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Spin resonance in EuTiO3probed by time-domain GHz ellipsometry

J.L.M. van Mechelen,1D. van der Marel,1I. Crassee,1and T. Kolodiazhnyi2

1D´ epartement de Physique de la Mati` ere Condens´ ee, Universit´ e de Gen` eve, Gen` eve, Switzerland.

2National Institute of Materials Science, Tsukuba, Ibaraki, Japan.

(Dated: May 19, 2011)

We show an example of a purely magnetic spin resonance in EuTiO3 and the resulting new record

high Faraday rotation of 590 deg/mm at 1.6T for 1 cm wavelengths probed by a novel technique

of magneto-optical GHz time-domain ellipsometry. From our transmission measurements of linear

polarized light we map out the complex index of refraction n =√?µ in the GHz to THz range.

We observe a strong resonant absorption by magnetic dipole transitions involving the Zeeman split

S = 7/2 magnetic energy levels of the Eu2+ions, which causes a very large dichroism for circular

polarized radiation.

The magnetic state of solids can be measured and ma-

nipulated through the interaction with photons. The in-

teraction of the electric field component of electromag-

netic radiation with the orbital motion of electrons is de-

scribed by the dielectric permeability ?±(ω), where the

suffix indicates left handed (LCP, −) and right handed

circular polarization (RCP, +). Interaction with the elec-

tron spin occurs through the magnetic field component

and is described by the magnetic susceptibility µ±(ω).

Photons interact differently with magnetically polarized

matter depending on whether their angular momentum

(±¯ h) is parallel or antiparallel to the magnetic polar-

ization. This so-called circular dichroism transforms in-

cident linear polarized light (which is a superposition of

equal amounts of LCP and RCP) to elliptical after trans-

mission (Faraday effect) or reflection (Kerr effect). The

magnetic field component of the electromagnetic field in

the THz range is the relevant component which interacts

with the local magnetic moments in EuTiO3, because

the 4f7ground state of the Eu2+ions has only spin- and

no orbital component. Photons in the THz range, when

absorbed by a 4f7moment, transfer their angular mo-

mentum with the matching chirality to the magnetic ion.

Bulk EuTiO3has the same perovskite crystal structure

as room temperature SrTiO3. It is magnetic due to the

seven parallel spins on the Eu site and has thus S = 7/2

and L = 0 and a Land´ e g-factor of 2. Neutron diffraction

at low temperatures has shown that EuTiO3orders an-

tiferromagnetically below TN= 5.5 K in a G-type struc-

ture [1]. The rare-earth perovskite phase diagram shows

EuTiO3to be on the borderline between AFM and FM

ordering [2]. At 4.5K application of a small external mag-

netic field of about 0.2 T provokes a spin-flop transition

and above 0.7T the magnetization rapidly saturates [3].

EuTiO3 can be made FM by applying a biaxial tensile

strain of 1.1% [4]. Bulk EuTiO3is a band insulator and

is transparent in the THz range.

Here we present a spectroscopic study of the spin dy-

namics of insulating EuTiO3probed in the GHz to THz

range simultaneously for LCP and RCP. In prior work

on AFM and FM spin resonances in various oxides [5–

10] both spin and orbital degrees of freedom determine

FIG. 1: Transmitted electric field vs. time delay through a 315

µm thick EuTiO3 slab for selected values of the applied mag-

netic field at 4.5 K. The incident radiation is linearly polarized

and after transmission is recorded by a linearly polarized de-

tector. The inset shows the electric field as a function of the

magnetic field at 51 ps; the red curve is a cosine function.

the resonance spectrum. In the present study we directly

probe the 4f orbitals of EuTiO3which allows us to in-

vestigate a purely magnetic spin resonance. Highly dense

(97-98%) polycrystalline EuTiO3pellets with the SrTiO3

structure were synthesized by spark plasma sintering as

described in Ref. [11]. Optical measurements are per-

formed on circular samples with a thickness of 265 µm

and 315 µm and a diameter of 10 mm, resulting from

different fabrication batches. Optical polishing of both

samples resulted in a black optical appearance with al-

most single crystal like shiny surfaces.

The transmitted electric field E of a linearly polar-

ized GHz-THz pulse was measured in the time-domain

at 4.5K (see Fig. 1). The emitting and receiving anten-

nas of the spectrometer (Teraview Ltd., Cambridge, UK)

are linearly polarized. The frequency range has been ex-

tended from 60 GHz down to 25 GHz by choosing an

appropriate Austin switch emitter and receiver. As a

arXiv:1105.3553v1 [cond-mat.str-el] 18 May 2011

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FIG. 2: The (a) real and (b) imaginary part of the complex

Faraday angle ΘF = θF+ iηF of the first transmitted pulse

as a function of photon energy for selected magnetic fields at

4.5 K.

function of time delay, Fig. 1 shows a pulse which cor-

responds to the directly transmitted beam followed by

a pulse which exits the material after two internal re-

flections. Application of a magnetic field H, parallel to

the propagation of the light, has the effect of initially

decreasing the amplitudes of both pulses. Demagnetiza-

tion effects are negligible for this sample/field geometry.

For the second pulse the influence of H is approximately

three times stronger than for the first one. As a function

of increasing field, E(t) passes through zero and starts to

grow again with opposite sign. The inset of Fig. 1 clearly

demonstrates the periodic cosine dependence on H. This

behavior can be understood if we assume that the pho-

tons, which are linearly polarized, pick up a Faraday ro-

tation θF proportional to H after passing through the

sample once. Taking into account that the detecting and

emitting antenna are aligned parallel to each other, the

detected field amplitude of the jth pulse (which has tra-

versed the sample 1+2j times due to multiple internal re-

flection) is expected to be proportional to cos[(1+2j)θF].

This is indeed the experimentally observed behavior dis-

played in the inset of Fig. 1.

In order to determine the complex index of refraction

n±(ω) =?µ±(ω)?±(ω) for both chiralities, we measured

mission using a fixed linear wire-grid polarizer in front

of the sample and an identical rotatable polarizer behind

the sample. In this way, the time dependent electric field

strength E(t) is obtained for analyzer angles α up to over

2π radians. Making use of the Jones matrix formalism,

the electric field at each time t has been fitted to the

relationship

the change of polarization state of the light after trans-

E(α)|t= Exx(t)cos2α − Exy(t)cosαsinα.

This gives the transmitted electric fields Exxand Exyin

(1)

the time-domain. Fourier transformation of both quan-

tities provides the complex electric fields E±(ω) for each

chirality. For the Fourier transformation, the signal in

the time domain 0 < t < 30ps was used. This corre-

sponds to the signal which has passed through the sam-

ple without multiple reflections and limits the frequency

resolution to 0.1 meV. Consequently the frequency do-

main spectra are smooth on the same energy scale. We

observe that E+(ω) and E−(ω) are significantly different,

as will be discussed later. This causes the incoming po-

larization to change from linear to elliptical, in agreement

with the result from Fig. 1. The ellipse is characterized

by the complex Faraday angle ΘF= θF+ iηF, where θF

is the rotation of the major axis as compared to the in-

cident linear polarization state, and ηFis related to the

ellipticity e (the ratio of the minor and major axes) by

e = tanhηF. The ellipsometric parameters ηF and θF

determined by

θF(ω) =1

2Im ln

?E+

E−

?

ηF(ω) =1

2Re ln

?E+

E−

?

,

(2)

are shown in Fig. 2. Since the sample is much thicker

than the attenuation length c/(ω Imn±) we can approx-

imate Eqs. 2 to

θF(ω) ?ωd

2cRe(n+− n−)ηF(ω) ? −ωd

2cIm(n+− n−),

(3)

where d is the sample thickness. The lower limit of 0.1

meV constitutes the diffraction limit below which no radi-

ation passes through the 8.5 mm wide aperture. The fact

that θF(ω) and ηF(ω) depend on the relative transmis-

sion of LCP and RCP photons removes most diffraction

effects from these spectra. The result is very intuitive

and shows that for a field of e.g. -1.3T, the absorption is

strongly peaked at 0.14meV for the RCP chirality, hence

the transmitted light has LCP chirality. Reversing the

sign of the magnetic field reverses the direction of the

local moments inside the material, hence now LCP pho-

tons are resonantly absorbed, allowing only RCP photons

to pass through the material. This selective absorption

of one particular chirality gives rise to a large Faraday

rotation in a broad band of GHz radiation (Fig. 2a) of

more than 250 degmm−1T−1which peaks up to an un-

precedented level of 590 deg mm−1at 0.14meV (34GHz)

at a relatively modest field of 1.6T. The largest actually

measured Faraday angle we obtained is about 560 deg

at 1.6T for an optical path length of 0.945 mm (cf. first

echo in Fig. 1). This rotation is well beyond measured

angles in previously known record bulk materials: ferrites

and garnets have typical rotations of 10 deg/mm in the

microwave X band (around 0.04 meV). Mn12Ac shows a

rotation in a very narrow photon energy region around

1.25 meV of at most 130 deg (for a 0.75 mm thick sam-

ple) which is present at zero applied magnetic field due

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FIG. 3: Transmitted amplitude (a,b) and phase (c,d) of 265

µm thick EuTiO3 as a function of photon energy for several

external magnetic fields H for LCP and RCP at 4.5K.

to the anisotropy field [12]. The measured angle in the

EuTiO3 samples is also large as compared to rotations

observed in thin materials like graphene and HgTe thin

films where a Faraday rotation is induced by cyclotron

resonance of charge carriers [13, 14]. The weak shoulder

around 0.25meV (cf. Fig. 2b) is due to wavelength depen-

dent transmission through the 8.5 mm aperture in which

the sample is mounted. Since the sample impedance for

LCP and RCP depends on the magnetic field, this effect

does not entirely cancel out in the ratio E+/E−.

To obtain the transmission T±(ω) of the first pulse,

the signal transmitted through the sample was calibrated

against a measurement of the empty aperture. The Fres-

nel equations T±(ω) then are

T±(ω) =

4Z±

(1 + Z±)2ei(n±−1)ωd/c,

??±/µ±. Fig. 3 shows the transmission

between 0.1 meV and 3.5 meV at magnetic fields H be-

tween 0T and −1.6T at 4.5 K. The curves show a pro-

nounced absorption and a step-like phase increase for

RCP light which strongly depend on the applied mag-

netic field whereas the transmission and phase for LCP

light do not show any magnetic field dependence.

The observed circular dichroic phenomenon is present

on an energy scale which corresponds to a magnetic

dipole transition inside the Zeeman split S = 7/2 mo-

ment of the Eu2+moments. Since in this case g = 2, the

Zeeman energy is 0.12 meV per Tesla which is compatible

with the observed resonance frequencies. If the resonance

seen in the transmission spectra would originate from a

(4)

where Z± =

amplitude and phase for LCP (−) and RCP (+) light

FIG. 4: Real and imaginary part of the index of refraction

n±(ω) = n±

function of photon energy and magnetic field for LCP and

RCP. The inset in (c) shows the energy of the maxima in

µ+

energy ¯ hω0(H) = 0.1158H (black line).

1(ω) + in±

2(ω), where n(ω) =

?

?(ω)µ(ω), as a

2(ω) as a function of magnetic field (circles) and the Larmor

peak in Im?±(ω), this would imply huge changes of ?±(0)

as a function of H. However, this is excluded by the ob-

servation of Katsufuji et al. [15] where ?(0) only changes

7% in a magnetic field of 1.6T. Therefore the resonance

seen in Fig. 3 must have its counterpart in the frequency

dependence of µ±(ω).

In order to obtain n±(ω) from the T±spectra we as-

sume that far above the Zeeman energy µ±(ω) ≈ 1. We

used a single Lorentz oscillator corresponding to the fer-

roelectric soft mode to model ?±(ω). The parameters of

this oscillator were fitted to the real and imaginary part

of the transmission spectra between 1.25 meV and 3.7

meV. We finally calculated n±(ω) between 0.1 and 3.5

meV by inversion of Eq. 4 using the low energy extrapo-

lation of aforementioned parametrization of ?±(ω) ≈ 500

(Fig. 4). At energies above the resonance, Fig. 4 con-

firms that n2→ 0 for both chiralities as expected. We

verified that the real and imaginary part of n±(ω) are

Kramers-Kronig consistent, as required by causality.

At low energies the imaginary part of n+(ω) shows a

peak which corresponds to the absorption of RCP light

(cf. Fig. 3b). In order to verify the hypothesis that this

absorption is due to purely magnetic dipole transitions

within the Zeeman split Eu 4f levels, corresponding to a

spin resonance, we plot the maxima of µ+

tion of the applied magnetic field H (inset Fig. 4c). This

shows a linear behavior which goes through the origin

when extrapolated to H = 0.

the Larmor energy ¯ hω0 = ¯ hγH, with γ = gµB/¯ h for

g = 2, with µBthe Bohr magneton. This is the energy

2(ω) as a func-

The figure also shows

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required to bring a spin-system into resonance in the FM

state.[17] The perfect agreement illustrates the absence

of an anisotropy field and thus of an orbital component

in the magnetic ground state of the Eu ions. The width

of the peak has the smallest value for an applied field

of 1.4 Tesla, and may indicate a cross-over in the mag-

netic phase diagram characterized by a small value of the

Gilbert damping [18]. The resonance contributes ∼0.1 to

µ(ω) for ω < ω0, which is comparable to spin resonances

observed in ferrite [6].

Interestingly the resonance shown in Fig. 4d is a rather

symmetric function of frequency for Imn(ω).

spondingly, the real part of n(ω) has an almost purely

dispersive line shape as expected from Kramers-Kronig

relations between these two quantities. Yet, this observa-

tion is at first glance surprising, in view of the fact that

we expect a symmetric resonance in Imµ(ω) with dis-

persive counterpart in Reµ(ω). [Note that ?(ω) should

be almost constant at these low frequencies.]

n(ω) =??(ω)µ(ω), an asymmetric line shape should oc-

inary part of n(ω)2(not shown) is strongly asymmetric.

Several reasons for this behavior can be considered. (i) In

view of anticipated multiferroic properties of this mate-

rial [19] it is tempting to speculate that the asymmetry is

induced by additional resonances at the same frequency

occurring in ?(ω) and/or the magneto-electric susceptibil-

ity. However, no mechanisms are known which can cause

such strong coupling between spin and electric field. (ii)

Asymmetry could in principle arise from a departure of

the condition of local response of n(k,ω), in other words,

if n(k,ω) depends strongly on the wave vector k. How-

ever, presumably the electric or magnetic response to the

external field is confined to regions of the order of the

grain-size of the polycrystalline sample (of order 10−6m),

i.e., far smaller than the sample thickness thus excluding

this scenario. (iii) The wavefront has a distortion due

to the 8.5 mm aperture. The wavefront distortion, and

the corresponding transmission and phase, are necessar-

ily wavelength dependent which becomes progressively

weakened for wavelengths much smaller than the aper-

ture. Since the spectral range of Fig. 4 corresponds to

wavelengths between 4 and 12 mm, the third scenario of-

fers the most plausible explanation for the observed line

shape anomaly.

This work presents the first frequency and magnetic

field dependence of the spin resonance in EuTiO3. In

contrast to other magnetic materials where ferromagnetic

resonances have been observed [6, 10] an orbital compo-

nent is absent in the magnetic ground state of the Eu2+

moments. We probe the transmission of EuTiO3 by a

novel spectroscopic technique of GHz time-domain ellip-

Corre-

Since

cur both in Ren(ω) and Imn(ω). Vice versa, the imag-

sometry, which provides the complex index of refraction

function for right and left handed circular polarized light.

These functions show a strong dichroism which causes

the rotation of linearly polarized GHz light by a record

amount of 590 deg/mm at 1.6 Tesla.

This work was supported by the Swiss National Sci-

ence Foundation through through grant number 200020-

125248 and the NCCR Materials with Novel Electronic

Properties (MaNEP). T.K. was supported by GASR C-

21560025 MEXT, Japan.

stimulating discussions with J.N. Hancock and R. Vi-

ennois.

We gratefully acknowledge

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