Inhomogeneous broadening of the EPR signal of Yb 3+ ions in domain walls of lightly doped antiferromagnetic cuprates

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ISSN 2072−5981
Volume 14, 2012 No. 1, 12 102 — 5 pages
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Inhomogeneous broadening of the EPR signal of Yb3+ ions in domain walls of lightly doped antiferromagnetic cuprates
A.A. Vishina1*, A. Maisuradze2, A. Shengelaya3, B.I. Kochelaev1, H. Keller2
'-Kazan Federal University, Kremlevskaya 18, Kazan 420 008, Russia 2Physik-Institut der Universitat Zurich, Winterhurerstrasse 190, ZH-8057, Switzerland 3Department of Physics, Tbilisi State University, Chavchavadze av. 3, GE-0128, Georgia
*E-mail: alenavishina@gmail. com
(Received November 21, 2012- accepted November 24, 2012)
Distortion of the long-range antiferromagnetic order in the YBa2Cu3O6+y is investigated by the electron paramagnetic resonance (EPR) measurements for y = 0.1 — 0.4. In the case of the doping level y = 0. 2,0.3 the EPR signal consists of narrow and broad lines, which we relate to formation of the charged domain walls. Our theoretical analysis of the inhomogeneous EPR broadening due to the local antiferromagnetic order distortion in domain walls is well consistent with experimental results for the case of coplanar elliptical domain walls.
PACS: 76. 30. -v, 71. 27. +a, 74. 72. -h Keywords: YBCO, elliptical domain wall, EPR
1. Introduction
The electron paramagnetic resonance (EPR) proved to be a powerful method of studying electronic properties of the high-temperatures superconductors (see review [1]). The low-frequency spin kinetics of the parent compound YBa2Cu3O6+y with y = 0.1 was investigated recently using the Yb3+ ion as the EPR-probe [2, 3]. At this level of oxygen doping the /"-holes do not yet appear in the CuO2 planes, and the ideal antiferromagnetic (AF) order is not affected [4]. The broadening of the Yb3+ EPR signal was explained by the spin-spin indirect interaction via magnons and the usual magnetic dipole-dipole interactions [2−3]. It is widely accepted that at y & gt- 0. 15 the holes in the CuO2 planes start to destroy the long-range magnetic order by creating polarons, domain walls, vortices and skyrmions [5−8]. This evolution of the AF state could be detected by the additional broadening of the EPR linewidth.
In this paper we report the results of our EPR signal investigations in Y0. 98Yb0. 02Ba2Cu3O6+y with y = 0. 2,0. 3,0.4. We have found that the Yb3+ EPR signal can be described by the sum of two lorentzians with sufficiently different linewidths. Figure 1 shows the temperature dependence of the narrow and the broad lines for different levels of oxygen doping. The intensity of the broad line increases with doping and disappears at y = 0.4. In the case y = 0.3 almost only the broad line is seen.
We assume that this EPR signal behavior can be explained by the electronic phase separation into the rich and poor in holes regions in the CuO2 planes. The separation can be related naturally to creation of charged domain walls (stripes). The local distortions of the antiferromagnetic order in the domain walls should give an additional inhomogeneous broadening to the Yb3+ EPR signal due to exchange coupling between the ytterbium and copper ions. We will consider separately the collinear and coplanar antiphase domain walls, which are created by the /-holes localized in the CuO2 planes on the oxygen ions around the Cu2+ ions.
T (K)
Figure 1. EPR linewidths for the broad and narrow lines fitted with Lorentzian lineshape.
2. Collinear domain walls
The detailed investigation of this type of charged domains was performed by Giamarchi and Lhuillier based on the two-dimensional Hubbard model [9]
H = -t Z ciacja+ UZ n, t%. (1)
(ij), o- i
Here cia (c+a*) are annihilation (creation) operators for an electron with spin a at the site i, and
nia = c+acia. U is the on-site Hubbard repulsion (U & gt- 0), and t is the hopping parameter. The numerical solutions were investigated by the Monte Carlo variational technique using the HartreeFock trial function. For the strong enough Hubbard repulsion (U /1 & gt- 4) the stable collinear domainwall solutions were found, where the doped /"-holes are localized within a stripe around the each Cu2+ site. This stripe separates two AF ordered regions with opposite signs in the AF order parameter. In the U /1 = 10 case the calculated spin texture of the collinear domain wall along the j-axis could be well reproduced by the phenomenological model for the x-component of the order parameter for two sublattices:
(S?) = So tanh (Xn /4), (S?) = -S0tanh (Xn /4). (2)
Here xn is the position of the site with respect to the stripe, 4 gives a width of the domain wall and S0 is the order parameter on a long distance from the stripe. These results were confirmed later by Seidbold, Sigmund and Hizhnyakov by numerical calculations within the slave-boson mean-field approximation for the two-dimensional Hubbard model [10].
In the presence of the external magnetic field directed along the stripe the order parameter component along the magnetic field appears [2]:
{Snr) = (Synb) = So sin^tanh (xn / 4) —
sin^ = § cuMbH0 /4J.
An angle y between the sublattices'- magnetizations and the x-axis is defined by the relation between the Zeeman energy of the Cu2+ ions gCuJuBH0 and the exchange coupling J between them [2]. This magnetizations components of the AF sublattices give a contribution to the Yb3+ ions Zeeman energy due to their exchange coupling with the neighboring Cu2+ ions:
HYbCu = 8A sin y S0X Yy tanh (xB / #). (4)
Here A is the exchange coupling between the ytterbium and copper ions, Y/ is the y-component of the Yb3+ ion spin operator. This interaction is the source of the additional inhomogeneous EPR signal broadening due to the Yb3+ ions located in the domain walls. The corresponding contribution to the EPR linewidth can be estimated by the moments method. The second moment has the form
M 2 = Sp{[YoX, H YbCu ][YX, H YbCu ]}{Sp (YXYX)}-1 = ?(4A siny)2 [tanh (Xn)]2. (5)
We here put S0 = 1/ 2. In the similar way the forth moment can be calculated. Transforming the sum over the sites inside the domain wall into the integral (-2? & lt- x & lt- 2?) we can find the EPR linewidth:
M2 = 0. 5(4A siny)2, M4 = 0. 35(4A siny)4 —
, / 3 ½, , (6)
AHthelor ~ 2(M23/M4) «4. 81 A sin y «90 G.
The obtained value is much less than the experimental value of the broad EPR line AHexroad «1200 G. The smallness of the contribution calculated appears due to a very small value of sin y which is defined by the relation of Zeeman energy to the exchange coupling between the nearest Cu2+ ions, which is sin y «6 • 10−5 in our case. This argument stimulates the investigation of a possible role of the coplanar domain walls.
3. The elliptical domain wall
An existence of the coplanar domain walls in the AF order of the CuO2 planes was predicted by Zachar, Kivelson, and Emery on the basis of the Landau theory of phase transitions [11]. Particular spin and charge textures for elliptical domain walls were calculated by Seibold within the twodimensional Hubbard model [12]. It was shown that for the completely filled domain wall (i.e. one hole per site along the stripe) only the collinear solutions exist whereas the coplanar structures become stable for half-filled walls for small hole concentrations. Figure 2a shows the spin texture for the case when two holes occupy alternatively the neighboring sites along the charged stripe. In this case the spin texture is similar to the coupled vortex-antivortex structure [12]. We suggest the following phenomenological model to reproduce the calculated spin texture.
a) The hole is present in the stripe:
s? = Sjb-=-S"sin^'-^XJ4 (7)
cosh (Xn / 4) cosh (Xn / 4)
b) The hole is absent in the stripe:
Si» = S0 sin a-----y------ Sf = -S0 sin a--------------------------------------1-. (8)
n 0 cosh (Xn / 4)' n 0 cosh (Xn / 4)
Here sin a defines the eccentricity of the elliptical domain wall- the case a = n/4 describes an ideal spiral solution, whereas a = 0 reduces the spin structure to a collinear domain wall.
Figure 2. Spin structures for the elliptical domain wall: the pattern (a) was calculated numerically by Seibold [12]- the pattern (b) shows our phenomenological model, calculated using formulas (7) and (8).
Hereafter we neglect an additional rotation of the magnetic moments caused by the external magnetic field. One can see (Figure 2b) that this model reproduces the calculated spin texture quite well.
The secular part of the corresponding Hamiltonian for the exchange interaction between the ytterbium ion and the elliptical domain wall takes the following form
HYbCu = Asin"ZYnyF (Xn /4),
(X ^
tanh (xn / 4)
tanh [(xn + a)/ 4]
cosh (xn /4) cosh (xn /4) cosh[(xn + a)/4] cosh[(xn + a)/4]J Calculations similar to the case of the collinear domain wall give
M2 = 8.5 -10−3 (A sin a)2, M4 = 1.9 -10−4 (A sin a)4-
= 0. 132І A sina.
Taking again the value |A| = 120K [2], we can achieve the experimental value for the broad EPR line AHbpoad «1200 G with a rather small eccentricity of the elliptical domain wall: sin a = 2. 9• 10−2. One could expect that at the level of oxygen doping approaching y = 0.4 the AF order will be destroyed, the holes in the CuO2 planes delocalized, and the inhomogeneous broadening of the Yb3+ EPR line will vanish. Such a behavior was actually observed in our case.
To conclude, we have investigated both experimentally and theoretically the evolution of the AF order in the Y0. 98Yb0. 02Ba2Cu3O6+y system on the basis of the EPR measurements. We have found that the EPR results can be explained on the basis of the electronic phase separation in the CuO2 planes due to a formation of the antiphase elliptical domain walls by the doped oxygen p-holes.
This work was supported by the Swiss National Science Foundation, the SCOPES grant No. IZ73Z0_128 242, and partially by the Ministry of Education and Science of the Russian Federation.
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