TRIM Simulations Tool for Stopping Fraction in Hydrostatic Pressure Cells Frank Elson1 Debarchan Das2 Gediminas Simutis34 Ola Kenji

2025-05-06 0 0 1.91MB 8 页 10玖币

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TRIM Simulations Tool for µ+Stopping Fraction in

Hydrostatic Pressure Cells

Frank Elson1,∗, Debarchan Das2, Gediminas Simutis3,4, Ola Kenji

Forslund4, Ugne Miniotaite1, Rasmus Palm1, Yasmine Sassa4, Jonas

Weissenrieder1, and Martin M˚ansson1,+

1Department of Applied Physics, KTH Royal Institute of Technology, SE-106 91 Stockholm,

Sweden

2Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI,

Switzerland

3Laboratory for Neutron and Muon Instrumentation, Paul Scherrer Institut, CH-5232 Villigen

PSI, Switzerland

4Department of Physics, Chalmers University of Technology, G¨oteborg, SE-412 96, Sweden

E-mail: ∗elson@kth.se, +condmat@kth.se

Abstract. For quantum systems or materials, a common procedure for probing their

behaviour is to tune electronic/magnetic properties using external parameters, e.g. temperature,

magnetic ﬁeld or pressure. Pressure application as an external stimuli is a widely used

tool, where the sample in question is inserted into a pressure cell providing a hydrostatic

pressure condition. Such device causes some practical problems when using in Muon Spin

Rotation/Relaxation (µ+SR) experiments as a large proportion of the muons will be implanted

in the pressure cell rather than in the sample, resulting in a higher background signal. This

issue gets further ampliﬁed when the temperature dependent response from the sample is much

smaller than that of the pressure cell,which may cause the sample response to be lost in the

background and cause diﬃculties in aligning the sample within the beam. To tackle this issue,

we have used pySRIM [1] to construct a practical and helpful simulation tool for calculating

muon stopping fractions, speciﬁcally for the pressure cell setup at the µE1 beamline using the

GPD spectrometer at the Paul Scherrer Institute, with the use of TRIM simulations. The

program is used to estimate the number of muon stopping in both the sample and the pressure

cell at a given momentum. The simulation tool is programmed into a GUI, making it accessible

to user to approximate prior to their experiments at GPD what fractions will belong to the

sample and the pressure cell in their ﬁtting procedure.

1. Introduction

High pressure studies using muon spin resonance (µ+SR) has become very popular as a ’clean’

approach for probing and tuning material properties, and especially within the ﬁeld of magnetic

materials and quantum criticality [2,3,4]. The purpose of this is to investigate the phase

diagram of a given material as a function of an external perturbation (i.e. pressure but also e.g.

temperature and magnetic ﬁeld). Through such an approach, it is possible to shed light onto

a plethora of complex phenomena, such as unconventional superconductivity [5], quantum spin

liquids [6] or frustrated magnetism [7]. The combination of pressure and the µ+SR technique,

in which a microscopic understanding of the ground state of these quantum materials can be

arXiv:2210.15437v1 [physics.comp-ph] 27 Oct 2022

obtained, provides a uniquely powerful tool to get insight into the intrinsic properties of the

material. However, to apply hydrostatic pressure (e.g. at GPD, which will be the spectrometer

used as the example throughout this paper), the samle needs to be compressed into a pellet

and inserted into the pressure cell made of either MP45N or Cu-Be. Before starting any

measurements, the muon beam and its momentum need to be adjusted to guarantee the maximal

signal from the sample. With surface muon beamlines (e.g. GPS at PSI), the energy of the muons

is usually 5 - 40 MeV/c. This is enough to penetrate a thin layer of mylar foil or capton tape

which is used to mount the sample to the sample holder. However, this energy is not enough to

penetrate the thick layers of metal that make up a pressure cell. For this, decay muon beamlines

are needed, which can provide muons in the energy range of 40 - 125 MeV/c. For the surface

muon case, alignment is simple as there is essentially only the sample signal to detect. When the

pressure cell is introduced, it gets slightly more diﬃcult as there is now another material in very

close proximity to the sample that will give a signiﬁcant signal. This is not an issue when the

sample gives a very strong response, as the sample signal will be much greater than the pressure

cell signal. Consequently, determining the optimal muon momentum for alignment is not very

diﬃcult. However, if the sample response is weak, then it may be diﬃcult to distinguish the

sample contributions from the pressure cell (as mentioned in Ref [8]). Additionally, there are

diﬀerent types of pressure cells (MP35N, CuBe and a combination of the two) with diﬀerent

signals. Further, each individual pressure cell made from same material are in fact also slightly

diﬀerent. As a result, there are several cases where it is incredibly diﬃcult to extract the sample

response from the total signal.

One way around this is to ﬁrst employ an indirect alignment using another sample with a

strong response (but same pressure cell), and then using this alignment result also for the sample

of interest (with weak signal). However, this can be a problem as slight diﬀerences in the sample

densities can drastically change the stopping fraction of muons in the sample (a higher density

means less muons pass through the sample). This then translates into issues in the ﬁtting process

as you need to have a correct estimate for the signal fraction from the sample. Consequently, if

your assumed stopping fraction is incorrect, the obtain ﬁtting results do not completely reﬂect

the intrinsic physical properties and behaviour of the sample.

In this paper, we present an eﬃcient and user friendly simulation method based using TRIM

[9] combined with the pySRIM python module [1]. In such approach, it is possible to simulate,

with higher level of accuracy, the number of muons that will be stopping in the pressure cell

and the sample, respectively, for any given muon momentum input. This is useful as a tool for

user to employ both before and after experiments. This is because it will both give the user

an idea on feasibility of their proposed experiment (in the respect of how easy it will be to see

their sample signal) and also for supporting the data analysis when ﬁtting the percentages of

the contributions from each ﬁt function (pressure cell and sample).

2. Basis of Simulation

2.1. Beam setup

The GUI software is a python package that determines the stopping fractions in a beamline

setup. The software runs TRIM calculations in the background and presents the results as early

interpretable ﬁgures and stopping percentages.

There are three key aspects that make this software more accurate for modelling stopping

fractions compared to running the standard TRIM simulations:

(i) The software utilises a Gaussian distribution of momentums/energies.

(ii) The input beam can be collimated to any area.

(iii) There is a random small angular divergence on each muon as each muon will not be

completely parallel to the beam.

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摘要：

TRIMSimulationsToolfor+StoppingFractioninHydrostaticPressureCellsFrankElson1;,DebarchanDas2,GediminasSimutis3;4,OlaKenjiForslund4,UgneMiniotaite1,RasmusPalm1,YasmineSassa4,JonasWeissenrieder1,andMartinMansson1;+1DepartmentofAppliedPhysics,KTHRoyalInstituteofTechnology,SE-10691Stockholm,Sweden2Lab...

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TRIM Simulations Tool for Stopping Fraction in Hydrostatic Pressure Cells Frank Elson1 Debarchan Das2 Gediminas Simutis34 Ola Kenji

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