Angle-dependent electron spin resonance of \mathrm{YbRh}_{2}\mathrm{Si}_{2} measured with planar microwave resonators and in-situ rotation

Angle-dependent electron spin resonance of measured with planar microwave resonators and in-situ rotation

Linda Bondorf Manfred Beutel Markus Thiemann Martin Dressel Daniel Bothner111Present address: Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands Jörg Sichelschmidt Kristin Kliemt Cornelius Krellner Marc Scheffler [ 1. Physikalisches Institut, Universität Stuttgart, Germany Physikalisches Institut and Center for Quantum Science (CQ) in LISA+, Universität Tübingen, Germany Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden, Germany Goethe-Universität, Frankfurt am Main, Germany
Abstract

We present a new experimental approach to investigate the magnetic properties of the anisotropic heavy-fermion system as a function of crystallographic orientation. Angle-dependent electron spin resonance (ESR) measurements are performed at a low temperature of and at an ESR frequency of utilizing a superconducting planar microwave resonator in a He-cryostat in combination with in-situ sample rotation. The obtained ESR g-factor of as a function of the crystallographic angle is consistent with results of previous measurements using conventional ESR spectrometers at higher frequencies and fields. Perspectives to implement this experimental approach into a dilution refrigerator and to reach the magnetically ordered phase of are discussed.

keywords:
heavy fermion, , anisotropy, electron spin resonance, microwave chip

url]scheffl@pi1.physik.uni-stuttgart.de

1 Introduction

The tetragonal heavy-fermion metal shows pronounced magnetic anisotropy Trovarelli2000a (); Trovarelli2000b (); gegenwart2002 () and is an intensively studied model system for quantum criticality gegenwart2008 (). It exhibits antiferromagnetic order at temperatures below and in-plane magnetic fields below gegenwart2002 (). Its Néel temperature decreases with increasing field down to a quantum-critical point (with ) induced by the external magnetic field of (within the tetragonal -plane) or (along the -axis) gegenwart2008 (); custers2003 (). Due to the presence of the quantum-critical point, the system shows pronounced non-Fermi-liquid properties gegenwart2008 (); custers2003 (). As the antiferromagnetic state underlies the quantum-critical nature of , the details of the magnetic order are highly interesting in context of the peculiar properties of . However, due to major experimental challenges in commonly used methods such as neutron scattering stock2012 (), the magnetically ordered phase of is not sufficiently investigated and understood yet. ESR could be a promising alternative method to elucidate details of the antiferromagnetic order, but conventional ESR spectrometers are limited in both temperature and magnetic field to energies much higher than the magnetic order of . Multiple ESR investigations on have been performed sichelschmidt2003 (); sichelschmidt2007 (); wykhoff2007 (); Duque2009 (); schaufuss2009 (), but they could not reach the mK temperature range that is required to address the regimes that are key to understanding the quantum-critical nature of . As the ESR response of is a very interesting topic on its own sichelschmidt2003 () and as its possible relation to quantum criticality is not settled Kochelaev2009 (); Woelfle2009 (), ESR studies close to the quantum-critical point are also desired from a fundamental perspective of magnetic resonance. Planar microwave resonators can be used as ESR probes scheffler2013 (); Javaheri2016 (); Ghirri2015 () for to overcome the limitations of conventional ESR spectrometers: as such resonators Frunzio2005 (); Goeppl2008 (); Clauss2013 (); Malissa2013 () can be operated with a multimode measurement technique scheffler2013 (); DiIorio1988 (); Hafner2014 (); Thiemann2017 (), they can simultaneously address multiple ESR frequencies and thus multiple magnetic magnetic fields in the phase diagram scheffler2013 (), and they can also be employed at mK temperatures Thiemann2017 (); Frunzio2005 (); wiemann2015 (); Scheffler2015 (); Parkkinen2015 (); Voesch2015 ().

Figure 1: Probe and sample mounting for ESR measurements and orientation of static magnetic field . a) Construction inside the sample box with piezoelectric rotator (1), brass stamp (2), sample (3) and coplanar microwave resonator (4). b) Superconducting Nb resonator on sapphire substrate, with fundamental frequency of . c) Sample of on a brass stamp, with angle indicating the orientation of magnetic field with respect to crystallographic axes and .

2 Experiment

We performed microwave measurements on inside a He-cryostat equipped with a superconducting electromagnet. The arrangement of microwave probe and sample is shown in Fig. 1a): the flat sample is kept at a small distance parallel to the microwave resonator chip (see Fig. 1a)) and is mounted (see Fig. 1c)) via a brass stamp to a commercial piezoelectric rotator Attocube (), and thus can be rotated within the sample plane. The microwave chip with meander-type superconducting Nb resonator (see Fig. 1b)) is installed in a brass box and connected via coaxial cables to the vector network analyzer for microwave transmission measurements.

In this arrangement of resonator and sample, precise ESR measurements on high-quality single cystals krellner2012 () require sample dimensions of order one millimeter for the relevant surface, namely the -plane (or another plane that includes the -axis). While such sample dimensions can readily be obtained for the -plane, growing a crystal with millimeter dimension along the -direction is challenging. This work is the first demonstration of an ESR measurement that combines a planar resonator and a sample in -plane.

Figure 2: Transmission spectrum of the superconducting Nb resonator with equidistant resonance peaks. Frequency ranges that are used to investigate the resonances are indicated. Additional features in the transmission might be due to box modes of the resonator mounting.
Figure 3: ESR in at and . The quality factor as a function of external magnetic field and normalized to the zero-field value, shown for several angles between the external field and the symmetry axis of the crystal, exhibits a pronounced minimum at the ESR field .

3 Results

Fig. 2 shows a typical transmission spectrum of the microwave resonator, and it clearly features sharp resonances of the first four harmonics with roughly equidistant resonance frequencies around and . From such spectra, we determine the quality factor of the -th mode through a Lorentzian fit of the resonance peak in the transmission signal. is defined as the ratio between resonance frequency and bandwidth (resonance width at half maximum) :

(1)

The transmission in the frequency range close to a resonance peak is measured as a function of magnetic field, and a pronounced change of the resonance peak can be observed. Thus we obtain the field dependence of the quality factor, which is shown in Fig. 3 for different sample orientations. is generally decreasing with increasing field due to field-induced losses in the superconducting resonator Frunzio2005 (); Bothner2012a (); deGraaf2012 (); Bothner2012b (); Ebensperger2016 () and due to the microwave charge response of the heavy fermions scheffler2013 (); Parkkinen2015 (); Degiorgi1999 (); Scheffler2005c (); Scheffler2010 (), and additionally it has a dip at the resonance magnetic field , indicating ESR absorption and thus the spin response of . As can be seen in Fig. 3, the resonance field increases if the angle between the external magnetic field and the crystallographic -axis is decreased from 90 (-plane) towards the -axis.

Figure 4: ESR -factor for as a function of the crystallographic angle measured by coplanar resonator at and (circles). Previous results obtained with a conventional X-band ESR spectrometer at and are shown for comparison (stars) sichelschmidt2007 ().

After subtraction of the background the resonance magnetic field and ESR linewidth can be obtained through a fit of an inverse Dysonian function, which describes the absorbed power at ESR in dependence of the magnetic field strength joshi2004 ()

(2)

The obtained is inserted into the ESR resonance condition to determine the ESR -factor (with Planck constant and Bohr magneton ):

(3)

Fig. 4 shows the ESR -factor of the angle-dependent measurement at and between and . There is a maximum around , and continuously decreases when the crystal is rotated such that the orientation of the magnetic field moves from the -plane towards the -axis. This evolution is consistent with data obtained previously at higher temperatures () and higher field with a conventional X-band spectrometer sichelschmidt2007 (), which are shown as stars in Fig. 4 for comparison. The slightly higher absolute values of for the X-band measurement can be explained by the well-established decrease of the -factor with decreasing temperature sichelschmidt2003 (); scheffler2013 ().

4 Conclusions

The presented results prove that planar resonators are sensitive enough for ESR measurements of for magnetic-field directions within the -plane. We performed the first ESR measurement using a superconducting coplanar microwave resonator in combination with in-situ sample rotation, and this also includes the lowest temperature of any angle-dependent ESR measurement on so far. Our results agree well with former results obtained by conventional techniques at higher frequencies and higher temperatures.
To investigate the magnetically ordered phase of below and , this experimental approach for angle-dependent ESR measurements can now be implemented inside a dilution refrigerator. There the technical situation features additional challenges due to the smaller available cooling power (to be considered for the wiring and electrical power needed to drive the rotator). On the other hand, the generally increasing ESR intensity upon cooling promises strong signal for such an experiment.

Acknowledgments

We thank G. Untereiner for support during preparation of experiments and R. Kleiner and D. Koelle for support during resonator fabrication. We thank the Deutsche Forschungsgemeinschaft (DFG, projects KR 3831/4-1, SCHE 1580/2-1, SI 1339/1-1) for financial support of this project.

References

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