cell (Uwatoko et al., 2005), which is more useful for ND studies of neutron absorber materials. For ND at pressures above 2 GPa, a hybrid CuBe/NiCrAl cell was also developed. Its detailed design and other features were reported byAso et al. (2007). In the following two sections, we will review the applications of the present apparatus to study the magnetic properties of UGe2and CeRhIn5.
2.2.2 UGe2
UGe2is a ferromagnet crystallizing in the orthorhombic ZrGa2-type struc- ture (space group Cmmm) and exhibits pressure-induced SC (Huxley et al., 2001; Saxena et al., 2000). By using the 14-mm Cu–Be cell, a single crystal of UGe2 can be successfully pressurized up to 1.6 GPa at low temperature (Aso et al., 2006a,b).
48 FWHM (⬚)
4
1.2
NaCl, Q = (2,0,0) with FC75 Rocking Curve
Radial 1.0
0.8
0.6
0.4
0.2
0.00.0 0.5 1.0 P (GPa)
1.5 2.0
14
A B
FIGURE 24 (A) Schematic drawing of the pressure cell. Hardened CuBe alloy is used for a cylinder. (B) FWHM of Bragg profiles atQ¼(2, 0, 0) for single-crystalline NaCl as a function of pressure. The lines are guides to the eye (Aso et al., 2006b).
Figure 25A shows the temperature dependence of ferromagnetic Bragg peak intensities atQ ¼(0, 0, 1) against the temperatureTmeasured at various pressures. The temperature–pressure phase diagram deter- mined by these measurements as illustrated inFigure 25B. Curie temper- ature (TC) is about 52 K at ambient pressure, and it monotonically
20,000
60 50 40 30 20 10 0 A
B 15,000
10,000
5000
0
0 10
JRR-3M/ISSP-HER
0.28 GPa 0.5 GPa 0.8 GPa 0.97 GPa 1.1 GPa 1.23 GPa 1.4 GPa
Paramagnetism (PM)
Ferromagnetism (FM)
Perfectly polarized
E Px
Pc Tx Tx TFM
Superconductivity (Tateiwa et al.) ki= 1.555 A–1
UGe2, Q = (0,0,1)
Open-BeF-80¢-80¢
20 30
T (K)
T (K) Normalized D, Q¢
P (GPa)
Intensity-BG (a.u.)
40 50 60
0.0 0.5 1.0 1.5 2.00.0
0.5 1.0 1.5 2.0
q¢
D
FIGURE 25 (A) Temperature dependence of ferromagnetic Bragg peak intensities at Q¼(0, 0, 1) against temperatureTmeasured at various pressures (Aso et al., 2006a).
(B) Phase diagram of UGe2determined by ND measurements. Pressure dependences of the obtained parametersDandY0from the Stoner model are also plotted, which are normalized with respect to their corresponding values at ambient pressure, that is, D¼39.5 K andY0¼83.4 K. Characteristic temperaturesTxtaken fromTateiwa et al.
(2001)are also plotted. The solid lines are guides to the eye (Aso et al., 2006b).
decreases with increasing pressure. The characteristic temperature Tx, where a steep increase in the ferromagnetic Bragg peak intensities is observed, also decreases with increasing pressure from30 K observed at ambient pressure, and it becomes suppressed to zero at a critical pressure Px of 1.2 GPa. InFigure 25B, the pressure dependence of D andY0parameters obtained from theStoner model (1938)is also plotted;
the Stoner model was applied to the temperature dependence of ferro- magnetic Bragg peak intensities at Q¼(0, 0, 1) belowTx. In the Stoner model, the magnetization (square root of the neutron intensities) is expressed as follows:
M¼M01aT3=2expðD=TÞ
; (4)
a¼3 4
ffiffiffip p 1
EF
3=2; D¼2EF Y0 EF21=3
; (5)
where M0indicates the magnetization at zero temperature, Dis the so- called Stoner gap,EFis the Fermi energy, and Y0 is the molecular field coefficient. It should be noted that these quantities ofD,Y0, andTxlie on a single line, suggesting that the characteristic temperatureTxis related to the Stoner gapD(equivalentlyY0) in the heavy quasiparticle band. These observations imply that the perfectly polarized ferromagnetic state is realized belowPxin UGe2.
2.2.3 CeRhIn5
CeRhIn5, which is a member of the CeTIn5(T¼Rh, Ir, and Co) family with a tetragonal HoCoGa5-type crystal structure, is an ideal model for studying correlations between AFM and SC because its transition tem- peratures (Ne´el temperature,TN, and superconducting transition temper- ature,Tc) can be controlled by the application of external pressure. At the ambient pressure, CeRhIn5displays AFM ordering belowTN 3.8 K. As the pressure increases,TNpasses through a maximum of 4.0 K at approx- imately 0.8 GPa and then vanishes in the vicinity of the characteristic pressurePx1.85 GPa. At pressures abovePx, pure SC state emerges at Tc2.2 K.
The magnetic structure of CeRhIn5at ambient pressure is an incom- mensurate (IC) spiral helix along the tetragonalc-axis characterized by the propagation wave vectort¼(0.5, 0.5,d), whered ¼0.297. The pressure dependence ofdis controversial. Thus, according toLlobet et al. (2004),d is almost independent of pressure up to 1.63 GPa, whileMajumdar et al.
(2002)reported thatdexhibits a jump at approximately 1 GPa. To reveal the intrinsic magnetic structure at ambient and high pressures, measure- ments under hydrostatic pressure are highly needed.
By using the 8.8-mm Cu–Be cell, a single crystal of CeRhIn5can be successfully pressurized up to 1.48 GPa at low temperature using the pressure-transmitting medium of a 4:1 deutrated methanol/ethanol mix- ture with the hydrostatic limit of 10 GPa (Aso et al., 2009). Note that the signal-to-background ratio in the present experiment (0.75 GPa) is much better than those in the literature (Llobet et al., 2004; Majumdar et al., 2002; Raymond et al., 2008). With increasing pressure,dgradually increases to 0.326 at 1.48 GPa, exhibiting no anomaly near 1 GPa in contrast to the results obtained byMajumdar et al. (2002). This discrep- ancy may originate from the difference in the pressure-transmitting media, since Fluorinert used in the previous experiments has a hydro- static limit of approximately 1 GPa.
To obtain a clear picture of the relationship between AFM and SC in CeRhIn5, the magnetic structure above and belowTcatP¼1.48 GPa was investigated. Figure 26A illustrates ND profiles along the (0.5, 0.5, l) vector at T¼2.0 K (>Tc), 0.90 K (Tc), and 0.75 K (< Tc). Figure 26B shows theT dependence of the peak intensities atQ1¼(0.5, 0.5, 1.326) and Q2¼(0.5, 0.5, 1.391). Upon lowering the temperature, the peak intensity at Q1 starts to increase at TN3.0 K and then gradually decreases below the characteristic temperatureTx1.6 K before sharply
700 600 500 400
1.8 1.7 1.6 1.5 1.4 1.3 1.2
(0.5,0.5,l)
T= 0.75 K 700
600 500
Intensity (counts/5min) 400 T= 0.90 K
700 600 500 400
T= 2.0 K Q1 Q2
A
B
600 500 400 300 200 100 0 –100
Peak Intensity (counts/15min)
4 3 2 1 0
T (K)
Q1= (0.5, 0.5, 1.326) Q2= (0.5, 0.5, 1.391)
TN
Tc T*
CeRhIn5, JRR-3/GPTAS ki= 3.83 Å–1, P= 1.48 GPa
FIGURE 26 (A) Neutron diffraction profiles of CeRhIn5measured underP1.48 GPa at (top)T¼2.0 K (>Tc), (middle) 0.90 K (Tc), and (bottom) 0.75 K (<Tc). (B)Tdependence of the peak intensities atQ1¼(0.5, 0.5, 1.326) (triangles) andQ2¼(0.5, 0.5, 1.391) (circles). The intensities of the paramagnetic state are subtracted. The solid line is a guide to the eye (Aso et al., 2009).
dropping atTc0.90 K. The intensity at 0.75 K is as small as the back- ground level. Interestingly, the peak atQ2exhibits the opposite behavior.
The intensity at 0.75 K is almost the same as that ofQ1atTx. We found that the incommensurabilitydexhibits a drastic change at approximately 1 K, which is close to Tc, at 1.48 GPa, that is, the switching of the magnetic ordering occurs. This unexpected behavior suggests the possibility that the AFM order is affected by the SC state.